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| author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
|---|---|---|
| committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
| commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
| tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /3760 | |
| parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
| download | Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.tar.gz Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.tar.bz2 Scilab-TBC-Uploads-7f60ea012dd2524dae921a2a35adbf7ef21f2bb6.zip | |
initial commit / add all books
Diffstat (limited to '3760')
332 files changed, 7922 insertions, 0 deletions
diff --git a/3760/CH1/EX1.1/Ex1_1.sce b/3760/CH1/EX1.1/Ex1_1.sce new file mode 100644 index 000000000..e48d24398 --- /dev/null +++ b/3760/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,21 @@ + +clc;
+f=50; // frequency in Hz
+Et=13; // emf per turn in volts
+E1=2310; // primary voltage in volts
+E2= 220; // secondary voltage in volts
+B=1.4; // maximum flux density in Tesla
+// calculating the number of turns in primary and secondary side
+N2= round(E2/Et); //secondary side turns
+printf('Number of secondary turns is %f\n',N2);
+N1=round(N2*(E1/E2));// primary side turns
+printf('Number of primary turns is %f\n',N1);
+disp('The value of primary turns does not satisfy with the');
+disp('value of secondary turns so taking value of N2=18(next nearest integer)');
+N2=18; // new value of secondary turns
+N1=18*(E1/E2);
+printf('Number of primary turns is %f\n',N1);
+printf('Number of secondary turns is %f\n',N2);
+// calculating net core area
+A=(220/(18*sqrt(2)*%pi*B*50))*10^4; // where N2=18
+printf('Net area of core is %f cm^2',A);
diff --git a/3760/CH1/EX1.10/Ex1_10.sce b/3760/CH1/EX1.10/Ex1_10.sce new file mode 100644 index 000000000..2ab041e7c --- /dev/null +++ b/3760/CH1/EX1.10/Ex1_10.sce @@ -0,0 +1,33 @@ +
+clc;
+E1=250;// voltage on low tension side
+E2=2500; // voltage on high tension side
+k=E2/E1; //turns ratio
+Z=380+230*%i; // given load connected to high tension side
+Zl=Z/k^2; // load referred to low tension side
+zl=0.2+0.7*%i; // leakage impedance of transformer
+zt=Zl+zl; // total series impedance
+ztm=abs(zt); // magnitude of total series impedance
+I1=E1/zt;
+I1m=abs(I1); // magnitude of primary load current
+I2=I1m/k; // secondary load current
+vt=5*abs(Z);
+printf('secondary terminal voltage is %f V\n',vt);
+R=500; // shunt branch resistance
+X=250; // shunt branch leakage reactance
+Ic=E1/R; // core less component of current
+Im=E1/(%i*X); // magnetizing component of current
+Ie=Ic+Im;// total exciting current
+It=I1+Ie;// total current on low tension side
+Itm=abs(It);
+printf('primary current is %f A\n',Itm);
+pf=cos(atan(imag(It),real(It)));
+printf('power factor is %f lagging\n',pf),
+lpf=real(Z)/abs(Z);
+op=vt*I2*lpf;
+printf('output power is %f W\n',op);
+pc=Ic^2*R; // core less power
+poh=I1m^2*real(zl); // ohmic losses
+pin=E1*Itm*pf; // input power
+n=(op/pin)*100; // efficiency
+printf('efficiency of transformer is %f percent',n);
diff --git a/3760/CH1/EX1.11/Ex1_11.sce b/3760/CH1/EX1.11/Ex1_11.sce new file mode 100644 index 000000000..7f7c5a7b9 --- /dev/null +++ b/3760/CH1/EX1.11/Ex1_11.sce @@ -0,0 +1,31 @@ +clc;
+p=10000; // rated output of transformer
+E1=2500; // primary side rated voltage
+E2=250; // secondary side rated voltage
+k=E2/E1; // turn's ratio
+// initialising results of open circuit results on l.v side
+Vo=250; //open circuit voltage
+Io=1.4; // no load current
+Po=105; // open circuit voltage
+// initialising the results of short circuit results on h.v side
+Vsc=104; // short circuit voltage
+Isc=8; // short circuit current
+Psc=320; // power dissipated
+theta=Po/(Vo*Io); // no load power factor
+Ic=Io*theta; // core less component of current
+Im=Io*sqrt(1-theta^2); // magnetising component of current
+Ro=round(Vo/Ic); // shunt branch resistance
+Xo=round(Vo/Im); // shunt branch impedance
+Zsc=Vsc/Isc; // short circuit impedance
+reh=Psc/Isc^2; // total transformer resistance
+xeh=sqrt(Zsc^2-reh^2); // total transformer leakage impedance
+// equivalent circuit referred to l.v side
+rel=reh*k^2;
+xml=xeh*k^2;
+printf('shunt branch resistance and reactance is %f ohm and %f ohm\n',Ro,Xo);
+printf('value of transformer resistance and leakage reactance referred to l.v side is %f ohm and %f ohm\n',rel,xml);
+// equivalent circuit referred to h.v side
+Rch=Ro/k^2;
+Xmh=Xo/k^2;
+printf('shunt branch resistance and reactance referred to h.v side is %f ohm and %f ohm\n',Rch,Xmh);
+printf('value of transformer resistance and leakage reactance referred to h.v side is %f ohm and %f ohm\n',reh,xeh);
diff --git a/3760/CH1/EX1.12/Ex1_12.sce b/3760/CH1/EX1.12/Ex1_12.sce new file mode 100644 index 000000000..fdfb35e51 --- /dev/null +++ b/3760/CH1/EX1.12/Ex1_12.sce @@ -0,0 +1,28 @@ +clc;
+P=200000; // rated power output of transformer
+E1=11000; // primary side voltage
+E2=400; // secondary side voltage
+// initialising the results of the open circuit test performed on l v side
+Vo=400; // open circuit voltage in V
+Io=9; // no load current in A
+Po=1500; // core loss in W
+// initialising the results of short circuit test performed on h v side
+Vsc=350; // voltage applied in short circuit test
+Isc=P/(3*E1); // short circuit current
+Psc=2100; // power dissipated in short circuit test
+E2p=E2/sqrt(3); // per phase voltage
+pop=Po/3; // per phase core loss
+Ic=pop/E2p; // core loss current
+Im=sqrt(Io^2-Ic^2); // magnetising component of current
+R=E2p/Ic; // core loss resistance in ohm
+X=E2p/Im; // magnetizing reactance
+Rh=R*(E1/E2p)^2; // core loss resistance referred to h v side
+Xh=floor(X*(E1/E2p)^2); // magnetizing component referred to h v side
+printf('coreloss resistance and magnetizing reactance referred to h v side is %f ohm and %f ohm\n ',Rh,Xh);
+Pscp=Psc/3; // ohmic loss per phase
+Z=Vsc/Isc; // total impedance of transformer
+Re=Pscp/Isc^2; // Total resistance of transformer refrred to high voltage side
+Xe=sqrt(Z^2-Re^2); // total leakage impedance of transformer referred to h v side
+printf('transformer resistance and leakage impedance referred to h v side are %f ohm and %f ohm\n',Re,Xe);
+n=(1-(pop+Pscp/2^2)/(P/6+pop+Pscp/2^2))*100; // efficiency at half load
+printf('efficiency at half load is %f percent',n);
diff --git a/3760/CH1/EX1.14/Ex1_14.sce b/3760/CH1/EX1.14/Ex1_14.sce new file mode 100644 index 000000000..29d40e4b3 --- /dev/null +++ b/3760/CH1/EX1.14/Ex1_14.sce @@ -0,0 +1,27 @@ +clc;
+p=20000; // rated power of transformer
+vbh=2500; // base voltage in volts for h. v. side
+vbl=250; // base voltage in volts for l. v. side
+ibh=p/vbh; // base current in Ampere for h. v. side
+zbh=vbh/ibh; // base impedance in ohm
+ze=2.6+4.3*%i; // equivalent leakage impedance referred to h. v. side in ohm
+zepu=ze/zbh; // per unit value in ohm
+disp('Per unit value of equivalent leakage impedance referred to h. v. side is');
+disp(zepu);
+k=vbl/vbh; // turn's ratio
+zel=ze*k^2; // equivalent leakage impedance referred to l. v. side in ohm
+ibl=p/vbl; // base current in Ampere for l. v. side
+zbl=vbl/ibl; // base impedance for l. v. side
+zelpu=zel/zbl; // per unit value in ohm
+disp('Per unit value of equivalent leakage impedance referred to l. v. side is');
+disp(zelpu);
+zepum=abs(zepu); // magnitude of per unit impedance
+vhl=zepum*vbh; // total leakage impedace drop on h. v. side
+vbl=zepum*vbl; // total leakage impedace drop on l. v. side
+printf('Total leakage impedance drop on h. v. side and l. v. side are %f V and %f V respectively\n',vhl,vbl);
+Ieh=4.8; // exciting current in Ampere
+Iepu=Ieh/ibh; // p u value of exciting current referred to h. v. side
+printf('Per unit value of exciting current referred to h. v. side is %f p.u. \n',Iepu);
+Iel=Ieh/k; // exciting current referred to l. v. side
+Ielpu=Iel/ibl; // p u value of exciting current referred to l. v. side
+printf('Per unit value of exciting current referred to l. v. side is %f p.u. \n',Ielpu);
diff --git a/3760/CH1/EX1.15/Ex1_15.sce b/3760/CH1/EX1.15/Ex1_15.sce new file mode 100644 index 000000000..c524c7a30 --- /dev/null +++ b/3760/CH1/EX1.15/Ex1_15.sce @@ -0,0 +1,27 @@ +clc;
+P=10000; // rated power of transformer
+vbh=2000; // base voltage for h v side in volts
+ibh=P/vbh; // base current for h v side in Ampere
+vbl=200; // base voltage for l v side in volts
+ibl=P/vbl; // base current for l v side in Ampere
+k=vbl/vbh; // turns ratio
+r1=3.6; // resistance of h v side of transformer in ohm
+x1=5.2; //leakage reactace h v side of transformer in ohm
+z=vbh/ibh; // base impedance for h v side'
+r1pu=r1/z; // p u value for resistance of h v side of transformer in ohm
+x1pu=x1/z; // p u value for leakage reactance of h v side of transformer in ohm
+r2=0.04; //resistance of l v side of transformer in ohm
+x2=0.056; //leakage reactace l v side of transformer in ohm
+// total resistance referred to h v side
+re=r1+r2/k^2;
+repu=re/z;
+// total leakage impedance referred to h v side
+xe=x1+x2/k^2;
+xepu=xe/z;
+printf('total per unit resistance and per unit leakage impedance referred to h v side are %f and %f\n',repu,xepu);
+Z=vbl/ibl; // base impedance for l v side
+Re=r2+r1*k^2; // total resistance referred to l v side
+Repu=Re/Z;
+Xe=x2+x1*k^2; //total leakage impedance referred to l v side
+Xepu=Xe/Z;
+printf('total per unit resistance and per unit leakage impedance referred to l v side are %f and %f ',Repu,Xepu);
diff --git a/3760/CH1/EX1.16/Ex1_16.sce b/3760/CH1/EX1.16/Ex1_16.sce new file mode 100644 index 000000000..f7e463735 --- /dev/null +++ b/3760/CH1/EX1.16/Ex1_16.sce @@ -0,0 +1,30 @@ +clc;
+P=200000; //rated power of transformer
+E1=4000; // primary side rated voltage
+E2=1000; // secondary side rated voltage
+n=0.97; // efficiency
+pfn=0.25; // power factor at no load
+pff=0.8; // power factor at full load
+vr=5; // percentage voltage regulation
+Pl=((1/n)-1)*200000; // total losses at full load
+Pf=Pl*0.6; // total losses at 60% of full load
+Po=(Pl-Pf)/(1-0.36); // ohmic losses
+Pc=Pl-Po; // core losses
+re2=(Po/P)*100; // P U total resistance referred to l. v. side
+xe2=(vr-re2*pff)/sqrt(1-pff^2); // P U total leakage reactance referred to l. v. side
+re2=(re2*E2^2)/(100*P); // total resistance in ohms
+disp('Total resistance referred to l. v. side is ');
+printf('%f ohm',re2);
+xe2=(xe2*E2^2)/(100*P); // total leakage reactance in ohms
+disp('Total leakage reactance referred to l. v. side is ');
+printf('%f ohm',xe2);
+Rc=E2^2/Pc;
+disp('Coreloss resistance is');
+printf('%f ohm',Rc);
+Ie2=Pc/(E2*pfn); // exciting current in Ampere
+Ic=Pc/E2; // core loss current
+Im=sqrt(Ie2^2-Ic^2); // magnetizing component of exciting current
+Xm=E2/Im; // magnetizing reactance
+disp('Magnetizing reactance is ');
+printf('%f ohm',Xm);
+disp('All parameters are known. So, equivalent circuit diagram referred to l. v. side can be drawn.');
diff --git a/3760/CH1/EX1.18/Ex1_18.sce b/3760/CH1/EX1.18/Ex1_18.sce new file mode 100644 index 000000000..4dcbbda5d --- /dev/null +++ b/3760/CH1/EX1.18/Ex1_18.sce @@ -0,0 +1,26 @@ +clc;
+P=20000; // rated power of transformer
+E1=2500; // primary side voltage
+E2=500; // secondary side voltage
+r1=8; // primary resistance in ohm
+x1=17; // primary leakage reactance in ohm
+r2=0.3; // secondary resistance in ohm
+x2=0.7; // secondary leakage reactane in ohm
+k=E2/E1; // turns ratio
+re2=r2+r1*k^2; // equivalent resistance referred to secondary winding
+xe2=x2+x1*k^2; // equivalent leakage reactance referred to secondary winding
+Il=P/E2; // full load secondary current
+disp('case a');
+pf=0.8; // lagging power factor
+vd=Il*(re2*pf+xe2*sqrt(1-pf^2)); // Voltage drop in impedance in volts
+vt=E2-vd; // secondary terminal voltage
+printf('secondary terminal voltage for a lagging power factor is %f v\n',vt);
+vr=((E2-vt)/E2)*100; // voltage regulation
+printf('voltage regulation for a lagging power factor is %f percent\n',vr);
+disp('case b');
+pf=0.8; // leading power factor
+vd=Il*(re2*pf-xe2*sqrt(1-pf^2)); // Voltage drop in impedance in volts
+vt=E2-vd; // secondary terminal voltage
+printf('secondary terminal voltage for a leading power factor is %f v\n',vt);
+vr=((E2-vt)/E2)*100; // voltage regulation
+printf('voltage regulation for a leading power factor is %f percent\n',vr);
diff --git a/3760/CH1/EX1.19/Ex1_19.sce b/3760/CH1/EX1.19/Ex1_19.sce new file mode 100644 index 000000000..596f00942 --- /dev/null +++ b/3760/CH1/EX1.19/Ex1_19.sce @@ -0,0 +1,10 @@ +clc;
+rpu=0.02; // P U equivalent resistance
+xpu=0.05; // P U equivalent leakage reactance
+E2=440; // Secondary full load voltage
+pf=0.8; // lagging power factor
+vr=rpu*pf+xpu*sqrt(1-pf^2); // P U voltage regulation
+printf('Full load p.u. voltage regulation is %f or %f percent\n',vr,vr*100);
+dv=E2*vr; // change in terminal voltage
+V2=E2-dv; // secondary terminal voltage
+printf('Secondary terminal voltage is %f V',V2);
diff --git a/3760/CH1/EX1.2/Ex1_2.sce b/3760/CH1/EX1.2/Ex1_2.sce new file mode 100644 index 000000000..dce16da4e --- /dev/null +++ b/3760/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,15 @@ +clc;
+f=50; // frequency in hertz
+B=1.2; // maximum flux density in Tesla
+A=75*10^-4; // net core area in m^2
+E1=220; // primary side voltage in volts
+E2=600; // secondary side voltage in volts
+E3=11; // tertiary side voltage in volts
+n3=round(E3/2); // number of turns in half of the tertiary winding
+Et=round(sqrt(2)*%pi*50*B*A); // calculating emf per turn
+N3=Et*n3; // total number of turns in tertiary winding
+printf('total number of turns in tertiary winding is %f\n',N3);
+N2=round(E2*(n3/E3)); // total number of turns in secondary winding
+printf('total number of turns in secondary winding is %f\n',N2);
+N1=round(E1*(n3/E3)); // total number of turns in secondary winding
+printf('total number of turns in primary winding is %f',N1);
diff --git a/3760/CH1/EX1.20/Ex1_20.sce b/3760/CH1/EX1.20/Ex1_20.sce new file mode 100644 index 000000000..cb94ee7f0 --- /dev/null +++ b/3760/CH1/EX1.20/Ex1_20.sce @@ -0,0 +1,20 @@ +clc;
+P=10000; // rated power of transformer in VA
+E1=2000; // full load primary voltage
+E2=400; // full load secondary voltage
+k=E2/E1; // turns ratio
+pf=0.8; // lagging power factor
+// initialising results of short circuit test
+v=60; // voltage applied for short circuit test
+i=4; // short circuit current
+p=100; // power dissipated in short circuit;
+reh=p/i^2; // total resistance referred to h v side
+zeh=v/i; // total impedance referred to h v side
+xeh=sqrt(zeh^2-reh^2); // total leakage reactance referred to h v side
+rel=reh*k^2; // resistance referred to l v side
+xel=xeh*k^2; // reactance referred to l v side
+i2l=P/E2; // full load secondary current
+vr=i2l*(rel*pf+xel*sqrt(1-pf^2)); // voltage regulation
+v2=E2+vr; // total voltage of secondary when transformer is operating on full load
+v1=v2/k; // voltage applied to primary to deliver full load
+printf('voltage applied to primary to deliver full load is %f v',v1);
diff --git a/3760/CH1/EX1.21/Ex1_21.sce b/3760/CH1/EX1.21/Ex1_21.sce new file mode 100644 index 000000000..5f5ceb225 --- /dev/null +++ b/3760/CH1/EX1.21/Ex1_21.sce @@ -0,0 +1,29 @@ +clc;
+zf=30+120*%i; // feeder impedance
+E1=33000; // primary side voltage
+E2=3300; // secondary side voltage
+k=E2/E1; // turns ratio
+P=100000; // load power
+pf=0.8;// leading power factor of load
+zl=0.3+1.4*%i; // leakage impedance referred to l v side
+zfl=zf*k^2; // feeder impedance referred to l v side
+vt=3300; // terminal voltage
+il=P/(vt*pf); // load current
+R=real(zfl)+real(zl); // total resistance referred to l v side
+X=imag(zfl)+imag(zl); // total impedance referred to l v side
+vfl=vt+il*(R*pf-X*sqrt(1-pf^2)); // voltage at the sending end of feeder referred to l v side
+vf=vfl/k; // voltage at the sending end of feeder
+printf('Voltage at the sending end of feeder is %f v\n',vf);
+v2=vt+il*(real(zl)*pf-imag(zl)*sqrt(1-pf^2)); //voltage induced in secondary windings
+v1=round(v2/k);
+printf('voltage at the primary terminals of transformer is %f v\n',v1);
+ap=il^2*R;
+printf('active power loss is %f W\n',ap);
+ar=il^2*X;
+printf('reactive power loss is %f W\n',ar);
+cp=P-P*%i*tan(acosd(pf)*(%pi/180)); // complex power at load end in VA
+cps=cp+((ap+ar*%i) ); // complex power at feeder end in VA
+pfs=cos(atan(imag(cps),real(cps)));
+printf('power factor at the sending end is %f leading',pfs);
+
+
diff --git a/3760/CH1/EX1.22/Ex1_22.sce b/3760/CH1/EX1.22/Ex1_22.sce new file mode 100644 index 000000000..58977276d --- /dev/null +++ b/3760/CH1/EX1.22/Ex1_22.sce @@ -0,0 +1,28 @@ +clc;
+P=10000; // rated power of transformer
+E1=2000; // primary side voltage
+E2=200; // secondary side voltage
+f=50; // frequency in hertz
+po=125; // no load power
+pfo=0.15; // no load power factor
+zbh=E1^2/P; // base impedance on h v side
+k=E2/E1; // turns ratio
+zl=0.5+1*%i; // percent leakage impedance
+zlh=zl*(zbh*k^2); // percent leakage impedance referred to h v side
+Rc=E1^2/po; // coreloss resistance
+Io=po/(E1*pfo); // No load current
+Xm=E1/(Io*sqrt(1-pfo^2)); // magnetizing reactance
+p=10000; // load power
+pf=0.8; // power factor of load
+il=p/(E2*pf); // secondary load current
+ilp=il*k; // primary load current
+vp=E1+ilp*(real(zlh)*pf+imag(zlh)*sqrt(1-pf^2));
+ap=ilp^2*real(zlh); // active power loss in series resistance
+ar=ilp^2*imag(zlh); // reactive power loss in series reactance
+Ap=vp^2/Rc; // active power loss in coreloss resistance
+Ar=vp^2/Xm; // reactive power loss in magnetizing reactance
+cpl=p*(1+%i*tan(acos(0.8))); // complex power at load end in VA
+cpi=(real(cpl)+ap+Ap)+%i*(imag(cpl)+ar+Ar); // complex power input to transformer VA
+printf('real power input to transformer is %f W\n',real(cpi));
+ipf=cos(atan(imag(cpi),real(cpi)));
+printf('input power factor is %f lagging',ipf);
diff --git a/3760/CH1/EX1.24/Ex1_24.sce b/3760/CH1/EX1.24/Ex1_24.sce new file mode 100644 index 000000000..9ada287e8 --- /dev/null +++ b/3760/CH1/EX1.24/Ex1_24.sce @@ -0,0 +1,18 @@ +clc;
+pc1=52; // core loss at f=40
+f1=40; // frequency in hertz
+pc2=90; // core loss at f=60
+f2=60; // frequency in hertz
+f=[f1 f1^2;f2 f2^2];
+pc=[pc1;pc2];
+k=inv(f)*pc;
+// proportionality constants for hysteresis and eddy current losses are
+kh=k(1);disp(kh) // proportionality constants for hysteresis losses
+ke=k(2);disp(ke) // proportionality constants for eddy current losses
+// determining both losses at 50 hertz
+f=50;
+ph=kh*f;
+printf('hysteresis losses at 50 hertz is %f W\n',ph);
+pe=ke*f^2;
+printf('eddy current losses at 50 hertz is %f W',pe);
+// answer for eddy current losses is misprinted in book
diff --git a/3760/CH1/EX1.25/Ex1_25.sce b/3760/CH1/EX1.25/Ex1_25.sce new file mode 100644 index 000000000..3db00e075 --- /dev/null +++ b/3760/CH1/EX1.25/Ex1_25.sce @@ -0,0 +1,15 @@ +
+clc;
+// subscripts 1 and 2 are used the quantities referred to 60 hz and 50 hz frequency respectively
+v1=220; // rated voltage at 60 hz
+f1=60; // operating frequency
+ph1=340; // hysteresis loss at 60 hz
+pe1=120; // eddy current loss at 60 hz
+v2=230; // rated voltage at 50 hz
+f2=50; // operating frequency
+s=1.6; // Steinmetz's constant
+B=(f1/f2)*(v2/v1); // ratio of flux densities Bm2/Bm1
+ph2=ceil(ph1*(50/60)*B^s); // hysteresis loss at 50 hz
+pe2=pe1*(f2/f1)^2*(B)^2;// eddy current loss at 50 hz
+pc=ph2+pe2;
+printf('Total core loss at 50 hz is %f W',pc);
diff --git a/3760/CH1/EX1.26/Ex1_26.sce b/3760/CH1/EX1.26/Ex1_26.sce new file mode 100644 index 000000000..957f6cb13 --- /dev/null +++ b/3760/CH1/EX1.26/Ex1_26.sce @@ -0,0 +1,22 @@ +clc;
+// subscripts 1 and 2 are used to refer 50 hz and 60 hz quantity respectively
+// voltage and current is same for both the cases
+s=1.6; // Steinmetz's coefficient
+poh1=1.6; // percentage ohmic losses
+ph1=0.9; // percentage hysteresis losses
+pe1=0.6; // percentage eddy current losses
+f1=50; // frequency in hertz
+f2=60; // frequency in hertz
+B=f1/f2 // since voltage level are same for both cases ratio of flux densities i.e Bm2/Bm1=f1/f2
+ph2=ph1*(f2/f1)*B^s; // percentage hysteresis losses
+pe2=pe1*(f2/f1)^2*B^2; // percentage eddy current losses
+poh2=poh1; // since the voltage and current levels are same therefore ohmic losses are same
+// for the total losses to be remain same at both the frequencies only ohmic losses can be varied
+p=poh1+ph1+pe1; // total losses at 50 hz
+pc=ph2+pe2; // total core losses at 60 hz
+pnoh=p-pc; // permissible value for new ohmic losses
+x=sqrt(pnoh/poh1); // factor by which output at 50 hz should be multiplied to get the same output at 60 hz
+printf('ohmic losses at 60 hz is %f percent\n',poh2);
+printf('hysteresis losses at 60 hz is %f percent\n',ph2);
+printf('eddy current losses at 60 hz is %f percent\n',pe2);
+printf('factor by which output at 50 hz should be multiplied to get the same output at 60 hz is %f ',x);
diff --git a/3760/CH1/EX1.27/Ex1_27.sce b/3760/CH1/EX1.27/Ex1_27.sce new file mode 100644 index 000000000..c9332db01 --- /dev/null +++ b/3760/CH1/EX1.27/Ex1_27.sce @@ -0,0 +1,25 @@ +clc;
+// subscripts 1 and 2 are used to indicate transformer of 11kv at 25hz and 22kv at 50 hz respectively
+// for same current power is doubled therefore P2=2P1
+poh1=1.8; // ohmic losses as a percentage of total power P1
+ph1=0.8; // hysteresis losses as a percentage of total power P1
+pe1=0.3; // eddy current losses as a percentage of total power P1
+poh2=poh1/2; // ohmic losses do not change with frequency but changes with voltage since p1=2p1 we get the result shown
+// since frequency also gets doubled whwn voltage levels double therefore there is no change in flux density i.e is Bm1=Bm2
+f1=25; // frequency in hertz
+f2=50; // frequency in hertz
+ph2=(f2/f1)*ph1; // hysteresis losses are directly proportional to frequency
+pe2=(f2/f1)^2*pe1; // eddy current losses are directly proportional to frequency
+// we know p2=2p1
+ph2p=ph2/2; // hysteresis losses as a percentage of total power P2
+pe2p=pe2/2; // eddy current losses as a percentage of total power P2
+printf('ohmic losses as a percentage of total power at 50 hz is %f percent\n',poh2);
+printf('hysteresis losses as a percentage of total power at 50 hz is %f percent\n',ph2p);
+printf('eddy current losses as a percentage of total power at 50 hz is %f percent\n',pe2p);
+// efficiency at f1,v1
+n1=(1-((poh1+ph1+pe1)/100)/(1+((poh1+ph1+pe1)/100)))*100;
+printf('efficiency at 25 hz is %f percent\n',n1);
+// efficiency at f2,v2
+n2=(1-((poh2+ph2p+pe2p)/100)/(1+((poh2+ph2p+pe2p)/100)))*100;
+printf('efficiency at 50 hz is %f percent',n2);
+
diff --git a/3760/CH1/EX1.28/Ex1_28.sce b/3760/CH1/EX1.28/Ex1_28.sce new file mode 100644 index 000000000..8202e42a4 --- /dev/null +++ b/3760/CH1/EX1.28/Ex1_28.sce @@ -0,0 +1,51 @@ +clc;
+P=10000; // rated power of transformer in VA
+E1=2500; // primary side voltage
+E2=250; // secondary side voltage
+pf=0.8; // power factor
+//initialising the results of open circuit test
+vo=250; // open circuit voltage
+io=0.8; //no load current
+po=50; // open circuit voltage
+// initialising the results of open circuit test
+vsc=60; // short circuit voltage
+isc=3; // short circuit current
+psc=45; // power dissipated in test
+ifl=P/E1; // full load current on primary side
+poh=psc*(ifl/isc)^2; // ohmic losses at full load current
+disp('case a(1)');
+n=(1-(po+(poh/4^2))/(po+(poh/4^2)+(P*pf)/4))*100; // efficiency at 1/4 load
+printf('efficiency at 1/4 load is %f percent\n',n);
+disp('case a(2)');
+n=(1-(po+(poh/2^2))/(po+(poh/2^2)+(P*pf)/2))*100; // efficiency at 1/2 load
+printf('efficiency at 1/2 load is %f percent\n',n);
+disp('case a(3)');
+n=(1-(po+(poh/1^2))/(po+(poh/1^2)+(P*pf)/1))*100; // efficiency at full load
+printf('efficiency at full load is %f percent\n',n);
+disp('case a(4)');
+n=(1-(po+((poh*5^2)/4^2))/(po+((poh*5^2)/4^2)+(P*pf*5)/4))*100; // efficiency at 1*1/4 load
+printf('efficiency at 5/4 load is %f percent\n',n);
+// let maximum efficiency occurs at x times the rated KVA
+// maximum efficiency occurs when core loss becomes equal to ohmic losses
+x=sqrt(po/poh);
+nm=(x*P)/1000; // VA output at maximum
+nmax=(1-(2*po)/(nm*1000*pf+2*po))*100;
+printf('KVA load at which maximum efficiency occurs is %f KVA\n',nm);
+printf('Maximum efficiency is %f percent\n',nmax);
+// from short circuit test
+reh=psc/isc^2; // total resistance referred to h v side
+zeh=vsc/isc; // total impedance referred to h v side
+xeh=sqrt(zeh^2-reh^2); // total leakage reactance referred to h v side
+er=(ifl*reh)/E1; //p u resistance
+ex=(ifl*xeh)/E1; // p u reactance
+vr=(er*pf+ex*sqrt(1-pf^2))*100; // p u voltage regulation
+printf(' p u voltage regulation for lagging power factor is %f percent\n',vr);
+dv=E2*(vr/100); // voltage drop in series impedance
+v2=E2-dv;
+printf('secondary terminal voltage for lagging power factor of 0.8 is %f v\n',v2);
+// voltaage regulation for leading power factor
+vr=(er*pf-ex*sqrt(1-pf^2))*100; // p u voltage regulation
+printf(' p u voltage regulation for leading power factor is %f percent\n',vr);
+dv=E2*(vr/100); // voltage drop in series impedance
+v2=E2-dv;
+printf('secondary terminal voltage for leading power factor of 0.8 is %f v\n',v2);
diff --git a/3760/CH1/EX1.29/Ex1_29.sce b/3760/CH1/EX1.29/Ex1_29.sce new file mode 100644 index 000000000..44da56614 --- /dev/null +++ b/3760/CH1/EX1.29/Ex1_29.sce @@ -0,0 +1,11 @@ +clc;
+p=20000; // rated capacity of transformer
+n=0.98; // efficiency of transformer at full load and half load
+c=[ 1 1; 1 1/4];
+o=[ ((1/n)-1)*p; ((1/n)-1)*(p/2)];
+l=inv(c)*o;
+printf('Core losses are %f W\n',l(1));
+printf('Ohmic losses are %f W\n',l(2));
+re=l(2)/p;
+printf('p.u. value of equivalent resistance is %f ',re);
+
diff --git a/3760/CH1/EX1.3/Ex1_3.sce b/3760/CH1/EX1.3/Ex1_3.sce new file mode 100644 index 000000000..f3d33b98e --- /dev/null +++ b/3760/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,19 @@ +clc;
+f=50; // frequency in hertz
+E1=2200; // supply voltage in volts
+E2=220; // secondary side voltage in volts
+P=361; // core loss in watts
+Io=0.6; // exciting current in Ampere
+Is=60; // secondary load current in Ampere
+pf=0.8; // power factor
+Ic=P/E1; // core loss component of current
+printf('core loss component of exciting current is %f A\n',Ic);
+Im=sqrt(Io^2-Ic^2); // magnetising component of current
+printf('magnetising component of exciting current is %f A\n',Im);
+ip=Is*(E2/E1); // primary current required to neutralise the secondary current
+Iv=ip*pf+Ic; // total vertical compartment of primary current
+Ih=ip*0.6+Im; // total horizontal compartment of primary current,pf cos(theta)=0.8 so sin(theta)=0.6
+Ip=sqrt(Iv^2+Ih^2); // toatl primary current
+printf('Total primary current is %f A\n',Ip);
+ppf=Iv/Ip; // primary power factor
+printf('primary power factor is %f (lagging)',ppf);
diff --git a/3760/CH1/EX1.30/Ex1_30.sce b/3760/CH1/EX1.30/Ex1_30.sce new file mode 100644 index 000000000..4dccd83b3 --- /dev/null +++ b/3760/CH1/EX1.30/Ex1_30.sce @@ -0,0 +1,15 @@ +clc;
+P=100000; // VA of transformer
+nmax=0.98; // maximum efficiency of transformer
+pf=0.8; // power factor at which maximum efficiency occurs
+l=80; // percentage of full load at which maximum efficiency occurs
+po=P*pf*(l/100); // output at maximum efficiency
+pl=((1/nmax)-1)*po; // total losses
+pc=pl/2; // core loss
+poh=pc; // at maximum efficiency variable losses are equal to constant losses
+pohl=poh*(100/l)^2; // ohmic losses at full load
+z=0.05; // p u leakage impedance
+r=pohl/P; // p u resistance
+x=sqrt(z^2-r^2); // p u leakage reactance
+vr=(r*pf+x*sqrt(1-pf^2))*100; // voltage regulation
+printf('Voltage regulation at 0.8 p.f. lagging is %f percent ',vr);
diff --git a/3760/CH1/EX1.31/Ex1_31.sce b/3760/CH1/EX1.31/Ex1_31.sce new file mode 100644 index 000000000..b62b64521 --- /dev/null +++ b/3760/CH1/EX1.31/Ex1_31.sce @@ -0,0 +1,11 @@ +clc;
+vdr=2; // percentage full load voltage drop in resistance
+vdx=4; // percentage full load voltage drop in leakage reactance
+// full load ohmic losses are equal to 0.02*VA rating of transformer which is equal to iron losses
+n=100/(1+(vdr/100)+(vdr/100));
+printf('Efficiency on full load at unity p.f is %f percent\n',n);
+// maximum voltage drop means voltage regulation is also maximum
+pf=vdr/sqrt(vdr^2+vdx^2);
+printf('Full load power factor at which voltage regulation is maximum is %f lagging\n',pf);
+pf=vdx/sqrt(vdr^2+vdx^2);
+printf(' load power factor at which voltage regulation is zero is %f leading',pf);
diff --git a/3760/CH1/EX1.32/Ex1_32.sce b/3760/CH1/EX1.32/Ex1_32.sce new file mode 100644 index 000000000..4d63fa1b6 --- /dev/null +++ b/3760/CH1/EX1.32/Ex1_32.sce @@ -0,0 +1,28 @@ +clc;
+P=20000; // rated VA of transformer
+E1=3300; // rated voltage of primary
+E2=220; // rated voltage of secondary
+v2=220; // voltage at which load is getting delivered
+p=14960; // load power in Watts
+pf=0.8; // power factor at on load
+pc=160; // core loss
+pfo=0.15; // power factor at no load
+il=p/(v2*pf); // load current
+is=P/E2; // rated current of secondary
+vr=1 ; // percentage voltage drop of rated voltage in total resistance
+vx=3 ; // percentage voltage drop of rated voltage in total leakage reactance
+re2=(E2*vr)/(is*100); // total resistance referred to secondary
+xe2=(E2*vx)/(is*100); // total leakage reactance referred to secondary
+poh=il^2*re2; // ohmic losses
+pi=poh+pc+p; // total input power
+// E2 as a reference
+i2=il*(pf-%i*sqrt(1-pf^2));
+E2n=v2+i2*(re2+%i*xe2); // secondary winding voltage
+io=pc/(pfo*E2); // no load current
+ic=pc/E2; // core loss current
+im=sqrt(io^2-ic^2); // magnetizing current
+I=i2+(ic-im*%i); // total input current, negative sign before im indicates that it lags behind E2 by 90 degree
+pfi=cos(atan(imag(I),real(I))); // input power factor
+printf('Total input power is %f W \n',pi);
+printf('Input power factor is %f lagging',pfi);
+
diff --git a/3760/CH1/EX1.33/Ex1_33.sce b/3760/CH1/EX1.33/Ex1_33.sce new file mode 100644 index 000000000..4be6cb6f6 --- /dev/null +++ b/3760/CH1/EX1.33/Ex1_33.sce @@ -0,0 +1,19 @@ +clc;
+P=500000; // VA rating of transformer
+E2=400; // rated secondary voltage
+nmax=0.98; // maximum efficiency of transformer
+l=80; // percentage of full load at which maximum efficiency occurs
+ze2=4.5; // percentage impedance
+pt=((1/nmax)-1)*P*(l/100); // total losses
+pc=pt/2; // core loss = ohmic loss at maximum efficiency
+poh=pc; // ohmic loss
+pohl=poh*(100/l)^2; // full load ohmic losses
+re2=(pohl/P)*100; // percentage resistance
+xe2=sqrt(ze2^2-re2^2); // percentage leakage reactance
+pfl=re2/ze2; // load power factor
+vr=re2*pfl+xe2*sqrt(1-pfl^2); // voltage regulation
+dv=(E2*vr)/100; // change in terminal voltage
+V2=E2-dv; // Secondary terminal voltage
+printf('Load power factor at which secondary terminal voltage is minimum is %f\n',pfl);
+printf('Secondary terminal voltage is %f v',V2);
+// answer for total losses is given wrong in the book
diff --git a/3760/CH1/EX1.34/Ex1_34.sce b/3760/CH1/EX1.34/Ex1_34.sce new file mode 100644 index 000000000..0961f106a --- /dev/null +++ b/3760/CH1/EX1.34/Ex1_34.sce @@ -0,0 +1,26 @@ +clc;
+P=5000; // rated VA of transformer
+pc=40; // core loss , it remains fixed for whole day
+poh=100; // ohmic losses
+// data for duration 7 A.M to 1 P.M
+p1=3000; // power consumed
+pf1=0.6 // power factor of load
+pk1=p1/pf1; // VA load
+poh1=poh*(pk1/P)^2; // ohmic losses for given duration
+// data for duration 1 P.M to 6 P.M
+p2=2000; // power consumed
+pf2=0.8 // power factor of load
+pk2=p2/pf2; // VA load
+poh2=poh*(pk2/P)^2; // ohmic losses for given duration
+// data for duration 6 P.M to 1 A.M
+p3=6000; // power consumed
+pf3=0.9 // power factor of load
+pk3=p3/pf3; // VA load
+poh3=poh*(pk3/P)^2; // ohmic losses for given duration
+// data for duration 1 A.M to 7 A.m =no load
+poht=poh1*6+poh2*5+poh3*7; // energy lost in ohmic losses
+pct=(pc*24); // daily energy lost as core loss
+ptl=poht+pct; // total energy lost
+po=p1*6+p2*5+p3*7; // output
+n=(1-(ptl/(ptl+po)))*100;
+printf('All day efficiency is %f percent',n);
diff --git a/3760/CH1/EX1.35/Ex1_35.sce b/3760/CH1/EX1.35/Ex1_35.sce new file mode 100644 index 000000000..c2f4cf451 --- /dev/null +++ b/3760/CH1/EX1.35/Ex1_35.sce @@ -0,0 +1,46 @@ +clc;
+
+//V/f ratio is same for every case hence hysteresis losses and eddy current losses can be calculated separately
+// data for column 1
+vt1=214; // terminal voltage
+f1=50; // frequency in hz
+p1=100; // power input in Watts
+vp1=vt1; // per phase voltage
+pv1=p1/3; // per phase power
+pc1=pv1/f1; // core loss per cycle
+// data for column 2
+vt2=171; // terminal voltage
+f2=40; // frequency in hz
+p2=72.5; // power input in Watts
+vp2=vt2; // per phase voltage
+pv2=p2/3; // per phase power
+pc2=pv2/f2; // core loss per cycle
+// data for column 3
+vt3=128; // terminal voltage
+f3=30; // frequency in hz
+p3=50; // power input in Watts
+vp3=vt3; // per phase voltage
+pv3=p3/3; // per phase power
+pc3=pv3/f3; // core loss per cycle
+// data for column 4
+vt4=85.6; // terminal voltage
+f4=20; // frequency in hz
+p4=30; // power input in Watts
+vp4=vt4; // per phase voltage
+pv4=p4/3; // per phase power
+pc4=pv4/f4; // core loss per cycle
+// Values of k1 and k2 have been obtained from graph
+k1=0.39;
+k2=(pc1-k1)/50;
+F1=60; //frequency at which losses has to be calculated
+ph1=k1*F1; //per phase hysteresis loss at 60 hz
+pe1=k2*F1^2; // per phase eddy curent loss at 60 hz
+pht=3*ph1; // total hysteresis loss
+pet=3*pe1; // total eddy current loss
+printf('Total hysteresis and eddy current losses at 60 hz are %f W and %f W respectively\n',pht,pet);
+F2=40; //frequency at which losses has to be calculated
+ph2=k1*F2; //per phase hysteresis loss at 40 hz
+pe2=k2*F2^2; // per phase eddy curent loss at 40 hz
+pht=3*ph2; // total hysteresis loss
+pet=3*pe2; // total eddy current loss
+printf('Total hysteresis and eddy current losses at 40 hz are %f W and %f W respectively',pht,pet);
diff --git a/3760/CH1/EX1.36/Ex1_36.sce b/3760/CH1/EX1.36/Ex1_36.sce new file mode 100644 index 000000000..ad13631ce --- /dev/null +++ b/3760/CH1/EX1.36/Ex1_36.sce @@ -0,0 +1,23 @@ +clc;
+E1=230; // primary rating of transformer 1 and transformer 2
+E2=400; // secondary rating of transformer 1
+e2=410; // secondary rating of transformer 2
+iv=25; // current feeded by voltage regulator to h v series winding
+pc=200; // core loss in each transformer
+r=1 // assuming resistance of transformer to be 1
+x=3*r // as per question leakage reactance is thrice of resistance
+il1=(iv*E2)/E1; // primary current of transformer 1
+il2=(iv*e2)/E1; // primary current of transformer 2
+pf=r/sqrt(r^2+x^2); // power factor during short circuit
+// As per the circuit diagram given in question, by Kirchoffs current law current through current coil of wattmeter W1 is given by
+I=il2-il1;
+// 2*core loss is the reading of wattmeter 2
+W=E1*I*pf; // reading of wattmeter 1 connected on l v side
+// in circuit diagram if terminal a is connected to c and terminal b is connected to d the current I and Io (no load current) flow in the same direction of current coil of Wattmeter.Hence its reading is increased to
+Wt=2*pc+W;
+printf('reading of wattmeter as per the connection described is %f W\n',Wt);
+// in circuit diagram if terminal c is connected to b and terminal d is connected to a the current I and Io (no load current) flow in the opposite direction through current coil of Wattmeter.Hence its reading is decreased to
+Wt=2*pc-W;
+printf('reading of wattmeter as per the connection described is %f W',Wt);
+
+
diff --git a/3760/CH1/EX1.37/Ex1_37.sce b/3760/CH1/EX1.37/Ex1_37.sce new file mode 100644 index 000000000..9ed4f1f8e --- /dev/null +++ b/3760/CH1/EX1.37/Ex1_37.sce @@ -0,0 +1,12 @@ +clc;
+E1=3300; // rated phase voltage of primary of a three phase transformer
+v=360; // voltage injected in open delta h v winding to circulate full load current
+vph=v/3; // voltage across each phase
+P=300; // rated KVA of transformer
+Pph=P/3; // KVA per phase
+Iph=(Pph*1000)/E1; // per phase current
+z=vph/Iph;
+printf('Per Phase leakage impedance is %f ohms\n',z);
+zb=E1/Iph; // base impedance
+zpu=z/zb;
+printf('leakage impedance per phase in per unit system is %f p.u',zpu);
diff --git a/3760/CH1/EX1.38/Ex1_38.sce b/3760/CH1/EX1.38/Ex1_38.sce new file mode 100644 index 000000000..5df7964e5 --- /dev/null +++ b/3760/CH1/EX1.38/Ex1_38.sce @@ -0,0 +1,40 @@ +clc;
+P=20000; // rated VA of transformer
+E1=2300; // rated voltage of primary
+E2=230; // rated voltage of secondary
+pf=0.6; // power factor
+n=0.96; // efficiency
+ih=P/E1; // rated current of h v winding
+il=P/E2; // rated current of l v winding
+// As per the connections given in fig 14.1(a), two voltages are in series aiding
+Et=E1+E2; // output voltage of autotransformer
+disp('case a');
+// By Kirchoffs law at point b , supply current is given by
+I=il+ih;
+Pa1=Et*il; // VA rating of autotransformer
+Po1=(Pa1/1000); // power output at full load unity power factor
+Pt1=(E2*il)/1000; // power transformed
+Pc1=(Po1-Pt1); // power conducted
+printf('For the given connection, output power is %f kW\n',Po1);
+printf('For the given connection, transformed power is %f kW\n',Pt1);
+printf('For the given connection, conducted power is %f kW\n',Pc1);
+disp('case b');
+// As per the connections given in fig 14.1(b), two voltages are in series opposition
+Et=E1-E2; // output voltage of autotransformer
+// By Kirchoffs law at point b , supply current is given by
+I=il-ih;
+Pa2=E1*I; // VA rating of autotransformer
+Po2=Pa2/1000; // power output at full load unity power factor
+Pt2=(E2*il)/1000; // power transformed
+Pc2=(Po2-Pt2); // power conducted
+printf('For the given connection, output power is %f kW\n',Po2);
+printf('For the given connection, transformed power is %f kW\n',Pt2);
+printf('For the given connection, conducted power is %f kW\n',Pc2);
+pl=((1/n)-1)*P*pf; // losses in 2-winding transformer
+// autotransformer operates at rated current and rated voltage so efficiency and losses remain constant
+disp('Efficiency for case a');
+n1=(1-(pl/(Po1*1000*pf+pl)))*100;
+printf('Efficiency of autotransformer for %f VA is %f percent\n',Po1,n1);
+disp('Efficiency for case b');
+n2=(1-(pl/(Po2*1000*pf+pl)))*100;
+printf('Efficiency of autotransformer for %f VA is %f percent',Po2,n2);
diff --git a/3760/CH1/EX1.39/Ex1_39.sce b/3760/CH1/EX1.39/Ex1_39.sce new file mode 100644 index 000000000..a1e4ee69e --- /dev/null +++ b/3760/CH1/EX1.39/Ex1_39.sce @@ -0,0 +1,14 @@ +clc;
+// connections have been made in fig 1.42 in book to suit voltage requirement of 3000V, 3500V and 1000V.
+E1=1000; // primary winding of transformer
+E2=2000; // secondary winding of transformer
+E3=500; // tertiary winding of transformer
+l1=1050; // load in KVA across 3500 V
+l2=180; // load in KVA across 1000 V
+i1=(l1*1000)/(E1+E2+E3); // current through load of 1050 KVA
+i2=(l2*1000)/(E1); // current through load of 180 KVA
+kt=l1+l2; // Total KVA load supplied
+I=(kt*1000)/(E1+E2);
+printf('current through %f KVA load is %f A\n',l1,i1);
+printf('current through %f KVA load is %f A\n',l2,i2);
+printf('current drawn from supply is %f A',I);
diff --git a/3760/CH1/EX1.4/Ex1_4.sce b/3760/CH1/EX1.4/Ex1_4.sce new file mode 100644 index 000000000..e4dfeb90b --- /dev/null +++ b/3760/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,13 @@ +clc;
+disp('weight of laminations is directly proportion to core volume density, which is directly proportional to product of area and height of limbs and while taking the ratio of weight of CRGO laminations and hot rolled laminations, height of limbs gets cancelled out(height of limbs are assumed to be equal). So, in the end ratio of weights of laminations is equal to ratio of area of core.Now area of core is given by maximum flux/flux density.According to question maximum flux remain same so ,while taking ratio of areas the maximum flux gets cancelled')
+B1=1.2; //flux density in hot rolled steel laminations
+B2=1.6; //flux density in CRGO steel laminations
+W1=100; // weight of H.R core in kg
+W2=W1*(B1/B2); // calculating weight of CRGO laminations in kg
+s=((W1-W2)/W1)*100; // calculating saving in core material
+printf('percentage saving in core material is %f percent\n',s);
+disp('weight of wire is directly proportional to product of length of turn around core and cross section of wire.(Wire cross section is assumed to be same in CRGO and HR laminations so gets cancelled out while taking ratio) also the length of turn is inversely proportional to square root of flux density ')
+w1= 80 // weight of Hot rolled wire
+w2=w1*(sqrt(1.2/1.6)); // weight of CRGO wire
+s=((w1-w2)/w1)*100; //saving in weight of wire
+printf('Percentage saving in weight of wire is %f percent',s);
diff --git a/3760/CH1/EX1.40/Ex1_40.sce b/3760/CH1/EX1.40/Ex1_40.sce new file mode 100644 index 000000000..4a5976531 --- /dev/null +++ b/3760/CH1/EX1.40/Ex1_40.sce @@ -0,0 +1,17 @@ +clc;
+E1=2500; // primary side voltage
+E2=250; // secondary side voltage
+P=10000; // rated VA of transformer
+// to achieve a voltage level of 2625, two equal parts of 125 V each of secondary winding are connected in parallel with each other and in series with primary winding
+Eo=E1+E2/2; // desired output of autotransformer
+il=P/E2; // rated current of l v winding
+i=2*il; // Total output current
+K=(i*Eo)/1000; // Auto transsformer KVA rating
+ip=P/E1; // rated current of h v winding
+I=i+ip; // current drawn from supply
+Pt=(i*(E2/2))/1000; // KVA transformed
+Pc=K-Pt; // KVA conducted
+printf('KVA output of autotransformer is %f KVA\n',K);
+printf('KVA transformed is %f KVA\n',Pt);
+printf('KVA conducted is %f KVA',Pc);
+
diff --git a/3760/CH1/EX1.41/Ex1_41.sce b/3760/CH1/EX1.41/Ex1_41.sce new file mode 100644 index 000000000..e9499c8cf --- /dev/null +++ b/3760/CH1/EX1.41/Ex1_41.sce @@ -0,0 +1,12 @@ +clc;
+E1=440; // primary supply voltage
+E2=380; // voltage at which load at secondary terminal is being supplied
+l1=40000; // power rating of load in watts
+pf=0.8; // lagging power factor
+I2=l1/(sqrt(3)*E2*pf);
+// per phase KVA input=per phase KVA output
+I1=(E2/E1)*I2;
+In=I2-I1;
+printf('Current in primary branch is %f A\n',I1);
+printf('current in secondary branch is %f A\n',I2);
+printf('current between neutral and tapping points is %f A',In);
diff --git a/3760/CH1/EX1.42/Ex1_42.sce b/3760/CH1/EX1.42/Ex1_42.sce new file mode 100644 index 000000000..726360d18 --- /dev/null +++ b/3760/CH1/EX1.42/Ex1_42.sce @@ -0,0 +1,20 @@ +clc;
+// From fig 1.45
+N1=1000; // no of turns on primary
+N2=400; // no. of turns on secondary
+n2=300; // no. of turns across points A and B
+l1=600; // a load of 600 KW connected between points A and C
+l2=60+60*%i; // load connected between points A and B
+E=30000; // primary supply voltage
+vac=E*(N2/N1); // secondary side voltage
+I1=(l1*1000)/vac; // current through load of 600 KW
+vab=(vac/N2)*n2; // volatge across pints A and B
+I2=vab/l2 ; // load current through load of 60+60i
+iba=I1+I2; // current through section Ab of winding
+mfs=iba*n2+I1*(N2-n2); // seconadry mmf
+ip=mfs/N1;
+printf('primary current is %f%fi A\n',real(ip),imag(ip));
+Pi=(E*abs(ip)*cos(atan(imag(ip),real(ip))))/1000;
+printf('primary power input is %f KW\n',Pi);
+pf=cos(atan(imag(ip),real(ip)))
+printf('power factor at primary terminal is %f lagging',pf)
diff --git a/3760/CH1/EX1.43/Ex1_43.sce b/3760/CH1/EX1.43/Ex1_43.sce new file mode 100644 index 000000000..7effd027a --- /dev/null +++ b/3760/CH1/EX1.43/Ex1_43.sce @@ -0,0 +1,27 @@ +clc;
+E=400; // supply voltage
+l1=200; // load connected across 75% tapping
+l2=400; // load connected between 25% and 100% tapping
+t1=25; // 25% tapping point
+t2=50; // 50% tapping point
+t3=75; // 75% tapping point
+V2=(t3/100)*E; // voltage across 200 ohm load
+I2=V2/l1; // current through 200 ohm load
+I1=(V2*I2)/E;
+// from fig.(1.46 b), KCL at point d gives
+idb=I2-I1;
+// same secondary voltage is applied against load of 400 ohm
+I2=V2/l2; // current through 400 ohm load
+I1=(V2*I2')/E;
+// from fig (1.46 c), KCL at point c gives
+ica=I2-I1;
+// superimposing the currents of above results current in three portion of winding can be known
+icd=ica;
+disp('current in section cd of winding is')
+printf('%f A\n',icd);
+ibc=I1;
+disp('current in section bc of winding is')
+printf('%f A\n',ibc);
+iab=idb+I1;
+disp('current in section ab of winding is')
+printf('%f A\n',iab);
diff --git a/3760/CH1/EX1.44/Ex1_44.sce b/3760/CH1/EX1.44/Ex1_44.sce new file mode 100644 index 000000000..7d3c13848 --- /dev/null +++ b/3760/CH1/EX1.44/Ex1_44.sce @@ -0,0 +1,31 @@ +clc;
+P=100000; // VA rating of two winding transformer
+E1=2000; // rated voltage of h v side
+E2=200; // rated voltage of l v side
+l=2.5; // percentage of loss in two winding transformer
+vr=3; // percentage of voltage regulation in two winding transformer
+z=4; // percentage of leakage impedance in two winding transformer
+ih=P/E1; // full load current of h v side
+il=P/E2; // full load current of l v side
+V1=E1; // rated voltage on l v side of autotransformer
+V2=E1+E2; // rated voltage on h v side of autotransformer
+Il=il+ih; // rated current on l v side of autotransformer
+printf('Rated voltage on l v and h v side of autotransformer are %f v and %f v respectively\n,',V1,V2);
+printf('Rated current on h v and l v side of autotransformer are %f A and %f A respectively\n,',il,Il);
+k=E1/V2; // turns ratio for auto transformer
+K=((1/(1-k))*P)/1000;
+printf('Rated KVA of autotransformer is %f KVA\n',K);
+pl=(1-k)*l; //percent full load losses in autotransformer
+n=100-pl;
+printf('Efficiency of auto transformer is %f percent\n',n);
+Z=(1-k)*z;
+printf('Percentage impedance as an auto transformer is %f \n',Z);
+VR=(1-k)*vr;
+printf('percentage voltage regulation as an auto transformer is %f \n',VR);
+Is=(1/(1-k))*(100/z); // short circuit p u current
+Ish=(Is*il)/1000;
+printf('Short circuit of auto transformer on h v side is %f KA \n',Ish);
+Isl=(Is*Il)/1000;
+printf('Short circuit of auto transformer on l v side is %f KA \n',Isl);
+
+
diff --git a/3760/CH1/EX1.45/Ex1_45.sce b/3760/CH1/EX1.45/Ex1_45.sce new file mode 100644 index 000000000..3b79bf8dc --- /dev/null +++ b/3760/CH1/EX1.45/Ex1_45.sce @@ -0,0 +1,22 @@ +clc;
+v1=10; // voltage applied to primary when secondary is short circuited
+ip=60; // primary current when secondary is short circuited
+k=0.8; // turns ratio
+E1=250; // input voltage for load voltage has to be calculated
+E2=200; // rated voltage of secondary
+il=100; // load current
+pfo=0.24; // power factor during short circuit test
+f=(1-k)^2/k^2; // factor by which secondary impedance has to be multiplied for referring it to primary
+// ze1=z1+f*z2 therefore by ohm s law
+ze1=v1/ip; // total impedance referred to primary
+re1=ze1*pfo; // total resistance referred to primary
+xe1=ze1*sqrt(1-pfo^2); // total leakage reactance referred to primary
+disp('case a');
+pf=0.8; // lagging power factor of load
+Ip=(E2*il)/E1; // current in primary due to load current
+v2=(E1-Ip*(re1*pf+xe1*sqrt(1-pf^2)))*k;
+printf('Secondary terminal voltage at %f lagging power factor is %f v\n',pf,v2);
+disp('case b')
+pf=1; // unity power factor
+v2=(E1-Ip*(re1*pf+xe1*sqrt(1-pf^2)))*k;
+printf('Secondary terminal voltage at unity power factor is %f v',v2);
diff --git a/3760/CH1/EX1.46/Ex1_46.sce b/3760/CH1/EX1.46/Ex1_46.sce new file mode 100644 index 000000000..a68bd686a --- /dev/null +++ b/3760/CH1/EX1.46/Ex1_46.sce @@ -0,0 +1,8 @@ +clc;
+r1=9 ; // ratio of reactance to resistance for transformer 1
+r2=3 ; // ratio of reactance to resistance for transformer 2
+d=atand(r1)-atand(r2); // differene between angles of transformer's leakage impedance
+// leakage impedance of both transformers are equal z1=z2, threefore currents in both transformers are equal that is i1=i2;
+I=1/cos((d/2)*(%pi/180)); // ratio of numerical sum of i1 and i2 to phasor sum of i1 and i2
+k=cos((d/2)*(%pi/180));
+printf('ratio of full load KVA delivered to sum of both transformers KVA ratings is %f',k);
diff --git a/3760/CH1/EX1.48/Ex1_48.sce b/3760/CH1/EX1.48/Ex1_48.sce new file mode 100644 index 000000000..f0b27a94f --- /dev/null +++ b/3760/CH1/EX1.48/Ex1_48.sce @@ -0,0 +1,18 @@ +clc;
+P=400000; // rated KVA of transformer
+P1=11000; // rated primary voltage
+S2=6600; // rated secondary voltage
+v1=360; // voltage recorded during short circuit of l v winding for first transformer
+p1=3025; // power dissipated during short circuit of l v winding for first transformer
+v2=400; // voltage recorded during short circuit of l v winding for second transformer
+p2=3200; // power dissipated during short circuit of l v winding for second transformer
+v3=480; // voltage recorded during short circuit test of l v winding third transformer
+p3=3250; // power dissipated during short circuit of l v winding for third transformer
+l1=(P+(v1/v2)*P+(v1/v3)*P)/1000;
+printf('The greatest load that can be put on the transformers is %f KVA\n',l1);
+is=P/S2; // secondary rated current
+// transformer 1 is fully loaded , its carries full load current
+re2=p1/is^2; // total resistance referred to secondary side
+vd=is*re2; // voltage drop for transformer 1
+E2=S2-vd;
+printf('Secondary terminal voltage is %f v',E2);
diff --git a/3760/CH1/EX1.49/Ex1_49.sce b/3760/CH1/EX1.49/Ex1_49.sce new file mode 100644 index 000000000..8cc6265de --- /dev/null +++ b/3760/CH1/EX1.49/Ex1_49.sce @@ -0,0 +1,32 @@ +clc;
+disp('case b');
+// KVA ratings and leakage impedances for the transformers are
+k1=100; // KVA rating for transformer 1;
+z1=0.02; // p u impedance for transformer 1;
+k2=75; // KVA rating for transformer 2;
+z2=0.03; // p u impedance for transformer 2;
+k3=50; // KVA rating for transformer 3;
+z3=0.025; // p u impedance for transformer 3;
+disp('case b(1)');
+// assumng k1 as a base KVA
+S=225; // load which has to be shared by three transformers
+ze1=z1*100; // percentage impedance for transformer 1
+ze2=(k1/k2)*z2*100; // percentage impedance for transformer 2
+ze3=(k1/k3)*z3*100; // percentage impedance for transformer 3
+zt=(1/ze1)+(1/ze2)+1/(ze3); // total percentage leakage impedance
+s1=S/(ze1*zt);
+s2=S/(ze2*zt);
+s3=S/(ze3*zt);
+printf('load shared by transformer 1,2 and 3 are %f KVA, %f KVA and %f KVA respectively\n',s1,s2,s3);
+disp('case b(2)');
+// since transformer 1 has lowest leakage impedance among three, it will be loaded to its rated capacity
+S=k1*ze1*zt ; // total KVA shared
+printf('greatest load that can be shared by transformers is %f KVA\n',S);
+disp('case b(3)');
+// for successful parallel operation of transformer all the three leakage impedances based on their KVA rating should be equal.Since magnitude of leakage impedance of transformer1 is fixed that is 2 percent z2=z3=2 percent
+ze1=2;
+ze2=ze1*(k1/k2);
+ze3=ze1*(k1/k3);
+zt=(1/ze1)+(1/ze2)+(1/ze3); // Total leakage impedance
+printf('magnitude of equivalent leakage impedance is %f percent\n',zt);
+
diff --git a/3760/CH1/EX1.5/Ex1_5.sce b/3760/CH1/EX1.5/Ex1_5.sce new file mode 100644 index 000000000..919be6efe --- /dev/null +++ b/3760/CH1/EX1.5/Ex1_5.sce @@ -0,0 +1,40 @@ +clc;
+v1=240; // high voltage side voltage
+v2=120; // low voltage side voltage
+f1=50; // frequency in Hz
+disp('v1 is directly proportional to product of frequency and maximum flux. considering q1 be maximum flux for v1 and q2 be maximum flux for v11 then Q=q2/q1 can be calculated as follow ')
+disp('case a')
+v11=240; // new supply voltage
+f2=40; // new supply frequency
+Q=(v11*f1)/(v1*f2);
+v22=(v2*f2*Q)/f1;
+printf('secondary voltage for case a is %f v\n',v22);
+disp('case b')
+v11=120; // new supply voltage
+f2=25; // new supply frequency
+Q=(v11*f1)/(v1*f2);
+v22=(v2*f2*Q)/f1;
+printf('secondary voltage for case a is %f v\n',v22);
+disp('case c')
+v11=120; // new supply voltage
+f2=50; // new supply frequency
+Q=(v11*f1)/(v1*f2);
+v22=(v2*f2*Q)/f1;
+printf('secondary voltage for case a is %f v\n',v22);
+disp('case d')
+v11=480; // new supply voltage
+f2=50; // new supply frequency
+Q=(v11*f1)/(v1*f2);
+v22=(v2*f2*Q)/f1;
+printf('secondary voltage for case a is %f v\n',v22);
+disp('case e')
+v11=240; // new supply voltage
+f2=0; // new supply frequency
+disp('since frequency is zero. Source is a DC source so a very high current will flow in primary side which will damage the transformer and the secondary induced emf is zero ')
+
+
+
+
+
+
+
diff --git a/3760/CH1/EX1.50/Ex1_50.sce b/3760/CH1/EX1.50/Ex1_50.sce new file mode 100644 index 000000000..9420898b4 --- /dev/null +++ b/3760/CH1/EX1.50/Ex1_50.sce @@ -0,0 +1,38 @@ +clc;
+// shorts circuits test on two transformers gave the following results
+P1=200000; // KVA of transformer 1
+V1=3; // percentage rated voltage
+pf1=0.25; // lagging power factor for Xmer1
+P2=500000; // KVA of transformer 2
+V2=4; // percentage rated voltage
+pf2=0.3 // lagging power factor for Xmer2
+l=560000; // load connected across parallel combination of transformers in KW
+pf=0.8; // power factor of load
+E1=11000; // Rated primary voltage
+E2=400; // Rated secondary voltage
+ib=1; // base current
+vb=1; // base voltage
+z1=(V1/100)*1; // base impedance
+Ze1=z1*(pf1+%i*sqrt(1-pf1^2)); // p u impedance
+z2=(V2/100)*1; // base imedance
+Ze2=z2*(pf2+%i*sqrt(1-pf2^2)); // p u impedance
+pb=P2; // base for p u conversion
+ze1=(pb/P1)*Ze1;
+ze2=(pb/P2)*Ze2;
+zt=ze1+ze2; // total impedance
+s=l/pf; // KVA rating of transformer
+S=s*(pf-%i*sqrt(1-pf^2)); // complex form of KVA rating
+s1=(S*ze2)/(zt); // KVA shared by first transformer
+PF1=cos(atand(imag(s1),real(s1))*(%pi/180));
+s1w=round((abs(s1)*PF1)/1000);
+printf('KW load shared by transformer 1 is %f at %f power factor lagging\n',s1w,PF1);
+s2=(S*ze1)/(zt); // KVA shared by first transformer
+PF2=cos(atand(imag(s2),real(s2))*(%pi/180));
+s2w=ceil((abs(s2)*PF2)/1000);
+printf('KW load shared by transformer 2 is %f at %f power factor lagging\n',s2w,PF2);
+i1=abs(s1)/P1; // p u current shared by transformer 1
+i2=abs(s2)/P2; // p u current shared by transformer 2
+vr=i1*(real(Ze1)*PF1+imag(Ze1)*sqrt(1-PF1^2)); // voltag regulation
+dv=E2*vr; // change in terminal voltage
+Vt=E2-dv; // terminal voltage
+printf('Secondary terminal voltage is %f v',Vt);
diff --git a/3760/CH1/EX1.51/Ex1_51.sce b/3760/CH1/EX1.51/Ex1_51.sce new file mode 100644 index 000000000..5a68492b3 --- /dev/null +++ b/3760/CH1/EX1.51/Ex1_51.sce @@ -0,0 +1,17 @@ +clc;
+k1=1000; // Rated KVA of transformer1
+k2=500; // Rated KVA of transformer2
+ze1=0.02+%i*0.06; // p u leakage impedance of transformer 1
+ze2=0.025+%i*0.08; // p u leakage impedance of transformer 2
+zb=1000; // base impedance
+Z1=(zb/k1)*ze1; // impedance of transformer 1
+Z2=(zb/k2)*ze2; // impedance of transformer 2
+zt=Z1+Z2; // total impedance
+S=k1*(abs(zt)/abs(Z2)); // since ze1<ze2 transformer 1 reaches its rated KVA threrfore load shared by transformer 2 is given by
+l2=S-k1; // load shared by transformer 2
+printf('Largest KVA load that can be loaded on parallel combination of transformer is given by %f KVA',S);
+
+
+
+
+
diff --git a/3760/CH1/EX1.52/Ex1_52.sce b/3760/CH1/EX1.52/Ex1_52.sce new file mode 100644 index 000000000..e8cc26cc3 --- /dev/null +++ b/3760/CH1/EX1.52/Ex1_52.sce @@ -0,0 +1,21 @@ +clc;
+// two transformers are connected in parallel and has following data
+P1=100; // rated KVA of transformer 1
+E11=6600; // rated primary voltage for transformer 1
+E21=230; // rated secondary voltage for transformer 1
+z1=1.5+4*%i // percentage leakage impedance for transformer 1
+P2=200; // rated KVA of transformer 2
+E12=6600; // rated primary voltage for transformer 2
+E22=220; // rated secondary voltage for transformer 2
+z2=1+5*%i // percentage leakage impedance for transformer 2
+i1=(P1*1000)/E21; // full load current for transformer 1
+ze1=(z1/100)*(E21^2/(P1*1000)); // leakage impedance for transformer 1 in ohm
+i2=(P2*1000)/E22; // full load current for transformer 2
+ze2=(z2/100)*(E22^2/(P2*1000)); // leakage impedance for transformer 2 in ohm
+io=(E21-E22)/abs(ze1+ze2); // circulating current at no load
+printf('No load circulating current is %f A\n',real(io));
+poh=abs(io)^2*(real(ze1)+real(ze2));
+printf(' Ohmic losses due to circulting current is %f W\n',poh);
+vd=abs(io)*abs(ze1); // voltage drop in leakage impedance
+vt=E21-vd; // secondary terminal voltage
+printf('secondary terminal voltage is %f v',vt);
diff --git a/3760/CH1/EX1.53/Ex1_53.sce b/3760/CH1/EX1.53/Ex1_53.sce new file mode 100644 index 000000000..349d5d45a --- /dev/null +++ b/3760/CH1/EX1.53/Ex1_53.sce @@ -0,0 +1,41 @@ +clc;
+k1=500000; // rated VA of transformer 1
+r1=0.015; // p u resistance of transformer 1
+x1=0.05; // p u reactance of transformer 1
+s1=405; // secondary no load voltage for transformer 1
+k2=250000; // rated VA of transformer 2
+r2=0.01; // p u resistance of transformer 2
+x2=0.05; // p u reactance of transformer 2
+s2=415; // secondary no load voltage for transformer 2
+l=750000; // KVA rating of load
+pf=0.8; // power factor of load
+v=400; // voltage at which load is being delivered
+z1=(r1+%i*x1)*(v^2/k1); // impedance for transformer 1 in ohms
+z2= (r2+%i*x2)*(v^2/k2); // impedance for transformer 2 in ohms
+il=l/v; // load current
+zl=v/il; // load impedance
+zl=zl*(pf+%i*sqrt(1-pf^2)); // complex form of load impedance
+zt=z1+z2; // equivalent impedance of both transformer
+io=(s2-s1)/abs(zt); // circulating current at no load
+aio=cos(atand(imag(zt),real(zt))*(%pi/180)); // power factor
+printf('Circulating current at no load is %f A at a power factor of %f lag\n',io,aio);
+Ia=((s1*z2)+(s1-s2)*zl)/((z1*z2)+(zl*zt));
+ia=abs(Ia);
+printf('Current shared by transformer 1 is %f A\n',ia);
+Ib=((s2*z1)-(s1-s2)*zl)/((z1*z2)+(zl*zt));
+ib=abs(Ib);
+printf('Current shared by transformer 2 is %f A\n',ib);
+kv1=(ia*v)/1000;
+pf1=cos(atand(imag(Ia),real(Ia))*(%pi/180));
+kw1=kv1*pf1;
+printf('KVA shared by transformer 1 is %f KVA at %f lagging power factor\n',kv1,pf1);
+printf('KW shared by transformer 1 is %f KW\n',kw1);
+kv2=(ib*v)/1000;
+pf2=cos(atand(imag(Ib),real(Ib))*(%pi/180));
+kw2=kv2*pf2;
+printf('KVA shared by transformer 2 is %f KVA at %f lagging power factor\n',kv2,pf2);
+printf('KW shared by transformer 2 is %f KW\n',kw2);
+
+
+
+
diff --git a/3760/CH1/EX1.54/Ex1_54.sce b/3760/CH1/EX1.54/Ex1_54.sce new file mode 100644 index 000000000..49cf5e118 --- /dev/null +++ b/3760/CH1/EX1.54/Ex1_54.sce @@ -0,0 +1,11 @@ +clc;
+z1=0.4+2.2*%i; // leakage impedance referred to secondary for transformer 1
+s1=510; // secondary no load voltage for transformer 1
+z2=0.6+1.7*%i; // leakage impedance referred to secondary for transformer 2
+s2=500; // secondary no load voltage for transformer 2
+zl=5+3*%i; // load impedance
+// current shared by both transformers should be equal i.e. I1=I2
+t=(s2*(z1)-(s1-s2)*zl-(s1-s2)*zl)/s1;
+xn=sqrt(abs(t)^2-real(z2)^2);
+xe=xn-imag(z2); // external reactance to be added in series
+printf('External reactance connected in series with leakage impedance of transformer 2 so that the current shared by both transformers are equal is %f ohm',xe);
diff --git a/3760/CH1/EX1.55/Ex1_55.sce b/3760/CH1/EX1.55/Ex1_55.sce new file mode 100644 index 000000000..bf33cccaa --- /dev/null +++ b/3760/CH1/EX1.55/Ex1_55.sce @@ -0,0 +1,19 @@ +clc;
+k=100; // Kva rating of transformer
+disp('case(a)');
+l1=90; // KVA rating of load
+pf=0.8; // lagging pf of load
+z=0.0075+0.09*%i; // p u leakage impedance of transformer
+l1=l1/k; // load expressed in p u with base KVA=100
+vd=l1*(real(z)*pf+imag(z)*sqrt(1-pf^2)); // p u voltage regulation
+ts=vd*100; // tap setting
+printf('Number of turns in the primary winding should be tapped down by %f percent\n',ts);
+disp('case(b)');
+lk=100; // KW rating of load
+pf=0.8; // lagging pf of load
+l1=lk/pf; // KVA rating of load
+z=0.0075+0.09*%i; // p u leakage impedance of transformer
+l1=l1/k; // load expressed in p u with base KVA=100
+vd=l1*(real(z)*pf+imag(z)*sqrt(1-pf^2)); // p u voltage regulation
+ts=vd*100; // tap setting
+printf('Number of turns in the primary winding should be tapped down by %f percent\n',ts);
diff --git a/3760/CH1/EX1.56/Ex1_56.sce b/3760/CH1/EX1.56/Ex1_56.sce new file mode 100644 index 000000000..24bca8ca5 --- /dev/null +++ b/3760/CH1/EX1.56/Ex1_56.sce @@ -0,0 +1,20 @@ +clc;
+p=11000; // per phase h v side voltage
+s=433; // l v side voltage
+sp=s/sqrt(3); // per phase l v side voltage
+K=10000; // VA rating of star connected load
+pf=0.8; // power factor of load
+z=0.5+1*%i; // Impedance per lead
+zh=300+1500*%i; // per phase h v side leakage impedance
+zl=0.2+1*%i; // per phase l v side leakage impedance
+vl=400; // load voltage
+k=p/sp; // turns ratio
+zhl=zh/k^2; // h v side leakage impedance referred to l v side
+zt=zhl+zl+z; // total impedance per phase between transformer and seconday load
+il=K/(sqrt(3)*vl); // per phase load current
+vd=round(il*(real(zt)*pf+imag(zt)*sqrt(1-pf^2))); // voltage drop per phase
+vlp=vl/sqrt(3); // per phase load terminal voltage
+E2=vlp+vd; // per phase voltage that must maintained l v terminals
+vb=E2-sp; // voltage boost that tap changer must provide
+ts=round((vb/sp)*100);
+printf('tap down if the tapped coils are on h v side or tap up if the tapped coils are on l v side by %f percent',ts);
diff --git a/3760/CH1/EX1.57/Ex1_57.sce b/3760/CH1/EX1.57/Ex1_57.sce new file mode 100644 index 000000000..0ed8c7bec --- /dev/null +++ b/3760/CH1/EX1.57/Ex1_57.sce @@ -0,0 +1,11 @@ +clc;
+k=5; // Effective turns ratio
+E1=400; // supply voltage for primary
+il=10; // load current
+E2=E1/k; // magnitude of maximum secondary induced
+E1o=E1+E2; // maximum possibe value of output voltage
+P=(il*E2)/1000; // Rating of secondary winding
+ip=(il*E2)/E1; // neglecting noload current, primary winding current
+I=ip+il;
+printf('Total primary line current is %f A',I);
+
diff --git a/3760/CH1/EX1.58/Ex1_58.sce b/3760/CH1/EX1.58/Ex1_58.sce new file mode 100644 index 000000000..1d4c08ca5 --- /dev/null +++ b/3760/CH1/EX1.58/Ex1_58.sce @@ -0,0 +1,8 @@ +clc;
+E1=430; // supply voltage
+k=100000; // VA rating of load
+il=k/(sqrt(3)*E1); // load current
+v1=380; v2=460; // range in which voltage at feeder end varies
+vr=E1-v1; // maximum variation in output side of regulator
+P=(sqrt(3)*vr*il)/1000;
+printf('KVA rating of induction regulator is %f KVA',P);
diff --git a/3760/CH1/EX1.59/Ex1_59.sce b/3760/CH1/EX1.59/Ex1_59.sce new file mode 100644 index 000000000..71c96f204 --- /dev/null +++ b/3760/CH1/EX1.59/Ex1_59.sce @@ -0,0 +1,17 @@ +clc;
+V1=400; // supply voltage
+E2=50; // induced secondary voltage
+l=8; // KW rating of load
+pf=0.8; // power factor of load
+n=0.85; // efficiency of induction regulator
+ip=(l*1000)/(sqrt(3)*pf*n*V1); // input current
+vmo=V1-E2; // minimum output voltage
+imo=(l*1000)/(sqrt(3)*pf*vmo); // maximum output current
+ks=(sqrt(3)*E2*imo)/1000; // KVA rating of secondary winding
+Vmo=V1+E2; // maximum output voltage
+Imo=(l*1000)/(sqrt(3)*pf*Vmo); // minimum output current
+//primary winding has to carry the current induced in it by secondary current due to transformer action and the difference of input current and output current
+ipm=((Imo*E2)/V1)+ip-Imo; // maximum primary winding current
+kp=(sqrt(3)*V1*ipm)/1000;
+printf('Rating of primary winding is %f KVA\n',kp);
+printf('Rating of secondary winding is %f KVA\n',ks);
diff --git a/3760/CH1/EX1.6/Ex1_6.sce b/3760/CH1/EX1.6/Ex1_6.sce new file mode 100644 index 000000000..0cc98ada7 --- /dev/null +++ b/3760/CH1/EX1.6/Ex1_6.sce @@ -0,0 +1,15 @@ +clc;
+N1=100; // no. of primary turns
+N2=160; // No. of secondary turns
+N3=60; // No. of tertiary turns
+I2=10; // secondary side current
+I3=20; // tertiary side current
+F2=N2*I2; // mmf of secondary winding
+F3=N3*I3; // mmf of tertiary winding
+disp('load connected to secondary is purely resistive and load connected to tertiary is purely capacitive' );
+F23=sqrt(F2^2+F3^2); //resultant load mmf
+F1=F23; // primary winding mmf balances this load mmf
+I1=F1/N1;
+printf('primary current is %f A\n',I1);
+pf=F2/F1;
+printf('primary side power factor is %f leading',pf);
diff --git a/3760/CH1/EX1.60/Ex1_60.sce b/3760/CH1/EX1.60/Ex1_60.sce new file mode 100644 index 000000000..67409f91f --- /dev/null +++ b/3760/CH1/EX1.60/Ex1_60.sce @@ -0,0 +1,18 @@ +clc;
+p=10; // number of full pitch coil in stator
+t=120; // phase spread of coil
+q=10.5*10^-3; // flux per pole in Weber
+f=50; // frequency of induction regulator
+n=2; // number of turns in each coil;
+E1=230; // supply voltage
+il=30; // load current
+N=p*n; // Total number of turns
+kw=sin((t/2)*(%pi/180))/((t/2)*(%pi/180)); // distribution factor
+E2=sqrt(2)*%pi*f*N*q*kw; // maximum secondary induced EMF
+Vo1=E1+E2; Vo2=E1-E2; // range of output voltage
+k=(il*E2)/1000;
+printf('Maximum induced voltage is %f v\n',E2);
+printf('range of output voltage is %f v-%f v\n',Vo2,Vo1);
+printf('KVA rating of induction regulator is %f KVA',k);
+
+
diff --git a/3760/CH1/EX1.61/Ex1_61.sce b/3760/CH1/EX1.61/Ex1_61.sce new file mode 100644 index 000000000..52820d154 --- /dev/null +++ b/3760/CH1/EX1.61/Ex1_61.sce @@ -0,0 +1,34 @@ +clc;
+// subscript 1 and 2 indicates h v and l v winding
+P=10000; // rated VA of transformer
+E1=2300; // rated voltage
+E2=230; // rated voltage
+r1=10; // total resistance
+r2=0.10; // total resistance
+l1=40*10^-3 ; l2=4*10^-4; // self-inductances
+m=10; // mutual inductance
+k=E2/E1; // turns ratio
+f=50; // frequency of supply;
+disp('case 1');
+L1=(m/k)+l1;
+printf('Primary self inductance is %f H\n',L1);
+L2=(m*k)+l2;
+printf('Secondary self inductance is %f H\n',L2);
+disp('case b');
+r21=r2/k^2; // l v side resistance referred to h v side
+l21=l2/k^2; // l v side self inductance referred to h v side
+M1=m/k; // mutual inductance referred to h v side
+printf('circuit parameters referred to primary winding are R1=%f ohm,R2=%f ohm,L1=%f H,L2=%f H and Lm1=%f H\n',r1,r21,l1,l21,M1);
+r12=r1*k^2; // h v side resistance referred to l v side
+l12=l1*k^2; // h v side self inductance referred to l v side
+M2=m*k; // mutual inductance referred to l v side
+printf('circuit parameters referred to secondary winding are R1=%f ohm,R2=%f ohm,L1=%f H,L2=%f H and Lm2=%f H\n',r12,r2,l12,l2,M2);
+disp('case c');
+lo=5+5*%i; // load connected to secondary
+x1=2*%pi*f*l12; // leakage reactance
+x2=2*%pi*f*l2; // leakage reactance
+re2=real(lo)+r2+r12; // total resistance after referring to l v side
+xe2=imag(lo)+x1+x2; // total reactance after referring to l v side
+Z=re2+%i*xe2; // total impedance
+vt=(E2/abs(Z))*abs(lo);
+printf('Secondary terminal voltage is %f v',vt);
diff --git a/3760/CH1/EX1.62/Ex1_62.sce b/3760/CH1/EX1.62/Ex1_62.sce new file mode 100644 index 000000000..9f65ef99c --- /dev/null +++ b/3760/CH1/EX1.62/Ex1_62.sce @@ -0,0 +1,24 @@ +clc;
+n1=590; // primary side turns
+n2=295; // secondary side turns
+V1=230; // voltage source from which h v side was energised during test
+io1=0.35; // no load current for when h v side is energised
+V2=110; // induced voltage across open circuited l v winding due energised h v side
+v2=115; // voltage source from which l v side was energised during test
+io2=0.72; // no load current for when l v side is energised
+v1=226; // induced voltage across open circuited h v winding due energised l v side
+f=50; // frequency of supply;
+w1=V1/(sqrt(2)*%pi*50); // Maximum value of flux linkage with h v winding
+L1=w1*(1/(sqrt(2)*io1));
+printf('self inductance of h v winding i %f H\n',L1);
+w2=v2/(sqrt(2)*%pi*50); // Maximum value of flux linkage with l v winding
+L2=w2*(1/(sqrt(2)*io2));
+printf('self inductance of l v winding i %f H\n',L2);
+M=(V2/(sqrt(2)*%pi*f))*(1/(sqrt(2)*io1));
+printf('mutual inductance between h v and l v winding is %f H\n',M);
+k1=(n1/n2)*(M/L1); // coupling factor for h v side
+k2=(n2/n1)*(M/L2); // coupling factor for l v side
+k=sqrt(k1*k2); // coefficient of coupling
+printf('coupling factor for h v side is %f\n',k1);
+printf('coupling factor for l v side is %f\n',k2);
+printf('coefficient of coupling is %f\n',k);
diff --git a/3760/CH1/EX1.63/Ex1_63.sce b/3760/CH1/EX1.63/Ex1_63.sce new file mode 100644 index 000000000..1a9ee6c6d --- /dev/null +++ b/3760/CH1/EX1.63/Ex1_63.sce @@ -0,0 +1,17 @@ +clc;
+L1=4*10^-3; // self indutance of winding 1
+L2=6*10^-3; // self indutance of winding 2
+M=1.8*10^-3; // mutual inductance of two windings
+E1=130; // supply voltage for winding 1
+f=500/%pi; // frequency of supply
+l=0.2*10^-3; // load connected to winding 2
+// writing voltage in rms form in matrix form V1=r1*I1+jw*L1*I1-jw*m*I2, V2=-r2*I2-jw*L2*I2+jw*m*I1 to determine I1 and I2
+t1=%i*2*%pi*f*L1;
+t2=-%i*2*%pi*f*M;
+t3=%i*2*%pi*f*M;
+t4=-%i*2*%pi*f*l-%i*2*%pi*f*L2; // writing different terms of matrix
+s=[t1 t2;t3 t4];
+v=[130;0];
+i=inv(s)*v; // calculating current in two windings
+p=-imag(i(1));
+printf('magnitude of current in primary winding is %f A',p);
diff --git a/3760/CH1/EX1.64/Ex1_64.sce b/3760/CH1/EX1.64/Ex1_64.sce new file mode 100644 index 000000000..002b7f159 --- /dev/null +++ b/3760/CH1/EX1.64/Ex1_64.sce @@ -0,0 +1,18 @@ +clc;
+r=60; // resistive load which is coupled to electronic circuit
+v=5; R=3000; // electronic circuit represented by a voltage source in series with a internal resistance
+// for maximum transfer of power, load resistance referred to primary must be equal to internal resitance of source
+k=sqrt(R/r);
+printf('turns ratio for maximum transfer of power is %f\n',k);
+// referrig all quantities to load side
+vl=v/k; // source voltage referred to load side
+Rl=R/k^2; // source referred to load side
+il=(vl/(Rl+r))*1000 ; // load current
+vld=(il*r)/1000; // load voltage
+p=(il^2*r)/1000; // load power
+printf('load voltage is %f v\n',vld);
+printf('load current is %f mA\n',il);
+printf('load power is %f mW\n',p);
+
+
+
diff --git a/3760/CH1/EX1.65/Ex1_65.sce b/3760/CH1/EX1.65/Ex1_65.sce new file mode 100644 index 000000000..027d9a678 --- /dev/null +++ b/3760/CH1/EX1.65/Ex1_65.sce @@ -0,0 +1,26 @@ +clc;
+r1=20; // resistance of primary side
+l1=1*10^-3; // leakage inductance of primary side
+r2=0.5; // resistance of secondary side
+l2=0.025*10^-3; // leakage inductance of secondary side
+m=0.2; // mutual inductance
+l=50; // load in ohm connected to transformer
+v=5; // voltage source
+R=2000; // internal resistance of source
+k=sqrt(R/l); // turns ratio for maximum power transfer
+printf('Turns ratio is %f\n',k);
+r21=0.5*k^2; // secondary resistance referred to primary
+l21=l2*k^2; // secondary inductance referred to primary
+lp=l*k^2; // load resistance referred to primary
+rs=r1+r21+lp+R; // total series resistance
+rp=((R+r1)*(R+r1))/rs; // equivalent resistance
+leq=l1+l21; // equivalent inductance
+f1=100; // frequency in hertz at which load voltage has to be calculated
+Vl=(1/k)*(R/rs)*v*(1/(sqrt(1+(rp/(2*%pi*f1*m))^2)));
+printf('load voltage at %f hz is %f v\n',f1,Vl);
+f2=5000; // frequency in hertz at which load voltage has to be calculated
+Vl=(1/k)*(R/rs)*v;
+printf('load voltage at %f hz is %f v\n',f2,Vl);
+f3=15000; // frequency in hertz at which load voltage has to be calculated
+Vl=(1/k)*(R/rs)*(1/(sqrt(1+((2*%pi*f3*l1)/rs)^2)))*v;
+printf('load voltage at %f hz is %f v\n',f3,Vl);
diff --git a/3760/CH1/EX1.66/Ex1_66.sce b/3760/CH1/EX1.66/Ex1_66.sce new file mode 100644 index 000000000..3554b58e8 --- /dev/null +++ b/3760/CH1/EX1.66/Ex1_66.sce @@ -0,0 +1,49 @@ +clc;
+// Answer for case c , secondary line voltage is given wrong in book
+k=12; // per phase turns ratio
+E1=11000; // supply voltage from feeder line
+ip=20; // primary line current
+disp('case a:star-delta');
+vph=E1/sqrt(3); // primary phase voltage
+iph=ip; // phase current on primary
+sph=vph/k; // secondary phase voltage
+vls=sph;
+printf('Line voltage on secondary is %f v\n',vls);
+isph=k*iph; // phase current on secondary
+isl=sqrt(3)*isph;
+printf('line current on secondary is %f A\n',isl);
+Kv=(3*sph*isph)/1000;
+printf('Output KVA is %f KVA\n',Kv);
+disp('case b:delta-star');
+vph=E1; // primary phase voltage
+iph=ip/sqrt(3); // phase current on primary
+sph=vph/k; // secondary phase voltage
+vls=sqrt(3)*sph;
+printf('Line voltage on secondary is %f v\n',vls);
+isph=k*iph; // phase current on secondary
+isl=isph;
+printf('line current on secondary is %f A\n',isl);
+Kv=(3*sph*isph)/1000;
+printf('Output KVA is %f KVA\n',Kv);
+disp('case c:delta-delta');
+vph=E1; // primary phase voltage
+iph=ip/sqrt(3); // phase current on primary
+sph=vph/k; // secondary phase voltage
+vls=sph;
+printf('Line voltage on secondary is %f v\n',vls);
+isph=k*iph; // phase current on secondary
+isl=sqrt(3)*isph;
+printf('line current on secondary is %f A\n',isl);
+Kv=(3*sph*isph)/1000;
+printf('Output KVA is %f KVA\n',Kv);
+disp('case d:star-star');
+vph=E1/sqrt(3); // primary phase voltage
+iph=ip; // phase current on primary
+sph=vph/k; // secondary phase voltage
+vls=sqrt(3)*sph;
+printf('Line voltage on secondary is %f v\n',vls);
+isph=k*iph; // phase current on secondary
+isl=isph;
+printf('line current on secondary is %f A\n',isl);
+Kv=(3*sph*isph)/1000;
+printf('Output KVA is %f KVA\n',Kv);
diff --git a/3760/CH1/EX1.67/Ex1_67.sce b/3760/CH1/EX1.67/Ex1_67.sce new file mode 100644 index 000000000..691ab7d84 --- /dev/null +++ b/3760/CH1/EX1.67/Ex1_67.sce @@ -0,0 +1,16 @@ +clc;
+E1=11000; // line voltage of primary
+E2=415; // line voltage of secondary
+kw=30; // KW rating of 3 phase induction motor
+n=0.9; // efficieny
+pf=0.833; // power factor at which load is operating
+Kv=kw/(n*pf); // KVA rating of transformer
+printf('KVA rating of transformer is %f KVA\n',Kv);
+ilv=(Kv*1000)/(sqrt(3)*E2); // line current on l v side
+//secondary is star connected therefore line current=phase current
+printf('Line current on l v side is %f A\n',ilv);
+printf('Phase current on l v side is %f A\n',ilv);
+ilp=(Kv*1000)/(sqrt(3)*E1); // line current on h v side
+ipp=ilp/sqrt(3);
+printf('Line current on h v side is %f A\n',ilp);
+printf('Phase current on h v side is %f A\n',ipp);
diff --git a/3760/CH1/EX1.68/Ex1_68.sce b/3760/CH1/EX1.68/Ex1_68.sce new file mode 100644 index 000000000..74735cff8 --- /dev/null +++ b/3760/CH1/EX1.68/Ex1_68.sce @@ -0,0 +1,16 @@ +clc;
+il=100; // load current
+pf=0.8;
+E1=11000; // primary line voltage
+E2=400; // secondary line voltage
+p=(sqrt(3)*E2*il*pf)/1000;
+printf('power consumed by load is %f KW\n',p);
+k=(sqrt(3)*E2*il)/1000;
+printf('KVA rating of load is %f KVA\n',k);
+iph=(k*1000)/(sqrt(3)*11000); // phase current on h v side
+//primary is star connected therefore line current=phase current
+printf('Line current on h v side is %f A\n',iph);
+printf('Phase current on h v side is %f A\n',iph);
+ipl=il/sqrt(3);
+printf('Line current on l v side is %f A\n',il);
+printf('Phase current on l v side is %f A\n',ipl);
diff --git a/3760/CH1/EX1.69/Ex1_69.sce b/3760/CH1/EX1.69/Ex1_69.sce new file mode 100644 index 000000000..47f643661 --- /dev/null +++ b/3760/CH1/EX1.69/Ex1_69.sce @@ -0,0 +1,30 @@ +clc;
+B=1.2; // maximum flux density in core
+H=600; // magnetic field intensity in A/m
+d=7.8; // gram density in g/cm^3
+cl=2; // core loss per kg
+e=1200; // supply voltage
+f=50; // frequency of supply voltage
+t=10; // thickness of core in cm
+w=40;
+L=30; // dimensions of core
+s=0.9; // stacking factor
+ga=t^2*10^-4; // gross core area in m^2
+nga=ga*s; // net gross core area in m^2
+q=nga*B; // maximum flux in core
+N=(e)/(sqrt(2)*%pi*f*q);
+printf('Number of turns in primary is %f\n',N);
+ml=((w+t)+(L+t))*2; // mean flux path in cm
+mmf=H*(ml/100); // mmf of the core
+mi=mmf/N; // maximum value of magnetizing current
+irm=mi/sqrt(2); // rms value of magnetizing current
+cv=(ml/100)*nga; // core volume
+wc=cv*d*10^3; // weight of core
+pc=wc*cl; // total core loss
+Ic=pc/e; // core loss current
+io=sqrt(Ic^2+irm^2);
+printf('No load current on primary side is %f A\n',io);
+pf=Ic/io;
+printf('No load power factor is %f\n',pf);
+pf=e*io*pf;
+printf('power input at no load is %f W',pf);
diff --git a/3760/CH1/EX1.70/Ex1_70.sce b/3760/CH1/EX1.70/Ex1_70.sce new file mode 100644 index 000000000..c203be35d --- /dev/null +++ b/3760/CH1/EX1.70/Ex1_70.sce @@ -0,0 +1,28 @@ +clc;
+// Three core type transformers are given in fig 1.80
+// For first core type transformer
+im1=4; // magnetizing core
+e2=100; // emf induced in secondary winding
+B=1; // maximum flux density in Tesla
+// mmf is directly proportional maximum flux in core i.e im*N(no. of turns)=kq(flux), k is proportionality constant
+// for fig(80(b)),qm2(flux for core transformer 1)=qm1(flux for core transformer 2), that is flux in both coils in core transformer 2 is qm1/2;
+//for upper coil im2*N is directly proportional to qm1/2
+//for lower coil Im2*N is directly proportional to qm2/2
+//adding above relation we get im2+Im2=4(magnetizing current)
+Im2=im1/2;
+im2=Im2; // magnetizing current of each coil is 2 A
+imt=Im2+im2; //total magnetizing current for transformer 2
+// since flux is same for both transformer, emf induced is also same
+// since flux is same for both transformer, area is same , therefore magnetic flux density is also same
+printf('Magnetizing current for transformer 2 is %f A\n',imt);
+printf('emf induced in secondary for transformer 2 is %f v\n',e2);
+printf('Magnetic flux density in transformer 2 is %f T\n',B);
+// for fig (80(c)), qm3=qm1/2
+// qm1~im1*N,qm3~im3*N; ~-sign of directly proportional (assumption)
+// from above two relations, we get
+im3=im1/4;
+B3=B/2;
+E2=e2/2;
+printf('Magnetizing current for transformer 3 is %f A\n',im3);
+printf('emf induced in secondary for transformer 3 is %f v\n',E2);
+printf('Magnetic flux density in transformer 3 is %f T\n',B3);
diff --git a/3760/CH1/EX1.71/Ex1_71.sce b/3760/CH1/EX1.71/Ex1_71.sce new file mode 100644 index 000000000..08e1ab5fc --- /dev/null +++ b/3760/CH1/EX1.71/Ex1_71.sce @@ -0,0 +1,26 @@ +clc;
+P=20; // Rated KVA of transformer
+E1=250; // rated primary voltage
+E2=125; // rated secondary voltage
+r1=0.15; // resistance of primary side
+x1=0.25; // leakage reactance of primary side
+r2=0.03; // resistance of secondary side
+x2=0.04; // leakage reactance of secondary side
+// given E1=V1(primary terminal voltage)
+k=E2/E1; // turns ratio
+ip=(P*1000)/E1; // full load primary current
+// voltage regulation=0, because E1=V1 therefore
+pf=-atand(r1,x1); // phase angle between E1 and ip
+// negative sign indicates that current leads voltage
+re2=r2/k^2; // secondary resistance referred to primary
+xe2=x2/k^2; // secondary leakage reactance referred to primary
+ip=ip*(cos(pf*(%pi/180))-%i*sin(pf*(%pi/180))); // complex form of primary current
+V2=E1-ip*(re2+xe2*%i);
+pfl=-atand(imag(V2),real(V2))-pf; // phase angle by which primary current leads secondary terminal voltage referred to primary
+PF=cos(pfl*(%pi/180));
+vl=abs(V2)/2;
+isl=(P*1000)/E2;
+pl=vl*isl*PF;
+printf('Load voltage is %f v\n',vl);
+printf('Load power factor is %f leading\n',PF);
+printf('Load power is %f W',pl);
diff --git a/3760/CH1/EX1.72/Ex1_72.sce b/3760/CH1/EX1.72/Ex1_72.sce new file mode 100644 index 000000000..d35e395bf --- /dev/null +++ b/3760/CH1/EX1.72/Ex1_72.sce @@ -0,0 +1,28 @@ +clc;
+// from fig 1.82
+E1=5; // supply voltage
+E2=20; // induced secondary voltage
+k=E2/E1; // turns ratio
+r1=6; // primary parameters
+r2=16; // secondary parameters
+r21=r2/k; // secondary parameters referred to primary
+E21=(E2*2)/k; // secondary voltage referred to primary
+theta=60*(%pi/180); // phase angle assocoated with E2
+// after referring to primary side, with E1 as a reference
+V=E21*(cos(theta)-%i*sin(theta))-E1; //resultant voltage
+I=abs(V)/(r1+r21); // magnitude of current
+pd1=I^2*r1;
+pd2=I^2*r21;
+printf('power dissipated in %f ohm resistor is %f W\n',r1,pd1);
+printf('power dissipated in %f ohm resistor is %f W\n',r21,pd2);
+// Current lags E1 by 90 degree
+teta1=90*(%pi/180);
+// Since E2 lags E1 by 60 degree and Current due to resultant voltage lags E1 by 90, therefore phase difference Current I and E2 is
+teta2=(90-60)*(%pi/180);
+Pd1=E1*I*cos(teta1);
+Pd2=E21*I*cos(teta2);
+printf('power delivered by %f v source is %f W\n',E1,Pd1);
+printf('power delivered by %f v source is %f W\n',E2,Pd2);
+
+
+
diff --git a/3760/CH1/EX1.73/Ex1_73.sce b/3760/CH1/EX1.73/Ex1_73.sce new file mode 100644 index 000000000..321b19b91 --- /dev/null +++ b/3760/CH1/EX1.73/Ex1_73.sce @@ -0,0 +1,18 @@ +clc;
+P=1200; // rated VA of transformer
+E1=240; // rated primary voltage
+E2=110; // rated secondary voltage
+xe=5; // total leakage reactance of transformer referred to primary
+re=1; // total resistance of transformer referred to primary
+vl=240; // rated voltage of load
+R=2500; // core resistance
+pf=1; // power factor
+ip=P/E1; // full load primary current
+// assuming E1 as a reference
+Vin=sqrt((E1+ip*re)^2+(ip*xe)^2); // input voltage when load is connected
+pi=ip^2*re; // ohmic losses
+pc=Vin^2/R; // core loss
+n=(P*pf*100)/(P*pf+pi+pc);
+printf('Efficiency at full load is %f percent\n',n);
+vr=((Vin-E1)/Vin)*100;
+printf('Voltage regulation for full load is %f percent',vr);
diff --git a/3760/CH1/EX1.74/Ex1_74.sce b/3760/CH1/EX1.74/Ex1_74.sce new file mode 100644 index 000000000..253f7bbe1 --- /dev/null +++ b/3760/CH1/EX1.74/Ex1_74.sce @@ -0,0 +1,20 @@ +clc;
+k1=4; // turns ratio for transformer 1
+k2=3; // turns ratio for transformer 2
+E1=120; // supply across which two transformers are connected in parallel
+E21=E1/k1; // secondary voltage for transformer 1
+E22=E1/k2; // secondary voltage for transformer 2
+R=10; // load resistance
+// Secondary windings are connected in series with the polarity such that the voltages E21 and E22 aid each other
+E2=E21+E22; // resultant output voltage
+il=E2/R; // Load current
+// for mmf balance, primary current for T1
+ip1=il/k1;
+// for mmf balance, primary current for T2
+ip2=il/k2;
+ip=ip1+ip2; // total current drawn from source
+printf('Current drawn from source is %f A\n',ip);
+zi=E1/ip;
+printf('Primary input impedance is %f ohm\n',zi);
+pi=E2*il;
+printf('Primary input power is %f W',pi);
diff --git a/3760/CH1/EX1.75/Ex1_75.sce b/3760/CH1/EX1.75/Ex1_75.sce new file mode 100644 index 000000000..86dfaef29 --- /dev/null +++ b/3760/CH1/EX1.75/Ex1_75.sce @@ -0,0 +1,11 @@ +clc;
+// A and B are two transformer shown in fig 1.85
+im=0.1; // magnetizing current
+// Since SA(secondary winding for transformer A) is connected directly across 200 v supply, so the magnetizing current required to establish the flux must flow through SA, therefore current taken by winding PA(primary winding for transformer A) is zero
+// Since voltage across SA is 200 v , voltage across PA has to be 200 v by transformer action
+// As a result of it , voltage across PB is zero, therefore induced emf in SB is zero
+printf('Current in secondary winding of transformer A is %f A',im);
+disp('Current in primary winding of transformer A is zero');
+disp('Voltage across secondary winding of transformer B is zero');
+
+
diff --git a/3760/CH1/EX1.76/Ex1_76.sce b/3760/CH1/EX1.76/Ex1_76.sce new file mode 100644 index 000000000..eaed45aab --- /dev/null +++ b/3760/CH1/EX1.76/Ex1_76.sce @@ -0,0 +1,21 @@ +clc;
+// 1 and 2 subscripts are used for transformer 1 and transformer 2
+// P and S are used for primary and secondary winding
+E=230; // Rated primary voltage of both transformer
+disp('case 1');
+R=0; // load conneted across secondary of transformer 1
+// R=0 means winding is short circuited, therefore voltage across S1 is zero, therefore whole voltage is applied across s2 therefore
+printf('Reading of voltmeter for R=%f is %f v\n',R,E);
+disp('case 2');
+R=115; // load conneted across secondary of transformer 1
+// A resistance of 115 ohm should cause a current of 1 A because voltage across P1 is 115 v but this means that P1 and P2 carrying 1A current . According to this voltage across P2 is magnetizing impedance of transformer 2 times magnetizing current. But magnetizing impedance is very large, due to this voltage across P2 rises much above 115 v and voltage across P1 falls, due to which magnetizing current through S1 decreases.
+disp('Voltmeter reading is much more than 115 v but less than 230 v. Let it be Vb');
+disp('case 3');
+R=1000; // load conneted across secondary of transformer 1
+// For R=1000 ohm , current in P1 and S1 are reduced. Hence current in P2 is also reduced. Therefore voltage across P2 is also reduced but still it is more than 115 v
+disp('Voltmeter reading is more than 115 v but less than Vb');
+disp('case 4');
+// for R=infinity S1 is open circuited, therefore voltage across P1=115 v and P2=115 v
+disp('Reading of voltmeter is 115 v');
+
+
diff --git a/3760/CH1/EX1.77/Ex1_77.sce b/3760/CH1/EX1.77/Ex1_77.sce new file mode 100644 index 000000000..2e878a33f --- /dev/null +++ b/3760/CH1/EX1.77/Ex1_77.sce @@ -0,0 +1,11 @@ +clc;
+E1=200; // rated voltage of l v side
+E2=400; // rated voltage of h v side
+f=50; // frequency of supply
+W=80; // open circuit input wattage=core loss
+m=1.91; // mutual induction between h v and l v side
+Ic=W/E2; // core loss current
+Qmax=E1/(sqrt(2)*%pi*f); // maximum value of flux linkage with l v winding
+Im=Qmax/(sqrt(2)*m);
+Io=sqrt(Ic^2+Im^2);
+printf('Current taken by transformer when no load test is conducted on h v side is %f A',Io);
diff --git a/3760/CH1/EX1.78/Ex1_78.sce b/3760/CH1/EX1.78/Ex1_78.sce new file mode 100644 index 000000000..2790b26cb --- /dev/null +++ b/3760/CH1/EX1.78/Ex1_78.sce @@ -0,0 +1,15 @@ +clc;
+P=100000; // rated VA of transformer
+n=0.98; // maximum possible efficiency
+l=80000; // rated KVA of load
+vrm=0.04; // maximum possible voltage regulation is equal to ze2 in p u
+pf=0.8; // power factor at which efficiency anf voltage regulation has to be determined
+pl=((1/n)-1)*l; // total losses in transformer
+pc=pl/2; // core losses; at maximum efficiency ohmic losses = core losses
+po=(1/pf)^2*pc; // ohmic losses at given power factor
+N=(P*pf*100)/(l+po+pc);
+printf('Efficiency at %f lagging power factor is %f percent\n',pf,N);
+re2=po/P; // resistance in p u
+xe2=sqrt(vrm^2-re2^2);
+vr=(re2*pf+xe2*sqrt(1-pf^2))*100;
+printf('Voltage regulation at %f lagging power factor is %f percent',pf,vr);
diff --git a/3760/CH1/EX1.79/Ex1_79.sce b/3760/CH1/EX1.79/Ex1_79.sce new file mode 100644 index 000000000..24123a347 --- /dev/null +++ b/3760/CH1/EX1.79/Ex1_79.sce @@ -0,0 +1,16 @@ +clc;
+// after deriving the expression for both the transformer and auto transformer
+k=0.8; // ratio of V2/V1(turns ratio)
+W=100; // Power to be delivered in KW
+pf=1; // unity power factor
+n=0.96; // given efficiency
+disp('for two winding transformer');
+ks=W;
+printf('KVA rating for secondary of two winding transformer is %f KVA\n',ks);
+kp=ks/n;
+printf('KVA rating for primary of two winding transformer is %f KVA\n',kp);
+disp('for auto transformer');
+kab=(W/n)*(1-k);
+printf('KVA rating for section AB of autotransformer is %f KVA\n',kab);
+kbc=W*(1-k/n);
+printf('KVA rating for section BC of autotransformer is %f KVA\n',kbc);
diff --git a/3760/CH1/EX1.8/Ex1_8.sce b/3760/CH1/EX1.8/Ex1_8.sce new file mode 100644 index 000000000..57ec999c1 --- /dev/null +++ b/3760/CH1/EX1.8/Ex1_8.sce @@ -0,0 +1,34 @@ +clc;
+P=33000; // rated power of transformer
+E1=2200; // primary voltage
+E2=220; // secondary voltage
+k=E2/E1; // turn's ratio
+r1=2.4; //primary winding resistance in ohm
+x1=6; // primary winding reactance in ohm
+r2=0.03; //secondary winding resistance in ohm
+x2=0.07; //secondary winding reactance in ohm
+r12=r1*k^2; //primary resistance referred to secondary
+x12=x1*k^2; //primary reactance referred to secondary
+printf('primary resistance and reactance referred to secondary are %f ohm and %f ohm\n',r12,x12);
+r21=r2/k^2; //secondary resistance referred to primary
+x21=x2/k^2; //secondary reactance referred to primary
+printf('secondary resistance and reactance referred to primary are %f ohm and %f ohm\n',r21,x21);
+re1=r1+r21;
+xe1=x1+x21;
+printf('equivalent resistance and reactance referred to primary are %f ohm and %f ohm\n',re1,xe1);
+re2=r2+r12;
+xe2=x2+x12;
+printf('equivalent resistance and reactance referred to secondary are %f ohm and %f ohm\n',re2,xe2);
+Ip=P/E1;
+printf('primary full load current is %f A\n',Ip);
+Is=P/E2;
+printf('secondary full load current is %f A\n',Is);
+O=Ip^2*re1;
+printf('ohmic losses at full load is %f W\n',O);
+Ils=160; // secondary side load current
+Ilp=Ils*k; // primary side load current
+Ze1=sqrt(re1^2+xe1^2);
+V=Ilp*Ze1;
+printf('Voltage applied to h.v side in order to obtain 160A short circuit cirrent in low voltage winding is %f V\n',V);
+Pi=Ilp^2*re1;
+printf('power input is %f W',Pi);
diff --git a/3760/CH1/EX1.9/Ex1_9.sce b/3760/CH1/EX1.9/Ex1_9.sce new file mode 100644 index 000000000..5ca3a7246 --- /dev/null +++ b/3760/CH1/EX1.9/Ex1_9.sce @@ -0,0 +1,28 @@ +clc;
+P=10000; //rated power of transformer
+E1=2500; // rated primary side voltage
+E2=250; // rated secondary side voltage
+// initialising primary side parameters
+r1=4.8; // primary resistance in ohm
+x1=11.2; // primary leakage reactance in ohm
+//initialising secondary side parameters
+r2=0.048; // secondary resistance in ohm
+x2=0.112; // secondary leakage reactance in ohm
+k=E2/E1; // turn's ratio1
+z=5+%i*3.5;
+re2=r2+r1*k^2; //resistance referred to secondary
+xe2=x2+x1*k^2; //reactance referred to secondary
+ze2=re2+%i*xe2;
+zt=z+ze2; // total load on secondary
+Z=abs(zt);
+I2=E2/Z; // load current on secondary
+disp ('case a');
+V2=round(I2*abs(z));
+printf('secondary terminal voltage is %f V\n',V2 );
+disp ('case b');
+pf=0.8; // power factor
+I2l=P/E2; // rated current of secondary side
+VD=I2l*(re2*pf+xe2*sqrt(1-pf^2)); // voltage drop in transformer leakage impedance
+Vt=E2-VD;
+printf('secondary terminal voltage is %f V',Vt)
+
diff --git a/3760/CH2/EX2.13/Ex2_13.sce b/3760/CH2/EX2.13/Ex2_13.sce new file mode 100644 index 000000000..1c19a29b9 --- /dev/null +++ b/3760/CH2/EX2.13/Ex2_13.sce @@ -0,0 +1,42 @@ +clc;
+f=50; // frequency
+w=2*%pi*f; // angular speed
+y=60; // y=angular position of rotor
+Ls=0.6+0.2*cosd(2*y) // self inductance of stator
+dLs=-2*0.2*sind(2*y); // derivative of Ls with y
+Lr=0.75+0.3*cosd(2*y) // self inductance of rotor
+dLr=-2*0.3*sind(2*y); // derivative of Lr with y
+Ms=0.8*cosd(y) // mutual inductance of stator
+dMs=-0.8*sind(y); // derivative of Ms with y
+disp('case a');
+is=20; // stator current
+ir=10; // rotor current
+te=(is^2*dLs)/2+(ir^2*dLr)/2+(is*ir)*dMs;
+printf('Magnitude of torque is %f Nm and since it is negative it acts in such a direction so as to decrease angular position\n',-te);
+is=20; // stator current
+ir=-10; // rotor current
+te=((is^2*dLs)/2)+((ir^2*dLr)/2)+((is*ir)*dMs);
+printf('Magnitude of torque is %f Nm and it acts in clockwise direction\n',te);
+is=20; // stator current
+ir=0; // rotor current
+te=((is^2*dLs)/2)+((ir^2*dLr)/2)+((is*ir)*dMs);
+printf('Magnitude of torque is %f Nm and it acts in counter-clockwise direction\n',-te);
+disp('case b');
+// rotor winding is short circuited rotor voltage=0 and is=sqrt(2)*20*sin(wt) here average torque is needed so for calculation we need not to worry about sin(wt)
+is=sqrt(2)*20; // stator current
+ir=(-Ms/Lr)*is; // rotor current
+te=((is^2*dLs)/2)+((ir^2*dLr)/2)+((is*ir)*dMs);
+printf('Magnitude of torque is %f Nm and it acts in clockwise direction\n',te/2);
+disp('case c');
+// vs=sqrt(2)*314*sin(wt) again here average torque is needed so for calculation we need not to worry about sin(wt)
+vs=sqrt(2)*314; // stator winding voltage
+ls1=(Ls-(Ms^2/Lr)); // short circuit inductance of stator winding
+is=vs/(w*ls1); // stator current
+ir=(-Ms/Lr)*is; // rotor current
+te=((is^2*dLs)/2)+((ir^2*dLr)/2)+((is*ir)*dMs);
+printf('Magnitude of torque is %f Nm and it acts in clockwise direction\n',te/2);
+
+
+
+
+
diff --git a/3760/CH2/EX2.15/Ex2_15.sce b/3760/CH2/EX2.15/Ex2_15.sce new file mode 100644 index 000000000..e0f060796 --- /dev/null +++ b/3760/CH2/EX2.15/Ex2_15.sce @@ -0,0 +1,33 @@ +clc;
+B=[ 0.2 0.4 0.6 0.8 1 1.2];
+H=[ 50 100 160 225 300 400];
+plot(H,B);
+xlabel('magnetic field intensity');
+ylabel('magnetic flux density');
+title('B-H curve');
+p=0.2; // force exerted by spring
+g1=0.5*10^-2; // air gap length
+g2=0.1*10^-2; // reduced gap length after coil is energised
+n=2000; // coil turns
+l=0.2; // mean length of magnetic iron path
+A=0.2*10^-4; // area of cross-section
+g=9.81; // acceleration due to gravity
+l1=6; // gap length
+l2=3; // gap length between spring and core
+uo=4*%pi*10^-7; // free space permeability
+disp('case a');
+fe=(p*g*l2)/l1; // electromagnetic torque
+Bg=sqrt((2*fe*uo)/A); // air gap flux density
+printf('Air gap flux density is %f T\n',Bg);
+// corresponding to value of Bg from B-H curve H is
+Hg=87.7; // magnetic flux intensity
+ATi=l*Hg; // total ampere turn for iron path
+ATg=(Bg*g1)/uo; // ampere turn for air gap
+AT=ATi+ATg; // total ampere turns
+ie=AT/n;
+printf('Exciting current required to close the armature relay is %f A\n',ie);
+disp('case b');
+ATg=(Bg*g2)/uo; // ampere turn for air gap
+AT=ATi+ATg; // total ampere turns
+ie=AT/n;
+printf('Exciting current required to keep the armature closed is %f A\n',ie);
diff --git a/3760/CH2/EX2.16/Ex2_16.sce b/3760/CH2/EX2.16/Ex2_16.sce new file mode 100644 index 000000000..a8a63d532 --- /dev/null +++ b/3760/CH2/EX2.16/Ex2_16.sce @@ -0,0 +1,9 @@ +clc;
+x=0.1*10^-3; // displacement of armature
+B=0.8; // air gap flux density
+A=200*10^-4; // area under pole
+g=0.6*10^-2; // air gap length
+uo=4*%pi*10^-7; // free space permeability
+// after derived expression
+p=(B^2*A*g*x)/(uo*(g^2-x^2));
+printf('Unbalanced magnetic pull on armature is %f N',p);
diff --git a/3760/CH2/EX2.17/Ex2_17.sce b/3760/CH2/EX2.17/Ex2_17.sce new file mode 100644 index 000000000..3ac04f35d --- /dev/null +++ b/3760/CH2/EX2.17/Ex2_17.sce @@ -0,0 +1,9 @@ +clc;
+i=sqrt(2)*1000; // maximum current carried by conductors
+z=2; // number of conductors in slot
+l=1; // embedded length
+w=0.05; // slot width
+uo=4*%pi*10^-7; // free space permeability
+// after derived expression
+fe=(uo*z^2*l*i^2)/(2*w);
+printf('Magnitude of magnetic force is %f N and its direction is towards the bottom of the slot\n',fe/2);
diff --git a/3760/CH2/EX2.19/Ex2_19.sce b/3760/CH2/EX2.19/Ex2_19.sce new file mode 100644 index 000000000..baf6ef5e9 --- /dev/null +++ b/3760/CH2/EX2.19/Ex2_19.sce @@ -0,0 +1,27 @@ +clc;
+// L1=3+(1/(2*X)) -self inductance of coil 1
+// L1=2+(1/(2*X)) -self inductance of coil 2
+// M=1/(2*X) -mutual inductance
+// X is displacement
+i1=10; // current of coil 1
+i2=-5; // current of coil 2
+// from expression W=(L1*i1^2)/2 + (L2*i2^2)/2 + (i1*i2*M) where W is work done and is equal to 175+25/(4*x);
+// fe=-25/(4*x^2) where fe is electromagnetic force and is equal to rate of change of work done with respect to x
+disp('case a');
+x1=0.5;
+x2=1;
+Wm=integrate('-25/(4*x^2)','x',x1,x2);
+printf('Mechanical work done for given increment in displacement is %f watt-sec\n',Wm);
+disp('case b')
+// psi1=(3+(1/(2*x)))*i1+(1/(2*x))*i2 psi1 is flux linkage with coil 1
+// psi2=(2+(1/(2*x)))*i2+(1/(2*x))*i1 psi2 is flux linkage with coil 2
+We1=(((3+(1/(2*x2)))*i1+(1/(2*x2))*i2)-((3+(1/(2*x1)))*i1+(1/(2*x1))*i2))*i1;
+We2=(((2+(1/(2*x2)))*i2+(1/(2*x2))*i1)-((2+(1/(2*x1)))*i2+(1/(2*x1))*i1))*i2;
+printf('Electrical energy supplied by source 1 is %f watt-sec\n',We1);
+printf('Electrical energy supplied by source 2 is %f watt-sec\n',We2);
+disp('case c');
+// W=175+(25/(4*x));
+dw=175+(25/(4*x2))-(175+(25/(4*x1)));
+printf('Change in field energy is %f Watt-sec\n',dw);
+
+
diff --git a/3760/CH2/EX2.21/Ex2_21.sce b/3760/CH2/EX2.21/Ex2_21.sce new file mode 100644 index 000000000..f09f6f630 --- /dev/null +++ b/3760/CH2/EX2.21/Ex2_21.sce @@ -0,0 +1,7 @@ +clc;
+B=1.6; // flux density between magnetic surfaces
+a=1; // area of magnetic surfaces
+uo=4*%pi*10^-7; // free space permeability
+f=(B^2*a)/(2*uo);
+printf('Force between two magnetic surfaces is %f N',f);
+
diff --git a/3760/CH2/EX2.22/Ex2_22.sce b/3760/CH2/EX2.22/Ex2_22.sce new file mode 100644 index 000000000..25886f134 --- /dev/null +++ b/3760/CH2/EX2.22/Ex2_22.sce @@ -0,0 +1,8 @@ +clc;
+A=1; // area of plates
+E=3*10^6; // electric field intensity between plates
+Eo=(10^-9/(36*%pi)); // vaccum permittivity
+// after using both energy and coenergy method expression for force is derived
+f=(E^2*Eo*A)/2;
+printf('Force between two plates is %f N',f);
+
diff --git a/3760/CH2/EX2.23/Ex2_23.sce b/3760/CH2/EX2.23/Ex2_23.sce new file mode 100644 index 000000000..544593e04 --- /dev/null +++ b/3760/CH2/EX2.23/Ex2_23.sce @@ -0,0 +1,13 @@ +clc;
+w=5*10^-3; // counter weight
+a=30*10^-4; // area of cross section of plates
+d=1*10^-2; // distance between two plates
+g=9.81; // acceleration due to gravity
+Eo=(10^-9/(36*%pi)); // vaccum permittivity
+l1=8*10^-2; // horizontal distance between pivot and plates
+l2=10*10^-2; // horizontal distance between pivot and counter weight
+// for the bar to remain horizontal electrostatic force is given by
+fe=(w*l2*g)/l1;
+v=sqrt((fe*2*d^2)/(Eo*a));
+printf('Voltage applied between the plates is %f KV',v/1000);
+
diff --git a/3760/CH2/EX2.25/Ex2_25.sce b/3760/CH2/EX2.25/Ex2_25.sce new file mode 100644 index 000000000..1d6b86e2c --- /dev/null +++ b/3760/CH2/EX2.25/Ex2_25.sce @@ -0,0 +1,20 @@ +clc;
+n=1000; // number of turns in exciting coil
+a=5*5*10^-4; // cross section area of core
+g=1*10^-2; // length of air gap
+uo=4*%pi*10^-7; // free space permeability
+disp('case a');
+i=5; // coil current
+l=(n^2*uo*a)/(2*g);
+printf('Inductance of coil is %f H\n',l);
+E=(l*i^2)/2;
+printf('Field energy stored in inductor is %f Watt-sec\n',E );
+fe=(i^2*a*n^2*uo)/(4*g^2);
+printf('Force on the armature is %f N\n',fe);
+disp('case b');
+g1=0.5*10^-2; // reduced length of air gap
+We=((n^2*uo*a)/(2*g1)-(n^2*uo*a)/(2*g))*i^2;
+printf('Electrical energy supplied by source is %f Watt-sec\n',We);
+disp('case c');
+w=integrate('(n^2*uo*a*i^2)/(4*(g-x)^2)','x',0,g1);
+printf('Mechanical work done is %f Watt-sec',w);
diff --git a/3760/CH2/EX2.26/Ex2_26.sce b/3760/CH2/EX2.26/Ex2_26.sce new file mode 100644 index 000000000..48bcb514d --- /dev/null +++ b/3760/CH2/EX2.26/Ex2_26.sce @@ -0,0 +1,8 @@ +clc;
+de=110*(%pi/180); // pole pitch
+g=0.4*10^-2; // air gap length
+B=0.5; // air gap flux density
+d=0.3; // armature diameter
+uo=4*%pi*10^-7; // free space permeability
+fe=(B^2*d*de*g)/(2*uo);
+printf('Force that tends to pull the armature into alignment is %f N',fe)
diff --git a/3760/CH2/EX2.28/Ex2_28.sce b/3760/CH2/EX2.28/Ex2_28.sce new file mode 100644 index 000000000..f2bbc14a0 --- /dev/null +++ b/3760/CH2/EX2.28/Ex2_28.sce @@ -0,0 +1,15 @@ +clc;
+r=4; // resistance of inductor
+v=8; // maximum voltage
+L=2; // inductance
+t=2; // time required to reach maximum voltage value
+disp('case a');
+// after solving laplace equation we get expression for i(t) (transient current) i.e i(t)=((exp^-2*t)+(2*t-1))/2
+// for t=2 sec i(t) is given by
+it=((exp(-2*t))+2*t-1)/2;
+E=(L*it^2)/2;
+printf('Energy stored during %d sec is %f J\n',t,E);
+disp('case b');
+i=v/r; // current when transients are over
+E=(L*i^2)/2;
+printf('Energy stored after transients are over is %d J\n',E);
diff --git a/3760/CH2/EX2.29/Ex2_29.sce b/3760/CH2/EX2.29/Ex2_29.sce new file mode 100644 index 000000000..f956d2f4b --- /dev/null +++ b/3760/CH2/EX2.29/Ex2_29.sce @@ -0,0 +1,22 @@ +clc;
+l=1.2; // length of iron path
+a=5*5*10^-4; // area of cross section
+uo=4*%pi*10^-7; // permeability for free space
+ur=1500; // relative permeability for iron
+i=2; // exciting current
+n=1000; // number of turns of coil
+g=0.5*10^-2; // air gap length
+r=(l/(uo*ur*a))+(g/(uo*a)); // net reluctance
+f=(n*i)/r; // flux in coil
+fe1=((f^2*l)/(uo*ur*a))/2;
+printf('Field energy stored in iron is %f J\n',fe1);
+fe2=((f^2*g)/(uo*a))/2;
+printf('Field energy stored in air gap is %f J\n',fe2);
+r1=fe2/fe1;
+printf('Ratio of field energy stored in air gap to field energy stored in iron is %f \n',r1);
+d1=fe1/(l*a);
+printf('Energy density in iron is %f J/m^3\n',d1);
+d2=fe2/(g*a);
+printf('Energy density in air gap is %f J/m^3\n',d2);
+r2=d2/d1;
+printf('Ratio of energy density in air gap to energy density in iron is %f \n',r2);
diff --git a/3760/CH2/EX2.30/Ex2_30.sce b/3760/CH2/EX2.30/Ex2_30.sce new file mode 100644 index 000000000..cf746b3b8 --- /dev/null +++ b/3760/CH2/EX2.30/Ex2_30.sce @@ -0,0 +1,32 @@ +
+
+clc;
+n=1200; // number of turns in exciting coil
+a=6*5*10^-4; // area of cross section of core
+disp('case a');
+x=0.01; // displacement of coil
+i=2; // exciting current
+uo=4*%pi*10^-7; // free space permeability
+Wf=(n^2*uo*a*i^2)/(4*x);
+printf('Field energy stored is %f J\n',Wf);
+F=(-n^2*uo*a*i^2)/(4*x^2);
+printf('Force on armature is %f N\n',F);
+disp('case b');
+x1=0.005; // further displacement of coil
+v1=(n^2*uo*a*i)/(2*x); // flux linkage corresponding to displacement 1 cm
+v2=(n^2*uo*a*i)/(2*x1); // flux linkage corresponding to displacement 0.5 cm
+M=((v2-v1)*i)/2;
+printf('Mechanical energy output is %f J\n',M);
+disp('case c');
+// after deriving expression
+Wm=integrate('(-n^2*uo*a)/x^2','x',x,x1);
+printf('Mechanical work done is %f J\n',Wm);
+disp('case d');
+// for x=0.005 flux linkage is constant than current will change
+i2=v1/((2*n^2*uo*a)/(2*x));
+Wm=((i-i2)*v1)/2;
+printf('Mechanical work done if flux linkage are maintained constant is %f J\n',Wm);
+disp('case e');
+// after the expression is derived
+Wm=integrate('(-v1^2)/(n^2*uo*a)','x',x,x1);
+printf('Mechanical work done if flux linkage are maintained constant is %f J\n',Wm);
diff --git a/3760/CH2/EX2.4/Ex2_4.sce b/3760/CH2/EX2.4/Ex2_4.sce new file mode 100644 index 000000000..95272dbf3 --- /dev/null +++ b/3760/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,13 @@ +clc;
+l=0.02; // air gap length
+i1=20; // intermediate current
+i2=40; // current during armature movement from open to close position
+// from fig 2.11
+f1=0.04*i1; // flux linkage during open position at A
+f2=1.2+0.03*(i1-20); // flux linkage during close position at D
+f3=0.04*i2; // flux linkage during open position at B
+f4=1.2+0.03*(i2-20); // flux linkage during close position at C
+// Mechanical work done=area ODCFEO-area OABFEO
+W=((i1*f2)/2)+(((f2+f4)*i1)/2)-((i2*f3)/2);
+fe=W/l;
+printf('Average electromagnetic force is %d N',fe);
diff --git a/3760/CH2/EX2.6/Ex2_6.sce b/3760/CH2/EX2.6/Ex2_6.sce new file mode 100644 index 000000000..b94e01698 --- /dev/null +++ b/3760/CH2/EX2.6/Ex2_6.sce @@ -0,0 +1,8 @@ +clc;
+g=0.003; // gap length
+wp=0.006; // pole width
+B=0.8; // flux density in air gap
+uo=4*%pi*10^-7; // free space permeability
+// after the derivation of expression
+fe=(B^2*wp*g)/(2*uo);
+printf('Force tending to bring electromagnets into axial alignment is %f N',fe);
diff --git a/3760/CH2/EX2.7/Ex2_7.sce b/3760/CH2/EX2.7/Ex2_7.sce new file mode 100644 index 000000000..5f68fd898 --- /dev/null +++ b/3760/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,74 @@ +clc;
+N=1500; // number of turns in coil
+i=3; // current carried by coil
+uo=4*%pi*10^-7; // free space permeability
+l=0.04; // side of plunger
+A=%pi*(l/2)^2; // cross section area of plunger
+disp('case a');
+disp('for gap length G=2 cm');
+g=0.02; // air gap length in cm
+x=0; // displacement of plunger
+G1=g-x; // gap length
+B=(uo*i*N)/G1; // air gap flux density
+printf('Air gap flux density is %f Wb/m^2\n',B);
+L1=(N^2*uo*A)/G1;
+printf('Coil inductance is %f H',L1);
+disp('for gap length G=1.5 cm');
+g=0.02; // air gap length in cm
+x=0.005; // displacement of plunger
+G2=g-x; // gap length
+B=(uo*i*N)/G2; // air gap flux density
+printf('Air gap flux density is %f Wb/m^2\n',B);
+L2=(N^2*uo*A)/G2;
+printf('Coil inductance is %f H',L2);
+disp('for gap length G=1 cm');
+g=0.02; // air gap length in cm
+x=0.01; // displacement of plunger
+G3=g-x; // gap length
+B=(uo*i*N)/G3; // air gap flux density
+printf('Air gap flux density is %f Wb/m^2\n',B);
+L3=(N^2*uo*A)/G3;
+printf('Coil inductance is %f H',L3);
+disp('for gap length G=0.5 cm');
+g=0.02; // air gap length in cm
+x=0.015; // displacement of plunger
+G4=g-x; // gap length
+B=(uo*i*N)/G4; // air gap flux density
+printf('Air gap flux density is %f Wb/m^2\n',B);
+L4=(N^2*uo*A)/G4;
+printf('Coil inductance is %f H',L4);
+disp('case b');
+disp('for gap length G=2 cm');
+W=(i^2*L1)/2;
+printf('Energy stored is %f watt-sec\n',W);
+disp('for gap length G=1.5 cm');
+W=(i^2*L2)/2;
+printf('Energy stored is %f watt-sec\n',W);
+disp('for gap length G=1 cm');
+W=(i^2*L3)/2;
+printf('Energy stored is %f watt-sec\n',W);
+disp('for gap length G=0.5 cm');
+W=(i^2*L4)/2;
+printf('Energy stored is %f watt-sec\n',W);
+disp('case c');
+disp('for gap length G=2 cm');
+fe=round((i^2*g*L1)/(2*G1^2));
+printf('Electromagnetic force is %f N\n',fe);
+disp('for gap length G=1.5 cm');
+fe=(i^2*g*L1)/(2*G2^2);
+printf('Electromagnetic force is %f N\n',fe);
+disp('for gap length G=1 cm');
+fe=round((i^2*g*L1)/(2*G3^2));
+printf('Electromagnetic force is %f N\n',fe);
+disp('for gap length G=0.5 cm');
+fe=round((i^2*g*L1)/(2*G4^2));
+printf('Electromagnetic force is %f N\n',fe);
+disp('case 4');
+// for g=2 cm and g=0.5cm, displacement is given by
+xi=0;
+xf=0.015;
+Wm=integrate('(i^2*g*L1)/(2*(g-x)^2)','x',xi,xf);
+printf('Mechanical work done is %f watt-sec\n',Wm);
+disp('case e');
+We=integrate('(i^2*g*L1)/(g-x)^2','x',xi,xf);
+printf('Electrical energy supplied by source is %f watt-sec\n',We);
diff --git a/3760/CH2/EX2.8/Ex2_8.sce b/3760/CH2/EX2.8/Ex2_8.sce new file mode 100644 index 000000000..bb75a8786 --- /dev/null +++ b/3760/CH2/EX2.8/Ex2_8.sce @@ -0,0 +1,9 @@ +clc;
+r=50*10^-3; // radius of rotor
+g=2*10^-3; // air gap length
+l=10*10^-3; // length normal to radius r
+B=2.2; // maximum air gap flux density
+uo=4*%pi*10^-7; // free space permeability
+// after the derivation of the expression
+T=(B^2*g*r*l)/uo;
+printf('Magnitude of torque is %f N-m',T);
diff --git a/3760/CH2/EX2.9/Ex2_9.sce b/3760/CH2/EX2.9/Ex2_9.sce new file mode 100644 index 000000000..168346615 --- /dev/null +++ b/3760/CH2/EX2.9/Ex2_9.sce @@ -0,0 +1,10 @@ +clc;
+r=50*10^-3; // radius of rotor
+g=2*10^-3; // air gap length
+l=10*10^-3; // length normal to radius r
+B=2.2; // maximum air gap flux density
+uo=4*%pi*10^-7; // free space permeability
+// after the derivation of the expression
+T=(B^2*g*(r+(g/2))*l)/uo;
+printf('Magnitude of torque is %f N-m',T);
+
diff --git a/3760/CH3/EX3.10/Ex3_10.sce b/3760/CH3/EX3.10/Ex3_10.sce new file mode 100644 index 000000000..9d1e3c533 --- /dev/null +++ b/3760/CH3/EX3.10/Ex3_10.sce @@ -0,0 +1,30 @@ +clc;
+disp('case a');
+f1=2/3; // fraction of slot wound
+p1=f1*180; // phase spread , 2/3 of the slots are wound
+kd1=sin((p1/2)*(%pi/180))/((p1/2)*(%pi/180)); // distribution factor
+p2=180; // phase spread , All the slots are wound
+f2=1; // fraction of slot wound
+kd2=sin((p2/2)*(%pi/180))/((p2/2)*(%pi/180)); // distribution factor
+// output is directly proportional to the product of fraction of slots wound and distribution factor
+ro=(f2*kd2)/(f1*kd1); // It is assumed that frequency ,flux per pole and the conductor cross section is same
+printf('Ratio of outputs is %f \n',ro);
+rc=f2/f1;
+printf('ratio of copper required is %f\n',rc);
+disp('case b');
+p3=60; // for 3-phase winding ,phase spread is 60 degrees
+kd3=sin((p3/2)*(%pi/180))/((p3/2)*(%pi/180)); // distribution factor
+// since all the slots are wound for both 1-phase and 3-phase, fraction of the slots wound is 1
+f3=1; // fraction of the slots wound
+ro=kd3/kd2;
+printf('Ratio of outputs is %f \n',ro);
+rc=f2/f3;
+printf('ratio of copper required is %f\n',rc);
+disp('case c');
+f4=1; // fraction of the slots wound
+p4=90; // for 2-phase winding ,phase spread is 90 degrees
+kd4=sin((p4/2)*(%pi/180))/((p4/2)*(%pi/180)); // distribution factor
+ro=kd3/kd4;
+printf('Ratio of outputs is %f \n',ro);
+rc=f3/f4;
+printf('ratio of copper required is %f\n',rc);
diff --git a/3760/CH3/EX3.11/Ex3_11.sce b/3760/CH3/EX3.11/Ex3_11.sce new file mode 100644 index 000000000..4b1729239 --- /dev/null +++ b/3760/CH3/EX3.11/Ex3_11.sce @@ -0,0 +1,47 @@ +clc;
+d=0.28; // air gap diameter
+l=0.23; // core length of alternator
+spp=4; // slots per pole per phase
+b1=0.87; // amplitude of flux density in fundamental harmonic in Tesla
+b3=0.24; // amplitude of flux density in third harmonic in Tesla
+b5=0.14; // amplitude of flux density in fifth harmonic in Tesla
+p=6; // number of poles in alternator
+np=3; // number of phases
+c=8; // number of conductor per slot
+f=50; // frequency of supply
+f1=(2*d*l*b1)/p; // flux for fundamental harmonic
+f3=(2*d*l*b3)/(p*3); // flux for third harmonic
+f5=(2*d*l*b5)/(p*5); // flux for fifth harmonic
+ap=180/(spp*np); // slot angular pitch
+kd1=sin(((spp*ap)/2)*(%pi/180))/(spp*sin((ap/2)*(%pi/180))); // distribution factor for fundamental harmonic
+kd3=sin(((3*spp*ap)/2)*(%pi/180))/(spp*sin(((3*ap)/2)*(%pi/180))); // distribution factor for third harmonic
+kd5=sin(((5*spp*ap)/2)*(%pi/180))/(spp*sin(((5*ap)/2)*(%pi/180))); // distribution factor for fifth harmonic
+// coil is short pitched by one slot, therefore
+e=180/(spp*np); // chording angle
+cs1=cos((e/2)*(%pi/180)); // coil span factor for fundamental harmonic
+cs3=cos(((3*e)/2)*(%pi/180)); // coil span factor for third harmonic
+cs5=cos(((5*e)/2)*(%pi/180)); // coil span factor for fifth harmonic
+kw1=cs1*kd1; // winding factor for fundamental harmonic
+kw3=cs3*kd3; // winding factor for third harmonic
+kw5=cs5*kd5; // winding factor for fifth harmonic
+ts=spp*np*p; // total number of slots
+tt=(ts*c)/2; // total number of turns
+nph=tt/np; // series turn per phase
+ep1=sqrt(2)*%pi*f*kw1*nph*f1; // emf per phase for fundamental harmonics
+ep3=(ep1*kw3*3*f3)/(kw1*f1); // emf per phase for third harmonics
+ep5=(ep1*kw5*5*f5)/(kw1*f1); // emf per phase for fifth harmonics
+disp('case a(1): star connected alternator');
+ep=sqrt(ep1^2+ep3^2+ep5^2);
+printf('Resultant EMF per phase is %f V\n',ep);
+// third frequency line emf doesnot appear in line voltage
+el=sqrt(3)*sqrt(ep1^2+ep5^2);
+printf('Resultant line voltage is %f V\n',el);
+disp('case a(2): Delta connected alternator');
+// third frequency line emf doesnot appear in line and phase voltage as they are short circuited by closed delta
+ep=sqrt(ep1^2+ep5^2);
+printf('Resultant EMF per phase(also line voltage) is %f V\n',ep);
+disp('case b: delta connected alternator ');
+rpp=10; // reactance per phase
+// emf to due first and third harmonic cancels each other but third harmonic gives rise to circulating current
+I=(3*ep3)/(3*np*rpp);
+printf('Circulating current is %f A',I);
diff --git a/3760/CH3/EX3.12/Ex3_12.sce b/3760/CH3/EX3.12/Ex3_12.sce new file mode 100644 index 000000000..c69386c56 --- /dev/null +++ b/3760/CH3/EX3.12/Ex3_12.sce @@ -0,0 +1,19 @@ +clc;
+spp=3; // slots per pole per phase
+np=3; // number of phases
+cs=8; // coil span
+fp=0.20; // fraction of third harmonic in flux density wave in air gap
+sp=spp*np; // slots per pole
+v=180/sp; // slot angular pitch
+kd1=sin(((spp*v)/2)*(%pi/180))/(spp*sin((v/2)*(%pi/180))); // distribution factor
+// for a coil span of 8 slots the coil is short pitched by one slot
+e=v; // chording angle
+kp1=cos((e/2)*(%pi/180)); // coil span factor
+kw1=kp1*kd1; // winding factor
+kd3=sin(((3*spp*v)/2)*(%pi/180))/(spp*sin(((v*3)/2)*(%pi/180))); // distribution factor for third harmonic
+kp3=cos(((3*e)/2)*(%pi/180)); // coil span factor for third harmonic
+kw3=kd3*kp3; // winding factor for third harmonic
+er=(kw3/kw1)*fp; // ratio of third harmonic emf to fundamental emf
+ep=sqrt(1+er^2); // ratio of net emf to fundamental emf
+pi=((ep-1)/1)*100;
+printf('Percentage increase in per phase rms emf is %f percent',pi);
diff --git a/3760/CH3/EX3.13/Ex3_13.sce b/3760/CH3/EX3.13/Ex3_13.sce new file mode 100644 index 000000000..86c0bf447 --- /dev/null +++ b/3760/CH3/EX3.13/Ex3_13.sce @@ -0,0 +1,29 @@ +clc;
+p=6; // number of poles in alternator
+s=42; // number of slots in alternator
+f=0.012; // flux per pole
+t=8; // number of turns in full pitch coil
+F=50; // frequency of alternator
+disp('case a');
+np=2; // number of phases
+spp=42/(p*np); // slots per pole per phase
+// spp is not an integer, the 2-phase winding is a fractional slot winding, therefore Sk is given by
+Sk=spp*2;
+v=90; // phase spread for 2-phase winding
+kd=sind(v/2)/(Sk*sind(v/(2*Sk))); // distribution factor
+kw=kd; // winding factor as kp=1
+nph=(s*t)/np; // per phase series turn
+eph=sqrt(2)*F*%pi*kw*nph*f;
+el=sqrt(2)*eph;
+printf('Phase emf is %f V\n',eph);
+printf('Line emf is %f V\n ',el);
+disp('case b');
+np=3; // number of phases
+v=60; // phase spraed for 3-phase winding
+kd=sind(v/2)/(Sk*sind(v/(2*Sk))); // distribution factor
+kw=kd; // winding factor as kp=1
+nph=(s*t)/np; // per phase series turn
+eph=sqrt(2)*F*%pi*kw*nph*f;
+el=sqrt(3)*eph;
+printf('Phase emf is %f V\n',eph);
+printf('Line emf is %f V\n ',el);
diff --git a/3760/CH3/EX3.14/Ex3_14.sce b/3760/CH3/EX3.14/Ex3_14.sce new file mode 100644 index 000000000..0755c00db --- /dev/null +++ b/3760/CH3/EX3.14/Ex3_14.sce @@ -0,0 +1,30 @@ +clc;
+s=81; // number of slots
+p=6; // number of poles
+np=3; // number of phases
+cs=13; // coil span in terms of slot pitches
+v=60; // phase spread for three phase winding
+f3=0.4; // ratio of third harmonic flux to first harmonic flux
+f5=0.25; // ratio of fifth harmonic flux to first harmonic flux
+spp=s/(p*np); // // spp is not an integer, the 2-phase winding is a fractional slot winding, therefore Sk is given by
+Sk=spp*2;
+ap=(p*180)/s;
+Cs=cs*ap; // coil span
+e=180-Cs; // chording angle
+kd1=sind(v/2)/(Sk*sind(v/(2*Sk))); // distribution factor for fundamental harmonic
+kp1=cosd(e/2); // coil span factor
+kd3=sind((3*v)/2)/(Sk*sind((3*v)/(2*Sk))); // distribution factor for third harmonic
+kp3=cosd((3*e)/2); // coil span factor for third harmonic
+kd5=sind((5*v)/2)/(Sk*sind((5*v)/(2*Sk))); // distribution factor for fifth harmonic
+kp5=cosd((5*e)/2); // coil span factor for fifth harmonic
+kw1=kd1*kp1; // winding factor for fundamental harmonics
+kw3=kd3*kp3; // winding factor for third harmonic
+kw5=kd5*kp5; // winding factor for fifth harmonic
+ep3=(kw3*f3)/kw1;
+printf('rms value of third harmonic emf is %f times the fundamental harmonic emf\n',ep3);
+ep5=(kw5*f5)/kw1;
+printf('rms value of fifth harmonic emf is %f times the fundamental harmonic emf\n',ep5);
+ep=sqrt(1+ep3^2+ep5^2); // resultant phase emf
+el=sqrt(3)*sqrt(1+ep5^2); // resultant line emf
+r=el/ep;
+printf('Ratio of resultant line emf to resultant phase emf is %f',r);
diff --git a/3760/CH3/EX3.15/Ex3_15.sce b/3760/CH3/EX3.15/Ex3_15.sce new file mode 100644 index 000000000..56ea082a9 --- /dev/null +++ b/3760/CH3/EX3.15/Ex3_15.sce @@ -0,0 +1,11 @@ +clc;
+B=1; // peak flux density in Tesla
+l=0.8; // length of armature conductor
+v=20; // velocity of coil
+// for 0< theta <30 coil aa' is moving in zero B-wave, emf for this range is zero
+// for 30< theta < 60 coil side a is cutting through B-wave and coil side a' is cutting zero B-wave, therefore
+e1=B*l*v; // emf at given position of coil
+// for 60< theta < 150 both coil sides are cutting through B-wave
+e2=2*B*l*v; // net emf at given position of coil
+rms=sqrt((1/%pi)*(((e1^2*%pi*2)/6)+((e2^2*%pi)/2)));
+printf('RMS value of generated emf in one single turn coil is %f V',rms);
diff --git a/3760/CH3/EX3.16/Ex3_16.sce b/3760/CH3/EX3.16/Ex3_16.sce new file mode 100644 index 000000000..035a5678e --- /dev/null +++ b/3760/CH3/EX3.16/Ex3_16.sce @@ -0,0 +1,15 @@ +clc;
+f=50; // frequency of alternator
+B=1; // peak flux density
+t=360; // total turns
+v=60; // phase spread
+pi=0.6; // pole pitch
+l=0.8; // stator length
+cs=180; // coil span in electrical degrees
+nph=t/3; // series turn per phase
+Bp=(4*B*cosd(v/2))/%pi; // fundamental value of peak flux density
+F=(2*l*pi*Bp)/%pi; // Fundamental air-gap flux per pole
+kd=sind(v/2)/((v/2)*(%pi/180)); // distribution factor
+kw=kd; // winding factor , as kp=1
+eph=sqrt(2)*%pi*f*F*kw*nph;
+printf('RMS value of fundamental emf per phase is %f V',eph);
diff --git a/3760/CH3/EX3.18/Ex3_18.sce b/3760/CH3/EX3.18/Ex3_18.sce new file mode 100644 index 000000000..fd107806a --- /dev/null +++ b/3760/CH3/EX3.18/Ex3_18.sce @@ -0,0 +1,22 @@ +clc;
+p=6; // number of poles
+s=54; // number of slots
+n=1000; // speed of alternator in rpm
+t=80; // number of turn in coils A and B
+f=0.015; // flux per pole
+F=50; // given frequency of alternator
+// Coil A is over pitched by one slot and coil B is short pitched by one slot
+pp=s/p; // pole pitch
+sap=(p*180)/s; // slot angular pitch
+e1=(%pi*F*f*t)/sqrt(2); // EMF generated in one coil side of coil A or B
+// same EMF is generated in col side 11 but with a phase of (180+sap) degrees. Resultant of emf in coil side 1 and 11 is given by
+Ea=2*e1*cosd(sap/2); // net emf in coil side 1
+Eb=Ea; // net emf in coil side 2
+//Ea and Eb are in phase with each other from phasor diagram (fig. 3.26)
+disp('case a');
+en=Ea+Eb;
+printf('Resultant e.m.f when coils A and B are connected in series aiding is %f V\n',en);
+disp('case b');
+en=Ea-Eb;
+printf('Resultant e.m.f when coils A and B are connected in series opposing is %f V\n',en);
+
diff --git a/3760/CH3/EX3.19/Ex3_19.sce b/3760/CH3/EX3.19/Ex3_19.sce new file mode 100644 index 000000000..6814446d3 --- /dev/null +++ b/3760/CH3/EX3.19/Ex3_19.sce @@ -0,0 +1,14 @@ +clc;
+np=3; // number of phases
+p=2; // number of poles
+spp=5; // slots per pole per phase
+n=4; // number of turns in coil
+i=20; // per phase current
+v=(spp*180)/(spp*np); // phase spread
+imax=sqrt(2)*i; // maximum value of current
+mmf=spp*n*imax; // resultant amplitude of mmf
+kd=sind(v/2)/((v/2)*(%pi/180)); // distribution factor
+fp=(4*mmf*kd)/%pi; // peak value of fundamental component
+fr=(4*3*spp*n*i)/%pi^2; // rms value of fundamental component
+printf('Maximum value of the peak of fundamental m.m.f wave is %f AT/pole\n',fp);
+printf('RMS value of the peak of fundamental m.m.f wave is %f AT/pole\n',fr);
diff --git a/3760/CH3/EX3.2/Ex3_2.sce b/3760/CH3/EX3.2/Ex3_2.sce new file mode 100644 index 000000000..2de444f82 --- /dev/null +++ b/3760/CH3/EX3.2/Ex3_2.sce @@ -0,0 +1,25 @@ +clc;
+n=24; // Number of armature conductor
+v=2; // average voltage per conductor
+i=5; // current carrying capacity of each conductor
+disp('case a');
+a=2; // number of parallel path
+sc=n/a; // series connected conductor in each path
+Ea=sc*v; // output voltage
+Ia=i*a; // output current
+p=Ea*Ia; // power rating
+printf('Generator rating is %f W\n',p);
+disp('case b');
+a=4; // number of parallel path
+sc=n/a; // series connected conductor in each path
+Ea=sc*v; // output voltage
+Ia=i*a; // output current
+p=Ea*Ia; // power rating
+printf('Generator rating is %f W\n',p);
+disp('case c');
+a=6; // number of parallel path
+sc=n/a; // series connected conductor in each path
+Ea=sc*v; // output voltage
+Ia=i*a; // output current
+p=Ea*Ia; // power rating
+printf('Generator rating is %f W\n',p);
diff --git a/3760/CH3/EX3.20/Ex3_20.sce b/3760/CH3/EX3.20/Ex3_20.sce new file mode 100644 index 000000000..522ef1775 --- /dev/null +++ b/3760/CH3/EX3.20/Ex3_20.sce @@ -0,0 +1,17 @@ +clc;
+p=2; // number of pole
+i=24; // phase current
+t=300; // full pitched turns
+v=60; // phase spread
+np=3; // number of phases
+nph=t/np; // series turn per phase
+j=(nph*sqrt(2)*i*180)/(v*%pi); // peak value of uniform current density
+disp('case a');
+A=(j*v*%pi)/(2*180); // peak amplitude of trapezoidal m.m.f wave
+printf('Peak amplitude of trapezoidal m.m.f wave is %f ATs/pole\n',A);
+disp('case b');
+kd=sind(v/2)/((v/2)*(%pi/180)); // distribution factor
+fp=(4*kd*A)/%pi;
+printf('Peak value of fundamental mmf wave is %f AT/pole\n',fp);
+fr=(4*3*A)/(%pi^2*sqrt(2));
+printf('RMS value of fundamental mmf wave is %f AT/pole\n',fr);
diff --git a/3760/CH3/EX3.3/Ex3_3.sce b/3760/CH3/EX3.3/Ex3_3.sce new file mode 100644 index 000000000..75b386d92 --- /dev/null +++ b/3760/CH3/EX3.3/Ex3_3.sce @@ -0,0 +1,22 @@ +clc;
+p=4; // number of poles
+s=60; // number of slots
+c=8; // number of conductors per slot
+f=20*10^-3; // flux per pole
+nr=1500; // relative speed in rpm between field flux and armature winding
+disp('case a');
+// winding is lap connected
+a=p; // for lap connected winding , number of parallel path=number of pole
+z=s*c; // total number of conductors
+n=nr/60; // speed in rps
+E=(f*z*n*p)/a;
+printf('Generated EMF is %f V\n',E);
+disp('case b');
+kw=0.96; // winding factor
+nt=z/2; // Total number of turns
+nph=nt/3; // number of series turns per phase
+fg=(p*n)/2; // generated EMF frequency
+E=sqrt(2)*%pi*fg*nph*kw*f;
+printf('Generated EMF per phase is %f V\n',E);
+e=round(sqrt(3)*E);
+printf('Generated EMF between line terminal is %f V\n',e);
diff --git a/3760/CH3/EX3.30/Ex3_30.sce b/3760/CH3/EX3.30/Ex3_30.sce new file mode 100644 index 000000000..04c1b63de --- /dev/null +++ b/3760/CH3/EX3.30/Ex3_30.sce @@ -0,0 +1,7 @@ +clc;
+p=6; // number of poles in induction motor
+f=50; // frequency of motor
+d=1.2; // stator bore diameter
+// in one revolution peripheral distance of Pi*diameter is transversed
+v=(2*f*%pi*d)/p;
+printf('Linear velocity of travelling mmf wave is %f m/sec',v);
diff --git a/3760/CH3/EX3.32/Ex3_32.sce b/3760/CH3/EX3.32/Ex3_32.sce new file mode 100644 index 000000000..b73327fe2 --- /dev/null +++ b/3760/CH3/EX3.32/Ex3_32.sce @@ -0,0 +1,26 @@ +clc;
+p=2; // number of poles
+f=50; // frequency of machine
+D=1.6; // diameter of cylindrical rotor
+l=1.8; // length of cylindrical rotor
+g=0.012; // air gap length
+rm=4000; // peak value of rotor mmf
+rs=6000; // peak value of stator mmf
+ph=140; // phase difference between stator mmf and rotor mmf
+uo=4*%pi*10^-7; // free space permeability0
+disp('a');
+rp=sqrt(rm^2+rs^2+2*rm*rs*cosd(ph));
+printf('Resultant peak gap mmf is %f AT/pole\n',rp);
+disp('b');
+Bp=(uo*rp)/g;
+printf('Peak gap flux density is %f T\n',Bp);
+disp('c');
+ge=(uo*%pi*D*l*rp^2)/(4*g);
+printf('Total gap energy is %f Joules\n',ge);
+disp('d');
+T=(p*uo*%pi*D*l*rs*rm*sind(ph))/(4*g);
+printf('Electromagnetic torque is %f Nm\n',T);
+disp('e');
+wm=(4*%pi*f)/2; // synchronous speed
+P=(T*wm)/1000
+printf('Electromagnetic power is %f KW',P);
diff --git a/3760/CH3/EX3.33/Ex3_33.sce b/3760/CH3/EX3.33/Ex3_33.sce new file mode 100644 index 000000000..3b8035b69 --- /dev/null +++ b/3760/CH3/EX3.33/Ex3_33.sce @@ -0,0 +1,21 @@ +clc;
+d=0.8; // diameter of rotor machine
+l=0.5; // length of rotor machine
+g=0.005; // air gap length
+as=10000; // peak current density for stator
+ar=6000; // peak current density for rotor
+t=60; // torque angle
+disp('case a');
+p=2; // number of pole
+uo=4*%pi*10^-7; // free space permeability
+Fs=(as*d)/p; // peak stator mmf per pole
+Fr=(ar*d)/p; // peak rotor mmf per pole
+Te=(p*uo*%pi*d*l*Fs*Fr*sind(t))/(4*g);
+printf('Torque for given number of poles is %f Nm\n',Te);
+disp('case b');
+p=6; // number of pole
+uo=4*%pi*10^-7; // free space permeability
+Fs=(as*d)/p; // peak stator mmf per pole
+Fr=(ar*d)/p; // peak rotor mmf per pole
+Te=(p*uo*%pi*d*l*Fs*Fr*sind(t))/(4*g);
+printf('Torque for given number of poles is %f Nm\n',Te);
diff --git a/3760/CH3/EX3.35/Ex3_35.sce b/3760/CH3/EX3.35/Ex3_35.sce new file mode 100644 index 000000000..f295338c2 --- /dev/null +++ b/3760/CH3/EX3.35/Ex3_35.sce @@ -0,0 +1,34 @@ +clc;
+p=4; // number of poles
+np=3; // number of phases
+f=50; // frequency of alternator
+sap=8; // slot angular pitch
+c=12; // number of concentric coils in field winding
+tf=6; // turns per field coil
+ta=28; // series armature turn per phase
+ar=0.6; // armature radius
+la=4; // armature length
+g=0.06; // gap length
+w=0.96; // winding factor for armature winding
+fc=1000; // field current
+disp('case a');
+kd=sind((np*sap)/2)/(np*sind(sap/2)); // distribution factor
+kp=1; // coil span factor
+kf=kd*kp; // winding factor for field winding
+nf=tf*c; // number of field turn
+F=(4*kf*nf*fc)/(%pi*p);
+printf('Peak value of fundamental mmf produced by field winding is %f AT/pole\n',F);
+disp('case b');
+uo=4*%pi*10^-7; // free space permeability
+B=(uo*F)/g;
+printf('Peak value of fundamental flux density wave is %f T\n',B);
+disp('case c');
+v=(4*B*la*ar)/p;
+printf('Fundamental value of air gap flux per pole is %f W\n',v);
+disp('case d');
+eph=sqrt(2)*%pi*f*v*ta*w;
+printf('EMF per phase is %f V\n',eph);
+el=sqrt(3)*round(eph);
+printf('Line EMF is %f V',el);
+
+
diff --git a/3760/CH3/EX3.36/Ex3_36.sce b/3760/CH3/EX3.36/Ex3_36.sce new file mode 100644 index 000000000..29f3dfd5d --- /dev/null +++ b/3760/CH3/EX3.36/Ex3_36.sce @@ -0,0 +1,40 @@ +clc;
+np=3; // number of phases
+p=6; // number of poles
+f=50; // frequency of alternator
+e=415; // open circuit emf;
+s=36; // number of slots in armature
+t=4; // number of turns per coil
+g=0.18; // air gap diameter
+l=0.4; // core length
+G=0.002; // gap length
+T=42; // number of turns in field winding
+kf=0.96; // winding factor
+uo=4*%pi*10^-7; // free space permeability
+disp('case a');
+nph=(s*t)/np; // series turn per phase
+spp=s/(p*np); // slots per pole per phase
+v=180/p; // slot angular pitch
+kd=sind((spp*v)/2)/(spp*sind(v/2)); // distribution factor
+Flu=e/(sqrt(2)*sqrt(3)*%pi*f*nph*kd); // flux per pole
+B=(p*Flu*2)/(4*l*g);
+printf('Peak value of fundamental flux density wave is %f T\n',B);
+disp('case b');
+Fl=(G*B)/uo; // peak fundamental field mmf wave
+printf('Peak value of fundamental mmf wave is %f AT/pole\n',Fl);
+If=(%pi*Fl*p)/(4*kf*T);
+printf('DC field current is %f A\n',If);
+disp('case c');
+Te=114; // given torque
+Ta=146; // torque angle
+Fm=floor((Te*4*G)/(p*uo*%pi*g*l*Fl*sind(Ta)));
+printf('Peak value of fundamental armature mmf is %f AT/pole\n',Fm);
+Fr=sqrt(Fl^2+Fm^2+2*Fl*Fm*cosd(Ta));
+printf('Resultant mmf per pole is %f AT/pole\n',Fr);
+disp('case d')
+ia=(Fm*2*%pi*p)/(12*kd*nph*sqrt(2));
+printf('RMS value of armature current is %f A\n',ia);
+ns=1000; // speed in rpm
+wm=(2*%pi*ns)/60; // angular speed in rps
+pf=(Te*wm)/(sqrt(3)*e*ia);
+printf('Power factor is %f lagging',pf);
diff --git a/3760/CH3/EX3.37/Ex3_37.sce b/3760/CH3/EX3.37/Ex3_37.sce new file mode 100644 index 000000000..2dfb9ff79 --- /dev/null +++ b/3760/CH3/EX3.37/Ex3_37.sce @@ -0,0 +1,6 @@ +clc;
+n1=0.95; // efficiency of transformer 1
+lo=((1/n1)-1); // fraction of output lost
+d=2; // Linear dimension of transformer B is two times the Linear dimension of transformer A
+nb=(1/(1+((1*lo)/d)))*100;
+printf('Full load efficiency of transformer B is %f percent',nb);
diff --git a/3760/CH3/EX3.39/Ex3_39.sce b/3760/CH3/EX3.39/Ex3_39.sce new file mode 100644 index 000000000..01cbed2b9 --- /dev/null +++ b/3760/CH3/EX3.39/Ex3_39.sce @@ -0,0 +1,18 @@ +clc;
+t0=0; // accelerating period
+t1=30; // decelerating period
+l1=2000; // maximum load during accelerating period
+lf=600; // maximum load during decelerating period
+l=1000; // load during full load
+tf=60; // full load duration
+td=10; // decelerating duration
+tde=20; // decting period
+sa=l1/t1; // slope during accelerating
+sd=lf/td; // slope during decelerating
+e1=integrate('(sa*t)^2','t',t0,t1); // term 1 for finding motor rating
+e2=l^2*tf; // term 2 for finding motor rating
+e3=integrate('(sd*t)^2','t',t0,td); // term 3 for finding motor rating
+T=t1+tf+td+tde; // total duration
+R=sqrt((1/120)*(e1+e2+e3));
+printf('KW rating of motor is %f KW',R);
+disp('Choose a motor of rating above the calculated rating');
diff --git a/3760/CH3/EX3.4/Ex3_4.sce b/3760/CH3/EX3.4/Ex3_4.sce new file mode 100644 index 000000000..438dae1c9 --- /dev/null +++ b/3760/CH3/EX3.4/Ex3_4.sce @@ -0,0 +1,25 @@ +clc;
+p1=4; // number of poles in slip ring induction motor
+p2=6; // number of poles in synchronous motor
+f=50; // frequency of supply
+ns=(120*f)/p2; // synchronous motor speed
+ni=(120*f)/p1; // induction motor speed
+disp('case a(1)');
+// when synchronous motor is driven in direction opposite to the rotating field produced the induction motor stator
+nr=ns+ni; // relative speed
+F=(p1*nr)/120;
+printf('Frequency of EMF at rotor slip ring terminals is %f Hz\n',F);
+disp('case a(2)');
+// when synchronous motor is driven in direction of the rotating field produced the induction motor stator
+nr=ni-ns; // relative speed
+F=(p1*nr)/120;
+printf('Frequency of EMF at rotor slip ring terminals is %f Hz\n',F);
+disp('case b');
+fn=150; // frequency of rotor terminal voltage required
+// let new number of pole be pn then relative speed is nr=ns+(120*50)/pn;
+pn=((fn*120)-(120*f))/ns;
+printf('Number of poles that the induction motor must have is %f \n',pn);
+disp('case c');
+pi=8; // number of poles in induction motor
+ps=(120*f*pi)/((fn*120)-(120*f));
+printf('Number of synchronous motor poles required is %f',ps);
diff --git a/3760/CH3/EX3.40/Ex3_40.sce b/3760/CH3/EX3.40/Ex3_40.sce new file mode 100644 index 000000000..32f2f8b04 --- /dev/null +++ b/3760/CH3/EX3.40/Ex3_40.sce @@ -0,0 +1,20 @@ +clc;
+T=80; // total duration
+t1=5-0; // duration of first increasing loading period
+t2=36-5; // duration of second increasing loading period
+t3=39-36; // duration of first decreasing loading period
+t4=55-39; // duration of second decreasing loading period
+t5=80-55; // duration of uniform loading
+l1=150; // initial load
+l2=1000; // load at 5th sec
+l3=1400; // load at 36th sec
+l4=300; // load at 39th sec
+l5=150; // load during uniform loading
+T1=(t1/3)*(l1^2+l2^2+l1*l2); // term 1 for evaluating rms power
+T2=(t2/3)*(l2^2+l3^2+l2*l3); // term 2 for evaluating rms power
+T3=(t3/3)*(l3^2+l4^2+l3*l4); // term 3 for evaluating rms power
+T4=(t4/3)*(l4^2+l5^2+l4*l5); // term 4 for evaluating rms power
+T5=t5*l5^2; // term 5 for evaluating rms power
+R=sqrt((1/T)*(T1+T2+T3+T4+T5));
+printf('As per the load time graph rating is %f KW',R);
+disp('Choose a motor of rating above the calculated rating');
diff --git a/3760/CH3/EX3.41/Ex3_41.sce b/3760/CH3/EX3.41/Ex3_41.sce new file mode 100644 index 000000000..98b2ed0b7 --- /dev/null +++ b/3760/CH3/EX3.41/Ex3_41.sce @@ -0,0 +1,21 @@ +clc;
+p=200; // rated KVA of transformer
+n=0.98; // efficiency
+t1=20; // temperature after one hour of operation
+t2=34; // temperature after two hour of operation
+r=1/3; // ratio of full load core losses to ohmic loss
+disp('case a');
+t=[(t2/t1)-1];
+th=-1/log(t); // heating time constant in hours
+theta=t1/(1-exp(-1/th));
+printf('Final steady temperature rise of the transformer on rated load is %f degree celsius\n',theta);
+disp('case b');
+f=1.2; //with increased heat dissipation ,ratio of new loss to old loss
+Pn=sqrt((f*(1+r))-r)*p;
+printf('New KVA rating of transformer is %f KVA\n',Pn);
+// for a temperature rise of 78 degree
+t3=78;
+f=(t3/theta)*f; // ratio of new loss to old loss
+Pn=sqrt((f*(1+r))-r)*p;
+printf('New KVA rating of transformer is %f KVA\n',Pn);
+
diff --git a/3760/CH3/EX3.42/Ex3_42.sce b/3760/CH3/EX3.42/Ex3_42.sce new file mode 100644 index 000000000..35e15d311 --- /dev/null +++ b/3760/CH3/EX3.42/Ex3_42.sce @@ -0,0 +1,14 @@ +clc;
+p=100; // KW rating of transformer
+al=1; // ratio of core loss to ohmic loss
+th=3; // heating time constant in hours
+h=1; // duration in hour for which KVA rating has to be determined
+disp('case a');
+// constant losses are equal to variable losses
+pn=p*sqrt(((1+al)/(1-exp(-h/th)))-al);
+printf('One hour rating is %f KW\n',pn);
+disp('case b');
+// consatant losses are neglected
+al=0; // ratio of core loss to ohmic loss
+pn=p*sqrt(((1+al)/(1-exp(-h/th)))-al);
+printf('One hour rating is %f KW\n',pn);
diff --git a/3760/CH3/EX3.43/Ex3_43.sce b/3760/CH3/EX3.43/Ex3_43.sce new file mode 100644 index 000000000..1755e5c53 --- /dev/null +++ b/3760/CH3/EX3.43/Ex3_43.sce @@ -0,0 +1,5 @@ +clc;
+t=1/2; //ratio of continuous rating to one hour rating
+p=2; // ratio of new KVA rating to old KVA rating
+al=2*(p*t);
+printf('Ratio of core loss to ohmic loss is %f ',al);
diff --git a/3760/CH3/EX3.5/Ex3_5.sce b/3760/CH3/EX3.5/Ex3_5.sce new file mode 100644 index 000000000..5d835efab --- /dev/null +++ b/3760/CH3/EX3.5/Ex3_5.sce @@ -0,0 +1,37 @@ +clc;
+p=4; // number of pole
+f=50; // frequency of supply
+ns=420; // stator turns
+nr=240; // rotor turns
+F=30*10^-3; // flux per pole
+kw=0.96; // winding factor for both stator and rotor
+nsph=ns/3; // stator turn per phase
+nrph=nr/3; // rotor turn per phase
+es=sqrt(2)*%pi*f*kw*nsph*F; // stator turn per phase
+disp('case a');
+// rotor is stationary
+s=1; // at standstill slip=1
+er=sqrt(2)*%pi*f*kw*nrph*F;
+printf('frequency of EMF in stator is %f Hz\n',f);
+printf('frequency of EMF in rotor is %f Hz\n',f);
+printf('Per phase stator EMF is %f V\n',es);
+printf('Per phase rotor EMF is %f V\n',er);
+disp('case b');
+sr=1440; // speed of rotor in rpm in direction of rotating flux
+Ns=(120*f)/p; // speed of rotating flux
+s=(Ns-sr)/Ns; // slip
+fr=s*f; // frequency of EMF in rotor
+er=sqrt(2)*%pi*fr*kw*nrph*F;
+printf('frequency of EMF in stator is %f Hz\n',f);
+printf('frequency of EMF in rotor is %f Hz\n',fr);
+printf('Per phase stator EMF is %f V\n',es);
+printf('Per phase rotor EMF is %f V\n',er);
+disp('case c');
+sr=1440; // speed of rotor in rpm opposite to the direction of rotating flux
+s=(Ns+sr)/Ns; // slip
+fr=s*f; // frequency of EMF in rotor
+er=sqrt(2)*%pi*fr*kw*nrph*F;
+printf('frequency of EMF in stator is %f Hz\n',f);
+printf('frequency of EMF in rotor is %f Hz\n',fr);
+printf('Per phase stator EMF is %f V\n',es);
+printf('Per phase rotor EMF is %f V\n',er);
diff --git a/3760/CH3/EX3.6/Ex3_6.sce b/3760/CH3/EX3.6/Ex3_6.sce new file mode 100644 index 000000000..db8332e66 --- /dev/null +++ b/3760/CH3/EX3.6/Ex3_6.sce @@ -0,0 +1,25 @@ +clc;
+disp('case a');
+s=54; // number of slots in stator,3 phase
+p=6; // number of poles
+spp=s/(3*p); // slots per pole per phase
+v=(p*180)/s; // slot angular pitch
+k1=sin(((spp*v)/2)*(%pi/180))/(spp*sin((v/2)*(%pi/180))); // fundamental harmonics
+k3=sin(((3*spp*v)/2)*(%pi/180))/(spp*sin(((3*v)/2)*(%pi/180))); // third harmonic
+k5=sin(((5*spp*v)/2)*(%pi/180))/(spp*sin(((5*v)/2)*(%pi/180))); // fifth harmonic
+printf('First harmonic component is %f\n',k1);
+printf('Third harmonic component is %f\n',k3);
+printf('Fifth harmonic component is %f\n',k5);
+disp('case b');
+s=48; // number of slots in stator,3 phase
+p=6; // number of poles
+spp=s/(3*p); // slots per pole per phase
+sk=spp*3;
+v=(p*180)/s; // slot angular pitch
+ps=spp*v; // phase spread
+k1=sin(((ps)/2)*(%pi/180))/(sk*sin(((ps)/(sk*2))*(%pi/180))); // fundamental harmonics
+k3=sin(((3*ps)/2)*(%pi/180))/(sk*sin(((3*ps)/(sk*2))*(%pi/180))); // third harmonic
+k5=sin(((5*ps)/2)*(%pi/180))/(sk*sin(((5*ps)/(sk*2))*(%pi/180))); // fifth harmonic
+printf('First harmonic component is %f\n',k1);
+printf('Third harmonic component is %f\n',k3);
+printf('Fifth harmonic component is %f\n',k5);
diff --git a/3760/CH3/EX3.8/Ex3_8.sce b/3760/CH3/EX3.8/Ex3_8.sce new file mode 100644 index 000000000..5a126aa39 --- /dev/null +++ b/3760/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,23 @@ +clc;
+disp('case a');
+cs=160*(%pi/180); // coil span in radian
+ps=120*(%pi/180); // phase spread
+kd=sin(ps)/(ps/2); // distribution factor for uniformly distributed winding
+e=180-(cs*(180/%pi)); // chording angle
+kp=cos((e/2)*(%pi/180)); // Coil span factor
+wf=kd*kp; // winding factor
+disp('Distribution factor is');
+disp(kd);
+disp('Winding factor is');
+disp(wf);
+disp('case b');
+s=9; // number of slots per pole
+sa=180/s; // slot angular pitch
+// for a phase spread of 120 , 6*20=120, 6 adjacent slots must belong to the same phase, therefore
+p=6; // poles belonging to same phase
+kd=sin(ps/2)/(p*sin(ps/(2*6)));
+wf=kd*kp;
+disp('Distribution factor is');
+disp(kd);
+disp('Winding factor is');
+disp(wf);
diff --git a/3760/CH4/EX4.11/Ex4_11.sce b/3760/CH4/EX4.11/Ex4_11.sce new file mode 100644 index 000000000..63ecf5694 --- /dev/null +++ b/3760/CH4/EX4.11/Ex4_11.sce @@ -0,0 +1,13 @@ +clc;
+P=4;//No of poles
+Pout=100000;//Output power in watts
+Vt=200;//terminal voltage
+Z=256;//No of conductors
+A=4;//no of parallel paths of armature conductors
+Ia=Pout/Vt;//armature current
+Bcp=0.25;//interpolar flux density in tesla
+gcp=0.01;//interpolar air gap length
+U=4*%pi*0.0000001;//permeability of air
+Fcp=((Ia*Z)/(2*A*P))+((Bcp/U)*(gcp));//The interpolar m.m.f. per pole
+Ncp=Fcp/Ia;
+printf('The turns on each interpoles should be equal to %f.',round(Ncp));
diff --git a/3760/CH4/EX4.12/Ex4_12.sce b/3760/CH4/EX4.12/Ex4_12.sce new file mode 100644 index 000000000..eca9b106a --- /dev/null +++ b/3760/CH4/EX4.12/Ex4_12.sce @@ -0,0 +1,7 @@ +clc;
+D=50;//diameter of commutator
+N=1000;//speed of rotation of commutator in rpm
+Wb=1.5;//brush width
+V=%pi*D*N/60;//peripheral velocity of commutator
+Tc=(Wb*1000)/V;//time of commutation in ms
+printf('Time of commutation is %f ms.',Tc);
diff --git a/3760/CH4/EX4.13/Ex4_13.sce b/3760/CH4/EX4.13/Ex4_13.sce new file mode 100644 index 000000000..0e19f3bb0 --- /dev/null +++ b/3760/CH4/EX4.13/Ex4_13.sce @@ -0,0 +1,16 @@ +//The answer given in book for this question is wrong.
+
+clc;
+P=4;//No of poles
+Ia=120;//armature current
+A=4;//No of parallel paths for armature conductor
+L=0.02//inductance in mH
+//Et=L*(di/dt),Transformer emf in coil
+//di=2*Ia/A,change of current during commutation
+//dt=Tc,time of commutation
+//Et=0.02*0.001*(60/Tc) ....(1)
+//Er=2*(Bav*l*v),rotational emf in single turn coil
+//Er=2*(phi_c/Tc) ....(2),phi_c is the avg value of flux in the commutating zone
+//For linear commutation, Er=Et, from equation (1)&(2)
+phi_c=60*0.02*0.001/2;//phi_c is the avg value of flux in the commutating zone
+printf('THE AVG. VALUE OF FLUX IN THE COMMUTATING ZONE IS %f Wb.',phi_c)
diff --git a/3760/CH4/EX4.14/Ex4_14.sce b/3760/CH4/EX4.14/Ex4_14.sce new file mode 100644 index 000000000..8e6de404d --- /dev/null +++ b/3760/CH4/EX4.14/Ex4_14.sce @@ -0,0 +1,13 @@ +clc;
+Pout=2000000;//output power in watts
+Vt=400;//output voltage
+P=14;//No of poles
+A=14;//No of parallel paths of conductor
+Pr=0.7;//pole arc to pole pitch ratio
+Z=1100;//total armature conductors
+Ia=Pout/Vt;//armature current
+A_z=(Ia*Z)/(A*P);//armature ampere conductors per pole
+A_z1=Pr*A_z;//armature ampere conductors per pole to be compensated by pole face winding
+//The compensating winding carries the entire armature current of 5000 A.
+Wc=A_z1/Ia;//compensating winding conductors per pole
+printf('Total compensating winding conductors per pole are %f.',round(Wc));
diff --git a/3760/CH4/EX4.15/Ex4_15.sce b/3760/CH4/EX4.15/Ex4_15.sce new file mode 100644 index 000000000..d33226095 --- /dev/null +++ b/3760/CH4/EX4.15/Ex4_15.sce @@ -0,0 +1,14 @@ +clc;
+ATp=15000;//armture ampere turns per pole
+Pr=0.68;//ratio of pole arc to pole pitch
+Ia=850;//rated armature current
+Bcp=0.25;//interpolar flux density in tesla
+gcp=0.01;//interpolar air gap length
+U=4*%pi*0.0000001;//permeability of air
+ATc=Pr*ATp;//compensating winding ampere turns per pole
+C=2*(ATc/Ia);//compensating winding conductors per pole
+MMF_ag=(Bcp/U)*gcp;//M.M.F. required for the air gap under the interpole
+MMF=MMF_ag+ATp;//interpole M.M.F. without compensating winding
+MMF_c=MMF-ATc;//ampere turns furnished by each interpole
+N=MMF_c/Ia;//No. of turns on each interpole
+printf('Number of turns on each interpole is %f.',round(N));
diff --git a/3760/CH4/EX4.16/Ex4_16.sce b/3760/CH4/EX4.16/Ex4_16.sce new file mode 100644 index 000000000..f2356dd3f --- /dev/null +++ b/3760/CH4/EX4.16/Ex4_16.sce @@ -0,0 +1,13 @@ +clc;
+Pout=10000;//output power of dc generator in watts
+Vt=250;//terminal voltage in volts
+If=2;//field current in ampere at no load
+If1=2.2;//field current in ampere at rated load
+Tp=1400;//turns on each pole
+Ia=Pout/Vt;//armature current
+MMF_rl=If1*Tp;//M.M.F. required at rated load
+MMF_nl=If*Tp;//M.M.F. required at no load
+MMF_s=MMF_rl-MMF_nl;//M.M.F. supplied by series winding
+Is=Ia;//series current at full load
+Ts=MMF_s/Is;//series field turns
+printf('Series field turns are equal to %f.',Ts);
diff --git a/3760/CH4/EX4.17/Ex4_17.sce b/3760/CH4/EX4.17/Ex4_17.sce new file mode 100644 index 000000000..d49dae65c --- /dev/null +++ b/3760/CH4/EX4.17/Ex4_17.sce @@ -0,0 +1,19 @@ +clc;
+// table is given in question for plotting magnetising curve
+if1=[ 0 0.2 0.4 0.6 1 1.4 1.8 2 ];
+Ea=[ 6 40 80 120 194 246 269 274];
+plot(if1,Ea);
+xlabel('If');
+ylabel('Ea');
+title('magnetising curve')
+v=230; // rated voltage of generator
+p=10000; // rated power of generator
+n=1500; // rated speed of generator
+rf=184; // shunt field resistance
+ra=0.443; // armature resistance
+ifl=1.7; // rated field current
+il=p/v; // full load current
+printf('Total armature current is %f A\n',il+ifl);
+printf('Armature resistance drop is %f ohms\n',(il+ifl)*ra);
+disp('In fig 4.17(textbook),AB is made equal to armature resistance drop then through B a horizontal line is made meeting curve at c');
+disp('Demagnetising effect is given by BC which is equal to 0.25 A');
diff --git a/3760/CH4/EX4.18/Ex4_18.sce b/3760/CH4/EX4.18/Ex4_18.sce new file mode 100644 index 000000000..e83ae6038 --- /dev/null +++ b/3760/CH4/EX4.18/Ex4_18.sce @@ -0,0 +1,25 @@ +clc;
+vt1=50; // terminal voltage
+rf=100; // resistance of field circuit
+n1=1000; // speed corresponding to vt1=50
+vt2=225; // terminal voltage
+n2=2000; // speed corresponding to vt2=225
+vt3=405; // terminal voltage
+n3=3000; // speed corresponding to vt3=405
+disp('case a');
+ifl1=vt1/rf; // field current for n=1000 rpm
+ifl2=vt2/rf; // field current for n=2000 rpm
+ifl3=vt3/rf; // field current for n=3000 rpm
+printf('Field current for speed=%f rpm is %f A\n',n1,ifl1);
+printf('Field current for speed=%f rpm is %f A\n',n2,ifl2);
+printf('Field current for speed=%f rpm is %f A\n',n3,ifl3);
+vt11=vt1*(n2/n1);
+printf('Terminal voltage=%f V at %f rpm is equivalent to %f V at %f rpm\n',vt1,n1,vt11,n2);
+vt33=vt3*(n2/n3);
+printf('Terminal voltage=%f V at %f rpm is equivalent to %f V at %f rpm\n',vt3,n3,vt33,n2);
+disp('Using above data, magnetising curve is drawn for n=2000 rpm');
+// from fig 4.37
+disp('For field resistance=80 ohms terminal voltage is given by BC');
+disp('BC=253, hence terminal voltage corresponding to field resistance of 80 ohms is 253 V');
+disp('For field resistance=70 ohms terminal voltage is given by QP');
+disp('QP=268, hence terminal voltage corresponding to field resistance of 70 ohms is 268 V');
diff --git a/3760/CH4/EX4.19/Ex4_19.sce b/3760/CH4/EX4.19/Ex4_19.sce new file mode 100644 index 000000000..e5e438788 --- /dev/null +++ b/3760/CH4/EX4.19/Ex4_19.sce @@ -0,0 +1,45 @@ +clc;
+n=1500; // speed of generator
+// data is given in question for magnetising curve at n=1500 rpm
+If=[ 0 0.4 0.8 1.2 1.6 2 2.4 2.8 3];
+Ea=[6 60 120 172.5 202.5 221 231 237 240];
+subplot(221);
+plot(If,Ea);
+xlabel('field current');
+ylabel('generated EMF');
+title('Magnetising curve for n=1500');
+disp('case a')
+rf=100; // field resistance
+// rf=100 lets say voltage=240 and field current=2.4 which is shown by point A, straight line passing through A and origin meets magnetising current at B which is no load voltage
+Eo=230;
+printf('No load voltage is %f V\n',Eo);
+disp('case b');
+// a line OF is drawn passing through origin slope of this line gives critical resistance
+vt=180; // terminal voltage
+ifl=1.2; // field current corresponding to terminal voltage
+rfl=vt/ifl;
+printf('Critical value of shunt field resistance is %f ohms\n',rfl);
+disp('case c');
+// Choose S (any point) on linear part of magnetising curve.A vertical line from S meets field resistance line at t and horizontal line at y. Now
+e1=90; // terminal voltage corresponding to point s
+e2=60; // terminal voltage corresponding to point t
+n2=(e2/e1)*n;
+printf('Critical speed for given shunt field resistance is %f rpm\n',n2);
+disp('case d');
+n3=1200; // speed at which magnetising curve is drawn
+// data for magnetising curve at n=1200 can be obtained by multiplying voltage of magnetising curve at n=1500 by factor 1200/1500 and at point C field resistance line for 100 ohms meet at magnetising curve .This point gives no load EMF
+EAn=Ea*(n3/n);
+subplot(222);
+plot(If,EAn);
+xlabel('field current');
+ylabel('generated EMF');
+title('Magnetising curve for n=1200');
+Eo=165;
+printf('No load EMF is %f V\n',Eo);
+disp('case e');
+ia=50; // armature current
+ra=0.3; // armature resistance
+vd=ia*ra; // armature resistance drop
+// To obtain terminal voltage cut OD equal to vd and draw DG parallel to field resistance line. From G draw vertical line meeting field resistance line at H. Point corresponding to H gives terminal voltage which is
+vt=207;
+printf('Terminal voltage is %f V\n',vt);
diff --git a/3760/CH4/EX4.2/Ex4_2.sce b/3760/CH4/EX4.2/Ex4_2.sce new file mode 100644 index 000000000..84878809e --- /dev/null +++ b/3760/CH4/EX4.2/Ex4_2.sce @@ -0,0 +1,17 @@ +clc;
+l=0.3;//core length
+r=0.2;//radius
+n=20;//speed in r.p.s.
+Ia=20;//armature current
+Z=500;//total conductors
+Bav=0.5;//avg. flux density
+a=4;//lap-wound
+P=4;//no of poles
+Wm=2*%pi*n
+phi=((0.5*2*%pi*0.2*0.3)/4);
+Ea=((P*n*Z*phi)/a);//generated emf
+Pm=Ea*Ia;//gross mechanical power developed
+Te=((Ea*Ia)/Wm);//internal torque
+printf('Generated E.M.F. is %f V.\n',Ea);
+printf('Gross mechanical power developed is %f W.\n',Pm);
+printf('Internal Torque is %f Nm.',Te);
diff --git a/3760/CH4/EX4.20/Ex4_20.sce b/3760/CH4/EX4.20/Ex4_20.sce new file mode 100644 index 000000000..325aef40b --- /dev/null +++ b/3760/CH4/EX4.20/Ex4_20.sce @@ -0,0 +1,51 @@ +clc;
+ra=0.5; // armature resistance
+rf=180; // shunt field resistance
+n=1100; // speed at which generator is being driven
+n1=1000; // speed for which data is given
+disp('case a');
+// from the data given in question magnetising curve is drawn (fig 4.46)
+If=[ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ];
+Ea=[5 50 100 140 170 190 200 205];
+Ean=(n/n1)*Ea
+plot(If,Ean);
+xlabel('field current');
+ylabel('generated EMF');
+title('Magnetising curve for n=1100');
+// line corresponding to rf=180 ohms to meet saturation curve at 221 V which is no load EMF
+Eo=221;
+printf('No load EMF is %f V\n',Eo);
+disp('case b');
+vt=190; // terminal voltage
+// from curve armature resistance drop is given by line BC
+vd=22.5; // armature resistance drop
+ia=vd/ra; // armature current
+ifl=vt/rf; // field current
+printf('Shunt field current is %f A\n',ifl);
+printf('Output current is %f A\n',ia-ifl);
+disp('case c');
+// OP represents maximum armature resistance drop i.e OP=46.5 V
+vd=46.5;
+ia=vd/ra; // armature resistance
+// tangent point at R gives field current which is
+ifl=0.635;
+printf('Maximum output current is %f A',ia-ifl);
+disp('case d');
+// under steady state short circuit terminal voltage=0 V and residual flux EMF is
+E=5.5; // residual flux EMF
+printf('Steady state short circuit current is %f A\n',E/ra);
+disp('case e');
+Eo=210; // no load voltage
+// for Eo OD represents field resistance field current is 1.015
+ifl=1.015; // field current
+rfn=Eo/ifl; // field resistance
+printf('Additional resistance required is %f ohms\n',rfn-rf);
+disp('case f');
+rf=150; // shunt field resistance
+vt=180; // terminal voltage
+p=0.04; // reduction in flux due to armature reaction
+ifl=vt/rf; // field current
+Ea=220*(1-p); // generated voltage
+ia=(Ea-vt)/ra; // armature current
+il=ia-ifl; // load current
+printf('Load power is %f KW',(vt*il)/1000);
diff --git a/3760/CH4/EX4.21/Ex4_21.sce b/3760/CH4/EX4.21/Ex4_21.sce new file mode 100644 index 000000000..82f432f09 --- /dev/null +++ b/3760/CH4/EX4.21/Ex4_21.sce @@ -0,0 +1,46 @@ +clc;
+Vrated=30;//rated output voltage of generater
+Irated=200;//rated output current of generator
+Ra=0.03;//armature resistance(including brushes)
+Rf=2.4;//field winding resistance
+//No-load saturation curve at 2200rpm
+If=[2 4 6 8 10 12];
+Ea=[15 27 35 40 43 45];
+plot(If,Ea);//magnetization curve at 2200 rpm
+
+
+//(1)AT 2200 rpm
+//at no load
+Ea1=28;//induced voltage in armature
+//for this voltage, the field current required, from magnetization curve is-
+If1=4.23;//field current in ampere
+Rt1=Ea1/If1;//total shunt field resistance
+Re=Rt1-Rf;//external resistance
+
+//at full load
+Ea1_=28+Irated*Ra;//induced voltage in armature
+//for this voltage, the field current required, from magnetization curve is-
+If1_=5.67;//field current
+Rt1_=Ea1/If1_;//total shunt field resistance
+Re_=Rt1_-Rf;//external resistance
+
+
+//(2)AT 4500 rpm
+//at no load
+Ea2__=28;//induced voltage in armature at 4500 rpm
+Ea2=28*(2200/4500);//Ea at 2200 rpm
+//for this voltage, the field current required, from magnetization curve is-
+If2=1.833;//field current in ampere
+Rt2=Ea2__/If2;//total shunt field resistance
+Re__=Rt2-Rf;//external resistance
+
+//at full load
+Ea2___=28+Irated*Ra;//induced voltage in armature at 4500 rpm
+Ea2_=34*(2200/4500);//Ea at 4500 rpm
+//for this voltage, the field current required, from magnetization curve is-
+If2_=2.17;//field current
+Rt2_=Ea2__/If2_;//total shunt field resistance
+Re___=Rt2_-Rf;//external resistance
+Pmax=If1_*If1_*min(Re,Re_,Re__,Re___);
+printf('The minimum & maximum value of external resistance is %f & %fohm respectively.\nMaximum power dissipated through rheostat is %f ohm.',min(Re,Re_,Re__,Re___),max(Re,Re_,Re__,Re___),Pmax);
+
diff --git a/3760/CH4/EX4.22/Ex4_22.sce b/3760/CH4/EX4.22/Ex4_22.sce new file mode 100644 index 000000000..b2fbe535b --- /dev/null +++ b/3760/CH4/EX4.22/Ex4_22.sce @@ -0,0 +1,20 @@ +clc;
+Vt=100;//terminnal voltage
+P=2;//no of poles
+Z=1000;//no of conductors
+A=2;//no of parallel paths for armature conductors
+Ra_=2*10e-3;//resistance of each armature
+Ra=500*Ra_*(1/2);//total armature resistance
+//Let If be field current
+//Ea=Vt+(Il+If)*0.5
+//Ea1=100+(10+If)*0.5,because at 1055 rpm Il=10.
+//Ea2=100+(20+If)*0.5,because at 1105 rpm Il=20.
+//But, Ea=k1*If*speed
+//Therefore,((If*1055)/(If*1105))=((100+(10+If)*0.5)/(100+(20+If)*0.5)),which gives-
+If=1;//field current
+Ea1=100+(10+1)*0.5;//at 1055 rpm
+N=1055;//speed of rotor
+phi=(Ea1*60*A)/(Z*N*P);
+Rf=Vt/If;//field circuit resistance
+printf('Field circuit resistance is %f ohm.\n',Rf);
+printf('Flux per pole is %f Wb.',phi);
diff --git a/3760/CH4/EX4.23/Ex4_23.sce b/3760/CH4/EX4.23/Ex4_23.sce new file mode 100644 index 000000000..d84a2ece1 --- /dev/null +++ b/3760/CH4/EX4.23/Ex4_23.sce @@ -0,0 +1,41 @@ +clc;
+disp('case a');
+v=90; // voltage build up by regulating resistance
+rs=(v*v)/(2*v); // shunt winding resistance
+IF=[500 1000 1500 2000 2500 3000];
+VA=[154 302 396 458 505 538 ];
+subplot(313);
+plot(IF,VA);
+xlabel('Field ATs/pole');
+ylabel('Generated e.m.f E,(V)');
+title('Magnetizing curve for n=500 r.p.m.');
+// from magnetizing curve for v=90, field current is 0.89 A
+ifl=0.89; // field current
+re=(v/(2*ifl))-rs;
+printf('Value of the resistance in the regulator is %f ohms\n',re);
+disp('case b');
+t1=800; // turns per pole of separately excited winding
+r1=160; // resistance of winding
+vc=220; // constant supply voltage
+t2=500; // turns per pole of shunt winding
+r2=200; // resistance of winding
+AT1=(vc*t1)/r1; // Ampere turns of separately excited winding
+// AT2=(t2/r2)*E is Ampere turns of shunt winding and E is generated EMF
+AT3=AT1+(t2/r2)*VA
+n1=500;
+n2=600; // given speeds
+VA2=(n2/n1)*VA; // generated EMF for n=600 rpm
+subplot(323);
+plot(IF,VA2);
+xlabel('Field ATs/pole');
+ylabel('Generated e.m.f E,(V)');
+title('Magnetizing curve for n=600 r.p.m.');
+subplot(333);
+plot(AT3,VA);
+ylabel('Generated e.m.f E,(V)');
+xlabel('Total ATs/pole due to both field winding');
+title('Generated e.m.f E,(V) vs total Ampere turns/pole ');
+// plot of variation of generated e.m.f with total Ampere turns per pole intersects magnetizing curve for n=500 rpm at P and magnetizing curve for n=600 rpm at Q. (refer fig. 4.48)
+// Point P gives no-load terminal voltage at 500 rpm and Q gives no-load terminal voltage at 600 rpm
+disp('No load voltage at 500 rpm is 490 V and at 600 rpm is 621 V');
+
diff --git a/3760/CH4/EX4.24/Ex4_24.sce b/3760/CH4/EX4.24/Ex4_24.sce new file mode 100644 index 000000000..4af125f9f --- /dev/null +++ b/3760/CH4/EX4.24/Ex4_24.sce @@ -0,0 +1,33 @@ +clc;
+//magnetization curve at 1200 rpm
+If=[0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8];//field current in rpm
+Ea=[6 53 106 160 209 241 258 272 282 288];//induced voltage in armature
+plot(If,Ea);xlabel('If');ylabel('Ea');//magnetization curve at 1200 rpm
+Pout=10000;//genertor output in watts
+Vt=230;//Terminal Voltage
+Ra=0.5;//armature resistance with brushes
+Ns=1000;//turns of shunt winding
+Nf=4;//turns of field winding
+Z=1000;//No of conductors
+
+//PART (A)
+//At rated output current the speed is 1150 rpm & shunt field current is 1 A
+If_=1;//field current at rated o/p current
+Il=Pout/Vt;//rated output current
+Ia=Il+If;//armature current at rated load
+Is=Ia;//for long shunt compound generator the series field current is equal to armature current
+//Since the compound geenerator is cumulatively compounded ,the total pole per m.m.f. is (Nf*If+Ns*Is)ampere turns
+//Thus the equivalent shunt field current is given by 1/Nf*(Nf*If+Ns*Is)=1+(4*44.5/1000)=1.18 A. The generated emf for this field currenr from the magnetization curve is 257 volts.
+//For speed of 1150 rpm the generated emf is-
+Ea_=257*(1150/1200);
+Vt_=Ea_-Ia*Ra;//terminal voltage
+
+//PART(B)
+Eg=Vt+Ia*Ra;//generated emf in the armature at 1150 rpm
+//By using the magnetization curve, the generated emf at 1200 rpm will be 252.25*(1200/1500)=263.3 volts.
+//From the open circuit characteristics, the field current corresponding to 263.3 volts is 1.26 A.
+MMFt=1.26*1000;//Total MMF
+//Total MMF must be produced by the combined action of shunt & series windings.
+//1.26*1000=1.00*1000+Ns*(44.5);
+Ns_=(0.26*1000)/44.5;//series field turns
+printf('The number of series field turns should be %f.',round(Ns_));
diff --git a/3760/CH4/EX4.25/Ex4_25.sce b/3760/CH4/EX4.25/Ex4_25.sce new file mode 100644 index 000000000..4010123ca --- /dev/null +++ b/3760/CH4/EX4.25/Ex4_25.sce @@ -0,0 +1,18 @@ +clc;
+//repeat part (b) of example 4.21
+
+//PART(a)-
+//When the demagnetizing effect is accounted for, then from equation :-Net mmf = Nf*If+Ns*Is-ATd ....(1)
+//1.26*1000=1.00*1000+10Is-0.022Is*1000
+Ns=round(0.3578*1000/44.5);//no of turns in series field winding
+
+//PART(b)-
+//If there are 10 series field turns, then from equation (1),
+//1.26*1000=1.00*1000+10Is-0.0022Is*1000
+Is=0.26/0.0078
+//Out of the total armature current of 44.5 A, only Is(33.3) should flow through the series field.
+//This can be achieved by putting a resistor in parallel with the series field winding.
+//33.3=(44.5*Rdi)/(0.05+Rdi)
+Rdi=0.05/0.3363;
+printf('NO OF TURNS IN SERIES FIELD WINDING ARE %f.',Ns);
+printf('\nTHE RESISTANCE OF DIVERTER Rdi SHOULD BE %f OHMS.',Rdi);
diff --git a/3760/CH4/EX4.26/Ex4_26.sce b/3760/CH4/EX4.26/Ex4_26.sce new file mode 100644 index 000000000..2344fb06c --- /dev/null +++ b/3760/CH4/EX4.26/Ex4_26.sce @@ -0,0 +1,29 @@ +clc;
+Vt=250;//rated o/p voltage of generator
+Pout=10000;//o/p of generator in watts
+Ra=0.4;//armature resistance
+Rse=0.2;//series field resistance
+Rs=125;//shunt field reesistance
+Vb=2;//total brush cotact drop
+Il=Pout/Vt;//load current
+
+//PART(a)-LONG SHUNT CONNECTION
+If=Vt/Rs;//shunt field current
+Ia=Il+If;//armature current
+//series field winding also carries Ia.
+Eal=Vt+Ia*(Rse+Ra)+Vb;//generated emf in armature
+printf('The generated EMF in armature when the generated is connected as long shunt machine is %f.\n',Eal);
+
+//PART(b)-SHORT SHUNT CONNECTION
+V=Vt+Il*Rse;//voltage across shunt field and armature terminals
+If_=V/Rs;//shunt field current
+Ia_=Il+If_;//armature current
+Eas=V+Ia*Ra+Vb;//generated emf in armature
+printf('The generated EMF in armature when the generated is connected as short shunt machine is %f.',Eas);
+
+//PART(c)-
+//Series field ampere turns are proportional to series-field current I
+//Is=0.3/0.5*I, where , Is is series field current with diverter.
+//series field ampere-turns with dvider = K*0.6*Is, where K is a constant.
+//percentage reduction in series field ampere turns is - ((I-O.6I)/I)*100.
+disp('Percentage reduction in series field ampere turns is 40%.');
diff --git a/3760/CH4/EX4.27/Ex4_27.sce b/3760/CH4/EX4.27/Ex4_27.sce new file mode 100644 index 000000000..42c166d91 --- /dev/null +++ b/3760/CH4/EX4.27/Ex4_27.sce @@ -0,0 +1,23 @@ +clc;
+Vt=230;//output voltage
+Ra=0.3;//armature circuit resistance
+Rf=160;//field circuit resistance
+Il=40;//line current at full load & rated voltage
+Ia1=3.33//armature current at rated voltage & no load speed of 1000 rpm
+//No load counter emf is-
+Ea1=Vt-Ia1*Ra;
+If=Vt/Rf;//field current
+//At full load armature current is-
+Ia2=Il-If;
+Ea2=Vt-Ia2*Ra;//Counter emf at full load
+//At full load, the field flux is-
+//Phi_2=0.96*phi_1
+//The conter emf Ea, is given by- Ea=Ka*phi*Wm
+//Ea1/Ea2=(Ka*phi_1*Wm1)/(Ka*phi_2*Wm2)=(phi_1*n1)/(phi_2*n2) or 229/218.43=(1000*phi_1)/n2*(0.96*phi_1)...(1)
+//from equation (1)
+n2=995;//full load speed
+//At full load, Ea2=Ka*phi_2*Wm
+//Ka*phi_2=Ea2/Wm
+//Electromagnetic or developed, torque at full load is, Te=Ka*phi_2*Ia2
+Te=(Ea2*60)/(2*%pi*n2)*Ia2;//Electromagnetic torque developed.
+printf('Electromagnetic or developed, torque at full load is %f.',Te);
diff --git a/3760/CH4/EX4.28/Ex4_28.sce b/3760/CH4/EX4.28/Ex4_28.sce new file mode 100644 index 000000000..724f97ad8 --- /dev/null +++ b/3760/CH4/EX4.28/Ex4_28.sce @@ -0,0 +1,24 @@ +clc;
+//Armature reaction is neglected
+Vt=220;//output voltage
+Ra=0.2;//armature circuit resistance
+Rf=110;//field circuit resistance
+n1=1500;//speed of rotor at no load
+Il1=5;//curent drawn by motor in ampere at no load & 1500 rpm
+Il2=52;//curent drawn by motor in ampere at rated load & rated voltage
+If=Vt/Rf;//shunt field current
+Ia1=Il1-If;//armature current at no load
+Ea1=Vt-Ia1*Ra;//counter emf at no load
+Pr=Ea1*Ia1;//rotational losses at no load
+//Rotational losses at full load & no load are same
+Ia2=Il2-If;//armature current at full load
+Ea2=Vt-Ia2*Ra;//counter emf at full load
+Pem=Ia2*Ea2;//electromagnetic power
+//Here phi_1(no load flux)=phi_2(full load flux), because the field current is constant & effect of AR is neglected.
+//Ea1/Ea2=(n1*phi_1)/(n2*phi_2);where n1 & n2 are speed of rotor at no load & full load respectively.
+n2=fix((n1*Ea2)/(Ea1));
+Psh=Pem-Pr;//shaft power
+Wm=(2*%pi*n2)/60;//angular velocity of shaft at full load
+Tsh=Psh/Wm//shaft torque
+printf('The motor speed is %f rpm.\n',n2);
+printf('Rated shaft torque is %f Nm.',Tsh);
diff --git a/3760/CH4/EX4.29/Ex4_29.sce b/3760/CH4/EX4.29/Ex4_29.sce new file mode 100644 index 000000000..db9759cd8 --- /dev/null +++ b/3760/CH4/EX4.29/Ex4_29.sce @@ -0,0 +1,16 @@ +
+clc;
+Ra=0.4;//armature resistance in ohm
+Rf=200;//field circuit resistance in ohm
+Vt=230;//terminal voltage for dc motor
+If_1=1.1;//field current for dc generator at open circuit voltage of 210 V.
+If_2=0.9;//field current for dc generator at open circuit voltage of 230 V.
+Ia=24;//armature current for dc shunt motor at 1500 rpm
+Ea=Vt-Ia*Ra;//counter e.m.f. for dc motor at 1500 rpm and full load
+//For generated e.m.f., Ea=230 V, field current is 1.1 A & for Ea=210 V, field current is 0.9 A
+//The change in generated e.m.f. is 20 V for field variation of 0.2 A & this change is linear.
+//Therefore for a generated e.m.f. of Ea=220.4 V at 1500 rpm, the field current would be-
+If=0.9+(0.2/20)*10.4;//0.9 A for 210 V & (0.2/20)*10.4 for remaining 10.4 V.
+Rsh=Vt/If;//Shunt field resistance required for a field current(If) with terminal voltage(Vt).
+Rext=Rsh-Rf;//External resistance that must be inserted in shunt field circuit
+printf('The external resistance that must be inserted in shunt field circuit = %f ohm.',Rext);
diff --git a/3760/CH4/EX4.3/Ex4_3.sce b/3760/CH4/EX4.3/Ex4_3.sce new file mode 100644 index 000000000..08080fdf5 --- /dev/null +++ b/3760/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,28 @@ +clc;
+P=6;//no of poles
+Z=300;//no of conductors
+phi=0.015;//flux per pole in webers
+n=30;//speed in r.p.s.
+Ic=80;//current per conductor
+Wm=2*%pi*n;
+Eav=P*n*phi;//avg. emf per conductor
+//when conductors are wave connected
+disp('Wave Connected')
+a1=2;//no of parallel paths
+Ia=Ic*a1;//total current
+Ea=Eav*(Z/a1);//E.M.F.
+Pa=Ea*Ia;//power developed in armature
+Te=Ea*Ia/Wm;//Electromagnetic torque
+printf('Generated E.M.F. is %f V.\n',Ea);
+printf('Power developed in armature is %f W.\n',Pa);
+printf('Electromagnetic Torque is %f Nm.\n',Te);
+//when conductors are lap connected
+disp('Lap Connected')
+a2=4;//no of parallel paths
+Ia2=Ic*a2;//total current
+Ea2=Eav*(Z/a2);//E.M.F.
+Pa2=Ea2*Ia2;//power developed in armature
+Te2=Ea2*Ia2/Wm;//Electromagnetic torque
+printf('Generated E.M.F. is %f V.\n',Ea2);
+printf('Power developed in armature is %f W.\n',Pa2);
+printf('Electromagnetic Torque is %f Nm.',Te2);
diff --git a/3760/CH4/EX4.30/Ex4_30.sce b/3760/CH4/EX4.30/Ex4_30.sce new file mode 100644 index 000000000..c9600bb48 --- /dev/null +++ b/3760/CH4/EX4.30/Ex4_30.sce @@ -0,0 +1,32 @@ +clc;
+//Armature reaction is neglected.
+Vt=250;//Supply voltage
+P=4;//No of poles
+A=2;//No of parallel paths for armature conductors
+Z=500;//No of armature conductors
+Ra=0.25;//armature circuit resistance in ohm
+Rf=125;//field resistance in ohm
+phi=0.02;//flux per pole in weber
+Il=14;//current drawn by motor from supply mains
+Ish=Vt/Rf;//constant shunt field current
+Pr=300;//rotational losses in watts
+Pi=Vt*Il;//power input in watts
+
+//PART(a)-
+Ia=Il-Ish;//armature current
+Ea=Vt-Ia*Ra;//counter/back emf
+//Ea=(P*phi*Z*N)/(60*A)
+N=(60*A*Ea)/(P*phi*Z);//speed of rotation of motor in rpm
+Wm=(2*%pi*N)/60;//angular velocity of motor
+Pe=Ea*Ia;//electromagnetic power
+Ti=Pe/Wm;//Internal torque developed in Nm.
+printf('Speed of rotation of motor is %f rpm.',N);
+printf('\nInternal torque developed = %f Nm.',Ti);
+
+//PART(b)-
+Psh=Pe-Pr;//shaft power
+Tsh=Psh/Wm;//shaft torque
+%n=(Psh/Pi)*100;//percentage eficiency
+printf('\nShaft power = %f watts.',Psh);
+printf('\nShaft torque = %f Nm.',Tsh);
+printf('\nEfficiency of motor is %f percent.',%n);
diff --git a/3760/CH4/EX4.31/Ex4_31.sce b/3760/CH4/EX4.31/Ex4_31.sce new file mode 100644 index 000000000..dc65331df --- /dev/null +++ b/3760/CH4/EX4.31/Ex4_31.sce @@ -0,0 +1,35 @@ +clc;
+Vt=230;//Supply voltage
+P=4;//No of poles
+A=2;//No of parallel paths for armature conductors
+Z=600;//No of armature conductors
+Ra=0.25;//armature circuit resistance in ohm
+phi=0.01;//flux per pole in weber
+Pr=500;//rotational losses in watts
+//generated emf in armature, Ea=(phi*Z*P*n)/(60*A) if n is speed in armature
+//Counter emf is Ea=(0.01*600*4*n)/(60*2)=0.2n volts
+//Vt=Ea+Ia*Ra
+//Ia=(Vt-Ea)/Ra/
+//Shaft o/p in watts, Psh=Ea*Ia-Pr, Psh=(0.2n)*(920-0.8n)-500 ....(1)
+n=[700 800 900 1000 1100];//different speeds of motor for which the shaft o/p power is to be measured
+//Psh=(0.184*n)-(1.6*(10e-4)*n*n)-0.5, Shaft o/p power in KW.
+Psh1=49.1;//Shaft o/p power in KW at n=700 rpm
+Psh2=44.3;//Shaft o/p power in KW at n=800 rpm
+Psh3=33.5;//Shaft o/p power in KW at n=900 rpm *Psh1,Psh2,Psh3,Psh4,Psh5 are calclulated from equation (1)*
+Psh4=23.5;//Shaft o/p power in KW at n=1000 rpm
+Psh5=8.3;//Shaft o/p power in KW at n=1100 rpm
+Psh=[Psh1 Psh2 Psh3 Psh4 Psh5];
+Pi=[4.5 8.5 14 21.1 30];//i/p power supplied to fan in KW.
+plot(n,Psh,n,Pi);xlabel('RPM');ylabel('KW');//Shaft o/p power versus speed of motor and power i/p versus speed of fan are plotted on the same graph
+//For plot :-*blue line- motor characteristic,green line- fan charactestic*
+//The intesecton of these two curves is called as OPERATING POINT.
+//At operating point the speed is 1012 rpm & pwer o/p of motor or power i/p to the fan is 22 KW ....(from the intersection point of two curves)
+n_=1012;//speed at operating point
+P_o=22000;//Power output loss
+Ia=920-(0.8*n_);//armature current
+Parm=Ia*Ia*Ra;//armature loss
+P_ip=P_o+Pr+Parm;//Power input
+%n=(P_o/P_ip)*100;//motor efficiency
+printf('Armature current is %f A\n.',Ia);
+printf('Operating speed is %f rpm\n.',n_)
+printf('Motor efficiency is %f percent.',%n);
diff --git a/3760/CH4/EX4.32/Ex4_32.sce b/3760/CH4/EX4.32/Ex4_32.sce new file mode 100644 index 000000000..8f3532ec8 --- /dev/null +++ b/3760/CH4/EX4.32/Ex4_32.sce @@ -0,0 +1,21 @@ +clc;
+Vt=230;//Supply voltage
+P=4;//No of poles
+A=2;//No of parallel paths for armature conductors
+Z=500;//No of armature conductors
+Ra=0.2;//armature circuit resistance in ohm
+Rs=0.1;//field resistance in ohm
+Il=40;//line current
+N=1000;//rated speed in rpm
+Ia1=40;//armature current for dc series motor at 40 A line current
+Ia2=20;//armature current for dc series motor at 20 A line current
+//For 40A line current
+Ea1=Vt-Ia1*(Ra+Rs);//counter emf
+//For 20A line current
+Ea2=Vt-Ia2*(Ra+Rs);//counter emf
+//Let, phi_1=flux at 40 A, phi_2=flux at 20 A line current
+//phi_2=0.6*(phi_1)
+//(Ea1/Ea2)=(n1*phi_1)/(n2*phi_2)
+//(218/224)=(1000*(phi_1))/(n2*(0.6*(phi_1))
+n2=(1000*224)/(218*0.6);//speed of motor at line current of 20 A at 230 V
+printf('Speed of motor at line current of 20 A at 230 V is %f rpm.',round(n2));
diff --git a/3760/CH4/EX4.33/Ex4_33.sce b/3760/CH4/EX4.33/Ex4_33.sce new file mode 100644 index 000000000..a0cb162e5 --- /dev/null +++ b/3760/CH4/EX4.33/Ex4_33.sce @@ -0,0 +1,35 @@ +//ANSWER GIVEN IN THE BOOK FOR THIS QUESTION IS INCORRECT.
+
+clc;
+//Neglecting armature reaction & magnetic saturation
+//Assuming rotational losses to remain constant
+V=230;//Supply voltage
+P=15000;//power rating of dc series motor in watts
+Il_1=80;//line current rated
+Il_2=40;//line current assuming that motor draws half the rated current at rated voltage
+Ia_1=Il_1;//armature current at line current equal to 80 A.
+Ia_2=Il_2;//armature current at line current equal to 40 A.
+n1=1000;//rated speed in rpm
+//Full load losses expressed as percentage of motor input:-
+//Armature ohmic loss=2.8%(including brush loss)
+//Field ohmic loss=2.2%
+//Rotational loss=2.2%
+P_ip=V*Il_1;//full load input
+P_ohmic=P_ip*(5.4/100)//As percent of total ohmic losses=2.2+2.8=5.4%
+//But P_ohmic=Il*Il*(Ra+Rs); where (Ra+Rs)=(armature + series field) resistance
+//(Ra+Rs)=P_ohmic/(Il*Il)=0.115 ohms
+//Let, r=(Ra+Rs)
+r=0.115;
+
+//PART(a)-
+Ea1=V-(Ia_1*r);//counter emf at line current = 80 A
+Ea2=V-(Ia_2*r);//counter emf at line current = 40 A
+//Since the magnetic saturation is neglected, phi_1=k*80 & phi_2=k*40; where k=constant & phi_1 & phi_2 are flux per pole at line currents 80 & 40 A respectively.
+//(Ea1/Ea2)=(n1*phi_1)/(n2*phi_2) or (220.8/225.4)=(1000*80)/(n2*40); where Ea1=220.8 V Ea2=225.4 V.
+n2=(1000*80*225.4)/(40*220.8);//speed in rpm
+printf('The speed of rotation of motor when the motor draws half the rated current at rated voltage is %f rpm.',round(n2));
+
+//PART(b)-
+Pr=P_ip*(2.2/100);//rotational losses
+Psh=Ea2*Ia_2-Pr;
+printf('\nThe shaft output power is %f W.',Psh);
diff --git a/3760/CH4/EX4.34/Ex4_34.sce b/3760/CH4/EX4.34/Ex4_34.sce new file mode 100644 index 000000000..e234e7b7b --- /dev/null +++ b/3760/CH4/EX4.34/Ex4_34.sce @@ -0,0 +1,41 @@ +
+clc;
+Pout=40000;//output power
+V=250;//supply voltage in volts
+r=0.2;//sum of armature circuit resistance & series field circuit resistance
+n=1500;//speed of dc series motor at rated current
+
+//PART(a)-
+
+Ir=Pout/V;//rated current
+Ea=V-Ir*r;//counter emf at rated load
+Wm=(2*%pi*n)/60;//angular speed of rotation of motor
+Te=round((Ea*Ir)/Wm);//rated electromagnetic torque in Nm.
+//Now the relation giving the torque speed characteristics of series motor must be developed.
+//Since the magnetic saturation is neglected
+//Te=Ka*phi*I
+//Te=K1*Ia^2
+K1=Te/(Ir^2);//Ia=rated current
+//Ea=K2*phi*n=K2*Ia*n
+K2=Ea/(Ir*n);// values of constant of proportionality
+//The values of constants k1 & K2 are obtained from rated conditions
+//Ia=(V-Ea)/r & Ea=K2*Ia*n ; Ia=1250-0.00454*Ia*n
+//Ia=1250/(1+0.00454n) ....(1); Ia=armature current at any speed
+//Te=K1*Ia^2
+n=[1400 1450 1500 1550 1600 1650 1700];
+Te=K1.*(((V/r)^2)./(1+(K2/r).*n).^2); // Electromagnetic torque
+Tl=5.*sqrt(n); // load torque
+plot(Te,n,Tl,n);
+xlabel('T(Nm)');
+ylabel('Speed(rpm)');
+title('Speed-torque characteristics for Series-motor and for load');
+
+//THE INTERSECTION OF SERIES MOTOR & LOAD CHARACTERISTICS GIVES THE OPERATING POINT
+
+//From the curve the operating point is obtained at 1591 rpm & torque is 199.5 Nm
+disp('The operating speed of motor is 1591 rpm.');
+
+//PART(b)-
+//Current drawn from the source is -
+Ia=(V/r)/(1+(K2/r)*1591);//From equation (1)
+printf('Current drawn from the source is %f A.',Ia);
diff --git a/3760/CH4/EX4.35/Ex4_35.sce b/3760/CH4/EX4.35/Ex4_35.sce new file mode 100644 index 000000000..d3e359167 --- /dev/null +++ b/3760/CH4/EX4.35/Ex4_35.sce @@ -0,0 +1,27 @@ +clc;
+V=230;//supply current
+Pout=15000;//output voltage
+Ra=0.2;//armature circuit resistance
+Rse=0.1;//resistance of series field winding
+Nf=1000;//shunt field turns per pole
+//Data for magnetization curve at 1500 rpm
+If_=[0 0.2 0.4 0.6 0.8 1.02 1.15 1.32 1.56 1.92 2.4];//field current at 1500 rpm
+Ea=[6 40 80 120 160 200 220 240 260 280 300];//counter emf at 1500 rpm and respective field current
+plot(If_,Ea);//Magnetization curve at 1500 rpm
+Ia_1=4;//armature current at rated voltage and rated load
+Ia_2=70;//armature current at 1200rpm
+
+//At no load
+Ea_=V-Ia_1*Ra;//counter emf
+//field current required for Ea_(ie.229.2 V),from O.C.C. is 1.23 A.
+
+//At load
+Ea__=V-Ia_2*(Ra+Rse);//counter emf at 1200 rpm
+Ea___=209*(1500/1200);//Ea at speed of 1500 rpm
+//Field current corresponding to Ea___(ie.261.25 V),from O.C.C. is 1.575 A.
+//Total D-axis mmf per pole=Nf*If+Ns*Is
+If=1.23;//field current at 229.2 V is 1.23 A
+If1=1.23;//field current at 261.25 V is 1.575 A
+//1.575*1000=1.23*1000+Ns*(70)
+Ns=(0.345*1000)/70;//series field turns
+printf('For long-shunt connection, series field turns is equal to %f.',round(Ns));
diff --git a/3760/CH4/EX4.36/Ex4_36.sce b/3760/CH4/EX4.36/Ex4_36.sce new file mode 100644 index 000000000..1919b0db3 --- /dev/null +++ b/3760/CH4/EX4.36/Ex4_36.sce @@ -0,0 +1,55 @@ +//Answer for part(e) in book is incorrect.
+clc;
+//Magnetization curve is same as that of example 4.33
+Ra=0.2;//armature resistance (including brushes)
+Nf=2000;//shunt field turns
+N=1500;//motor speed in rpm at no load as well as rated load.
+Ia=36;//motor armature current in Amperes at rated load
+
+//PART(a)-At no load,
+Vt=230;//supply mains in volts
+Ea_a=Vt;//counter emf, neglecting armature circuit resistance
+If_a=1.23;//field current in amperes
+printf('(a) Shunt field current is %f A.\n',If_a);
+//Thus constant shunt field current If from O.C.C. is 1.23 A corresponding to 230V.
+
+//PART(b)-At full load,
+Ea_b=Vt-Ia*Ra;//counter emf
+//A point is drawn on magnetization curve with coordinates A(If,Ea_b).
+//The horizontal distance between Pt. A & the magnetization curve, gives the effective armature reaction in terms of shunt field current, its value is 0.06 A.
+AT_arm=Nf*0.06;//armature reaction in amopere turns per pole
+printf('(b) Effective armature reaction is %f ampere turns per pole.\n',AT_arm);
+
+//PART(c)-At rated load, with series winding in circuit & motor is cumulatively compounded,
+Rse=0.05;//series field resistance in ohm
+Ea__c=Vt-Ia*(Ra+Rse);//counter emf at 1350 rpm
+Ea_c=Ea__c*(1500/1350);//Ea at 1500 rpm
+//From magnetization curve, Ea=245.5 V requires If_c=1.365 A.
+//From equation - Net MMF =Nf*If+Ns*Is-ATd ....(1)
+//1.365*2000=1.23*2000+Ns*(36)-120
+Ns=round(65/6);//Series field current
+printf('(c) Required no of series field turns are %f.\n',Ns);
+
+//PART(d)-If the series field winding has 20 turns -
+Ns_=20;//no of turns of series field winding
+//Net mmf = Nf*If+Ns_*Is-AT_arm ....(formula)
+mmf_net=If_a*Nf+Ns_*Ia-AT_arm;//Net field mmf in terms of ATs
+If_d=(If_a*Nf+Ns_*Ia-AT_arm)/Nf;//Net field mmf in terms of the equivalent shunt field current(A).
+//From the magnetization curve, the value of Ea corresponding to If=1.53A is 258V at 1500rpm.
+//But the counter emf,Ea corresponding to rated current is 230-36(0.2+0.05)=221 V.
+//Therefore the motor speed n corresponding to Ea=221V is-
+//(221/258)=(n/1500)
+n=(221/258)*1500;
+printf('(d) Speed at rated voltage rated armature current is %f rpm.\n',round(n));
+
+//PART(e)-Assuming demagnetizing effect of armature reaction to be 200 ampere turns per pole.
+ATarm=200;//demagnetizing effect of armature reaction in ampere turns per pole.
+Ia_e=50;//armature current in amperes ....(given)
+mmfnet=If_a*Nf+Ns_*Ia_e-ATarm;//from equation no ....(1)
+If_e=mmfnet/Nf;//Net field mmf in terms of the equivalent shunt field current(A).
+//From the magnetizing curve, corresponding to field current If_e(1.63 A), Ea at 1500 rpm is 264 V.
+//But, Ea=Ka*phi*Wm ; where, phi = flux per pole
+//Thus, Ka*phi=(264*60)/(2*%pi*1500)
+Kaphi=264/(50*%pi);//Ka*phi
+Test=Kaphi*Ia_e;//starting torque
+printf('(e) When the armature current is limited to 50 A the starting torque is %f Nm.',Test);
diff --git a/3760/CH4/EX4.37/Ex4_37.sce b/3760/CH4/EX4.37/Ex4_37.sce new file mode 100644 index 000000000..574204290 --- /dev/null +++ b/3760/CH4/EX4.37/Ex4_37.sce @@ -0,0 +1,22 @@ +
+clc;
+V=230;//supply voltage in volts
+Ra=0.5;//armature resistance in ohm
+N=250;//rated speed of motor
+I=100;//rated current in ampere
+//For the separately excited dc motor torque-speed characteristics is given by Tl=500-W, where W is rotational speed in rad/sec & Tl is load torque in Nm.
+//At rated load, motor counter emf is -
+Ea=V-I*Ra;
+//Ea=Km*Wr; Km = motor constant, Wr = rated motor speed in rad/sec
+Wr=(2*%pi*250)/60;//rated motor speed in rad/sec
+Km=Ea/Wr;//motor constant in V-s/rad
+//Armature current at any speed W is given by-
+Ia=(V-Ea)/Ra;// ie. Ia=(230-Km*W)/0.5
+//Motor torque, Te=Km*Ia=(Km/0.5)*(230-Km*W)
+//Under steady state, motor torque ,Te=load torque, Tl
+//Thus, (Km/0.5)*(230-Km*W)=500-10*W
+W=(((V*Km)/Ra)-500)/((Km^2/Ra)-10);//angular speed in rpm
+N_=(W*60)/(2*%pi);//Speed in rpm
+Ia_=(230-Km*W)/0.5//armature current
+printf('Steady state speed of motor is %f rpm\n.',N_);
+printf('Armature current drawn by motor at steady state is %f A.',Ia_);
diff --git a/3760/CH4/EX4.38/Ex4_38.sce b/3760/CH4/EX4.38/Ex4_38.sce new file mode 100644 index 000000000..3c16a651c --- /dev/null +++ b/3760/CH4/EX4.38/Ex4_38.sce @@ -0,0 +1,28 @@ +clc;
+v=230; // rated voltage of dc motor
+p=10000; // rated power of dc motor
+rf=115; // field resistance
+ra=0.348; // net armature resistance
+ifs=v/rf; // shunt field current
+ia=(p/v)-ifs; // rated armature current
+disp('case a');
+rx1=(v/(2*ia))-ra;
+printf('External resistance required at the time of starting is %f ohms\n',rx1);
+disp('case b');
+Ea1=v-ia*(rx1+ra); // counter emf at stud 1
+r2=(v-Ea1)/(2*ia); // resistance when handle is moved to 2nd stud
+rx2=r2-ra; // external resistance
+rc=rx1-rx2;
+printf('Resistance that must be cut out in first step is %f ohms\n',rc);
+disp('case c');
+Ea2=v-ia*rc; // counter emf at stud 2
+r3=(v-Ea2)/(2*ia); // resistance when handle is moved to 3rd stud
+rc=rc-r3;
+printf('Resistance that must be cut out in second step is %f ohms\n',rc);
+disp('case d');
+Ea3=v-ia*rc; // counter emf at stud 3
+r4=(v-Ea3)/(2*ia); // resistance when handle is moved to 4th stud
+rc=rc-r4;
+printf('Resistance that must be cut out in third step is %f ohms\n',rc);
+disp('Total number of steps is 3');
+
diff --git a/3760/CH4/EX4.39/Ex4_39.sce b/3760/CH4/EX4.39/Ex4_39.sce new file mode 100644 index 000000000..c0663f32d --- /dev/null +++ b/3760/CH4/EX4.39/Ex4_39.sce @@ -0,0 +1,67 @@ +clc;
+v=240; // rated voltage of dc shunt motor
+i=50; // rated current of dc shunt motor
+ra=0.2; // armature resistance
+n=4; // number of resistance element
+N=1500; // rated speed of motor
+vb=1; // pu base voltage
+ia=1; // pu base current
+rb=v/i; // pu base resistance
+ra=ra/rb; // per unit armature resistance
+disp('case a');
+ia1=1.4; // pu maximum allowable armature current
+R=vb/ia1; // net resistance
+al=(ra/R)^(1/n); // ratio of total resistances on two adjacent studs
+r1=R*(1-al);
+printf('Resistance cut out when handle is at stud 2 is %f pu or %f ohms\n',r1,r1*rb);
+r2=al*r1;
+printf('Resistance cut out when handle is at stud 3 is %f pu or %f ohms\n',r2,r2*rb);
+r3=al*r2;
+printf('Resistance cut out when handle is at stud 4 is %f pu or %f ohms\n',r3,r3*rb);
+r4=al*r3;
+printf('Resistance cut out when handle is at stud 5 is %f pu or %f ohms\n',r4,r4*rb);
+disp('case b');
+ia2=al*ia1; // pu minimum armature current
+// at stud 1 armature current=ia2 after t1 where t is time reckoned from the instant motor is switched on
+Ea1=vb-ia2*R; // counter EMF at stud 1
+Va1=Ea1+ia2*ra; // voltage across at armature terminal at instant t1
+printf('The first contactor should close at %f pu or %f V\n',Va1,Va1*v);
+// at stud 2 armature current=ia2 after t2 where t is time reckoned from the instant motor is switched on
+Ea2=vb-ia2*(R-r1); // counter EMF at stud 2
+Va2=Ea2+ia2*ra; // voltage across at armature terminal at instant t2
+printf('The second contactor should close at %f pu or %f V\n',Va2,Va2*v);
+// at stud 3 armature current=ia2 after t3 where t is time reckoned from the instant motor is switched on
+Ea3=vb-ia2*(R-r1-r2); // counter EMF at stud 3
+Va3=Ea3+ia2*ra; // voltage across at armature terminal at instant t3
+printf('The third contactor should close at %f pu or %f V\n',Va3,Va3*v);
+// at stud 4 armature current=ia2 after t4 where t is time reckoned from the instant motor is switched on
+Ea4=vb-ia2*(R-r1-r2-r3); // counter EMF at stud 4
+Va4=Ea4+ia2*ra; // voltage across at armature terminal at instant t4
+printf('The fourth contactor should close at %f pu or %f V\n',Va4,Va4*v);
+disp('case c');
+Ea=vb-ia*ra; // pu full load counter EMF
+n1=Ea1/Ea; // pu speed when handle is at stud 1
+printf('Speed of dc shunt motor when handle is at stud 1 is %f pu or %f rpm\n',n1,n1*N);
+n2=Ea2/Ea; // pu speed when handle is at stud 2
+printf('Speed of dc shunt motor when handle is at stud 2 is %f pu or %f rpm\n',n2,n2*N);
+n3=Ea3/Ea; // pu speed when handle is at stud 3
+printf('Speed of dc shunt motor when handle is at stud 3 is %f pu or %f rpm\n',n3,n3*N);
+n4=Ea4/Ea; // pu speed when handle is at stud 4
+printf('Speed of dc shunt motor when handle is at stud 4 is %f pu or %f rpm\n',n4,n4*N);
+disp('Using above data sketch of variation of armature current and speed can be obtained with time');
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3760/CH4/EX4.4/Ex4_4.sce b/3760/CH4/EX4.4/Ex4_4.sce new file mode 100644 index 000000000..db8015c8a --- /dev/null +++ b/3760/CH4/EX4.4/Ex4_4.sce @@ -0,0 +1,24 @@ +clc;
+p=6; // number of poles
+c=240; // number of coils
+t=2; // number of turns per coil
+rt=0.03; // resistance of one turn
+l=0.5; // length of armature
+d=0.4; // diameter of armature
+B=0.6; // air gap flux density
+a=p; // number of parallel paths is same as number of poles foe lap winding
+an=40; // mechanical angle subtended by pole
+n=1200; // armature speed
+th=an*(p/2); // electrical angle subtended by pole
+f=(2*%pi*(d/2)*l*th*B)/(p*180); // flux per pole
+Z=2*c*t; // total conductors
+disp('case a');
+Ea=(f*Z*n*p)/(60*a);
+printf('Generated EMF at no load is %f V\n',ceil(Ea));
+disp('case b');
+ia=40; // armature current
+at=(c*t)/a; // number of armature turns per path
+r=at*rt; // resistance of one path
+Ra=r/a; // resistance of armature circuit
+vt=Ea-ia*Ra;
+printf('Terminal voltage at full load is %f V\n',ceil(vt));
diff --git a/3760/CH4/EX4.40/Ex4_40.sce b/3760/CH4/EX4.40/Ex4_40.sce new file mode 100644 index 000000000..3976a0aba --- /dev/null +++ b/3760/CH4/EX4.40/Ex4_40.sce @@ -0,0 +1,33 @@ +clc;
+v=200; // rated voltage of shunt motor
+i=22; // rated current of dc shunt motor
+n1=1000; // speed at which motor is running
+rf=100; // field resistance
+ra=0.1; // armature resistance
+n2=800; // reduced speed at which motor is to run
+iF=v/rf; // field current
+ia=i-iF; // armature current
+disp('case a');
+// load torque is independent of speed
+Ea1=v-ia*ra; // counter EMF at 1000 rpm
+rg=(v-ia*ra-(n2*Ea1)/n1)/ia;
+printf('Additional resistance inserted in armature circuit is %f ohms\n',rg);
+printf('Loss in additional resistance is %f W\n',ia^2*rg);
+disp('case b');
+// load torque is directly proportional to speed
+ia2=(n2/n1)*ia; // armature current at 800 rpm
+rg=(v-ia2*ra-(n2*Ea1)/n1)/ia2;
+printf('Additional resistance inserted in armature circuit is %f ohms\n',rg);
+printf('Loss in additional resistance is %f W\n',ia2^2*rg);
+disp('case c');
+// load torque varies as the square of speed
+ia2=(n2/n1)^2*ia; // armature current at 800 rpm
+rg=(v-ia2*ra-(n2*Ea1)/n1)/ia2;
+printf('Additional resistance inserted in armature circuit is %f ohms\n',rg);
+printf('Loss in additional resistance is %f W\n',ia2^2*rg);
+disp('case d');
+// load torque varies as the cube of speed
+ia2=(n2/n1)^3*ia; // armature current at 800 rpm
+rg=(v-ia2*ra-(n2*Ea1)/n1)/ia2;
+printf('Additional resistance inserted in armature circuit is %f ohms\n',rg);
+printf('Loss in additional resistance is %f W\n',ia2^2*rg);
diff --git a/3760/CH4/EX4.41/Ex4_41.sce b/3760/CH4/EX4.41/Ex4_41.sce new file mode 100644 index 000000000..f555bf515 --- /dev/null +++ b/3760/CH4/EX4.41/Ex4_41.sce @@ -0,0 +1,16 @@ +clc;
+V=240; // rated voltage of dc shunt motor
+n=800; // rated speed of dc shunt motor
+i=50; // rated current of dc shunt motor
+ra=0.2; // armature resistance
+pr=0.6; // reduction in load torque as a fraction of full load torque
+rg=2; // series resistance in armature circuit
+fr1=0.04; // weakening of field flux at full load
+fr2=0.02; // weakening of field flux at 60% of full load
+Ea1=V-(i*ra); // counter EMF at rated load
+ia2=(i*pr)*((1-fr1)/(1-fr2)); // armature current at reduced load torque
+Ea2=V-ia2*(rg+ra); // counter EMF at reduced load torque
+n2=(n*Ea2*(1-fr1))/(Ea1*(1-fr2));
+printf('Motor speed at reduced load torque is %f rpm',n2);
+
+
diff --git a/3760/CH4/EX4.42/Ex4_42.sce b/3760/CH4/EX4.42/Ex4_42.sce new file mode 100644 index 000000000..8952674cd --- /dev/null +++ b/3760/CH4/EX4.42/Ex4_42.sce @@ -0,0 +1,16 @@ +clc;
+N=1000; // speed of dc series motor
+v=250; // supply from mains
+i=50; // current drawn from mains
+r=0.6; // armature + field resistance
+rg=4.4; // additional resistance
+// field flux is proportional to armature current
+Ea1=v-i*r; // counter EMF at 1000 rpm
+// Ea2=v-(n2/20)*(r+rg) where Ea2 is counter EMf at speed n2 . taking ratio of Ea2/Ea1 we obtain a quadratic equation in n2 whose terms are given by
+t1=(Ea1*i)/N;
+t2=(N*i)*((r+rg)/(N/i));
+t3=-(N*i*v);
+p=[ t1 t2 t3];
+n=roots(p);
+printf('New speed of motor is %f rpm',ceil(n(2)));
+
diff --git a/3760/CH4/EX4.43/Ex4_43.sce b/3760/CH4/EX4.43/Ex4_43.sce new file mode 100644 index 000000000..f5e08494a --- /dev/null +++ b/3760/CH4/EX4.43/Ex4_43.sce @@ -0,0 +1,22 @@ +clc;
+v=230; // rated voltage of dc shunt motor
+n1=900; // speed at which motor is running
+ia1=2; // armature current at n=900 rpm
+ra=0.5; // armature resistance
+ia2=20; // armature current at rated load and rated voltage
+Ea=v-ia1*ra; // counter EMF at no load
+k=(Ea*60)/(2*%pi*n1); // constant term used for calculating back EMF
+disp('case a');
+rs=2; // resistance in series with armature
+rp=3; // resistace in parallel with series combination of rs and ra
+A=rp/(rp+rs);
+wmo=(1/k)*(A*v-ia1*(A*rs+ra)); // no-load speed
+wml=(1/k)*(A*v-ia2*(A*rs+ra)); // full-load speed
+sr=((wmo-wml)/wml)*100; // percent speed regulation
+printf('Speed regulation for first case is %f percent\n',sr);
+disp('case b');
+rs=3; // resistance in series with armature
+wmo=(1/k)*(v-ia1*(rs+ra)); // no-load speed
+wml=(1/k)*(v-ia2*(rs+ra)); // full-load speed
+sr=((wmo-wml)/wml)*100; // percent speed regulation
+printf('Speed regulation for second case is %f percent\n',sr);
diff --git a/3760/CH4/EX4.44/Ex4_44.sce b/3760/CH4/EX4.44/Ex4_44.sce new file mode 100644 index 000000000..9f09c2a59 --- /dev/null +++ b/3760/CH4/EX4.44/Ex4_44.sce @@ -0,0 +1,19 @@ +clc;
+v=200; // rated voltage of dc shunt motor
+ra=0.1; // armature resistance
+n=1000; // running speed of motor
+ia=50; // armature current at n=1000 rpm
+re=0.1; // reduction in field flux
+disp('case a');
+Ea1=v-ia*ra; // initial counter EMF
+Ea2=Ea1*(1-re); // counter EMF after reduced field flux
+iam=(v-Ea2)/ra;
+printf('Maximum value of armature current is %f A\n',iam);
+T=(iam/ia)*(1-re);
+printf('Torque corresponding to maximum armature current is %f times initial torque\n',T);
+disp('case b');
+ia2=(1/(1-re))*ia;
+printf('Armature current when transients are over is %f A\n',ia2);
+Ea2=v-ia2*ra; // counter EMF when transients are over
+n2=(Ea2*n)/(Ea1*(1-re));
+printf('Ultimate speed after transients are over is %f rpm',ceil(n2));
diff --git a/3760/CH4/EX4.45/Ex4_45.sce b/3760/CH4/EX4.45/Ex4_45.sce new file mode 100644 index 000000000..46ee3ce95 --- /dev/null +++ b/3760/CH4/EX4.45/Ex4_45.sce @@ -0,0 +1,14 @@ +clc;
+clc;
+v=200; // rated voltage of dc shunt motor
+ra=0.1; // armature resistance
+n=1000; // running speed of motor
+ia=50; // armature current at n=1000 rpm
+re=0.1; // reduction in field flux
+ia2=(1/(1-re))*ia; // armature current when transients are over
+Ea1=v-ia2*ra; // counter EMF when transients are over
+// with sudden increase from 0.9*f to f (f=flux), counter EMF rises to
+Ea2=Ea1*(1/(1-re));
+i=(v-Ea2)/ra;
+printf('Armature current is %f A',i);
+disp('Since armature current is negative, machine acts as a generator. Speed reduces till counter EMF becomes less than supply voltage,so that motor action takes place and torque balance is obtained')
diff --git a/3760/CH4/EX4.46/Ex4_46.sce b/3760/CH4/EX4.46/Ex4_46.sce new file mode 100644 index 000000000..a3934172b --- /dev/null +++ b/3760/CH4/EX4.46/Ex4_46.sce @@ -0,0 +1,12 @@ +clc;
+v=220; // supply voltage
+n1=2000; // speed of fan motor
+ia1=60; // current corresponding to n=2000 rpm
+// flux is directly proportional to exciting current and load torque increase as square of speed
+// four field coils are connected in two parallel groups also n^2 is directly proportional to armature current therefore
+r=sqrt((2*ia1^2)/n1^2); // ratio of armature current corresponding to n2 and n2 where n2=new speed
+// counter EMF are directly proportional to product n*ia and ra(armature resistance) and rs(series) resistance are not given, therefore takig ratio of n1*ia1 and n2*ia2 we can determine value of n2
+n2=sqrt((ia1*n1*2)/r);
+printf('New speed is %f rpm\n',n2);
+ia2=n2*r;
+printf('New armature current is %f A\n',ia2);
diff --git a/3760/CH4/EX4.48/Ex4_48.sce b/3760/CH4/EX4.48/Ex4_48.sce new file mode 100644 index 000000000..2fcdb5218 --- /dev/null +++ b/3760/CH4/EX4.48/Ex4_48.sce @@ -0,0 +1,20 @@ +clc;
+v=230; // rated voltage of dc shunt motor
+ra=0.4; // armature circuit resistance
+rf=115; // field resistance
+n1=800; // initial speed
+n2=1000; // final speed
+ia1=20; // armature current at n=800 rpm
+// torque at both speed is same therefore f1*ia1=f2*ia2 where f=field flux therefore
+Ea1=v-ia1*ra; // counter EMF at 800rpm
+// ia2=ia1*k where k=f1/f2 now writing Ea2(counter EMF at 1000rpm) in terms of k and finding value of k by solving quadratic equation in k whose terms are
+t1=ia1*ra*n1;
+t2=-v*n1;
+t3=Ea1*n2;
+p=[ t1 t2 t3];
+k=roots(p);
+if1=v/rf; // initial field current
+if2=if1/k(2); // final field current correponding to n=1000rpm
+rs=v/if2; // new shunt field circuit resistance
+re=rs-rf;
+printf('Resistance that must be inserted in shunt field circuit is %f ohms\n',floor(re));
diff --git a/3760/CH4/EX4.49/Ex4_49.sce b/3760/CH4/EX4.49/Ex4_49.sce new file mode 100644 index 000000000..2dc47cbce --- /dev/null +++ b/3760/CH4/EX4.49/Ex4_49.sce @@ -0,0 +1,15 @@ +clc;
+v=250; // rated voltage of dc shunt motor
+ra=0.5; // armature resistance
+rf=250; // field resistance
+n1=600; // speed of motor
+i=21; // current drawn by motor when n=600 rpm
+re=250; // additional resistance in field circuit
+if1=v/rf; // field current
+ia=i-if1; // armature current
+Ea1=v-ia*ra; // counter EMF at n=600 rpm
+if2=v/(rf+re); // field current after addition of external resistance
+ia2=ia*(if1/if2); // armature current after addition of external resistance
+Ea2=v-ia2*ra; // counter EMF at new speed
+n2=(n1*Ea2*if1)/(Ea1*if2);
+printf('New speed of motor is %f rpm',n2);
diff --git a/3760/CH4/EX4.5/Ex4_5.sce b/3760/CH4/EX4.5/Ex4_5.sce new file mode 100644 index 000000000..6d425637c --- /dev/null +++ b/3760/CH4/EX4.5/Ex4_5.sce @@ -0,0 +1,14 @@ +clc
+Pout=24000;//rated output power in watts
+Et=250;//rated terminal voltage
+Ra=0.1;//armature resistance
+N=1600;//speed in rpm
+//Ea(terminal voltage)= k*(N*phi),where k is constant & phi is flux per pole
+//At no load, 260=k*1600*phi ....(1)
+Ia=Pout/Et;
+//if the generated voltage under rated load is Ea1,then
+//Ea=k*1500*phi ....(2)
+//From equation (1)&(2), (Ea1/260)=((1500*phi)/(1600*phi))
+Ea1=(1500*260)/1600;
+Vt=Ea1-Ia*Ra//terminal voltage at rated load
+printf('The terminal voltage of generator under given conditions is %f V.',Vt)
diff --git a/3760/CH4/EX4.50/Ex4_50.sce b/3760/CH4/EX4.50/Ex4_50.sce new file mode 100644 index 000000000..3256f2ca3 --- /dev/null +++ b/3760/CH4/EX4.50/Ex4_50.sce @@ -0,0 +1,16 @@ +clc;
+v=250; // supply voltage
+i=50; // current drawn from supply
+ic=0.4; // percentage increase in speed
+T=1.2; // ratio of final and initial torque
+n=1.4;// ratio of final and initial speed
+ra=0.5; // armature resistance
+Ea1=v-i*ra; // counter EMF at initial speed
+// ia2=(T2/T1)*ia1*k where k=f1/f2 and T1 is initial torque and T2 is final torque now writing Ea2(counter EMF at 1000rpm) in terms of k and finding value of k by solving quadratic equation in k whose terms are
+t1=T*ra*i;
+t2=-v;
+t3=n*Ea1;
+p=[ t1 t2 t3 ];
+k=roots(p);
+fr=(1-(1/k(2)))*100;
+printf('Percentage reduction in field flux is %f percent',fr);
diff --git a/3760/CH4/EX4.51/Ex4_51.sce b/3760/CH4/EX4.51/Ex4_51.sce new file mode 100644 index 000000000..d2ea83bef --- /dev/null +++ b/3760/CH4/EX4.51/Ex4_51.sce @@ -0,0 +1,27 @@ +clc;
+v=250; // rated voltage of dc shunt motor
+n1=1200; // no load speed
+N=1000; // turns per pole in shunt field winding
+n2=900; // reduced speed
+ia=100; // full load armature current
+rf=0.2; // series field resistance
+ra=0.1; // armature resistance
+ar=0.04; // armature reaction as afraction of main field m.m.f
+// At no load counter EMF=v therefore from magnetization curve given in fig 4.76 field current is
+IF=[ 0.38 0.58 0.8 1.1 1.36 1.76];
+EA=[125 180 215 250 275 300];
+plot(IF,EA);
+xlabel('field current');
+ylabel('counter EMF');
+title('Magnetising curve');
+ifs1=1.1; // field current
+Ats1=ifs1*N; // ampere turns for field current
+Ea2=v-ia*(ra+rf); // counter EMF at full load
+// magnetization curve is for 1200 rpm, therefore full load counter EMF corresponding to it is
+Ea2=Ea2*(n1/n2);
+// corresponding to above counter EMF field current from magnetization curve is
+ifs2=1.62;
+Ats2=(ifs2*N)/(1-ar); // ampere turns for field current at full load
+at=Ats2-Ats1; // series field
+t=at/ia;
+printf('Number of series turns per pole to reduce speed to %f rpm is %f ',n2,ceil(t));
diff --git a/3760/CH4/EX4.52/Ex4_52.sce b/3760/CH4/EX4.52/Ex4_52.sce new file mode 100644 index 000000000..596f792b3 --- /dev/null +++ b/3760/CH4/EX4.52/Ex4_52.sce @@ -0,0 +1,14 @@ +clc;
+v=240; // supply voltage
+n=1000; // speed of motor
+i=40; // current drawn from supply
+rf=0.2; // field resistance
+ra=0.25; // armture resistance
+rd=0.3; // diverter resistance
+// torque is constant for different speeds
+// when diverter is put in parallel with series resistance then some fraction of armature current flows through series circuit this current for constant torque is given by
+ia2=sqrt(i^2/(rd/(rf+rd)));
+Ea1=v-i*(ra+rf); // counter EMf at n=1000 rpm
+Ea2=v-ia2*(ra+((rf*rd)/(rf+rd))); // counter EMF at new speed
+n2=(Ea2*n*i)/(Ea1*(rd/(rf+rd))*ia2);
+printf('Motor speed after diverter is put in parallel with series field winding is %f rpm',ceil(n2));
diff --git a/3760/CH4/EX4.53/Ex4_53.sce b/3760/CH4/EX4.53/Ex4_53.sce new file mode 100644 index 000000000..c51bc0de5 --- /dev/null +++ b/3760/CH4/EX4.53/Ex4_53.sce @@ -0,0 +1,23 @@ +clc;
+v=230; // rated voltage of motor
+p=6; // number of poles
+f=4*10^-3; // flux per pole in Wb/A
+T=20; // load torque
+n=800; // speed at T=20 N-m
+a=2; // for wave connected conductors number of parallel path
+z=432; // number of conductors
+r=1; // total resistance of motor
+// it is given that T=kn^2, therefore
+k=T/n^2; // proportionality of constant
+r1=(f*z*p)/(60*a); // ratio of back EMF to product of speed and armature current
+t=(r1*60)/(2*%pi); // ratio of full load torque to square of armature current
+// also Ea(back EMf)=v-ia*ra and r1=Ea/(n*ia) compairing both we get ia=v/(1+r1*n);
+// Also k*n2^2=t*ia^2 , in this expression putting value of ia and solving quadratic equation in n2
+t1=sqrt(k)*r1;
+t2=sqrt(k);
+t3=-sqrt(t)*v;
+p=[ t1 t2 t3 ];
+n2=roots(p);
+printf('Speed of motor is %f rpm\n',n2(2));
+ia=v/(1+r1*n2(2));
+printf('Armature current when motor is connected to rated supply is %f A',ia);
diff --git a/3760/CH4/EX4.54/Ex4_54.sce b/3760/CH4/EX4.54/Ex4_54.sce new file mode 100644 index 000000000..9b83a4ecc --- /dev/null +++ b/3760/CH4/EX4.54/Ex4_54.sce @@ -0,0 +1,28 @@ +clc;
+v=230; // rated voltage of dc shunt motor
+n=1000; // rated speed of motor
+rf=115; // field resistance
+ra=0.5; // armature resistance
+ia=4; // no load armature current
+k=(v-ia*ra)/(2*%pi*n/60); // constant term in formula of back EMF
+disp('case a');
+t=80; // load torque
+ia2=t/k; // armature load current
+Ea2=v-ia2*ra; // counter EMF corresponding to load armature current
+printf('Armature current for given load is %f A\n',ia2);
+n2=(Ea2*60)/(k*2*%pi);
+printf('Speed of motor at given load is %f rpm\n',n2);
+disp('case b');
+pd=8000; // power developed by motor
+n3=1250; // speed at power is developed
+// determining value of armature current corresponding to power by solving quadratic equation whose terms are
+t1=ra;
+t2=-v;
+t3=pd;
+p=[ t1 t2 t3];
+ia3=roots(p);
+Ea3=v-ia3(2)*ra; // counter EMF for load armature current
+k1=k/(v/rf); // constant term in formula of back EMF for field current = 1 A
+ifn=(Ea3*60)/(2*%pi*n3*k1);
+rfn=v/ifn;
+printf('External resistance that must be inserted in series with field winding is %f ohms',rfn-rf);
diff --git a/3760/CH4/EX4.55/Ex4_55.sce b/3760/CH4/EX4.55/Ex4_55.sce new file mode 100644 index 000000000..e294b6705 --- /dev/null +++ b/3760/CH4/EX4.55/Ex4_55.sce @@ -0,0 +1,22 @@ +clc;
+v=250; // rated voltage of dc series motor
+ra=0.25; // armature resistance
+rf=0.15; // series field resistance
+disp('case a');
+t=80; // developed torque
+n1=1200; // speed at developed torque
+// solving quadratic equation in ia
+t1=ra+rf;
+t2=-v;
+t3=(t*2*%pi*n1)/60;
+p=[ t1 t2 t3];
+ia=roots(p);
+printf('Current for developing given torque is %f A\n',ia(2));
+disp('case b');
+n2=1800;
+ia2=ia(2)/2;
+Ea1=v-ia(2)*(ra+rf); // counter EMF corresponding to armature current of case 1
+Ea2=v-ia2*(ra+rf); // counter EMF corresponding to armature current ia2
+fr=(n1*Ea2)/(n2*Ea1); // ratio of fluxes for two armatures current
+pr=(1-fr)*100;
+printf('Percentage reduction in flux is %f pecent',pr);
diff --git a/3760/CH4/EX4.56/Ex4_56.sce b/3760/CH4/EX4.56/Ex4_56.sce new file mode 100644 index 000000000..14a2cccb7 --- /dev/null +++ b/3760/CH4/EX4.56/Ex4_56.sce @@ -0,0 +1,15 @@ +clc;
+v=230; // rated voltage of dc series motor
+n=1500; // speed at rated output
+i=20; // current drawn at rated output
+ra=0.3; // armature resistance
+rf=0.2; // field resistance
+disp('case a');
+// At starting Ea=0, therefore
+re=(v/i)-(ra+rf);
+printf('External resistance to be added in motor armature circuit to develop rated torque is %f ohms\n',re);
+disp('case b');
+n2=1000; // speed at rated torque has to be developed
+Ea2=(n2/n)*(v-i*(ra+rf)); // counter EMF at n=1000 rpm
+re=(v-Ea2-i*(ra+rf))/i;
+printf('External resistance to be added in motor armature circuit to develop rated torque is %f ohms\n',re);
diff --git a/3760/CH4/EX4.57/Ex4_57.sce b/3760/CH4/EX4.57/Ex4_57.sce new file mode 100644 index 000000000..b9a3152e2 --- /dev/null +++ b/3760/CH4/EX4.57/Ex4_57.sce @@ -0,0 +1,22 @@ +clc;
+// in book voltages are calculated for r=0.5 not for r=0.4(as asked in question) that is why answer is differing
+v=230; // supply voltage
+n1=800; // speed at supply voltage
+i=20; // current drawn from supply
+r=0.4; // dc series motor resistance
+n2=1000; // raised speed
+Ea1=v-i*r; // counter EMF at 800 rpm
+disp('case a');
+// when magnetic circuit is saturated flux is constant.Under steady state condition full load torque=torque at any load therefore
+i2=i*(n2/n1)^2; // new current drawn from supply
+Ea2=Ea1*(n2/n1); // counter EMF at 1000 rpm
+vt=Ea2+i2*r;
+printf('Current for saturated magnetic circuit is %f A\n',i2);
+printf('Voltage for saturated magnetic circuit is %f V\n',vt);
+disp('case b');
+// when magnetic circuit is not saturated flux is directly proportional to armature current and torque is directly proportional to square of armature current
+i3=(n2/n1)*i;
+Ea3=(n2*Ea1*i3)/(n1*i); // counter EMF at 1000 rpm
+vt=Ea3+i3*r;
+printf('Current for unsaturated magnetic circuit is %f A\n',i3);
+printf('Voltage for unsaturated magnetic circuit is %f V\n',vt);
diff --git a/3760/CH4/EX4.58/Ex4_58.sce b/3760/CH4/EX4.58/Ex4_58.sce new file mode 100644 index 000000000..46d572954 --- /dev/null +++ b/3760/CH4/EX4.58/Ex4_58.sce @@ -0,0 +1,14 @@ +clc;
+s=4; // speed range
+ia=60; // armature current at speed n
+disp('Field flux control');
+// For constant power load Ea*Ia is constant therefore ia is conatant at 4*n
+printf('The armature current at required speed is %f A\n',ia);
+// For constant torque load, speed is 4 times of initial speed therefore flux changes by 1/4 times and hence to maintain torque constant armature current should be four times
+printf('The armature current at required speed is %f A\n',4*ia);
+disp('Armature voltage control');
+// For constant power load Ea*Ia is constant therefore at 4 times speed armature voltage is 4 times and the armature current gets reduced by 1/4 times
+printf('The armature current at required speed is %f A\n',ia/4);
+// For constant power load Ea*Ia is constant therefore at 4 times speed ,flux is constant therefore
+// armature current is constant
+printf('The armature current at required speed is %f A\n',ia);
diff --git a/3760/CH4/EX4.59/Ex4_59.sce b/3760/CH4/EX4.59/Ex4_59.sce new file mode 100644 index 000000000..b729febb0 --- /dev/null +++ b/3760/CH4/EX4.59/Ex4_59.sce @@ -0,0 +1,47 @@ +clc;
+v=220; // rated voltage of motor
+i=15; // rated current of motor
+ra=0.4; // net armature resistance
+n=1500; // speed for which magnetization curve is given
+IF=[ 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.2 1.45];
+EA=[120 160 197 210 220 228 232 236 243 248];
+plot(IF,EA);
+xlabel('field current');
+ylabel('voltage');
+title('magnetising curve');
+disp('case a');
+ifg1=0.15; // initial generator field current
+ifg2=1.4; // final generator field current
+ifm=0.6; // motor field current
+// corresponding ifg1 counter EMF of generator from magnetization curve is
+Ea1=60;
+vd=i*(ra+ra); // voltage drop in two armature resistance
+Ea2=Ea1-vd; // counter EMF of motor
+// but motor counter EMF for 0.6 A field current at 1500 rpm is
+Ea3=210;
+nmin1=(Ea2/Ea3)*n; // minimum motor speed
+// corresponding ifg2 counter EMF of generator from magnetization curve is
+Ea4=247;
+Ea5=Ea4-vd; // counter EMF of motor
+nmax1=(Ea5/Ea3)*n; // maximum motor speed
+sr=nmax1/nmin1; // speed range
+printf('Speed range for full load armature current is %f:1\n',sr);
+// for no load generator counter EMF= motor counter EMf
+nmin2=(Ea1/Ea3)*n; // minimum motor speed
+pr=((nmin2-nmin1)/nmin2)*100;
+printf('Percent speed drop from no load to full load for condition of minimum speed is %f percent\n',pr);
+// for maximum generator field current generator counter EMF= motor counter EMf at no load
+nmax2=(Ea4/Ea3)*n; // maximum motor speed
+sr=nmax2/nmin2; // speed range
+printf('Speed range for full load armature current is %f:1\n',sr);
+pr=((nmax2-nmax1)/nmax2)*100;
+printf('Percent speed drop from no load to full load for condition of maximum speed is %f percent\n',pr);
+disp('case b')
+// for generator field current=1 A counter EMF from magnetization curve is
+Ea6=236;
+Ea7=Ea6-vd; // motor counter EMF at full load
+Ea8=(Ea7/(2*nmax1))*n;
+printf('Motor counter EMF for %f rpm is %f V\n',n,Ea8);
+// Corresponding to Ea8, field current is
+ifmi=0.25;
+printf('Minimum motor field current is %f A\n',ifmi);
diff --git a/3760/CH4/EX4.6/Ex4_6.sce b/3760/CH4/EX4.6/Ex4_6.sce new file mode 100644 index 000000000..c2dd1ecbf --- /dev/null +++ b/3760/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,17 @@ +clc;
+Vt=230;//terminal voltage of dc shunt machine
+Il=40;//Line current
+Ra=0.5;//Armature circuit resistance
+Rf=115;//Field circuit resistance
+//GENERATOR OPERATION
+If=Vt/Rf;//field current
+Ia1=If+Il;//armature current
+Ea1=Vt+Ia1*Ra;//generated emf
+//Ea1=k*Ng*phi ....(1), where Ng is the generator speed & phi is flux per pole proportional to If
+//MOTOR OPERATION
+Ia2=Il-If;//armature current
+Ea2=Vt-Ia2*Ra;//generated emf
+//Ea2=k*Nm*phi ....(2), where Nm is the motor speed & phi is flux per pole proportional to If
+//From equation (1)&(2), (Ea1/Ea2)=((Ng*phi)/(Nm*phi))
+N=Ea1/Ea2;//ratio of speed of generator to motor,N=Ng/Nm
+printf('The ratio of speed as a generator to the speed as a motor is %f.',N)
diff --git a/3760/CH4/EX4.60/Ex4_60.sce b/3760/CH4/EX4.60/Ex4_60.sce new file mode 100644 index 000000000..ad3872ab3 --- /dev/null +++ b/3760/CH4/EX4.60/Ex4_60.sce @@ -0,0 +1,17 @@ +clc;
+p=4000; // rated power of separately excited dc series motor
+v=230; // rated voltage of motor
+n=1000; // rated speed of motor
+e=260; // ac voltage supplied to motor through converter
+i=2; // current drawn at no load
+no=1100; // speed at no load
+ra=0.5; // armature resistance
+vd=2; // voltage drop in thyristor
+de=30; // firing angle delay
+ia=20; // rated armature current
+k=((((2*sqrt(2)*e)/%pi)-(i*ra)-vd)*60)/(2*%pi*no); // conatant term in formula of back EMf
+disp('case a');
+printf('Motor torque is %f Nm\n',k*ia);
+disp('case b');
+wm=((((2*sqrt(2)*e*cosd(de))/%pi)-vd)/k)-((ra*ia)/k);
+printf('Motor speed is %f rpm',ceil((wm*60)/(2*%pi)));
diff --git a/3760/CH4/EX4.61/Ex4_61.sce b/3760/CH4/EX4.61/Ex4_61.sce new file mode 100644 index 000000000..407a2e271 --- /dev/null +++ b/3760/CH4/EX4.61/Ex4_61.sce @@ -0,0 +1,52 @@ +clc;
+n=800; // speed at which magnetization curve is given
+// case a
+v=600; // dc voltage source
+ra=0.3; // armature resistance
+rf=0.25; // field resistance
+T=300; // given torque
+VT=[ 200 375 443 485 510 518]; // terminal voltage
+IF=[ 15 30 45 60 75 90 ]; // field current
+EA1=VT+IF*ra; // generated EMF
+EA2=v-IF*(ra+rf); // generated EMF for v=600 V
+N2=n*(EA2./EA1); // speed for v= 600 V
+TE=(EA2.*IF.*EA1*60)./(2*%pi*n*EA2); //torque
+subplot(221);
+plot(TE,N2);
+xlabel('Torque(Nm)');
+ylabel('speed(rpm)');
+title('speed-torque');
+subplot(222);
+plot(TE,IF);
+xlabel('Torque(Nm)');
+ylabel('current(A)');
+title('current-torque');
+disp('from curves, for a torque of 300 Nm, speed is 940 rpm and current is 52.5 A');
+disp('case b');
+rd=0.25; // diverter resistance put in parallel with series combination of armature and field resistance
+ia1=30;
+ia2=60; // armature currents
+if1=ia1*(rd/(rd+rf)); // field current corresponding to ia1
+Ea1=204.5; // given counter EMF for field current
+Ea2=v-ia1*(ra+((rd*rf)/(rd+rf))); // counter EMF for voltage supply of 600 V
+n2=n*(Ea2/Ea1);
+printf('Speed at %f A armature current is %f rpm\n',ia1,n2);
+T=(Ea1*60*ia1)/(2*%pi*n);
+printf('Torque at %f A armature current is %f Nm\n',ia1,T);
+if1=ia2*(rd/(rd+rf)); // field current corresponding to ia1
+Ea1=384; // given counter EMF for field current
+Ea2=v-ia2*(ra+((rd*rf)/(rd+rf))); // counter EMF for voltage supply of 600 V
+n2=n*(Ea2/Ea1);
+printf('Speed at %f A armature current is %f rpm\n',ia2,n2);
+T=(Ea1*60*ia2)/(2*%pi*n);
+printf('Torque at %f A armature current is %f Nm\n',ia2,T);
+disp('case c');
+ia3=75; // armature current
+t=0.8; // tapping percentage of field winding as a fration of full series turn
+ifl=t*ia3; // corresponding field current
+Ea=503; // given counter EMF for field current
+Ea2=v-ia3*(ra+t*rf); // counter EMF for voltage supply of 600 V
+n2=n*(Ea2/Ea);
+printf('Speed at %f A armature current is %f rpm\n',ia3,n2);
+T=(Ea*60*ia3)/(2*%pi*n);
+printf('Torque at %f A armature current is %f Nm\n',ia3,T);
diff --git a/3760/CH4/EX4.62/Ex4_62.sce b/3760/CH4/EX4.62/Ex4_62.sce new file mode 100644 index 000000000..6cca34dfc --- /dev/null +++ b/3760/CH4/EX4.62/Ex4_62.sce @@ -0,0 +1,22 @@ +clc;
+ra=0.3; // armature resistance
+n=0.7; // efficiency of dc shunt motor
+l=800; // weight of load
+v=3; // speed of raising a load
+vi=230; // initial value of supply voltage
+vf=190; // final value of supply voltage
+g=9.81; // acceleration due to gravity
+f=l*g; // resisting force due to gravitational pull
+p=f*v; // power required for lifting the load
+P=p/n; // power rating of dc machine
+printf('Required rating of power is %f KW\n',P/1000);
+// for supply voltage of 230 V Ea=230-ia*ra finding quadratic equation in ia whose terms are
+t1=ra;
+t2=-vi;
+t3=P;
+p=[ t1 t2 t3 ] ;
+ia=roots(p);
+Ea=vf-ia(2)*ra; // counter EMF for supply voltage of 190 V
+v=(Ea*ia(2)*n)/(l*g);
+printf('New hoist speed is %f m/s',v);
+
diff --git a/3760/CH4/EX4.63/Ex4_63.sce b/3760/CH4/EX4.63/Ex4_63.sce new file mode 100644 index 000000000..9afe8568e --- /dev/null +++ b/3760/CH4/EX4.63/Ex4_63.sce @@ -0,0 +1,10 @@ +clc;
+v1=6; // hoist speed
+i=60; // series current
+v=600; // supply voltage
+r=0.5; // net resistance
+g=9.81; // acceleration due to gravity
+v2=4; // reduced hoist speed
+Ea1=v-i*r; // counter EMf corresponding to v1
+rx=((v-((v2/v1)*Ea1))/i)-r;
+printf('External resistance to be added is %f ohms',rx);
diff --git a/3760/CH4/EX4.64/Ex4_64.sce b/3760/CH4/EX4.64/Ex4_64.sce new file mode 100644 index 000000000..8db1039f5 --- /dev/null +++ b/3760/CH4/EX4.64/Ex4_64.sce @@ -0,0 +1,16 @@ +clc;
+v=450; // supply voltage
+i=25; // current drawn from supply
+n=600; // full load speed
+z=500; // number of conductors
+f=1.7*10^-2*sqrt(i); // flux per pole
+p=4; // number of poles
+a=p; // number of parallel paths for wave wound winding is same as number of poles
+Ea1=(f*n*z*p)/(60*a); // counter EMF
+ra=(v-Ea1)/i; // armature resistance
+// T=k*f*ia where f is flux and ia is armature current As per question new torque is half of initial torque
+i2=((i^1.5)/2)^(1/1.5); // new armature current
+Ea2=(v/2)-i2*ra; // counter EMF for new armature current
+n2=(Ea2*f*sqrt(i)*n)/(Ea1*f*sqrt(i2));
+printf('New speed at which motor will run is %f rpm',floor(n2));
+
diff --git a/3760/CH4/EX4.66/Ex4_66.sce b/3760/CH4/EX4.66/Ex4_66.sce new file mode 100644 index 000000000..c54ec073a --- /dev/null +++ b/3760/CH4/EX4.66/Ex4_66.sce @@ -0,0 +1,16 @@ +clc;
+// answer is calculated for torque=30 but it is asked for torque=40 i.e why answer varies
+p=4; // number of dc series motor
+f=4*10^-3; // ratio of flux per pole to armature current
+T=40; // torque of fan
+n=1000; // speed of motor
+a=2; // number of parallel path for waave winding
+z=480; // number of conductors
+ra=1; // armature resistance
+v=230; // supply voltage
+re=sqrt((T*2*%pi*a)/(p*z*f*n^2)); // ratio of armature current and new speed
+// Ea=vt-ia*ra writing ia in terms of n solving for n (n is new speed)
+n2=v/(re+((p*f*z)/(60*a)));
+printf('Motor speed is %f rpm\n',n2);
+ia=re*n2;
+printf('Armature current is %f A',ia);
diff --git a/3760/CH4/EX4.67/Ex4_67.sce b/3760/CH4/EX4.67/Ex4_67.sce new file mode 100644 index 000000000..5043f2b36 --- /dev/null +++ b/3760/CH4/EX4.67/Ex4_67.sce @@ -0,0 +1,23 @@ +clc;
+p=10000; // rated power of generator
+v=250; // rated voltage of generator
+l1=400; // rotationl losses
+ra=0.5; // armature resistance
+rf=250; // shunt field resistance
+ifl=v/rf; // constant field current
+lc=ifl*rf+l1; // constant losses
+io=p/v; // output current of generator
+ia=io+ifl; // armature current
+la=ia^2*ra; // armature circuit loss
+ps=p+lc+la; // generator shaft power input
+printf('Generator shaft power input is %f W\n',ps);
+ng=(1-((lc+la)/ps))*100;
+printf('Efficiency at rated load is %f percent\n',ng);
+// at maximum efficiency variable losses= constant losses
+ia=sqrt(lc/ra); // armature current at maximum efficiency
+io=floor(ia)-ifl; // output current of generator
+po=v*io; // output power
+printf('Generator output at maximum efficiency is %f W\n',po);
+pi=po+2*lc;
+nm=(1-((lc+lc)/pi))*100;
+printf('Maximum efficiency is %f percent\n',nm);
diff --git a/3760/CH4/EX4.68/Ex4_68.sce b/3760/CH4/EX4.68/Ex4_68.sce new file mode 100644 index 000000000..a3e11aca5 --- /dev/null +++ b/3760/CH4/EX4.68/Ex4_68.sce @@ -0,0 +1,25 @@ +clc;
+v=250; // rated voltage of shunt motor
+p=15000; // rated power of motor
+nm=0.88; // maximumu efficiency of motor
+n=700; // speed of motor
+rf=100; // resistance of shunt field
+i=78; // current drawn by mains
+f=0.8; // fraction of rated output being delivered
+l=((1/nm)-1)*f*p; // total losses
+// at maximum losses constant losses= variable losses
+lc=l/2; // constant losses
+pi=f*p+l; // input to motor at maximum efficiency
+il=pi/v; // input line current
+ia=il-(v/rf); // armature current
+ra=lc/ia^2; // armature resistance
+ia2=i-(v/rf); // armature current at given load
+pi=i*v; // total power input
+tl=ia2^2*ra+lc; // total losses
+n1=(1-(tl/pi))*100; // efficiency at line current of 75 A
+Ea1=v-ia*ra; // counter EMF
+Ea2=v-ia2*ra; // counter EMF corresponding to line current of 75 A
+// field current is constant so flux is constant
+n2=(Ea2/Ea1)*n;
+printf('Efficiency at line current of %d A is %f percent\n',i,ceil(n1));
+printf('Speed at line current of %d A is %f rpm',i,floor(n2));
diff --git a/3760/CH4/EX4.69/Ex4_69.sce b/3760/CH4/EX4.69/Ex4_69.sce new file mode 100644 index 000000000..5b359c51f --- /dev/null +++ b/3760/CH4/EX4.69/Ex4_69.sce @@ -0,0 +1,29 @@ +clc;
+p=10000; // rated power of transformer
+n=900; // speed of motor
+v=400; // rated voltage of motor
+ra=1; // armatyre resistance
+rf=400; // field resistance
+ne=0.85; // efficiency at rated load
+l=((1/ne)-1)*p; // total losses
+disp('case a');
+pi=p+l; // power input
+il=pi/v; // line current
+ia=il-(v/rf); // armature current
+la=ia^2*ra; // armature circuit losses
+lf=v*(v/rf); // shunt field losses
+wo=l-la-lf; // no load losses
+iao=wo/v; // no load current neglecting armature losses at no load
+printf('No load armature current is %f A\n',iao);
+disp('case b');
+Ea1=v-ia*ra; // counter EMF at rated load
+il=20; // current drawn by motor
+ia=il-(v/rf); // armature current
+Ea2=v-ia*ra; // counter EMF at line current of 20 A
+n2=(Ea2/Ea1)*n;
+printf('Speed of motor while drawing current of %d A from mains is %f rpm\n',il,ceil(n2));
+disp('case c');
+k=(Ea1*60)/(2*%pi*n); // constant term in counter EMF formula
+T=98.5; // electromagnetic torque
+ia=T/k;
+printf('Armature current at given torque is %f A',ceil(ia));
diff --git a/3760/CH4/EX4.70/Ex4_70.sce b/3760/CH4/EX4.70/Ex4_70.sce new file mode 100644 index 000000000..6af9d35e4 --- /dev/null +++ b/3760/CH4/EX4.70/Ex4_70.sce @@ -0,0 +1,19 @@ +clc;
+v=240; // rated voltage of motor and supply voltage
+i=5.2; // line current
+p=10000; // rated power of motor
+no=1200; // no load speed
+ra=0.25; // armature resistance
+rf=160; // field resistance
+ifl=v/rf; // constant field current
+iao=i-ifl; // no load armature current
+wo=v*iao-iao^2*ra; // no load rotational losses
+// by using equation of electromagnetic power solving quadratic equation in armature current whose terms are
+t1=ra;
+t2=-v;
+t3=p+wo;
+P=[ t1 t2 t3 ];
+ia=roots(P);
+pi=(v-ia(2)*ra)*ia(2)+ia(2)^2*ra+ifl*v; // motor input
+nm=(p/pi)*100;
+printf('Motor efficiency at rated load is %f percent',nm);
diff --git a/3760/CH4/EX4.71/Ex4_71.sce b/3760/CH4/EX4.71/Ex4_71.sce new file mode 100644 index 000000000..eb8bb0baf --- /dev/null +++ b/3760/CH4/EX4.71/Ex4_71.sce @@ -0,0 +1,10 @@ +clc;
+v=440; // rated voltage of mootor
+no=2000; // no load speed
+n1=1000; // speed at full load torque
+Tl=0.5; // load torque as a fraction of rated torque
+n2=1050; // increased speed due to redued torque
+// field current is constant so flux is constant
+// since torqu gets reduced by half new armature current also gets reduced half i.e ia2=ia1/2;
+vd=(v*(n2-n1))/(n2-(n1/2));
+printf('Armature voltage drop at full load is %d V',vd);
diff --git a/3760/CH4/EX4.72/Ex4_72.sce b/3760/CH4/EX4.72/Ex4_72.sce new file mode 100644 index 000000000..25a5d501b --- /dev/null +++ b/3760/CH4/EX4.72/Ex4_72.sce @@ -0,0 +1,19 @@ +clc;
+v=230; // source voltage
+ra=0.1; // resistance of armature
+ia=100; // armature current
+n=1600; // speed of dc shunt motor
+wl=300; // friction and windage losses
+lo=1200; // no load core loss
+lc=2500; // copper losses
+Ls=0.01; // stray losses as a fraction of output
+Ea=v-ia*ra; // counter EMF
+pe=Ea*ia; // electromagnetic power
+wo=wl+lo; // no load rotational losses
+po=pe-wo; // shaft power + stray load losses
+psh=po/(1+Ls);
+Tsh=(psh*60)/(2*%pi*n);
+printf('Shaft torque is %f Nm\n',Tsh);
+pi=pe+lc; // power input to motor
+nm=(psh/pi)*100;
+printf('Motor efficiency is %f percent',nm);
diff --git a/3760/CH4/EX4.73/Ex4_73.sce b/3760/CH4/EX4.73/Ex4_73.sce new file mode 100644 index 000000000..452c2217f --- /dev/null +++ b/3760/CH4/EX4.73/Ex4_73.sce @@ -0,0 +1,17 @@ +clc;
+// shaft power is given little bit more than actual value in question
+w1=25;
+w2=9; // spring balance readings in kg
+d=19.5*10^-2; // outside pulley diameter
+t=0.5*10^-2; // belt thickness
+g=9.81; // acceleration due to gravity
+n=1500; // motor speed
+v=230; // applied voltage
+il=12.5; // line current
+Ts=(w1-w2)*((d/2)+(t/2))*g;
+printf('Shaft torque is %f Nm\n',Ts);
+psh=(2*%pi*n*Ts)/60;
+printf('Shaft power is %f W\n',psh);
+pi=v*il; // motor input
+nm=(psh/pi)*100;
+printf('Motor efficiency at rated load is %f percent',nm);
diff --git a/3760/CH4/EX4.74/Ex4_74.sce b/3760/CH4/EX4.74/Ex4_74.sce new file mode 100644 index 000000000..aca6ba82f --- /dev/null +++ b/3760/CH4/EX4.74/Ex4_74.sce @@ -0,0 +1,22 @@ +clc;
+v=400; // rated voltage of dc shunt motor
+io=5; // current at no load
+ra=0.5; // armature resistance
+rf=200; // field resistance
+i=50; // current at full load
+ifl=v/rf; // constant shunt field current
+iao=io-ifl; // no load armature current
+wo=v*iao-iao^2*ra; // no load rotational losses
+ia=i-ifl; // full load armature current
+la=ia^2*ra; // full load armature circuit losses
+lf=v*ifl; // constant shunt feld losses
+tl=la+lf+wo; // total field losses
+pi=i*v; // motor input at full load
+nm=(1-(tl/pi))*100;
+printf('Output power is %f KW\n',(pi-tl)/1000);
+printf('Efficiency on full load is %f percent\n',nm);
+Ea1=v-iao*ra; // no load counter EMF
+Ea2=v-ia*ra; // full load counter EMF
+pr=((Ea1-Ea2)/Ea1)*100; // Ea is directly proportioal to speed so percentage change in Ea is same as percentage in speed;
+
+printf('Percentage change in speed from no load to full load is %f percent',pr);
diff --git a/3760/CH4/EX4.75/Ex4_75.sce b/3760/CH4/EX4.75/Ex4_75.sce new file mode 100644 index 000000000..daab32a6c --- /dev/null +++ b/3760/CH4/EX4.75/Ex4_75.sce @@ -0,0 +1,23 @@ +clc;
+v=400; // rated voltage of dc shunt motor
+p=20000; // rated power of motor
+i=2.5; // no load current
+ra=0.5; // armature resistance
+rf=800; // field current
+vb=2; // voltage drop in brush
+ifl=v/rf; // constant shunt field current
+iao=i-ifl; // no load armature current
+wo=v*iao-iao^2*ra; // no load rotational losses
+tl=wo+v*ifl; // total losses
+// by using equation of power input= output power + losses, solving quadratic equation in armature current whose terms are
+t1=ra;
+t2=vb-v;
+t3=p+tl-v*(v/rf);
+P=[ t1 t2 t3];
+ia=roots(P);
+lo=ia(2)^2*ra; // armature ohmic losses
+lb=ia(2)*vb; // brush drop loss
+tl=tl+lo+lb; // total losses at rated load
+pi=p+tl; // input power
+nm=(p/pi)*100;
+printf('Full load efficiency is %f percent',nm);
diff --git a/3760/CH4/EX4.77/Ex4_77.sce b/3760/CH4/EX4.77/Ex4_77.sce new file mode 100644 index 000000000..6978ed6bb --- /dev/null +++ b/3760/CH4/EX4.77/Ex4_77.sce @@ -0,0 +1,24 @@ +clc;
+// Hopkinson's method gave following result for two identical dc shunt machines
+v=230; // line voltage
+il=30; // line current excluding both field currents
+ia=230; // motor armature current
+ifl1=4; ifl2=5; // field currents
+ra=0.025; // armature current
+// from fig 4.85
+ig=ia-il; // generator armature current
+la1=ig^2*ra; // armature circuit losses in generator
+la2=ia^2*ra; // armature circuit losses in motor
+pd=v*il; // power drawn from supply (excluding field loss)
+wo=pd-la1-la2; // no load rotational losses for both machines
+pg=v*ig; // generator outputk
+tl=(wo/2)+v*ifl2+la1; // total losses for generator
+ng=(1-(tl/(tl+pg)))*100;
+pi=v*(ia+ifl1); // input power for motor
+tl=(wo/2)+v*ifl1+la2; // total losses for motor
+nm=(1-(tl/pi))*100;
+printf('Motor efficiency is %f percent\n',nm);
+printf('Generator efficiency is %f percent\n',ng);
+// If both machine are assumed to have same efficiency then
+n=sqrt(ig/ia)*100;
+printf('Efficiency of machine is %d percent',n);
diff --git a/3760/CH4/EX4.78/Ex4_78.sce b/3760/CH4/EX4.78/Ex4_78.sce new file mode 100644 index 000000000..776ee4989 --- /dev/null +++ b/3760/CH4/EX4.78/Ex4_78.sce @@ -0,0 +1,22 @@ +clc;
+// fields test on two similar machine gave following test
+iam=60; // motor armature current
+vam=500; // voltage across armature
+vfm=40; // voltage across field
+vt=450; // terminal voltage for generator
+io=46; // output current for generator
+vfg=40; // voltage across field
+ra=0.25; // armture resistance
+pi=(vam+vfm+vfg)*iam; // power input to whole set
+pog=vt*io; // generator output
+tl=pi-pog; // total loss in whole set
+poh=iam^2*ra+iam*(vfm+vfg)+io^2*ra; // total ohmic losses
+wo=(tl-poh)/2; // no load roational losses for each machines
+pim=(vam+vfm)*iam; // motor power input
+plm=iam^2*ra+iam*vfm+wo; // total motor loss
+nm=(1-(plm/pim))*100;
+printf('Motor efficiency is %f percent\n',nm);
+plg=io^2*ra+iam*vfm+wo; // total motor loss
+pgm=pog+plg; // generator input
+ng=(1-(plg/pgm))*100;
+printf('Generator efficiency is %f percent',ng);
diff --git a/3760/CH4/EX4.81/Ex4_81.sce b/3760/CH4/EX4.81/Ex4_81.sce new file mode 100644 index 000000000..fff8aab41 --- /dev/null +++ b/3760/CH4/EX4.81/Ex4_81.sce @@ -0,0 +1,23 @@ +clc;
+p=3000; // power of amplidyne
+v=300; // voltage of amplidyne
+w=200; // angular velocity of amplidyne
+rf=50; // field resistance
+ra=5; // armature resistance
+rc=1; // compensating winding resistance
+kqf=250;
+kdq=100;
+kqd=80; // voltage constants
+A=(kdq*kqf)/(ra*rf); // voltage amplification factor
+id=p/v; // rated current
+vf=(v+id*(ra+rc))/A; // field voltage
+ifl=vf/rf; // field current
+pk=(v*id)/(vf*ifl); // power gain
+printf('Field current is %f A\n',ifl);
+printf('Power gain at rated output is %f \n',pk);
+// when compensation is zero
+vf=(v+id*(((kdq*kqd)/ra)+ra))/A; // field voltage
+ifl=vf/rf;
+printf('Field current at zero compensation is %f A\n',ifl);
+pk=(v*id)/(vf*ifl); // power gain
+printf('Power gain at rated output at zero compensation is %f \n',pk);
diff --git a/3760/CH4/EX4.82/Ex4_82.sce b/3760/CH4/EX4.82/Ex4_82.sce new file mode 100644 index 000000000..ce3ec351d --- /dev/null +++ b/3760/CH4/EX4.82/Ex4_82.sce @@ -0,0 +1,31 @@ +clc;
+// plot for open circuit characteristics is given in fig 4.10
+IF=[ 0 11.5 23 36.5 59.5 79 110 160];
+EA=[0 40 80 120 160 180 200 220 ];
+subplot(221);
+plot(IF,EA);
+xlabel('field ATs');
+ylabel('voltage');
+title('magnetising curve');
+nf=800; // field winding turns
+rd=0.5; // total armature resistance along d-axis
+ifl=0.2; // field winding current
+d=10; // product of (difference between mmf of compensating winding and armature mmf along d-circuit)and load current
+nf1=nf*ifl; // field winding turns for field current of 200mA
+il=nf1/d; // maximum load current
+printf('Maximum field current is %d A\n',il);
+IL=[0 2 4 6 8 10 12 14 16]; // load currents
+ATD=nf1-d*IL; // net d-axis ATs
+disp('Net d-axis ATs is');
+disp(ATD);
+// corresponding to each ATD open circuit EMF is obtained from magnetising curve
+EO=[220 213 204.7 194 180.5 161.4 128 70 0 ]; // open circuit EMF
+VRD=rd*IL; // d-axis resistance drop
+VO=EO-VRD;
+disp('Output voltage(V) is ');
+disp(VO);
+subplot(222);
+plot(IL,VO);
+xlabel('load current(A)');
+ylabel('Output voltage(v)');
+title('Output voltage vs Load current');
diff --git a/3760/CH4/EX4.83/Ex4_83.sce b/3760/CH4/EX4.83/Ex4_83.sce new file mode 100644 index 000000000..e4ea7029e --- /dev/null +++ b/3760/CH4/EX4.83/Ex4_83.sce @@ -0,0 +1,12 @@ +clc;
+// from fig 4.79
+vo=206; // output voltage
+il=8; // load current
+ifl=0.2; // field current
+Eo=280; // open circuit voltage for which field winding current is to be determined
+r=0.5; // net resistance
+n=800; // d-axis ampere turns
+// with saturation ignored output voltage vd is given by vd=(n*if-10*il)K-il*r
+K=(vo+il*r)/(800*ifl-10*il); // slope of straight line in curve
+ifl=Eo/(K*n);
+printf('For given open circuit voltage field current is %f mA',ifl*1000);
diff --git a/3760/CH4/EX4.84/Ex4_84.sce b/3760/CH4/EX4.84/Ex4_84.sce new file mode 100644 index 000000000..d22ba4c14 --- /dev/null +++ b/3760/CH4/EX4.84/Ex4_84.sce @@ -0,0 +1,16 @@ +clc;
+A=100; // amplidyne voltage amplification
+vo=200; // DC generator output voltage
+rf=125; // field winding resistance
+vfb=0.1; // ratio of feedback voltage to output voltage of generator
+vr=50; // reference voltage
+// amplidyne output voltage,Va =(vr-vfb*vt)*A
+// ig=va/rf ig is generator field current
+// vog=ig*vo vog is generator output voltage-1
+// simplifying 1 we get
+vt=(vr*A)/((vfb*A)+(rf/vo));
+printf('Output voltage of generator is %f V\n',vt);
+// now feedback voltage is reduced to zero
+vr=(vt*rf)/(A*vo);
+printf('Reference voltage to obtain required output generator voltage is %f V ',vr);
+
diff --git a/3760/CH4/EX4.85/Ex4_85.sce b/3760/CH4/EX4.85/Ex4_85.sce new file mode 100644 index 000000000..f8a4ca7d2 --- /dev/null +++ b/3760/CH4/EX4.85/Ex4_85.sce @@ -0,0 +1,12 @@ +clc;
+g1=1.5; // gain factor of amplifier
+g2=80; // gain factor of generator
+vo=250; // output voltage at no load
+s=0.2; // feedback potentiometer setting
+// for generated voltage= 80V field current is 1 A
+ifl=vo/g2; // field current for generated voltage= 250V
+vi=ifl/g1; // amplifier input voltage for field current corresponding to generated voltage= 250V
+vfb=s*vo; // feedback voltage
+vr=vfb+vi;
+printf('Reference voltage for given potentiometer setting is %f V\n',vr);
+printf('When feedback setting is zero, reference voltage is %f V',vi);
diff --git a/3760/CH4/EX4.86/Ex4_86.sce b/3760/CH4/EX4.86/Ex4_86.sce new file mode 100644 index 000000000..5ccb21051 --- /dev/null +++ b/3760/CH4/EX4.86/Ex4_86.sce @@ -0,0 +1,20 @@ +clc;
+p=4000; // rated power of generator
+v=250; // rated voltage of generator
+ra=0.25; // armature resistance
+rf=100; // fiel resistance
+vr=20; // improving factor for voltage regulation
+g1=120; // generator gain
+// after deriving required expression
+il=p/v; // load current
+vgr=((il*ra)/v)*(1/vr); // pu full load generator regulation
+dvt=-vgr*v; // decrease in terminal voltage of generator from no load to full load
+disp('case a');
+s=0.1; // feedback potentiometer setting
+A=(-dvt*rf-il*ra*rf)/(dvt*s*g1);
+printf('Amplifier gain is %f\n',A);
+disp('case b');
+s=1; // feedback potentiometer setting
+A=(-dvt*rf-il*ra*rf)/(dvt*s*g1);
+printf('Amplifier gain is %f\n',A);
+
diff --git a/3760/CH4/EX4.87/Ex4_87.sce b/3760/CH4/EX4.87/Ex4_87.sce new file mode 100644 index 000000000..ba9953d61 --- /dev/null +++ b/3760/CH4/EX4.87/Ex4_87.sce @@ -0,0 +1,24 @@ +clc;
+v=48; // supply voltage
+n=2400; // speed of permanent magnet DC motor
+i=0.8; // current drawn by motor
+ra=1; // armature resistance of motor
+disp('case a');
+Ea=v-i*ra; // generated EMF
+l=Ea*i;
+printf('No load rotational losses is %f W\n',l);
+disp('case b');
+km=(Ea*60)/(2*%pi*n); // speed voltage constant
+v=40; // supply voltage
+n1=1600; // speed at supply voltage
+Ea=(km*2*%pi*n1)/60; // generated EMF
+ia=(v-Ea)/ra; // new armature current
+pe=Ea*ia; // Electromagnetic power developed
+po=pe-l;
+printf('Output power is %f W\n',po);
+disp('case c');
+v=20; // supply voltage
+// when motor stalls Ea=0
+ia=v/ra; // stall current
+T=km*ia;
+printf('Stall torque is %f Nm',T);
diff --git a/3760/CH4/EX4.9/Ex4_9.sce b/3760/CH4/EX4.9/Ex4_9.sce new file mode 100644 index 000000000..6a46c5607 --- /dev/null +++ b/3760/CH4/EX4.9/Ex4_9.sce @@ -0,0 +1,22 @@ +clc;
+A=2;//No of parallel paths for armature conductors
+P=6;//No. of poles
+If=2;//Field current
+Il=148;//Line current
+Ia=If+Il;//Armature current
+Z=480;//No of conductors
+//brushes on GNA, theta=0
+ATd1=0//demagnetizing ampere turns
+ATc1=((Ia*Z)/(2*A*P))//Cross magnetizing ampere turns
+printf('When brushes are on GNA the demagnetizing ampere turns & Cross magnetizing ampere turns are equal to %f & %f ATs/pole respectively.\n',ATd1,ATc1);
+//brushes are shifted from GNA by 5 degrees electrical, theta=5
+theta=5;
+ATd2=((2*theta*Ia*Z)/(180*2*A*P))//demagnetizing ampere turns
+ATc2=3000-ATd2;//Cross magnetizing ampere turns
+printf('When the brushes are shifted from GNA by 5 degrees electrical the demagnetizing ampere turns & Cross magnetizing ampere turns are equal to %f & %f ATs/pole respectively.\n',ATd2,ATc2);
+//brushes are shifted from GNA by 5 degrees mechanical, theta_m=5
+theta_m=5;//mechanical angle
+theta_e=(P/2)*theta_m;//electrical angle
+ATd3=((2*theta_e*Ia*Z)/(180*2*A*P))//demagnetizing ampere turns
+ATc3=3000-ATd3;//Cross magnetizing ampere turns
+printf('When the brushes are shifted from GNA by 5 degrees mechnical the demagnetizing ampere turns & Cross magnetizing ampere turns are equal to %f & %f ATs/pole respectively',ATd3,ATc3);
diff --git a/3760/CH5/EX5.1/Ex5_1.sce b/3760/CH5/EX5.1/Ex5_1.sce new file mode 100644 index 000000000..18c2c993b --- /dev/null +++ b/3760/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,99 @@ +clc;
+v=220; // rated voltage of alternator
+f=50; // frequency of supply
+r=0.06; // resistance per phase
+p=6; // number of poles
+i=40; // full load current
+pf=0.8; // lagging power factor
+vt=v/sqrt(3); // rated per phase voltage
+IF=[ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.8 2.2 2.6 3 3.4];
+EA=[ 29 58 87 116 146 172 194 232 261.5 284 300 310];
+subplot(313);
+plot(IF,EA/sqrt(3));
+xlabel('Field current');
+ylabel('open circuit voltage');
+title('open circuit characteristics');
+IF1=[ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.8 ];
+ISC=[ 6.6 13.2 20 26.5 32.4 40 46.3 59 ];
+subplot(323);
+plot(IF1,ISC);
+xlabel('Field current');
+ylabel('short circuit current');
+title('short circuit characteristics');
+ZPF=[ 0 0 0 0 0 0 29 88 140 177 208 230];
+subplot(333);
+plot(IF,ZPF);
+xlabel('Field current');
+ylabel('terminal voltage');
+title('full load zero power factor characteristics');
+disp('EMF method');
+// value of synchronous reactance is taken from given table
+EA1=[ 29 58 87 116 146 172 194 232]
+ZS=EA1./(ISC*sqrt(3));
+disp('synchronous impedance (ohms) is');
+disp(ZS);
+XS=ZS; // RS^2 is negligible
+disp('synchronous reactance (ohms) is');
+disp(XS);
+xs=2.27;
+ia=i*(pf-%i*sqrt(1-pf^2)); // full load current in complex form
+E=vt+ia*(r+%i*xs); // Excitation voltage
+vr=floor(((abs(E)-vt)/vt)*100);
+printf('Voltage regulation is %f percent\n',vr);
+disp('Mmf method');
+// with ia as reference
+E=vt*(pf+%i*sqrt(1-pf^2))+i*r; // Excitation voltage
+// from fig 5.30 ,E=127 V
+oc=1.69; // current for given excitation voltage obtained from open circuit characteristics
+sc=1.2; // field current required to circulate full load short circuit current
+al=atand(imag(E),real(E)); // angle between ia and E
+Ff=(oc*(-sind(al)+%i*cosd(al)))-sc; // field mmf
+printf('field mmf is %f A\n',abs(Ff));
+// corresponding to Ff,E=163.5 v from O.C.C
+Ef=163.5;
+vr=((Ef-vt)/vt)*100;
+printf('Voltage regulation is %f percent\n',vr);
+disp('Zero power factor method');
+// As per the description given in method
+vd=30; // voltage drop armature leakage reactance
+xa=vd/i; // armature leakage reactance
+// with ia as reference
+Er=vt*(pf+%i*sqrt(1-pf^2))+i*(r+%i*xa); // Excitation voltage
+// from fig 5.30 ,E=148.6 V
+oc=2.134; // current for given excitation voltage obtained from open circuit characteristics
+Fa=0.84; // armature mmf from potier triangle
+be=atand(imag(Er),real(Er)); // angle between ia and E
+Ff=(oc*(-sind(be)+%i*cosd(be)))-Fa; // field mmf
+printf('field mmf is %f A\n',abs(Ff));
+// corresponding to Ff=2.797 A,E=169 v from O.C.C
+Ef=169;
+vr=((Ef-vt)/vt)*100;
+printf('Voltage regulation is %f percent\n',vr);
+disp('New A.S.A method');
+// parameters needed in this method are calculated in part c
+id=0.366; // difference in field current between OCC and air gap line from fig 5.30
+th=acosd(pf);
+ig=1.507; // field current corresponding to rated rated per phase voltage
+Ff=ig+sc*(%i*pf+sqrt(1-pf^2)); // field mmf without saturation
+Ff=abs(Ff)+id; // ield mmf with saturation
+printf('field mmf is %f A\n',Ff);
+// corresponding to Ff=2.791 A,E=169 v from O.C.C
+Ef=169;
+vr=((Ef-vt)/vt)*100;
+printf('Voltage regulation is %f percent\n',vr);
+disp('Saturated synchronous reactance method');
+// for E=148.5 v (from part c),
+Era=179.5; // air line gap voltage
+k=Era/abs(Er); // saturation factor
+vdg=100.5; // voltage drop in unsaturated synchronous reactance
+xag=vdg/i; // unsaturated synchronous reactance
+xas=xa+((xag-xa)/k); // saturated synchronous reactance
+// with vt as reference
+Ef=vt+ia*(r+%i*xas);
+ok=2.15; // resultant mmf from fig 5.30
+Ff=(abs(Ef)/abs(Er))*ok;
+printf('field mmf is %f A\n',Ff);
+// corresponding to Ff=2.78 A,E=169 v from O.C.C
+Ef=169;
+vr=((Ef-vt)/vt)*100;
+printf('Voltage regulation is %f percent\n',vr);
diff --git a/3760/CH5/EX5.10/Ex5_10.sce b/3760/CH5/EX5.10/Ex5_10.sce new file mode 100644 index 000000000..552e5ef19 --- /dev/null +++ b/3760/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,36 @@ +clc;
+v=6600; // rated voltage of motor
+xs=20 ; // per phase synchronous reactance
+p=500000; // VA rating of motor
+il=p/(sqrt(3)*v); // rated armature current
+vt=v/sqrt(3); // per phase rated voltage
+disp('case a');
+de=10; // load angle
+c1=1;
+c2=-2*vt*cosd(de);
+c3=vt^2-(il*xs)^2; // coefficients of quadratic equation in Ef
+p= [ c1 c2 c3 ];
+Ef=roots(p);
+printf('Per phase excitation EMF at lagging pf is %f v\n',Ef(2));
+printf('Excitation line EMF at lagging pf is %f v\n',sqrt(3)*Ef(2));
+printf('Per phase excitation EMF at leading pf is %f v\n',Ef(1));
+printf('Excitation line EMF at leading pf is %f v\n',sqrt(3)*Ef(1));
+disp('case b');
+disp('For lagging pf');
+pd=(3*vt*Ef(2)*sind(de))/xs;
+pf=pd/(sqrt(3)*v*il);
+printf('Mechanical power developed is %f W\n',pd);
+printf('Power factor is %f lagging\n',pf);
+disp('For leading pf');
+pd=(3*vt*Ef(1)*sind(de))/xs;
+pf=pd/(sqrt(3)*v*il);
+printf('Mechanical power developed is %f W\n',pd);
+printf('Power factor is %f leading\n',pf);
+disp('case c');
+p=200000; // delivered power
+de=90; // load angle for falling out of step
+// motor falls out of step at de= 90 degrees
+Ef=(p*xs)/(3*sind(de)*vt);
+printf('Minimum excitation voltage per phase is %f v',Ef);
+
+
diff --git a/3760/CH5/EX5.11/Ex5_11.sce b/3760/CH5/EX5.11/Ex5_11.sce new file mode 100644 index 000000000..0ff034a65 --- /dev/null +++ b/3760/CH5/EX5.11/Ex5_11.sce @@ -0,0 +1,15 @@ +clc;
+v=415; // rated voltage of motor
+f=50; // frequency of motor
+ef=520; // line to line excitation emf
+p=6; // number of poles
+xs=2; // per phase synchronous reactance
+t=220; // torque developed
+vt=v/sqrt(3); // rated per phase voltage
+eft=ef/sqrt(3); // per phase excitation emf
+ws=(4*%pi*f)/p; // synchronous speed
+de=asind((t*ws*xs)/(3*vt*eft)); // load angle
+ia=(sqrt(vt^2+eft^2-2*eft*vt*cosd(de)))/xs; // from phasor diagram(fig 5.48),armature current
+pf=(ef*sind(de))/(xs*ia*sqrt(3));
+printf('Current drawn from supply is %f A\n',ia);
+printf('Power factor is %f leading',pf);
diff --git a/3760/CH5/EX5.12/Ex5_12.sce b/3760/CH5/EX5.12/Ex5_12.sce new file mode 100644 index 000000000..83f2fa811 --- /dev/null +++ b/3760/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,16 @@ +clc;
+v=415; // rated volatge of motor
+pf=0.9; // leading power factor
+ps=15000; // shaft power
+E=400; // excitation emf
+r=0.5; // per phase resistance
+vt=v/sqrt(3); // rated per phase voltage
+e=E/sqrt(3); // per phase excitation emf
+c1=1.5;
+c2=-sqrt(3)*v*pf;
+c3=ps; // coefficients of quadratic equation in armature current
+p= [ c1 c2 c3 ];
+ia=roots(p);
+// higher value of armature current is neglected
+xs=((vt*sqrt(1-pf^2))-(sqrt(e^2-(vt*pf+ia(2)*r)^2)))/ia(2);
+printf('Synchronous reactance is %f ohm',xs);
diff --git a/3760/CH5/EX5.13/Ex5_13.sce b/3760/CH5/EX5.13/Ex5_13.sce new file mode 100644 index 000000000..56d1dc840 --- /dev/null +++ b/3760/CH5/EX5.13/Ex5_13.sce @@ -0,0 +1,14 @@ +clc;
+e=1.2; // pu excitation emf
+xs=0.8; // pu synchronous reactance
+vt=1; // pu rated voltage
+ia=1; // pu armature current for KVA=100 %, vt*ia=1 therefore ia=1;
+pf=cosd(asind((e^2-xs^2-1)/(-2*xs))); // leading power factor
+pd=vt*ia*pf;
+printf('Mechanical power developed by motor is %f pu\n',pd);
+e=1; // pu excitation emf reduced to generate 100% emf
+de=asind((pf*xs)/(vt*e)); // load angle
+ia=(sqrt(vt^2+e^2-2*e*vt*cosd(de)))/xs; // new armature current
+p=(vt*ia)*100;
+printf('New KVA rating is %f percent ',p);
+
diff --git a/3760/CH5/EX5.14/Ex5_14.sce b/3760/CH5/EX5.14/Ex5_14.sce new file mode 100644 index 000000000..6fda02973 --- /dev/null +++ b/3760/CH5/EX5.14/Ex5_14.sce @@ -0,0 +1,18 @@ +clc;
+xs=0.8; // pu reactance
+Ef=1.3; // pu excitation EMF
+p=0.5; // pu output power
+vt=1; // rated per phase voltage
+disp('case a');
+de=asind((p*xs)/(vt*Ef));
+printf('Load angle is %f degrees\n',de);
+ia=(sqrt(vt^2+Ef^2-2*vt*Ef*cosd(de)))/xs; // from phasor diagram (fig5.49)
+printf('Armature current is %f p.u.\n',ia);
+pf=p/(vt*ia);
+printf('Power factor is %f lagging\n',pf);
+disp('case b');
+// Under given condition magnitude of power factor remains same but it becomes leading
+Ef=sqrt((vt*pf)^2+(vt*sqrt(1-pf^2)-ia*xs)^2); // excitation EMF
+printf('Excitation EMF is %f p.u.\n',Ef);
+de=asind((p*xs)/(vt*Ef));
+printf('Load angle is %f degrees\n',de);
diff --git a/3760/CH5/EX5.15/Ex5_15.sce b/3760/CH5/EX5.15/Ex5_15.sce new file mode 100644 index 000000000..8633091ce --- /dev/null +++ b/3760/CH5/EX5.15/Ex5_15.sce @@ -0,0 +1,33 @@ +clc;
+v=11000; // rated voltage of motor
+zs=1+10*%i; // per phase synchronous impedance
+ia=100; // armature current at unity power factor
+vt=v/sqrt(3); // per phase voltage
+Ef=sqrt((vt+ia*real(zs))^2+(ia*imag(zs))^2); // excitation EMF from phasor diagram
+al=atand(real(zs),imag(zs));
+de=atand((ia*imag(zs))/(vt+ia)); // load angle
+p=(Ef*vt*sind(de+al)/abs(zs))-((vt^2*real(zs))/abs(zs)^2); // per phase power delivered
+disp('case a');
+Ef1=1.15*Ef; // Excitation EMF after an increment of 15%
+t1=p;
+t2=(vt^2/abs(zs)^2)*real(zs);
+t3=abs(zs)/(vt*Ef1); // terms needed to evaluate load angle
+di=asind((t1+t2)*t3)-al; // load angle
+ia1=(sqrt(vt^2+Ef1^2-2*Ef1*vt*cosd(di)))/abs(zs); // armature current
+pf=p/(vt*ia1);
+printf('New value of armature current is %f A\n',ia1);
+printf('New value of load angle is %f degrees\n',di);
+printf('New power factor is %f lagging\n',pf);
+disp('case b');
+// at unity pf
+pf=1;
+c1=1+imag(zs)^2;
+c2=2*vt;
+c3=vt^2-Ef1^2; // coefficients of quadratic equation in armature current
+p= [ c1 c2 c3 ];
+ia=roots(p);
+printf('Armature current under given condition is %f A\n',ia(2));
+P=(vt*ia(2)*pf)/1000;
+Pt=P*3;
+printf('Per phase power delivered is %f KW\n',P);
+printf('Net power delivered is %f KW\n',Pt);
diff --git a/3760/CH5/EX5.16/Ex5_16.sce b/3760/CH5/EX5.16/Ex5_16.sce new file mode 100644 index 000000000..0b212f9b1 --- /dev/null +++ b/3760/CH5/EX5.16/Ex5_16.sce @@ -0,0 +1,18 @@ +clc;
+vt=1; // rated per phase voltage
+zs=0.02+0.8*%i; // per phase p.u synchronous impedance
+// At the time of synchronization excitation EMF=rated per phase voltage and load angle=0
+ef=1; // pu excitation EMF
+ia=1; // pu armature current
+// from phasor diagram 5.51
+t1=ef^2-real(zs)^2-imag(zs)^2-1;
+t2=sqrt((2*real(zs))^2+(2*imag(zs))^2);
+t3=atand(-real(zs)/imag(zs)); // terms needed to find out power factor
+pf=cosd(asind(t1/t2)+ t3);
+printf('Operating power factor is %f leading\n',pf);
+al=atand(real(zs),imag(zs));
+t1=vt*ia*pf;
+t2=(vt^2/abs(zs)^2)*real(zs);
+t3=abs(zs)/(vt*ef); // terms needed to evaluate load angle
+de=floor(asind((t1+t2)*t3))-al; // load angle
+printf('Load angle of generator is %f degrees',de);
diff --git a/3760/CH5/EX5.17/Ex5_17.sce b/3760/CH5/EX5.17/Ex5_17.sce new file mode 100644 index 000000000..b3e20f88b --- /dev/null +++ b/3760/CH5/EX5.17/Ex5_17.sce @@ -0,0 +1,17 @@ +clc;
+p=40*10^6; // rated power of turbogenerator
+v=11000; // rated voltage of generator
+xs=0.8; // p.u. synchronous reactance
+ra=0.5; // series reactance of infinite bus
+vt=v/sqrt(3); // rated per phase voltage
+disp('case b');
+ia=p/(v*sqrt(3)); // armature current
+printf('Armature current is %f A\n',ia);
+xs=xs*(vt/ia); // xs in ohms
+vd=ia*ra; // voltage drop in series resistance
+pf=cosd(asind((vd/2)/vt));
+printf('Alternate power factor is %f lagging\n',pf);
+disp('case c');
+Ef=sqrt((vt*pf)^2+((vd/2)+(ia*xs))^2);
+printf('Excitation EMF line to neutral is %f V\n',Ef);
+printf('Excitation EMF line to line is %f V\n',sqrt(3)*Ef);
diff --git a/3760/CH5/EX5.18/Ex5_18.sce b/3760/CH5/EX5.18/Ex5_18.sce new file mode 100644 index 000000000..146b06fc9 --- /dev/null +++ b/3760/CH5/EX5.18/Ex5_18.sce @@ -0,0 +1,15 @@ +clc;
+v=400; // rated voltage of motor
+pi=5472; // input power
+np=3; // number of phases
+xs=10; // synchronous reactance
+ef=v; // excitation voltage
+vt=v/sqrt(3); // rated per phase voltage
+de=round(asind((pi*xs*np)/(np*v^2)));
+printf('Load angle is %f degrees\n',de);
+// from fig. 5.53, vt=ef(excitation voltage per phase) armature resistance=0
+pf=cosd(de/2);
+printf('Power factor is %f lagging\n',pf);
+// from fig. 5.53
+ia=floor((2*vt*sind(de/2))/xs);
+printf('Armature current is %f A',ia);
diff --git a/3760/CH5/EX5.19/Ex5_19.sce b/3760/CH5/EX5.19/Ex5_19.sce new file mode 100644 index 000000000..ca0b5df91 --- /dev/null +++ b/3760/CH5/EX5.19/Ex5_19.sce @@ -0,0 +1,40 @@ +clc;
+v=2000; // rated voltage of motor
+xsm=2; // synchronous reactance of motor
+xsg=3; // synchronous reactance of generator
+xt=1.5; // transmission line reactance
+ia=100; // current drawn by motor
+pf=1; // power factor
+disp('case a');
+vt=v/sqrt(3); // rated per phase voltage
+Efm=floor(sqrt(vt^2+(ia*xsm)^2)); // excitation EMF
+printf('Excitation EMF for motor is %f V\n',Efm);
+Efg=sqrt(vt^2+(ia*(xsg+xt))^2); // excitation EMF
+printf('Excitation EMF for alternator is %f V\n',Efg);
+disp('case b');
+de1=acosd(vt/Efm); // load angle for motor
+de2=acosd(vt/Efg); // load angle for alternator
+de=de1+de2; // power angle between Efm and Efg
+pt=(Efg*Efm*sind(de))/(xsm+xsg+xt);
+P=pt*3;
+printf('Per phase power transfer between alternator and motor is %f KW\n',pt/1000);
+printf('Net power transfer between alternator and motor is %f KW\n',P/1000);
+disp('case c');
+// from phasor diagram fig 5.54
+ia=sqrt(Efm^2+Efg^2)/(xsm+xsg+xt);
+// for maximum transfer of power , power angle=90 degrees
+de=90
+pmax=(Efg*Efm*sind(de))/(xsm+xsg+xt);
+P=pmax*3;
+printf('Per phase maximum power transfer between alternator and motor is %f KW\n',pmax/1000);
+printf('Net maximum power transfer between alternator and motor is %f KW\n',P/1000);
+// from phasor diagrams determining various parameters needed to find power factor
+be=acosd(Efm/(ia*(xsm+xsg+xt)));
+Vp=sqrt((Efm-ia*xsm*cosd(be))^2+(ia*xsm*sind(be))^2); // phase voltage
+Vl=sqrt(3)*Vp; // line voltage
+printf('Armature current for given condition is %f A\n',ia);
+printf('Terminal voltage of synchronous motor is %f V\n',Vp);
+// from phasor diagram
+aoc=asind((ia*xsm*sind(be))/Vp);
+pf=cosd(90-be-aoc);
+printf('Power factor angle of motor is %f leading',pf);
diff --git a/3760/CH5/EX5.20/Ex5_20.sce b/3760/CH5/EX5.20/Ex5_20.sce new file mode 100644 index 000000000..15edb3c24 --- /dev/null +++ b/3760/CH5/EX5.20/Ex5_20.sce @@ -0,0 +1,18 @@ +clc;
+p=20*10^6; // VA rating of alternator
+z=5; // impedance of alternator
+r=0.5; // resistance of alternator
+v=11000; // voltage rating of bus bars
+e=12000; // excitation voltage
+vt=v/sqrt(3); // alternator per phase voltage
+Ef=e/sqrt(3); // alternator per phase excitation voltage
+pmax=round((((Ef*vt)/z)-((vt^2*r)/z^2))/10^6);
+P=round(pmax*3);
+printf('Per phase maximum output power from alternator is %f MW\n',pmax);
+printf('Total maximum output power from alternator is %f MW\n',P);
+disp('case b');
+pf=r/z; // power factor
+ia=round((sqrt(vt^2+Ef^2-2*Ef*vt*pf))/z); // armature current
+printf('Armature current is %f A\n',ia);
+pf=(Ef*z-vt*r)/(ia*z^2);
+printf('Power factor under maximum power condition is %f leading',pf);
diff --git a/3760/CH5/EX5.21/Ex5_21.sce b/3760/CH5/EX5.21/Ex5_21.sce new file mode 100644 index 000000000..80ddbb6bb --- /dev/null +++ b/3760/CH5/EX5.21/Ex5_21.sce @@ -0,0 +1,27 @@ +clc;
+v=2200; // rated voltage of motor
+r=0.32; // per phase armature resistance
+p=1500; // KW rating of motor
+ie=15; // exciting current
+is=750; // short circuit current
+cl=60; // core loss in KW
+fl=40; // frictional and windage loss in KW
+IF=[5 10 15 20 25 30];
+EFO=[ 760 1500 2140 2650 3040 3340]; // excitation EMF per phase
+EFP=EFO/sqrt(3);
+disp('Excitation EMF per phase(V) is');
+disp(EFP);
+// from table given for ie=15,
+Ef=2140; // Excitation EMF
+np=3; // number of phases
+ef=Ef/sqrt(3); // per phase open circuit voltage
+zs=ef/is; // synchronous impedance
+vt=floor(v/sqrt(3)); // per phase terminal voltage
+i=floor(vt/zs); // current phasor lagging vt
+ia=vt/(2*r); // armature current
+pd=((p/2)+cl+fl)/np; // mechanical power developed per phase at half-full load output
+R=ceil(sqrt((ia^2-((pd*1000)/r))));
+printf('Radius of power circle is %f A\n',R);
+printf('Current phasor is %f A\n',i);
+printf('Synchronous impedance is %f ohm\n',zs);
+disp('using above data and table given in solution, V-curves and variation of p.f. with field currents can be plotted');
diff --git a/3760/CH5/EX5.22/Ex5_22.sce b/3760/CH5/EX5.22/Ex5_22.sce new file mode 100644 index 000000000..b8205f9a4 --- /dev/null +++ b/3760/CH5/EX5.22/Ex5_22.sce @@ -0,0 +1,21 @@ +clc;
+v=2200; // rated voltage of motor
+p=1500; // KW rating of motor
+ie=15; // exciting current
+is=750; // short circuit current
+cl=60; // core loss in KW
+fl=40; // frictional and windage loss in KW
+// from table given in question for ie=15,
+Ef=2140; // Excitation EMF
+np=3; // number of phases
+ef=Ef/sqrt(3); // per phase open circuit voltage
+xs=ef/is; // synchronous reactance
+vt=floor(v/sqrt(3)); // per phase terminal voltage
+i=floor(vt/xs); // current phasor lagging vt
+pd=((p/2)+cl+fl)/np; // mechanical power developed per phase at half-full load output
+ia=pd*1000/vt; // working component of armature current
+// as resistance =0 , armature current=0 therefore radius of power circle=0 that is it becomes line with centre at zero
+printf('Working component of armature current is %f A\n',ia);
+printf('Terminal voltage is %f A\n',vt);
+printf('Synchronous reactance is %f ohm\n',xs);
+disp('using above data and table given in solution, V-curves and variation of p.f. with field currents can be plotted');
diff --git a/3760/CH5/EX5.23/Ex5_23.sce b/3760/CH5/EX5.23/Ex5_23.sce new file mode 100644 index 000000000..384f5c428 --- /dev/null +++ b/3760/CH5/EX5.23/Ex5_23.sce @@ -0,0 +1,21 @@ +clc;
+v=1100; // rated voltage of motor
+ef=1650; // emf
+p=350; // input power in KW
+zs=0.7+3.2*%i; // synchronous impedance per phase
+vt=v/sqrt(3); // rated per phase voltage
+eft=ef/sqrt(3); // per phase emf
+i1=vt/abs(zs);
+printf('Current phasor lagging terminal voltage is %f A\n', i1);
+i2=eft/abs(zs);
+printf('Current phasor lagging excitation EMF is %f A\n', i2);
+ia=(p*1000)/(3*vt);
+printf('Working component of armature current is %f A',ia);
+disp('using this data vector diagram is drawn and value of ia and power factor is obtained');
+ia=194.5;
+pf=19.5;
+printf('Power factor is %f leading\n',pf);
+printf('Armature current is %f A\n',ia);
+de=acosd((ia^2-i1^2-i2^2)/(-2*i1*i2));
+printf('Load angle is %f degrees\n',de);
+
diff --git a/3760/CH5/EX5.24/Ex5_24.sce b/3760/CH5/EX5.24/Ex5_24.sce new file mode 100644 index 000000000..95035647e --- /dev/null +++ b/3760/CH5/EX5.24/Ex5_24.sce @@ -0,0 +1,26 @@ +clc;
+xd=1.2; // d axis synchronous reactance
+xq=0.8; // q axis synchronous reactance
+ra=0.025; // armature resistance
+vt=1; // pu rated per phase voltage
+disp('case a');
+disp('For lagging power factor')
+pf=0.8; // power factor
+ia=1*(pf-sqrt(1-pf^2)*%i); // armature current
+Ef1=vt+%i*(ia*xq)+ia*ra; // excitation EMF
+id=1*sind(atand(imag(Ef1),real(Ef1))+acosd(pf)); // d component of armature current
+iq=1*cosd(atand(imag(Ef1),real(Ef1))+acosd(pf)); // q component of armature current
+Ef=abs(Ef1)+id*(xd-xq); // excitation EMF
+printf('Excitation EMF is %f p.u. at a load angle of %f degrees\n',abs(Ef),atand(imag(Ef1),real(Ef1)));
+disp('case b');
+disp('For leading power factor')
+pf=0.8; // power factor
+ia=1*(pf+sqrt(1-pf^2)*%i); // armature current
+Ef1=vt+%i*(ia*xq)+ia*ra; // excitation EMF
+id=1*sind(atand(imag(Ef1),real(Ef1))-acosd(pf)); // d component of armature current
+iq=1*cosd(atand(imag(Ef1),real(Ef1))-acosd(pf)); // q component of armature current
+Ef=abs(Ef1)+id*(xd-xq); // excitation EMF
+printf('Excitation EMF is %f p.u.at a load angle of %f degrees\n',abs(Ef),atand(imag(Ef1),real(Ef1)));
+
+
+
diff --git a/3760/CH5/EX5.27/Ex5_27.sce b/3760/CH5/EX5.27/Ex5_27.sce new file mode 100644 index 000000000..1c51189a1 --- /dev/null +++ b/3760/CH5/EX5.27/Ex5_27.sce @@ -0,0 +1,25 @@ +clc;
+v=400; // rated voltage of synchronous machine
+vt=v/sqrt(3); // per phase rated voltage
+ps=9500; // shaft load
+xd=5; // per phase d-axis synchronous reactance
+xq=3.2; // per phase q-axis synchronous reactance
+l=500; // friction windage and core losses
+np=3; // number of phases
+// at rated voltage excitation EMF
+Ef=v/sqrt(3); // excitation EMF
+disp('case a');
+pt=ps+l; // power developed
+// by using formula pd=np*(((Ef*Ef*sind(de))/xd)+((Ef^2*sind(2*de)*0.5*(xd-xq))/(xd*xq))), and hit and trial method we obtain value of load angle
+de=11.623; // load angle
+id=(Ef-Ef*cosd(de))/xd; // d-axis component of armature current
+iq=(Ef*sind(de))/xq; // q-axis component of armature current
+ia=sqrt(id^2+iq^2);
+printf('Armature current is %f A\n',ia);
+pf=cosd(acosd(iq/ia)-de);
+printf('Power factor is %f lagging\n',pf);
+disp('case b');
+de=acosd((-Ef*xq)/(4*Ef*(xd-xq))+(sqrt(0.5+((Ef*xq)/(4*vt*(xd-xq)))^2)));
+pd=np*(((Ef*Ef*sind(de))/xd)+((Ef^2*sind(2*de)*0.5*(xd-xq))/(xd*xq))); // maximum power developed
+po=pd-l;
+printf('Maximum power output is %f W',po);
diff --git a/3760/CH5/EX5.29/Ex5_29.sce b/3760/CH5/EX5.29/Ex5_29.sce new file mode 100644 index 000000000..3aa0e3fac --- /dev/null +++ b/3760/CH5/EX5.29/Ex5_29.sce @@ -0,0 +1,12 @@ +clc;
+Ef=1.4; // p.u excitation EMF
+xs=1.2; // p.u synchronous reactance
+p=0.5; // p.u synchronous power being delivered
+i=1; // percentage increment in prime mover torque
+vt=1; // rated per phase voltage
+de=asind((p*xs)/(Ef*vt)); // load angle
+dp=(i*p)/100; // increase in p.u real power
+ip=(dp/p)*100;
+printf('Percentage increase in real power is %d percent of its previous value\n',ip);
+iq=-tand(de)*ip;
+printf('Percentage decrease in reactive power is %f percent of its previous value\n',-iq);
diff --git a/3760/CH5/EX5.3/Ex5_3.sce b/3760/CH5/EX5.3/Ex5_3.sce new file mode 100644 index 000000000..fe0626675 --- /dev/null +++ b/3760/CH5/EX5.3/Ex5_3.sce @@ -0,0 +1,26 @@ +clc;
+e=400; // rated voltage of motor
+E=510; // excitation emf
+zs=0.5+%i*4; // synchronous impedance per phase
+l=900; // net loss
+al=90-atand(imag(zs),real(zs));
+disp('case a');
+Pmax=((e*E)/abs(zs))-((E^2*real(zs))/abs(zs)^2); // maximum output power
+sp=Pmax*3-l;
+printf('Shaft power is %f W\n',sp);
+ia=(sqrt(e^2+E^2-2*e*E*cosd(atand(imag(zs),real(zs)))))/abs(zs);
+il=sqrt(3)*ia; // line current
+printf('Line current is %f A\n',il);
+di=acosd((e*abs(zs)-E*real(zs))/(ia*abs(zs)^2));
+pf=cosd(atand(imag(zs),real(zs))-di);
+printf('Power factor is %f lagging\n',pf);
+disp('case b');
+Pmax=((e*E)/abs(zs))+((e^2*real(zs))/abs(zs)^2); // maximum input power
+ia=(sqrt(e^2+E^2-2*e*E*cosd(90+al)))/abs(zs);
+sp=floor(Pmax*3-ia^2*real(zs)*3-900);
+printf('Shaft power is %f W\n',sp);
+il=sqrt(3)*ia; // line current
+printf('Line current is %f A\n',il);
+di=acosd((e+E*cosd(atand(imag(zs),real(zs))))/(ia*abs(zs)));
+pf=cosd(atand(imag(zs),real(zs))-di);
+printf('Power factor is %f lagging\n',pf);
diff --git a/3760/CH5/EX5.31/Ex5_31.sce b/3760/CH5/EX5.31/Ex5_31.sce new file mode 100644 index 000000000..37330d877 --- /dev/null +++ b/3760/CH5/EX5.31/Ex5_31.sce @@ -0,0 +1,17 @@ +clc;
+v=400; // rated voltage of motor
+xd=6; // d-axis synchronous reactance
+xq=4; // q-axis synchronous reactance
+vt=400/sqrt(3); // rated per phase voltage
+// As per the theory given in question, phasor diagram is drawn and formula is derived
+// After the derived expression, for maximum power load angle=45
+de=45;
+P=(vt^2/2)*((1/xq)-(1/xd))*sind(2*de);
+printf('Maximum load that can be put on synchronous motor is %f W per phase\n',P);
+printf('Maximum load that can be put on synchronous motor is %f W for 3-phase\n',3*P);
+iq=(vt*sind(de))/xq; // q-axis component of armature current
+id=(vt*sind(de))/xd; // d-axis component of armature current
+ia=sqrt(iq^2+id^2);
+printf('Armature current is %f A\n',ia);
+pf=(3*P)/(sqrt(3)*v*ia);
+printf('Power factor at maximum power is %f lagging',pf);
diff --git a/3760/CH5/EX5.32/Ex5_32.sce b/3760/CH5/EX5.32/Ex5_32.sce new file mode 100644 index 000000000..1b27288fc --- /dev/null +++ b/3760/CH5/EX5.32/Ex5_32.sce @@ -0,0 +1,15 @@ +clc;
+// Answer for minimum excitation voltage is given wrong in book
+v=400; // rated voltage of motor
+xd=6; // d-axis synchronous reactance
+xq=4; // q-axis synchronous reactance
+vt=400/sqrt(3); // rated per phase voltage
+p=21; // load carried by motor
+pph=(p/3)*1000; // per phase load carried by motor
+// As per the theory given in question, expression is derived
+// After the derived expression,
+// cos(de)=(vt^2*(xd-xq)*sin(de)^3)/(pph*xd*xq), value of de (load angle is obtained by trial and error method and value of load angle is)
+de=63.2;
+Ef=(pph-(vt^2/2)*((xd-xq)/(xd*xq))*sind(2*de))/((vt/xd)*sind(de));
+printf('Maximum stable load angle is %f degrees\n',de);
+printf('Minimum excitation voltage is %f v\n',Ef);
diff --git a/3760/CH5/EX5.34/Ex5_34.sce b/3760/CH5/EX5.34/Ex5_34.sce new file mode 100644 index 000000000..354bb19b3 --- /dev/null +++ b/3760/CH5/EX5.34/Ex5_34.sce @@ -0,0 +1,16 @@ +clc;
+vt=1; // pu rated voltage
+xd=1; // pu d-axis synchronous reactance
+xq=0.6; // pu q-axis synchronous reactance
+p=0.9; // pu power being delivered
+pf=0.8; // power factor
+ia=p/(vt*pf); // pu armature current
+de=atand((ia*xq+vt*sind(acosd(pf)))/(vt*pf))-acosd(pf);
+printf('Load angle is %f degrees\n',de);
+Ef=vt*cosd(de)+ia*sind(de+acosd(pf))*xd;
+printf('Excitation voltage is %f p.u.\n',Ef);
+// when loss of excitation takes place Ef=0, for maximum power load angle=45
+de=45; // load angle
+pmax=(vt^2*(xd-xq)*sind(2*de))/(2*xd*xq);
+printf('Maximum power is %f p.u.\n',pmax);
+disp('As maximum power is less than the power being delivered generator will lose synchronism');
diff --git a/3760/CH5/EX5.35/Ex5_35.sce b/3760/CH5/EX5.35/Ex5_35.sce new file mode 100644 index 000000000..592ace7a2 --- /dev/null +++ b/3760/CH5/EX5.35/Ex5_35.sce @@ -0,0 +1,37 @@ +clc;
+v=11000; // rated voltage of motor
+P=20*10^6; // rated power of motor
+p=12; // number of poles
+f=50; // frequency
+xd=5; // d-axis synchronous reactance
+xq=3; // q-axis synchronous reactance
+vt=v/sqrt(3); // per phase rated voltage
+ia=P/(sqrt(3)*v); // per phase armature current
+disp('case a');
+// from phasor diagram
+Ef=vt-%i*(ia*xq);
+de=atand((ia*xq),(vt)); // load angle
+id=ia*sind(de); // d-axis component of armature current
+Ef=ceil(abs(Ef)+id*(xd-xq));
+printf('Excitation voltage is %f V to neutral\n',Ef);
+disp('case b');
+po=(((Ef*vt*sind(de))/xd)+((vt^2*(xd-xq)*sind(2*de))/(2*xd*xq)))/1000;
+printf('Power is %f KW per phase\n',po);
+po=3*po*1000;
+printf('Calculated power %f W is almost equal to given rated power i.e %f W\n',po,P);
+disp('case c');
+ps=((Ef*vt*cosd(de))/xd)+((vt^2*(xd-xq)*cosd(2*de))/(xd*xq));
+printf('Synchronozing power per electrical degree is %f KW\n',(3*ps*%pi)/(180*1000));
+ws=(4*%pi*f)/p; // synchronous speed
+t=(3*ps*%pi)/(180*ws);
+printf('Torque corresponding to synchronous power is %f N-m\n',t);
+disp('case d');
+printf('Synchronozing power per mechanical degree is %f KW\n',(3*ps*%pi*p)/(2*180*1000));
+t=(3*ps*%pi*p)/(2*180);
+printf('Torque corresponding to synchronous power is %f N-m\n',t);
+disp('case e');
+de=acosd((-Ef*xq)/(4*Ef*(xd-xq))+(sqrt(0.5+((Ef*xq)/(4*vt*(xd-xq)))^2)));
+printf('Maximum value of power angle is %f degrees\n',de);
+pmax=(((Ef*vt*sind(de))/xd)+((vt^2*(xd-xq)*sind(2*de))/(2*xd*xq)))/1000;
+printf('Maximum power is %f KW per phase\n',pmax);
+printf('Maximum power is %f KW for 3 phase\n',pmax*3);
diff --git a/3760/CH5/EX5.36/Ex5_36.sce b/3760/CH5/EX5.36/Ex5_36.sce new file mode 100644 index 000000000..1e3fe2e6a --- /dev/null +++ b/3760/CH5/EX5.36/Ex5_36.sce @@ -0,0 +1,27 @@ +clc;
+v=6600; // rated voltage of motor
+p=8; // number of poles
+f=50; // frequency of motor
+xs=20; // percentage synchronous reactance
+P=3000; // rated power of motor
+m=3; // number of phases
+vt=v/sqrt(3); // per phase rated voltage
+ia=(P*1000)/(sqrt(3)*v); // per phase armature current
+xs=(xs*vt)/(100*ia); // synchronous reactance in ohm
+disp('case a');
+de=0; // at no load load angle=0 and excitation voltage=per phase rated voltage
+ps=ceil(((m*vt^2*cosd(de)*%pi*p)/(xs*360))/1000);
+printf('Synchronozing power per mechanical degree is %f KW\n',ps);
+T=((ps*1000*p*60)/(2*%pi*120*f))/1000;
+printf('Corresponding synchronizing torque is %f KN-m\n',T);
+disp('case b');
+pf=0.8; // lagging power factor
+Ef=vt+%i*ia*(pf-sqrt(1-pf^2)*%i)*xs; // Excitation EMF
+de=atand(imag(Ef),real(Ef));
+ps=((m*vt*abs(Ef)*cosd(de)*%pi*p)/(xs*360))/1000;
+printf('Synchronozing power per mechanical degree is %f KW\n',ceil(ps));
+T=((ps*1000*p*60)/(2*%pi*120*f))/1000;
+printf('Corresponding synchronizing torque is %f KN-m\n',T);
+
+
+
diff --git a/3760/CH5/EX5.37/Ex5_37.sce b/3760/CH5/EX5.37/Ex5_37.sce new file mode 100644 index 000000000..7c7b23253 --- /dev/null +++ b/3760/CH5/EX5.37/Ex5_37.sce @@ -0,0 +1,23 @@ +clc;
+vt=3300; // terminal voltage
+xs=11; // synchronous reactance per phase
+p=8; // number of poles
+f=50; // frequency of motor
+m=3; // number of phases
+// from fig 5.82
+// at no load load angle=0 and excitation voltage=terminal voltage
+de=0;
+s=p/2; // electrical degree equivalent of one mechanical degree in space
+es=2*vt*sind(s/2); // synchronizing voltage
+is=es/xs;
+printf('Synchronizing current in the armature is %f A\n',is);
+ps=m*vt*is*cosd(de+s/2);
+printf('synchonizing power is %f KW\n',floor(ps/1000));
+ws=(2*%pi*120*f)/(60*p);
+T=ps/ws;
+printf('Synchronizing torque tending to restore rotor to its previous position is %f Nm\n',T);
+disp('case b');
+ia=30; // armature current
+dde=2*(asind((ia*xs)/(2*vt))); // change in load angle in electrical degrees
+s=dde*(2/p);
+printf('Rotor slips back by %f mechanical degrees',s);
diff --git a/3760/CH5/EX5.38/Ex5_38.sce b/3760/CH5/EX5.38/Ex5_38.sce new file mode 100644 index 000000000..16b6c2408 --- /dev/null +++ b/3760/CH5/EX5.38/Ex5_38.sce @@ -0,0 +1,36 @@ +clc;
+v=400; // rated voltage of motor
+f=50; // frequency of motor
+r=1; // per phase resistance
+x=5; // per phase reactance
+m=3; // number of phases
+p=15000; // rated power of motor
+disp('case a');
+EF=480; // Excitation voltage
+ph=p/m; // per phase power
+vt=v/sqrt(3); // terminal voltage
+R0=vt/(2*r);
+printf('Radius of zero power circle is %f A\n',R0);
+R1=sqrt(R0^2-(ph/r));
+printf('Radius of per phase power circle is %f A\n',R1);
+Ef=EF/sqrt(3); // per phase excitation voltage
+i1=vt/sqrt(r^2+x^2);
+i2=Ef/sqrt(r^2+x^2); // current phasors lagging terminal and excitation voltage
+printf('Current phasors lagging terminal voltage is %f A\n',i1);
+printf('Current phasors lagging exciation voltage is %f A\n',i2);
+disp('using the above data power circle diagram is drawn and value of armature current and power factor is obtained');
+ia=26;
+pf=0.955;
+printf('Armature current is %f A\n',ia);
+printf('Power factor is %f leading\n',pf);
+disp('case b');
+// from power circle diagram, radius for maximum power is 61 A
+R2=61; // radius for maximum power
+pmax=(R0^2-R2^2)*r;
+printf('Maximum power per phase is %f KW\n',pmax/1000);
+printf('Maximum power for 3-phase is %f KW\n',(3*pmax)/1000);
+disp('case c');
+l=12; // load on motor in KW
+lp=(l/3)*1000; // per phase load
+ef=(sqrt(r^2+x^2))*(R0-sqrt(R0^2-lp/r));
+printf('Minimum excitation voltage is %f V',ef);
diff --git a/3760/CH5/EX5.4/Ex5_4.sce b/3760/CH5/EX5.4/Ex5_4.sce new file mode 100644 index 000000000..0ee46a4ec --- /dev/null +++ b/3760/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,17 @@ +clc;
+v=3300; // rated voltage of motor
+zs=0.4+%i*5; // synchronous impedance per phase
+E=4000; // excitation EMF
+pi=1000; // input power
+vp=v/sqrt(3); // per phase rated voltage
+ep=E/sqrt(3); // per phase excitation EMF
+al=atand(real(zs),imag(zs));
+t1=(pi*1000)/3;
+t2=(vp^2/abs(zs)^2)*real(zs);
+t3=abs(zs)/(vp*ep); // terms needed to evaluate load angle
+di=asind((t1-t2)*t3)+al; // load angle
+ia=(sqrt(vp^2+ep^2-2*ep*vp*cosd(di)))/abs(zs);
+pf=(pi*1000)/(3*ia*vp);
+// here ep*cos(di)+ia*ra*pf> vp; hence leading power factor
+printf('Line current is %f A\n',ia);
+printf('Power factor is %f leading',pf);
diff --git a/3760/CH5/EX5.41/Ex5_41.sce b/3760/CH5/EX5.41/Ex5_41.sce new file mode 100644 index 000000000..8c342dd70 --- /dev/null +++ b/3760/CH5/EX5.41/Ex5_41.sce @@ -0,0 +1,26 @@ +clc;
+n=1490; // speed of machine in rpm
+p=4; // number of poles
+f=50; // frequency
+v=11000; // rated voltage of machine
+p=20*10^6; // rated power of machine
+v1=30;
+v2=25; // per phase voltage for phase A of machine
+i1=10;
+i2=6.5; // per phase current for phase A of machine
+ns=(120*f)/p; // synchronous speed of machine
+xd=v1/i2; // d-axis synchronous reactance
+xq=v2/i1; // q-axis synchronous reactance
+disp('case a');
+ia=p/(sqrt(3)*v); // armature current
+vt=v/sqrt(3); // per phase armature voltage
+Ef=vt+ia*xq*%i;
+de=atand(imag(Ef),real(Ef)); // load angle
+id=ia*sind(de); // d-axis current
+Ef1=abs(Ef)+id*(xd-xq);
+printf('Per phase excitation value is %f V\n',ceil(Ef1));
+printf('Line value of excitation EMf is %f V\n ',ceil(sqrt(3)*Ef1));
+disp('case 2');
+pr=(vt^2*(xd-xq)*sind(2*de))/(2*xd*xq);
+printf('Reluctance power developed by machine is %f KW per phase\n',pr/1000);
+printf('Total reluctance power developed by machine is %f KW',(3*pr)/1000);
diff --git a/3760/CH5/EX5.43/Ex5_43.sce b/3760/CH5/EX5.43/Ex5_43.sce new file mode 100644 index 000000000..26382f727 --- /dev/null +++ b/3760/CH5/EX5.43/Ex5_43.sce @@ -0,0 +1,22 @@ +clc;
+p=100*10^3; // rated power of alternator
+v=440; // rated voltage of alternator
+m=3; // number of phases
+l1=340; // friction and windage losses
+l2=480; // open circuit core losses
+rf=180; // field winding resistance at 75 degree cel.
+ra=0.02; // armature resistance per phase
+vf=220; // voltage applied to field winding
+pf=0.8; // power factor
+disp('At half load');
+ia=p/(sqrt(3)*v); // full load armature current
+l3=(m*ia^2*ra)/4; // short circuit load loss at half load
+l4=vf^2/rf; // field circuit loss
+lt=l1+l2+l3+l4; // net loss
+n=(1-(lt/((p/2)*pf+lt)))*100;
+printf('Efficiency is %f percent\n',n);
+disp('At full load');
+l3=m*ia^2*ra; // short circuit load loss at full load
+lt=l1+l2+l3+l4; // net loss
+n=(1-(lt/(p*pf+lt)))*100;
+printf('Efficiency is %f percent\n',n);
diff --git a/3760/CH5/EX5.44/Ex5_44.sce b/3760/CH5/EX5.44/Ex5_44.sce new file mode 100644 index 000000000..ebb4f944b --- /dev/null +++ b/3760/CH5/EX5.44/Ex5_44.sce @@ -0,0 +1,16 @@ +clc;
+p=40000; // rated power of machine
+v=400; // rated voltage of machine
+l=1500; // short circuit load loss
+m=3; // number of phases
+ia1=1; // armature current in p.u.
+ra=0.118; // dc armature resistance at 30 degree cel.
+ia2=p/(sqrt(3)*v); // rated armature current
+l1=l/p; // short circuit loss in p.u.
+ra1=l1/ia1^2;
+printf('Effective armature resistance is %f p.u.\n',ra1);
+l2=l/m; // short circuit load loss per phase
+ra2=l2/ia2^2;
+printf('Effective ac armature resistance is %f ohm per phase\n',ra2);
+r=ra2/ra;
+printf('Ratio of ac to dc armature resistance is given as %f ',r);
diff --git a/3760/CH5/EX5.45/Ex5_45.sce b/3760/CH5/EX5.45/Ex5_45.sce new file mode 100644 index 000000000..d1e0cbb64 --- /dev/null +++ b/3760/CH5/EX5.45/Ex5_45.sce @@ -0,0 +1,22 @@ +clc;
+p=500*10^3; // rated power of alternator
+v=11000; // rated voltage of alternator
+m=3; // number of phases
+l1=1500; // friction and windage losses
+l2=2500; // open circuit core losses
+ra=4; // armature resistance per phase
+l3=1000; // field copper loss
+pf=0.8; // power factor
+disp('case a: Half load');
+ia=p/(sqrt(3)*v); // armature current
+l4=(m*ia^2*ra)/4; // short circuit load loss at half load
+lt=l1+l2+l3+l4; // net loss
+n=(1-(lt/((p/2)*pf+lt)))*100;
+printf('Efficiency is %f percent\n',n);
+disp('case b');
+// for maximum efficiency variable losses=constant losses
+iam=sqrt((l1+l2+l3)/(m*ra)); // armature current at maximum efficiency
+pout=m*(v/sqrt(3))*iam*pf; // output power ta maximum efficiency
+lt=2*(l1+l2+l3); // net losses
+nm=(1-(lt/(pout+lt)))*100;
+printf('Maximum efficiency is %f percent\n',nm);
diff --git a/3760/CH5/EX5.46/Ex5_46.sce b/3760/CH5/EX5.46/Ex5_46.sce new file mode 100644 index 000000000..20511a3a1 --- /dev/null +++ b/3760/CH5/EX5.46/Ex5_46.sce @@ -0,0 +1,16 @@ +clc;
+l=1800; // total load on factory
+pf=0.6; // power factor
+pfn=0.95; // desired power factor
+// from phasor diagram 5.107
+l1=l/pf; // load in VA
+a1=acosd(pf); // phase angle between terminal voltage and armature current
+a2=acosd(pfn); // phase angle corresponding to desired power factor
+k1=l1*sind(a1); // KVAr of load
+k2=l*tand(a2); // combined KVAr
+disp('case a');
+s=k1-k2;
+printf('Synchronous condenser rating is %f KVA\n',floor(s));
+disp('case b');
+r=sqrt(l^2+k2^2);
+printf('Total KVA of factory is %f KVA',r);
diff --git a/3760/CH5/EX5.47/Ex5_47.sce b/3760/CH5/EX5.47/Ex5_47.sce new file mode 100644 index 000000000..4665a68f7 --- /dev/null +++ b/3760/CH5/EX5.47/Ex5_47.sce @@ -0,0 +1,24 @@ +clc;
+l0=300; // total load on factory
+pf=0.6; // lagging power factor
+n=88; // percentage efficiency of motor
+pfn=0.9; // desired power factor
+l1=60; // mechanical load to be supplied
+// from phasor diagram 5.108
+pi=l1/(n/100); // synchronous motor input
+lt=pi+l0; // combined load
+disp('case a');
+k=lt/pfn;
+printf('Total load is %f KVA\n',k);
+disp('case b');
+a1=acosd(pf); // phase angle between terminal voltage and armature current
+a2=acosd(pfn); // phase angle corresponding to desired power factor
+k1=l0*tand(a1); // KVAr of load
+k2=lt*tand(a2); // combined KVAr
+s=k1-k2; // leading KVAr supplied by synchronous motor
+r=sqrt(s^2+pi^2);
+printf('Capacity of synchronous motor is %f KVA\n',r);
+disp('case c');
+pfs=pi/r;
+printf('Synchronous motor operating power factor is %f leading',pfs);
+
diff --git a/3760/CH5/EX5.48/Ex5_48.sce b/3760/CH5/EX5.48/Ex5_48.sce new file mode 100644 index 000000000..491c0f712 --- /dev/null +++ b/3760/CH5/EX5.48/Ex5_48.sce @@ -0,0 +1,15 @@ +clc;
+p0=1000; // full load power rating of substation
+pf=0.71; // lagging power factor
+pfn=0.87; // desired power factor
+// from phasor dagram 5.109
+p1=p0*pf; // load KW
+p2=sqrt(p0^2-p1^2); // load KVAr
+pn=p0*pfn; // new power delivered to load
+p0n=pn/pf; // new load KVA
+pl=p0n-p0;
+printf('Permissible additional load at %f lagging power factor is %f KVA\n',pf,pl);
+p2n=sqrt(p0n^2-pn^2); // new load KVAr
+p2ns=sqrt(p0^2-pn^2); // new load KVAr with the use of synchronous condensor
+R=p2n-p2ns;
+printf('Rating of synchronous condensor is %f KVA',R);
diff --git a/3760/CH5/EX5.49/Ex5_49.sce b/3760/CH5/EX5.49/Ex5_49.sce new file mode 100644 index 000000000..f17b1c6d4 --- /dev/null +++ b/3760/CH5/EX5.49/Ex5_49.sce @@ -0,0 +1,16 @@ +clc;
+p=4000; // load taken by industrial plant in KW
+pf=0.8; // lagging power factor
+l=400; // rating of induction motor to be replaced by synchronous motor
+n=0.9; // efficiency of induction motor and synchronous motor
+pf1=0.9; // lagging power factor at which induction motor operates
+pf2=0.8; // leading power factor at which synchronous motor operates
+A=p-%i*p*tand(acosd(pf)); // complex power of plant
+pi=l/pf1; // power input to induction motor
+B=pi-%i*pi*tand(acosd(pf1)); // complex power requirement of induction motor
+C=pi+%i*pi*tand(acosd(pf2)); // complex power requirement of synchronous motor
+pfn=cosd(atand(imag(A-B+C),real(A-B+C)));
+printf('New power factor of the plant is %f lagging\n',pfn);
+r=(abs(A-B+C)/sqrt(3))/(p/(sqrt(3)*pf)); // ratio of new line current to original line current
+pr=(1-r)*100;
+printf('Percentage reduction in line current is %f percent',pr);
diff --git a/3760/CH5/EX5.5/Ex5_5.sce b/3760/CH5/EX5.5/Ex5_5.sce new file mode 100644 index 000000000..4ea7fe6f3 --- /dev/null +++ b/3760/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,21 @@ +clc;
+v=230; // rated voltage of motor
+f=50; // frequency
+p=4; // number of poles
+zs=0.6+3*%i; // synchronous impedance
+ia1=10; // current drawn by motor at upf
+ia2=40; // final current after load is inceased to certain value
+vt=v/sqrt(3); // per phase voltage
+al=atand(real(zs),imag(zs));
+Ef=sqrt((vt-ia1*real(zs))^2+(ia1*imag(zs))^2); // excitation EMF
+t1=(ia2*abs(zs))^2;
+t2=Ef^2+vt^2;
+t3=-2*Ef*vt; // terms needed to evaluate load angle
+de=acosd((t1-t2)/t3); // load angle
+pi=(Ef*vt*sind(de-al))/abs(zs)+(vt^2*real(zs))/abs(zs)^2; // input power
+pf=pi/(vt*ia2);
+printf('Power factor is %f lagging\n',pf);
+pd=3*(pi-ia2^2*real(zs)); // developed power
+ns=(120*f)/p; // synchronous speed
+T=(pd*60)/(2*%pi*ns);
+printf('Torque developed is %f N-m',T);
diff --git a/3760/CH5/EX5.53/Ex5_53.sce b/3760/CH5/EX5.53/Ex5_53.sce new file mode 100644 index 000000000..a192ba3bd --- /dev/null +++ b/3760/CH5/EX5.53/Ex5_53.sce @@ -0,0 +1,44 @@ +clc;
+m=3; // number of phases
+p=2; // number of poles
+P=4*10^6; // rated power of generator
+v=11000; // rated voltage of generator
+as=72; // armature slots
+cs=4; // conductor per armature slot
+rs=24; // rotor slots
+rp=10; // rotor slot angular pitch
+cr=20; // conductors per rotor slot
+z=0.1+2*%i; // armature leakage impedance per phase
+pf=0.8; // lagging power factor
+vt=v/sqrt(3); // terminal voltage
+ia=P/(sqrt(3)*v); // full load armature current
+// Open circuit characteristics have been plotted using table given in question.Per phase value of excitation voltage is obtained fron table
+IF=[ 40 80 120 160 200 240 280 320 360];
+EA=[ 2490 4980 7470 9390 10620 11460 12030 12450 12660 ];
+plot(IF,EA/sqrt(3));
+xlabel('Field current');
+ylabel('open circuit voltage');
+title('open circuit characteristics');
+Er=vt+ia*(pf-%i*sqrt(1-pf^2))*z; // air gap voltage
+printf('Air gap voltage is %f V\n',abs(Er));
+disp('Corresponding to magnitude of air gap voltage value of field MMF in terms of field current is obtained from O.C.C (for textbook refer fig. 5.114)');
+Fr=242; // field MMF in terms of field current
+q=rs/p; // rotor slots per pole
+kd=sind(q*rp/2)/(q*sind(rp/2)); // distribution factor
+kp=1 ; // coil span factor for full pitch field coil
+kw=kd*kp; // winding factor
+Nf=(rs*cr)/p; // total field turns
+F1f=(4*kw*Nf)/(%pi*p); // ratio of fundamental field mmf per pole to field current
+Nph=(as*cs)/(m*p); // series turn per phase
+q1=as/(m*p); // armature slots per pole per phase
+v1=(p*180)/as; // armature slot angular pitch
+kd=(sind(q1*v1/2))/(q1*sind(v1/2)); // distribution factor
+kw=kd*kp; // winding factor
+Fa=(0.9*m*Nph*ia*kw)/(p*F1f); // armature mmf in terms of field current
+B=acosd(pf)+atand(imag(Er),real(Er)); // power factor angle + angle by which air gap voltage leads terminal voltage
+Ff=sqrt(Fr^2+Fa^2-2*Fr*Fa*cosd(90+B)); // equivalent field current
+printf('Equivalent field current is %f A\n',Ff);
+// corresponding to equivalent field current, excitation voltage is obtained from O.C.C
+Ef=7168; // excitation EMF per phase
+vr=((Ef-vt)/vt)*100;
+printf('Voltage regulation at full load %f lagging power factor is %f percent',pf,vr);
diff --git a/3760/CH5/EX5.54/Ex5_54.sce b/3760/CH5/EX5.54/Ex5_54.sce new file mode 100644 index 000000000..0959e9af5 --- /dev/null +++ b/3760/CH5/EX5.54/Ex5_54.sce @@ -0,0 +1,15 @@ +clc;
+p=2*10^6; // rated power of alternator
+v=11000; // rated voltage of alternator
+zs=0.3+5*%i; // synchronous impedance per phase
+pf=0.8; // lagging power factor
+vt=v/sqrt(3); // terminal voltage
+ia=p/(sqrt(3)*v); // full load armature current
+// with vt as reference phasor
+Ef=vt+ia*(pf-sqrt(1-pf^2)*%i)*zs;
+// now excitation level is same but load power fcator is leading
+printf('Load current is %f A\n',ia);
+de=cosd(atand(imag(Ef),real(Ef))); // angle between excitation and terminal voltage
+vt=abs(Ef)*(de+sqrt(1-de^2)*%i)-ia*(pf+sqrt(1-pf^2)*%i)*zs;
+printf('Terminal voltage at %f leading power factor is %f V per phase\n',pf,abs(vt));
+printf('Line terminal voltage is %f KV',(sqrt(3)*abs(vt))/1000);
diff --git a/3760/CH5/EX5.55/Ex5_55.sce b/3760/CH5/EX5.55/Ex5_55.sce new file mode 100644 index 000000000..2c0d0c89b --- /dev/null +++ b/3760/CH5/EX5.55/Ex5_55.sce @@ -0,0 +1,14 @@ +clc;
+p=30*10^6; // rated power of alternator
+v=11000; // rated voltage of alternator
+zs=0.005+0.70*%i; // p.u synchronous reactance
+Ef=1.5; // p.u. excitation EMF
+ia=1; // p.u. armature current
+vt=1; // p.u. terminal voltage
+t1=Ef^2-(real(zs)*ia)^2-(imag(zs)*ia)^2-1;
+t2=sqrt((2*ia*real(zs))^2+(2*ia*imag(zs))^2);
+t3=atand((2*ia*real(zs))/(2*ia*imag(zs))); // terms needed to find out power factor
+pf=cosd(asind(t1/t2)-t3);
+printf('Power factor is %f lagging\n',pf);
+de=acosd((ia*abs(zs)^2-Ef^2-vt^2)/(-2*Ef*vt));
+printf('Load angle is %f degrees',de);
diff --git a/3760/CH5/EX5.56/Ex5_56.sce b/3760/CH5/EX5.56/Ex5_56.sce new file mode 100644 index 000000000..583f094a1 --- /dev/null +++ b/3760/CH5/EX5.56/Ex5_56.sce @@ -0,0 +1,26 @@ +clc;
+xd=1.2; // pu d-axis synchronous reactance
+xq=0.8; // pu q-axis synchronous reactance
+xe=0.1; // pu external reactance
+vb=1; // voltage of infinite bus
+pf=0.9; // lagging power factor
+disp('case a');
+// vb=vt-j*ia*xe -(1)where ia is armature current
+// ia=ia*(pf-%i*sqrt(1-pf^2)); // complex form of armature current
+// vt*ia=1 therefore ia=1/vt solving equation 1 we get a quadratic equation in vt whose terms are
+t1=1;
+t3=-2*xe*sqrt(1-pf^2)-vb;
+t5=(xe*sqrt(1-pf^2))^2-(pf*xe)^2; // terms of quadratic equation in terminal voltage
+p= [t1 0 t3 0 t5];
+vt=roots(p);
+ia=1/vt(2); // pu armature current
+printf('Generator terminal voltage is %f pu\n',vt(2));
+printf('Armature current is %f pu\n',ia);
+disp('case b');
+Ef=vt(2)+ia*(pf-%i*sqrt(1-pf^2))*%i*xq;
+de=atand(imag(Ef),real(Ef));
+pa=acosd(pf); // power factor angle
+id=ia*sind(de+pa); // d-axis component of armature current
+Ef=abs(Ef)+id*(xd-xq);
+printf('Load angle is %f degrees\n',de);
+printf('Excitation voltage is %f pu',Ef);
diff --git a/3760/CH5/EX5.57/Ex5_57.sce b/3760/CH5/EX5.57/Ex5_57.sce new file mode 100644 index 000000000..ecc525058 --- /dev/null +++ b/3760/CH5/EX5.57/Ex5_57.sce @@ -0,0 +1,20 @@ +clc;
+xd=0.85; // reactance along d-axis
+xq=0.55; // reactance along q-axis
+vt=1; // pu bus voltage
+Ef=1.2; // pu excitation EMF
+// P=(Ef*vt*sin(de))/xd + (vt^2/2)*((1/xq)-(1/xd))*sin(2*de) where p is power and de is load angle
+// for maximum power dp/dde(derivative with respect to load angle) is zero. Solving we get a quadratic equation whose terms are
+p=[ (vt^2/2)*((1/xq)-(1/xd))*4 (Ef*vt)/xd -(vt^2/2)*((1/xq)-(1/xd))*2 ];
+l=roots(p);
+an=l(2);
+de=acos(an)*(180/%pi); // load angle
+
+pmax=(Ef*vt*sin(de*(%pi/180)))/xd + (vt^2/2)*((1/xq)-(1/xd))*sin(2*de*(%pi/180));
+printf('Maximum power output that motor can supply without loss of synchronization is %f pu\n',pmax);
+// cos(de)=(vt^2/p)*((xd-xq)/(xd+xq))*sin(de)^3 where de is load angle for minimum excitation EMF
+// by trial and error value of de is
+de=63;
+P=1; // pu power
+Ef=(P-((vt^2/2)*((xd-xq)/(xd*xq))*sind(2*de)))/((vt/xd)*sind(de));
+printf('Minimum excitation EMF for machine to stay in synchronism is %f pu\n',Ef);
diff --git a/3760/CH5/EX5.58/Ex5_58.sce b/3760/CH5/EX5.58/Ex5_58.sce new file mode 100644 index 000000000..70efa2c40 --- /dev/null +++ b/3760/CH5/EX5.58/Ex5_58.sce @@ -0,0 +1,17 @@ +clc;
+p=3*10^6; // rated power of alternator
+v=11000; // rated voltage of alternator
+r=0.4; // per phase effective resistance
+vl=12370; // line to line voltage at zero leading power factor
+i=100; // load current at zero power factor
+pf=0.8; // lagging power factor at which voltage regulation has to be determined
+vt=vl/sqrt(3); // per phase terminal voltage
+Ef=v/sqrt(3); // per phase excitation EMF
+ia=p/(sqrt(3)*v); // full load phase current
+// for zero power factor load angle=0
+zs=(vt-Ef)/i; // synchronous impedance
+xs=sqrt(zs^2-r^2); // synchronous reactance
+// From phasor diagram
+Ef1=sqrt((Ef*pf+ia*r)^2+(Ef*sqrt(1-pf^2)+ia*xs)^2); // excitation EMF at 0.8 power factor
+vr=((Ef1-Ef)/Ef)*100;
+printf('Voltage regulation at %f lagging power factor is %f percent',pf,vr);
diff --git a/3760/CH5/EX5.59/Ex5_59.sce b/3760/CH5/EX5.59/Ex5_59.sce new file mode 100644 index 000000000..970281870 --- /dev/null +++ b/3760/CH5/EX5.59/Ex5_59.sce @@ -0,0 +1,17 @@ +clc;
+v=11000; // voltage of infinite bus
+po=15*10^6; // output power of alternator
+pf=0.8; // operating power factor of synchronous machine
+p=130; // percentage increase in excitation EMF
+m=3; // number of phases
+ia=po/(sqrt(3)*pf*v); // per phase armature current
+vb=v/sqrt(3); // per phase bus voltage
+//from phasor diagrams in fig 5.117(a) and 5.117(b)
+xs=(sqrt(((p/100)*vb)^2-(vb*pf)^2)-(vb*sqrt(1-pf^2)))/ia; // synchronous reactance
+printf('Synchronous reactance of machine is %f ohms\n',xs);
+de=asind((po*xs)/(m*vb^2));
+printf('Load angle of machine before excitation EMF is increased is %f degrees\n',de);
+pf=cosd(de/2);
+printf('Power factor of the machine before excitation EMF is increased is %f leading\n',pf);
+ia=(2*vb*sind(de/2))/xs;
+printf('Armature current of the machine before excitation EMF is increased is %f A',ia);
diff --git a/3760/CH5/EX5.6/Ex5_6.sce b/3760/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..848eec94f --- /dev/null +++ b/3760/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,18 @@ +clc;
+v=6600; // rated voltage of motor
+zs=1.5+12*%i ; // per phase synchronous impedance
+pi1=1000; // input power
+pf=0.8; // power factor
+pi2=1500; // power at which power factor is to be found out
+vt=v/sqrt(3); // per phase voltage
+al=atand(real(zs),imag(zs));
+ia=(pi1*1000)/(sqrt(3)*v*pf);
+Ef=sqrt((vt*pf-ia*real(zs))^2+(vt*sqrt(1-pf^2)+ia*imag(zs))^2); // excitation EMF
+t1=(pi2*1000)/3;
+t2=(vt^2/abs(zs)^2)*real(zs);
+t3=abs(zs)/(vt*Ef); // terms needed to evaluate load angle
+di=asind((t1-t2)*t3)+al; // load angle
+ia=(sqrt(vt^2+Ef^2-2*Ef*vt*cosd(di)))/abs(zs); // new armature current
+pfn=((pi2-pi1)*1000)/(ia*vt);
+// as Ef*cos(di)+ia*ra> vt hence leading power factor
+printf('New power factor is %f leading',pfn);
diff --git a/3760/CH5/EX5.7/Ex5_7.sce b/3760/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..d74e6e665 --- /dev/null +++ b/3760/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,16 @@ +clc;
+v=2300; // rated voltage of motor
+xs=12 ; // per phase synchronous reactance
+p=200000; // VA rating of motor
+l1=120000; // initial load
+l2=60000; // final load
+vt=v/sqrt(3); // rated per phase voltage
+ia=l1/(3*vt); // minimum armature current
+ia1=1.5*ia; // armature current at reduced load (50% increment)
+pf=1/1.5; // power factor
+Ef=sqrt((vt*pf)^2+(vt*sqrt(1-pf^2)+ia1*xs)^2); // excitation EMF
+de=asind((l2*xs)/(3*vt*Ef)); // new load angle
+ia2=(sqrt(vt^2+Ef^2-2*Ef*vt*cosd(de)))/xs; // new armature current
+printf('New value of armature current is %f A\n',ia2);
+pfn=l2/(3*vt*ia2);
+printf('Power factor at new armature current is %f leading',pfn);
diff --git a/3760/CH5/EX5.8/Ex5_8.sce b/3760/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..f9282a7a3 --- /dev/null +++ b/3760/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,11 @@ +clc;
+ef=1.2; // ratio of excitation voltage to rated per phase voltage
+i=0.7; // ratio of armature current to rated current
+r=0.01; // percentage resistance of motor
+x=0.5; // percentage reactance of motor
+// as per the expression given in book
+t1=ef^2-(r*i)^2-(x*i)^2-1;
+t2=sqrt((2*i*r)^2+(2*i*x)^2);
+t3=atand((2*i*r)/(2*i*x)); // terms needed to find out power factor
+pf=cosd(asind(t1/t2)-t3);
+printf('Power factor is %f lagging',pf);
diff --git a/3760/CH5/EX5.9/Ex5_9.sce b/3760/CH5/EX5.9/Ex5_9.sce new file mode 100644 index 000000000..630bb9e06 --- /dev/null +++ b/3760/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,34 @@ +clc;
+v=400; // rated voltage of motor
+zs=0.13+%i*1.3 ; // per phase synchronous impedance
+p=100000; // VA rating of motor
+l=4000; // stray losses
+pl=75000; // power delivered to load
+disp('case a');
+il=p/(sqrt(3)*v); // line current
+vt=v/sqrt(3); // per phase rated voltage
+pd=pl+l ; // power developed
+poh=3*il^2*real(zs);
+lt=poh+l; // total losses
+pi=pl+lt; // input power
+pf=pi/p; // power factor
+n=(1-(lt/pi))*100; // efficiency
+printf('Power factor is %f\n',pf);
+printf('Efficiency is %f percent\n',n);
+Ef1=round(sqrt((vt*pf-il*real(zs))^2+(-vt*sqrt(1-pf^2)+il*imag(zs))^2)); // excitation EMF
+de=atand((-vt*sqrt(1-pf^2)+il*imag(zs))/(vt*pf-il*real(zs)))+acosd(pf); // load angle
+printf('Excitation EMf at under excitation is %f v\n',Ef1);
+printf('Load angle at under excitation is %f degrees \n',de);
+Ef2=round(sqrt((vt*pf-il*real(zs))^2+(vt*sqrt(1-pf^2)+il*imag(zs))^2)); // excitation EMF
+de=atand((vt*sqrt(1-pf^2)+il*imag(zs))/(vt*pf-il*real(zs)))-acosd(pf); // load angle
+printf('Excitation EMf at over excitation is %f v\n',Ef2);
+printf('Load angle at over excitation is %f degrees\n',de);
+i=pi/(sqrt(3)*v);
+printf('Input current is %f A\n',i);
+disp('caes b');
+de=acosd(real(zs)/abs(zs)); // load angle
+pmax=((vt*Ef1)/abs(zs))-((Ef1^2*real(zs))/abs(zs)^2);
+pt=pmax*3;
+printf('Load angle for maximum power output is %f degrees\n',de);
+printf('Maximum output per phase is %f W\n',pmax);
+printf('Total maximum output is %f W\n',pt);
diff --git a/3760/CH6/EX6.1/Ex6_1.sce b/3760/CH6/EX6.1/Ex6_1.sce new file mode 100644 index 000000000..d8590e025 --- /dev/null +++ b/3760/CH6/EX6.1/Ex6_1.sce @@ -0,0 +1,14 @@ +clc;
+// after changing dc supply terminals from phase a to phase b
+disp('case a');
+P=2; // number of poles
+te=(2/P)*120;
+printf('Number of mechanical degrees through which rotor moves is %d degrees\n',te);
+disp('case b');
+P=4; // number of poles
+te=(2/P)*120;
+printf('Number of mechanical degrees through which rotor moves is %d degrees\n',te);
+disp('case c');
+P=6; // number of poles
+te=(2/P)*120;
+printf('Number of mechanical degrees through which rotor moves is %d degrees\n',te);
diff --git a/3760/CH6/EX6.10/Ex6_10.sce b/3760/CH6/EX6.10/Ex6_10.sce new file mode 100644 index 000000000..634d1fc96 --- /dev/null +++ b/3760/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,78 @@ +
+
+clc;
+
+//from 6.9 problem
+P=4;
+r1=0.15;
+x1=0.45;
+r2=0.12;
+x2=0.45;
+Xm=28.5;
+s=0.04;
+V=400;
+f=50;
+Pfixed=400;
+t=1.2; // rotor effective turns ratio
+
+//for part a
+//According to the conditions and diagram
+t1=complex(r1,x1);
+t2=complex(0,Xm);
+t3=complex(r1,x2+Xm);
+Ze=(t1*t2)/(t3);
+Re=real(Ze);
+Xe=imag(Ze);
+t4=complex(Re,(x2+Xe));
+SmT=(r2)/(sqrt((Re*Re)+((x2+Xe)*(x2+Xe))));
+Ve=(V/sqrt(3))*(Xm/(x2+Xm));
+Ws=(4*%pi*f)/P;
+Tem=(3/Ws)*Ve^2*(1/2)*(1/(Re+sqrt(Re^2+(x2+Xe)^2)));
+Pm=Tem*(1-SmT)*Ws;
+Psh=Pm-Pfixed;
+Tsh=Psh/(Ws*(1-SmT));
+mprintf('for part a \n slip = %f \n maximun torque = %f Nm \n power output = %f KW \n',SmT,Tem, Psh/1000);
+
+
+//for part b
+s=1;
+I2st=(Ve)/(sqrt((r2+Re)*(r2+Re)+(x2+Xe)*(x2+Xe)));
+Test=(3/Ws)*I2st*I2st*(r2);
+mprintf(' for part b rotor current = %f A \n torque = %f Nm \n',I2st,Test);
+
+
+//for part c
+R=sqrt(Re^2+(x2+Xe)^2)-r2;
+Ra=R/(t^2);
+mprintf('for part c \n external resisitance value is = %f Ohm \n',Ra);
+
+//for part d
+s1=0.04;
+Pm=((3*(Ve)*(Ve))*r2*((1-s1)/s1))/(((Re+r2+((r2*(1-s1)/s1))))*((Re+r2+((r2*(1-s1)/s1))))+((x2+Xe)*(x2+Xe)));
+mprintf('for part d \n power developed is %f KW \n',Pm/1000);
+
+//for part e
+SmP=(r2)/(sqrt(((Re+r2)*(Re+r2))+((x2+Xe)*(x2+Xe)))+r2);
+Pmn=((3/2)*Ve*Ve)/(Re+r2+sqrt((r2+Re)*(r2+Re)+(x2+Xe)*(x2+Xe)));
+mprintf('for part e \n slip = %f \n power developed = %f KW',SmP,Pmn/1000);
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.11/Ex6_11.sce b/3760/CH6/EX6.11/Ex6_11.sce new file mode 100644 index 000000000..2e9a99d24 --- /dev/null +++ b/3760/CH6/EX6.11/Ex6_11.sce @@ -0,0 +1,73 @@ +clc;
+P=4;
+r1=0.15;
+x1=0.45;
+r2=0.12;
+x2=0.45;
+Xm=28.5;
+s=0.04;
+V=400;
+f=50;
+Pfixed=400;
+
+//from problem 6.10
+Re=0.1476;
+Xe=0.443;
+r2=0.12;
+x2=0.45;
+
+a=Xm/(x2+Xm);
+//Ve=a*V1;
+Wr=(4*%pi*f)/P;
+b=(3/Wr)*(1/2)*(1/((Re)+(sqrt((Re*Re)+((x2+Xe)*(x2+Xe))))));
+//Tem=b*Ve*Ve
+
+//for part a
+V1=230;
+Ve1=a*V1;
+Tem1=b*Ve1*Ve1;
+mprintf('for part a \n maximum internal torque developed is %f Nm \n',Tem1);
+
+//for part b
+V2=115;
+Ve2=a*V2;
+Tem2=b*Ve2*Ve2;
+mprintf('for part b \n maximum internal torque developed is %f Nm \n',Tem2);
+
+//for f=25 Hz
+Xe1=(1/2)*Xe;
+x21=(1/2)*x2;
+Ws1=(1/2)*Wr;
+
+
+//for part c
+V3=115;
+Ve3=a*V3;
+Tem3=(3/Ws1)*Ve3*Ve3*(1/2)*(1/((Re)+(sqrt((Re*Re)+((x21+Xe1)*(x21+Xe1))))))
+mprintf('for part c \n maximum internal torque developed is %f Nm \n',Tem3);
+
+//for f=5 Hz
+Xe2=(1/10)*Xe;
+x22=(1/10)*x2;
+Ws2=(1/10)*Wr;
+
+
+//for part d
+f3=5; //f3=(1/10)*f
+V4=23;
+Ve4=a*V4;
+Tem4=(3/Ws2)*Ve4*Ve4*(1/2)*(1/((Re)+(sqrt((Re*Re)+(((x22+Xe2)*(x22+Xe2)))))))
+mprintf('for part d \n maximum internal torque developed is %f Nm \n',Tem4);
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.13/Ex6_13.sce b/3760/CH6/EX6.13/Ex6_13.sce new file mode 100644 index 000000000..724c4c804 --- /dev/null +++ b/3760/CH6/EX6.13/Ex6_13.sce @@ -0,0 +1,82 @@ +//answer match + roots
+
+clc;
+Pm=10000;
+V=400;
+f=50;
+smT=0.1;
+P=4;
+Ns=(120*f)/P;
+
+//for (i)
+disp('(i)');
+//As per given conditions the slip is given by equation Sfl2-0.4Sfl+0.01=0
+V=[1 -0.4 0.01];
+R=roots(V);
+Sfl=R(2);
+Nr=Ns*(1-Sfl);
+mprintf('The slip is %f \n The rotor speed is %f r.p.m',Sfl,ceil(Nr));
+
+//for (ii)
+disp('(ii)');
+Pg=Pm/(1-Sfl);
+Prot=Sfl*Pg;
+mprintf('The rotor ohmic loss is %f W \n',Prot);
+
+//for (iii)
+disp('(iii)');
+Tefl=Pg/(2*3.14*(Ns/60));
+Test=(4*Tefl)/((smT)+(1/smT));
+mprintf('starting torque is %f Nm \n',Test);
+
+//for (iv)
+disp('(iv)');
+a=sqrt(((Sfl*Sfl)+(smT*smT))/((Sfl)*(Sfl)*(1+(smT)*(smT))));
+mprintf('starting current = %f full load current\n',a);
+
+//for (v)
+disp('(v)');
+// answer is slightly different in book
+b=sqrt((1/2)*(1+(smT/Sfl)^2));
+mprintf('stator current at maximun torque = %f full load current \n',b);
+
+//for (vi)
+disp('(vi)');
+E=(Pm/Pg)*100;
+mprintf('full load efficiency is = %f percent\n',E);
+
+//for (vii)
+disp('(vii)');
+//As per given conditions
+smT1=3*smT;
+mprintf('New slip value is %f \n',smT1);
+
+//for (viii)
+disp('(viii)');
+//According to the given conditions s1(2)-1.2s+0.09
+VV=[1 -1.2 0.09];
+RR=roots(VV);
+s1=RR(2);
+Nr1=Ns*(1-s1);
+mprintf('full load slip is %f rotor speed is %f r.p.m',s1,Nr1);
+
+//for (ix)
+disp('(ix)');
+Test1=((2)/((1/0.3)+(0.3)))*(2*Tefl);
+mprintf('starting torque is %f Nm \n',Test1);
+
+//for (x)
+disp('(x)');
+c=sqrt((s1^2+smT1^2)/(s1^2*(1+smT1^2)));
+mprintf('starting current = %f full load current \n',c);
+
+//for (xi)
+disp('(xi)');
+Protfl=s1*Pg;
+mprintf('Rotor ohmic loss at full load torque is %f W \n',Protfl);
+
+//for (xii)
+disp('(xii)');
+Pm1=(1-s1)*Pg;
+E=Pm1/Pg;
+mprintf('Efficiency is %f percent',E*100);
diff --git a/3760/CH6/EX6.14/Ex6_14.sce b/3760/CH6/EX6.14/Ex6_14.sce new file mode 100644 index 000000000..e72918dfc --- /dev/null +++ b/3760/CH6/EX6.14/Ex6_14.sce @@ -0,0 +1,40 @@ +
+clc;
+Pm=60000;
+P=6;
+s=0.04;
+V=400;
+smT=0.2;
+f=50;
+Ns=(120*f)/P;
+
+Ws=(2*%pi*Ns)/60;
+Wr=Ws*(1-s);
+Tefl=Pm/Wr;
+
+//for part a
+Tem=(((smT/s)+(s/smT))/2)*Tefl;
+mprintf('for part a \n the maximun torque is %f Nm\n',Tem);
+
+//for part b
+Prot=(s/(1-s))*(Pm);
+mprintf('for part b \n the rotor ohmic loss is %f W\n',Prot);
+
+//for part c
+smT1=2*smT;
+mprintf('for part c \n THe new slip is %f \n',smT1);
+
+//for part d
+//On analysis the slip is given by
+s2=0.084;
+mprintf('for part d \n full load slip is %f \n',s2);
+
+//for part e
+T2=Pm/((Ws)*(1-s2));
+mprintf('for part e \n the full load torque is %f Nm\n',T2);
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.15/Ex6_15.sce b/3760/CH6/EX6.15/Ex6_15.sce new file mode 100644 index 000000000..e3e1159cc --- /dev/null +++ b/3760/CH6/EX6.15/Ex6_15.sce @@ -0,0 +1,19 @@ +
+clc;
+sfl=0.05; //Full load slip
+//Test/Tem=a
+//Tfl/Tem=b
+a=1/2;
+b=1/1.6;
+//As per the given equation we get smT1^2-2.5smT1+1=0
+Q=[1 -2.5 1];
+R=roots(Q);
+smT1=R(2);
+
+//For full load slip of 0.05 we get the equation smT2^2-0.20smT2+0.0025
+Q1=[1 -0.20 0.0025];
+R1=roots(Q1);
+smT2=R1(1);
+
+P=((smT1-smT2)/smT1)*100;
+mprintf('Percentage reduction in rotor circuit resistance is %f percent',P);
diff --git a/3760/CH6/EX6.16/Ex6_16.sce b/3760/CH6/EX6.16/Ex6_16.sce new file mode 100644 index 000000000..9ddb18a45 --- /dev/null +++ b/3760/CH6/EX6.16/Ex6_16.sce @@ -0,0 +1,32 @@ +
+clc;
+r2=0.04;
+x2=0.2;
+
+//As per given conditions we get a quadratic equation in smT which is smT^2-4*smT+1
+t1=1; t2=-4; t3=1;
+p=[ t1 t2 t3];
+smT=roots(p);
+
+r22=x2*smT(2);
+R=r22-r2;
+mprintf('The external resistane needed to be inserted is %f Ohm \n',R);
+
+
+//say V=400(Input voltage)
+V=400;
+//without external resistance
+Ist=V/(sqrt((r2)*(r2)+(x2)*(x2)));
+pf=r2/(sqrt((r2)*(r2)+(x2)*(x2)));
+
+//with external resistance
+Ist1=V/(sqrt((r22)*(r22)+(x2)*(x2)));
+pf1=r22/(sqrt((r22)*(r22)+(x2)*(x2)));
+
+a=((Ist-Ist1)/Ist)*100;
+b=((pf1-pf)/pf)*100;
+mprintf('Percentage in starting current is %f \n',a);
+mprintf('Percentage in power factor is %f \n',b);
+
+
+
diff --git a/3760/CH6/EX6.17/Ex6_17.sce b/3760/CH6/EX6.17/Ex6_17.sce new file mode 100644 index 000000000..51e26e646 --- /dev/null +++ b/3760/CH6/EX6.17/Ex6_17.sce @@ -0,0 +1,20 @@ +clc;
+//r2/x2=a
+a=.5;
+Test=25;
+
+//for part a
+disp('For part a ');
+//b=3(V1)2/r2Ws
+//As per given conditions
+b=Test*5;
+//When rotor resistace is doubled
+Test1=b*(1/4);
+mprintf('The starting torque is %f Nm\n',Test1);
+//for part b
+disp('For part b');
+//resisance is half
+Test2=b*(2/17);
+
+
+mprintf('The starting torque is %f Nm',Test2);
diff --git a/3760/CH6/EX6.18/Ex6_18.sce b/3760/CH6/EX6.18/Ex6_18.sce new file mode 100644 index 000000000..a869e26dd --- /dev/null +++ b/3760/CH6/EX6.18/Ex6_18.sce @@ -0,0 +1,27 @@ +//equation
+clc;
+//Test/Tefl=1.5;
+d=1.5;
+//Tem/Tefl=2.5;
+e=2.5;
+
+//for part a
+
+//d=Test/Tefl;
+//equation of torque gives following equation
+Q=[1 -3.33 1];
+R=roots(Q);
+smT=R(2);
+mprintf('The slip at maximun torque is %f \n',smT)
+
+//for part b
+//equation of torque gives
+Q=[1 -1.665 0.111];
+R=roots(Q);
+sfl=R(2);
+mprintf('The slip at full load is %f \n',sfl)
+
+//for part c
+//I2st=c*Isfl As per torque equation
+c=sqrt((d)*(1/sfl));
+mprintf('The rotor current = %f times full load current \n',c)
diff --git a/3760/CH6/EX6.19/Ex6_19.sce b/3760/CH6/EX6.19/Ex6_19.sce new file mode 100644 index 000000000..676c0b650 --- /dev/null +++ b/3760/CH6/EX6.19/Ex6_19.sce @@ -0,0 +1,10 @@ +clc;
+Te=200;
+s=0.04;
+c=4; //given multiplying factor of leakage reactance
+
+//3V*V=a*WS
+a=Te*s*(((1+(1/s))*(1+(1/s)))+((c+c)*(c+c)));
+Test=a*(1/((1+1)*(1+1)+(c+c)*(c+c)));
+Tem=a*(1/2)*(1/(1+sqrt((1)*(1)+(c+c)*(c+c))));
+mprintf('The starting torque is %f Nm \n The maximun Torque is %f Nm',Test,Tem);
diff --git a/3760/CH6/EX6.2/Ex6_2.sce b/3760/CH6/EX6.2/Ex6_2.sce new file mode 100644 index 000000000..d9d044910 --- /dev/null +++ b/3760/CH6/EX6.2/Ex6_2.sce @@ -0,0 +1,40 @@ +clc;
+Nf=1440; //full load speed
+f=50; //frequency
+
+disp('case a');
+
+P=fix((120*f)/Nf); //formula for finding poles
+mprintf('The number of Poles is %d\n',P);
+
+disp('case b');
+
+
+Ns=(120*f)/P; //finding synchronous speed
+s=(Ns-Nf)/Ns; //finding slip at full load
+f2=s*f; //rotor frequency
+mprintf('The full load slip is %f and the rotor frequency is %f Hz\n',s,f2);
+
+disp('case c');
+
+
+//speed of stator field w.r.t stator structure is Ns
+Nss=Ns;
+// answer for speed of stator field with respect to stator structure is given wrong in book
+Wss=(2*%pi*Ns)/60;
+Nsr=Ns-Nf; //speed of stator field w.r.t rotor structure
+Wsr=(2*%pi*Nsr)/60;
+printf('The speed of stator field w.r.t stator is %f rad/sec ,%f rpm\n and w.r.t rotor is %f rad/sec ,%f rpm\n',Wss,Nss,Wsr,Nsr);
+
+disp('case d');
+
+
+//speed of rotor field w.r.t stator structure is Nf+Ns
+Nrr=(120*f2)/P; //speed of rotor field w.r.t rotor structure
+Nrs=Nf+Nrr;
+// answer for speed of rotor field with respect to rotor structure is given wrong in book
+Wrs=(2*%pi*Nrs)/60;
+
+Wrr=(2*%pi*Nrr)/60;
+//The stator and rotor fields are stationary w.r.t to each other
+printf('The speed of rotor field w.r.t stator structure is %f rad/sec, %f rpm\n and w.r.t rotor structure is %f rad/sec, %f rpm and speed of rotor field w.r.t stator field is 0',Wrs,Nrs,Wrr,Nrr);
diff --git a/3760/CH6/EX6.20/Ex6_20.sce b/3760/CH6/EX6.20/Ex6_20.sce new file mode 100644 index 000000000..8c7d78bca --- /dev/null +++ b/3760/CH6/EX6.20/Ex6_20.sce @@ -0,0 +1,36 @@ +clc;
+sA=0.05; //slip
+
+//for part a
+disp('for part a ');
+//Torque is proportional to s/r2
+//As per given conditions sB=a*sA
+a=4;
+sB=a*sA;
+mprintf('The slip is %d times previous slip and \n',a);
+
+//for part b
+disp('for part b ');
+//I2 is directly proportional to s/r2
+//As per given conditions I2B=b*I2A
+b=sB/(a*sA);
+//Rotor ohmic losses is directly proportional to I*I*r2
+//As per given conditions P2=c*P1
+c=a*b;
+//As per given conditions Pf2=d*Pf1
+d=b;
+mprintf('rotor current for new rotor resistance is equal to initial rotor current \n Rotor ohmic losses for new rotor resistance=%f times initial ohmic losses \n power factor for new rotor resistance is equal to initial power factor',c);
+
+//for part c
+disp('for part c ');
+//As per given conditions Wa=e*Ws
+e=1-sA;
+//Wb=f*Ws
+b=1-sB;
+//PB=g*PA
+g=b/e;
+mprintf('The power output is reduced to %f times previous value',g);
+
+
+
+
diff --git a/3760/CH6/EX6.21/Ex6_21.sce b/3760/CH6/EX6.21/Ex6_21.sce new file mode 100644 index 000000000..b48ac82d9 --- /dev/null +++ b/3760/CH6/EX6.21/Ex6_21.sce @@ -0,0 +1,27 @@ +clc;
+f=50;
+P=6;
+Pmsh=10000; //Shaft Output
+N=930;
+Pw=600;
+Pf=0.01*Pmsh; //Friction and Windage losses
+Ns=(120*f)/P;
+NmT=800; //Speed at maximum torque
+
+
+//for part a
+disp('for part a');
+sfl=(Ns-N)/Ns;
+Pm=Pmsh+Pf;
+Pg=Pm/(1-sfl);
+Pst=Pg+Pw;
+mprintf('Total Rotor input is %f W \n Total Stator input is %f W \n',Pg,Pst);
+
+//for part b
+disp('for part b');
+smT=(Ns-NmT)/Ns;
+Ws=(2*%pi*Ns)/60;
+Tefl=Pg/Ws;
+Test=(((smT/sfl)+(sfl/smT))/2)*(2/((smT)+(1/smT)))*Tefl;
+mprintf('Maximun Torque is %f Nm',Test);
+
diff --git a/3760/CH6/EX6.22/Ex6_22.sce b/3760/CH6/EX6.22/Ex6_22.sce new file mode 100644 index 000000000..c44f42765 --- /dev/null +++ b/3760/CH6/EX6.22/Ex6_22.sce @@ -0,0 +1,21 @@ +clc;
+Pm=7500;
+V=420;
+f=50;
+P=4;
+s=0.04;
+r1=1.2;
+x1=1.4;
+x2=1.4;
+Xm=38.6;
+
+//As per Thevenin's Equivalent circuit
+Re=(r1*Xm)/(Xm+x2);
+Xe=(x1*Xm)/(x2+Xm);
+Ve=(V/sqrt(3))*(Xm/(x2+Xm));
+r2=(3)*(1-s)*s*Ve*Ve*(1/Pm);
+smT=r2/(sqrt((Re*Re)+((Xe+x2)*(Xe+x2))));
+Tem=((3*Ve*Ve)/((((120*f)/P)/60)*2*%pi))*(1/2)*(1/(Re+(sqrt((Re*Re)+((Xe+x2)*(Xe+x2))))));
+Test=((3*Ve*Ve)/((((120*f)/P)/60)*2*%pi))*(r2/(((Re+r2)*(Re+r2))+((Xe+x2)*(Xe+x2))));
+mprintf('maximum torque is %f Nm \n slip is %f \n starting torque is %f Nm',Tem,smT,Test);
+
diff --git a/3760/CH6/EX6.23/Ex6_23.sce b/3760/CH6/EX6.23/Ex6_23.sce new file mode 100644 index 000000000..177f13087 --- /dev/null +++ b/3760/CH6/EX6.23/Ex6_23.sce @@ -0,0 +1,56 @@ +clc;
+Pm=100000;
+V=420;
+P=6;
+f=50;
+sfl=0.04;
+smT=0.2;
+
+//for part a
+disp('for part a');
+Pg=Pm/(1-sfl);
+Ws=(4*%pi*f)/P;
+Tefl=Pg/Ws;
+//a=Tefl/Tem
+a=(1/(2/((sfl/smT)+(smT/sfl))));
+Tem=a*Tefl;
+mprintf('Maximum Torque is %f Nm \n',Tem);
+
+//for part b
+disp('for part b');
+//b=Test/Tem
+b=2/((1/smT)+(smT));
+Test=b*Tem;
+mprintf('The starting Torque is %f Nm \n',Test)
+
+//for part c
+disp('for part c');
+Prot=sfl*Pg;
+mprintf('Rotor Ohmic losses are %f W \n',Prot)
+
+//for part d
+disp('for part d');
+//Output is proportional to (s(1-s))/r2
+//Given conditions gives the equation as s1*s1-s1+0.0768
+Q=[1 -1 0.0768];
+R=roots(Q);
+s1=R(2);
+mprintf('Slip is %f \n',s1)
+
+//for part e
+disp('for part e');
+Tefl=(Pm/(1-s1))/Ws;
+mprintf('full-load torque is %f Nm \n',Tefl)
+
+//for part f
+disp('for part f');
+smT1=2*smT;
+mprintf('slip at maximum torque is %f',smT1);
+
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.25/Ex6_25.sce b/3760/CH6/EX6.25/Ex6_25.sce new file mode 100644 index 000000000..d24e286fa --- /dev/null +++ b/3760/CH6/EX6.25/Ex6_25.sce @@ -0,0 +1,46 @@ +clc;
+P=10;
+f=50;
+Pm=48000;
+pf=0.8;
+f21=120; //min frequency range
+f22=300; //max frequency range
+Ns=(120*f)/P;
+
+//for f2=300
+Nr1=((120*f21)/P)-Ns;
+//for f2=600
+Nr2=((120*f22)/P)-Ns;
+mprintf('Thus the dc motor changes speed from %f to %f rpm \n',Nr1,Nr2)
+
+//for part b and c
+s1=(Nr1+Ns)/Ns;
+s2=(Nr2+Ns)/Ns;
+Pr=Pm/pf;
+Pr1=Pr/s1;
+Pr2=Pr/s2;
+R1=(s1-1)*Pr1*pf;
+R2=(s2-1)*Pr2*pf;
+T1=(R1*60)/(2*%pi*Nr1);
+T2=(R2*60)/(2*%pi*Nr2);
+// stator should be able to handle higher KVA
+mprintf('KVA rating of induction motor stator is %f KVA\n',Pr1/1000)
+mprintf('DC motor rating is %f KW \n Maximum torque output from DC motor is %f Nm \n',R2/1000,T1);
+
+//for part d
+//When speed is limited to 2700 rpm
+P1=((120*f22)-(120*f))/2700;
+P1=ceil(P1);
+mprintf('Number of Poles is %d \n',P1);
+
+//for part e
+Nr11=((f22*120)/P1)-((120*f)/P1);
+Nr22=((f21*120)/P1)-((120*f)/P1);
+mprintf('Thus the new speed range of dc motor is from %f to %f rpm \n',Nr22,Nr11);
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.26/Ex6_26.sce b/3760/CH6/EX6.26/Ex6_26.sce new file mode 100644 index 000000000..479c80f24 --- /dev/null +++ b/3760/CH6/EX6.26/Ex6_26.sce @@ -0,0 +1,15 @@ +clc;
+f=50;
+P=4;
+Pm=10000; //Rated output
+N=1425;
+Nm=1200; //Speed at which maximun torque is developed
+
+Ns=(120*f)/P;
+s=(Ns-N)/Ns;
+Ws=(2*%pi*Ns)/60;
+Tefl=(Pm/Ws)*(1/(1-s));
+smT=(Ns-Nm)/Ns;
+Tem=Tefl*((s/smT)+(smT/s))*(1/2);
+Test=Tem*(2)*(1/((1/smT)+(smT/1)));
+mprintf('The starting torque is %f Nm',Test);
diff --git a/3760/CH6/EX6.27/Ex6_27.sce b/3760/CH6/EX6.27/Ex6_27.sce new file mode 100644 index 000000000..d8556fde4 --- /dev/null +++ b/3760/CH6/EX6.27/Ex6_27.sce @@ -0,0 +1,49 @@ +clc;
+fs=2; //slip frequency
+V=400;
+f=50;
+V2=340; //New voltage
+f2=40; //New frequency
+smT=0.1; //slip at which it develops maximum torque
+
+//maximun torque's slip is directly proportional to (1/f)
+smT1=(f/f2)*smT;
+
+//Maximun Torque is directly proportional to ((V*V)/(f*f))
+s=fs/f;
+//Ted(Developed Torque) is proportional to (Tem/smT)*(s/smT)
+//Ted1(400V,50Hz)proportional a
+a=((V*V)/(f*f))*(s/smT);
+//equating the developed torque equation
+s1=a*(((f2)*(f2))/((V2)*(V2)))*(smT1);
+fs1=s1*f2;
+mprintf('The new slip frequency is %f Hz',fs1);
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.28/Ex6_28.sce b/3760/CH6/EX6.28/Ex6_28.sce new file mode 100644 index 000000000..3132bc636 --- /dev/null +++ b/3760/CH6/EX6.28/Ex6_28.sce @@ -0,0 +1,46 @@ +clc;
+f=50;
+V=440;
+P=4;
+N=1490; //Rated speed
+N1=1600; //New Speed
+
+Ns=(120*f)/P;
+s=(Ns-N)/Ns;
+//With neglecting resistances and leakage reactances
+//Torque is directly proportional to s/(fr2)
+//Appllying the condition for same torque we get
+//a=s/f
+a=(s/f);
+//Ns/s=b
+b=120/P;
+//s=(Ns-N1)/Ns
+//Using above equation we get equation (f*f)-7500f-400000
+Q=[1 -7500 400000]
+R=roots(Q);
+f1=R(2);
+mprintf('Value of new Frequency is %f Hz',f1);
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.29/Ex6_29.sce b/3760/CH6/EX6.29/Ex6_29.sce new file mode 100644 index 000000000..48d84d2cf --- /dev/null +++ b/3760/CH6/EX6.29/Ex6_29.sce @@ -0,0 +1,60 @@ +//debug
+clc;
+V1=420; //supply voltage
+r1=2.95;
+x1=6.82;
+r2=2.08;
+x2=4.11;
+Iml=6.7; //magnetizing line current
+Pw=269; //core loss
+s=0.03; //slip
+P=12;
+f=50;
+N=(120*f)/P;
+Ns=(120*f)/P;
+
+Im=Iml/sqrt(3);
+//V1=E1+Im(r1+jx1)
+//Above equation on solving gives the solution as E1*E1+52.8E1-175572.65
+Q=[1 52.8 -175572.62];
+R=roots(Q);
+E1=R(2);
+Xm=E1/Im;
+//As per the circuit diagram
+a=r2/s;
+Zf=(((r2/s)+x2*%i)*Xm*%i)/((r2/s)+((x2+Xm)*%i));
+Rf=real(Zf);
+Zab=complex((real(Zf)+r1),(imag(Zf)+x1));
+I1=420/Zab;
+I1M=sqrt((real(I1)*real(I1))+(imag(I1)*imag(I1)));
+an1=atand(imag(I1),real(I1));
+pf=cosd(atand(imag(I1)/real(I1)));
+I2=I1*(Xm*%i)*(1/((r2/s)+((x2+Xm)*%i)));
+an2=atand(imag(I2),real(I2));
+I2M=sqrt((real(I2)*real(I2))+(imag(I2)*imag(I2)));
+T=3*(60/(2*%pi*N))*I1M*I1M*Rf;
+
+mprintf('The power factor is %f Lag\n The input current is %f A lagging by an angle of %f degrees \n The output rotor current is %f A lagging by an angle of %f degrees \n The Torque developed is %f Nm \n',pf,I1M,-an1,I2M,-an2,T);
+
+
+//For maximun Torque
+X1=x1+Xm;
+Re=(r1*Xm)/X1;
+Xe=(x1*Xm)/X1;
+smT=r2/(sqrt((Re)*(Re)+(x2+Xe)*(x2+Xe)));
+Nm=Ns*(1-smT);
+Tem=3*(E1)*(E1)*(1/(Re+(sqrt((Re)*(Re)+(x2+Xe)*(x2+Xe)))))*(1/2)*(1/(2*%pi*(N/60)));
+mprintf('maximum torque developed is %f Nm \n corresponding speed is %f rpm',Tem,Nm);
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.3/Ex6_3.sce b/3760/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..0861c8ed8 --- /dev/null +++ b/3760/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,11 @@ +
+clc;
+f=50; //frequency of stator
+P=6;
+NofO=90; //number of oscillation
+f2=NofO/60; //rotor frequency
+s=f2/f; //slip
+Ns=(120*f)/P; //synchronous speed
+Nr=Ns*(1-s); //rotor speed
+
+mprintf('The rotor speed is %f rpm',Nr);
diff --git a/3760/CH6/EX6.30/Ex6_30.sce b/3760/CH6/EX6.30/Ex6_30.sce new file mode 100644 index 000000000..7db1313f8 --- /dev/null +++ b/3760/CH6/EX6.30/Ex6_30.sce @@ -0,0 +1,61 @@ + +//In solution they have taken different value of speed at rated torque from what is given in question that is why answer is varying
+clc;
+P=4;
+Pm=10000; //OUTPUT POWER
+f=50; //FREQUENCY
+N=1440; //SPEED AT WHICH RATED TORQUE IS OBTAINED
+Ns=(120*f)/P; //SYNCHRONOUS SPEED
+
+s=(Ns-N)/Ns;
+//Torque is directly proportional to the slip
+//As per given conditions
+s1=(1/2)*s;
+Nr=Ns*(1-s1);
+Pm1=(1/2)*(((Pm*60)/(2*%pi*N)))*((2*%pi*Nr)/(60));
+mprintf('The motor speed is %f rpm \n The power output is %f W',Nr,Pm1);
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/3760/CH6/EX6.31/Ex6_31.sce b/3760/CH6/EX6.31/Ex6_31.sce new file mode 100644 index 000000000..3dba3c754 --- /dev/null +++ b/3760/CH6/EX6.31/Ex6_31.sce @@ -0,0 +1,23 @@ +
+clc;
+N=1455;
+Ns=1500; //General case considered in the problem
+s1=(Ns-N)/Ns;
+
+//for V1=0.9V
+//V1/V=a
+a=0.9;
+//T=(3VVs)/(Wsr2)
+//As torque is constant
+s2=(s1)/(a*a);
+Nr=Ns*(1-s2);
+//I=s1V/r2
+//I22/I21=b
+b=(s2*a)/s1;
+//Losses Ratio=c
+R=b*b;
+
+d=((N-Nr)/N)*100;
+e=((R-1)/1)*100;
+mprintf('Percentage reduction in speed is %f percent\n',d);
+mprintf('Percentage reduction in ohmic losses is %f percent\n',e);
diff --git a/3760/CH6/EX6.32/Ex6_32.sce b/3760/CH6/EX6.32/Ex6_32.sce new file mode 100644 index 000000000..f4fa3c183 --- /dev/null +++ b/3760/CH6/EX6.32/Ex6_32.sce @@ -0,0 +1,14 @@ +clc;
+P=7500; // rated power of induction motor
+v=400; // rated voltage of motor
+To=6; // no load torque
+fs=0.04; // full load slip
+p=6; // number of poles
+f=50; // frequency
+ns=(120*f)/p; // synchronous speed
+Tl=(P*60)/(2*%pi*ns*(1-fs)); // full load torque
+s=(To*fs*v^2)/(Tl*(v/2)^2); // slip at no load
+no=ns*(1-s);
+printf('No load speed of motor is %f rpm\n',no);
+
+
diff --git a/3760/CH6/EX6.33/Ex6_33.sce b/3760/CH6/EX6.33/Ex6_33.sce new file mode 100644 index 000000000..56142dbbd --- /dev/null +++ b/3760/CH6/EX6.33/Ex6_33.sce @@ -0,0 +1,20 @@ +clc;
+tr=2.5; // ratio of maximum torque to full load torque
+sm=0.18; // maximum slip
+r=1; // per phase rotor resistance
+x2=r/sm; // rotor reactance
+// using expression for tr we obtain a quadratic equation is s(full load slip) whose terms are
+t1=1;
+t2=-tr*2*sm;
+t3=sm^2;
+t=[ t1 t2 t3 ];
+s=roots(t);
+x=sqrt((2*x2)/(((r/s(2))^2+x2^2)*s(2)));
+printf('Minimum voltage that could be impressed so that motor can supply rated torque is %f times rated voltage or %f percent of rated voltage\n',x,x*100);
+// from expression for maximum torque and full load torque we get a quadratic equation in R(externall resistance) whose terms are
+t1=1;
+t2=2-2*x2;
+t3=1+x2^2-2*x2;
+t=[ t1 t2 t3 ];
+R=roots(t);
+printf('External resistance inserted in rotor circuit is %f ohms\n',R(2));
diff --git a/3760/CH6/EX6.34/Ex6_34.sce b/3760/CH6/EX6.34/Ex6_34.sce new file mode 100644 index 000000000..69f94a821 --- /dev/null +++ b/3760/CH6/EX6.34/Ex6_34.sce @@ -0,0 +1,17 @@ +clc;
+f1=50; // rated frequency of 3- phase induction motor
+f2=40; // applied frequency
+vr=0.9; // ratio of applied voltage to rated voltage
+m=3; // number o phases
+fr=f2/f1; // ratio of frequencies
+ir=fr/vr;
+printf('Ratio of starting current at %d Hz to starting current at %d Hz is %f \n',f1,f2,ir);
+tr=(m/f1)*(f2/m)*(fr/vr)^2;
+printf('Ratio of starting torque at %d Hz to starting torque at %d Hz is %f \n',f1,f2,tr);
+tmr=(m/f1)*(f2/m)*(fr/(vr)^2);
+printf('Ratio of maximum torque at %d Hz to maximum torque at %d Hz is %f \n',f1,f2,tmr);
+vr1=sqrt((m/f1)*(f2/m)*fr^2);
+printf('For the same starting torque ratio of voltage at %d Hz to ratio of voltage at %d Hz is %f\n',f2,f1,vr1);
+vr2=sqrt((m/f1)*(f2/m)*fr);
+printf('For the same maximum torque ratio of voltage at %d Hz to ratio of voltage at %d Hz is %f\n',f2,f1,vr2);
+// answer for ratio of v2/v1 for same starting torque is slightly different from what is given in book
diff --git a/3760/CH6/EX6.35/Ex6_35.sce b/3760/CH6/EX6.35/Ex6_35.sce new file mode 100644 index 000000000..eecf2f645 --- /dev/null +++ b/3760/CH6/EX6.35/Ex6_35.sce @@ -0,0 +1,21 @@ +clc;
+P=60000; // rated power of 3-phase induction motor
+p=4; // number of poles
+f=50; // frequency
+po=3000; // no load losses
+i=0.3; // ratio of rated current to rated voltage when motor is prevented from rotating
+pi=4000; // power input when motor is prevented from rotating
+pr=0.3; //ratio of mechanical losses to no load losses
+pm=pr*po; // mechanical losses
+lsc1=po-pm; // stator core loss
+lsc2=pi/2; // stator copper loss=rotor copper loss
+disp('case a');
+pg=P+pm+lsc2; // air gap power
+s=lsc2/pg;
+printf('Slip at rated load is %f\n',s);
+disp('case b');
+pim=pi/i^2; // power input to motor during blocked rotor test
+pg=pim-lsc1-lsc2; // air gap power
+ws=(4*%pi*f)/p; // synchronous speed
+T=pg/ws;
+printf('Starting torque at rated applied voltage is %f Nm\n',T);
diff --git a/3760/CH6/EX6.36/Ex6_36.sce b/3760/CH6/EX6.36/Ex6_36.sce new file mode 100644 index 000000000..e6d377fe2 --- /dev/null +++ b/3760/CH6/EX6.36/Ex6_36.sce @@ -0,0 +1,11 @@ +clc;
+sm=0.2; // slip
+f1=50; // rated frequency of 3- phase induction motor
+f2=45; // applied frequency
+fr=f2/f1; // ratio of frequenciesir=fr/vr;
+ir=sqrt((sm^2+1)/(sm^2+fr^2));
+printf('Ratio of starting current at %d Hz to starting current at %d Hz is %f \n',f2,f1,ir);
+tr=(sm^2+1)/(sm^2+fr^2);
+printf('Ratio of starting torque at %d Hz to starting torque at %d Hz is %f \n',f2,f1,tr);
+tmr=1/fr;
+printf('Ratio of maximum torque at %d Hz to maximum torque at %d Hz is %f \n',f2,f1,tmr);
diff --git a/3760/CH6/EX6.37/Ex6_37.sce b/3760/CH6/EX6.37/Ex6_37.sce new file mode 100644 index 000000000..a921d307f --- /dev/null +++ b/3760/CH6/EX6.37/Ex6_37.sce @@ -0,0 +1,31 @@ +clc;
+P=20000; // rated power of induction motor
+v=400; // rated voltage of motor
+f=50; // frequency
+m=3; // number of phases
+p=4; // number of poles
+r1=0.2; // stator resistance
+x=0.45; // stator/rotor leakage reactance
+xm=18; // magnetising reactance
+s=0.04; // slip
+pg=P/(1-s); // air gap power
+pr=s*pg; // rotor copper loss
+vp=v/sqrt(3); // per phase voltage
+ve=(vp*xm)/(x+xm); // Thevenin voltage
+re=(r1*xm)/(x+xm); // Thevenin resistance
+xe=(x*xm)/(x+xm); // Thevenin reactance
+// using Thevenin's theorrm and rotor copper loss expression we get a quadratic equation in r2 (rotor resistance) whose terms are
+t1=pr/s^2;
+t2=((2*pr*re)/s)-(m*ve^2);
+t3=pr*((xe+x)^2+re^2);
+t=[ t1 t2 t3];
+r2=roots(t);
+disp('case a');
+ws=(4*%pi*f)/p; // synchronous speed
+Tm=(m*ve^2)/(ws*2*(re+sqrt(re^2+(x+xe)^2)));
+printf('Maximum internal torque is %f Nm\n',Tm);
+Ti=(m*ve^2*r2(1))/(ws*((re+r2(1))^2+(x+xe)^2));
+printf('Initial starting torque is %f Nm\n',Ti);
+disp('case b');
+sm=r2(1)/(sqrt(re^2+(xe+x)^2));
+printf('Slip at maximum torque is %f ',sm);
diff --git a/3760/CH6/EX6.4/Ex6_4.sce b/3760/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..cd614c991 --- /dev/null +++ b/3760/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,31 @@ +clc;
+f1=50; //frequency of supply
+f2=20; //frequency required by the load
+P=4;
+//for part a
+
+Nrf_ss=(120*f1)/P; //Speed of rotor field w.r.t stator structure
+Nrf_rs=(120*f2)/P; //Speed of stator field w.r.t rotor structure
+//Nr (+or-) speed of rotor field w.r.t rotor = speed of stator field w.r.t stator
+//for +ve sign rotor must be driven in the direction of stator field at a speed
+Nr1=Nrf_ss-Nrf_rs;
+Nr2=Nrf_ss+Nrf_rs;
+mprintf('The two speeds are %d and %d \n',Nr1,Nr2);
+
+
+//for part b
+
+//for rotor speed Nr1
+s1=(Nrf_ss-Nr1)/Nrf_ss;
+//for rotor speed Nr2
+s2=(Nrf_ss-Nr2)/Nrf_ss;
+//On evaluation the ratio of voltages is found as
+ R=s1/s2; //R=E1/E2
+mprintf('The ratio of two voltages available at the slip rings at the two speeds is %d',R);
+
+//for part c
+
+
+
+
+
diff --git a/3760/CH6/EX6.41/Ex6_41.sce b/3760/CH6/EX6.41/Ex6_41.sce new file mode 100644 index 000000000..1dcdd6c94 --- /dev/null +++ b/3760/CH6/EX6.41/Ex6_41.sce @@ -0,0 +1,31 @@ +clc;
+P=10000; // rated power of squirrel cage induction motor
+V=400; // rated voltage of motor
+m=3; // number of phases
+// no load test results
+Vo=400; // applied voltage
+io=8; // no load current
+Po=250; // no load power
+// blocked rotor test
+vb=90; // applied voltage
+ib=35; // current
+pb=1350; // input power
+// ac resistance is 1.2 times dc resistance
+rs=0.6; // per phase dc resistance of stator winding
+pr=Po-m*(io/sqrt(3))^2*(1.2*rs); // no load rotational losses
+znl=Vo/(io/sqrt(3)); // no load impedance
+rnl=Po/(m*(io/sqrt(3))^2); // no load resistance
+xnl=sqrt(znl^2-rnl^2); // no load reactance
+zbr=vb/(ib/sqrt(3)); // block rotor test impedance
+Rbr=pb/(m*(ib/sqrt(3))^2); // block rotor resistance
+xbr=sqrt(zbr^2-Rbr^2); // block rotor reactance
+x1=xbr/2;
+xm=xnl-x1;
+X2=xm+x1;
+r2=(Rbr-1.2*rs)*(X2/xm)^2;
+printf('Rotational losses are %f watts\n',pr);
+printf('Stator resistance is %f ohms\n',1.2*rs);
+printf('Rotor resistance is %f ohms\n',r2);
+printf('Magnetising reactance is %f ohms\n',xm);
+printf('Stator reactance is %f ohms\n',x1);
+printf('Rotor reactance is %f ohms',x1);
diff --git a/3760/CH6/EX6.43/Ex6_43.sce b/3760/CH6/EX6.43/Ex6_43.sce new file mode 100644 index 000000000..449e68d60 --- /dev/null +++ b/3760/CH6/EX6.43/Ex6_43.sce @@ -0,0 +1,21 @@ +clc;
+p=10000; // rated power of SCIM
+v=420; // rated voltage of SCIM
+p=4; // number of poles
+f=50; // frequency of SCIM
+// results of blocked rotor test
+vb=210; // applied voltage
+ib=20; // applied current
+pb=5000; // power dissipated
+l=300; // stator core loss
+rs=0.6; // dc stator resistance
+m=3; // number of phases
+R=(rs*3)/2; // per phase stator resistance
+Rs=1.2*R; // Effective stator resistance per phase
+pi=pb*(v/vb)^2; // power input at rated voltage during block rotor test
+is=ib*(v/vb); // stator current at rated voltage during block rotor test
+pg=pi-m*(is/sqrt(3))^2*Rs-l; // air gap power
+ws=(4*%pi*f)/p;
+printf('synchronous speed is %f rad/sec\n',ws);
+T=pg/ws;
+printf('Starting torque is %f Nm',T);
diff --git a/3760/CH6/EX6.44/Ex6_44.sce b/3760/CH6/EX6.44/Ex6_44.sce new file mode 100644 index 000000000..a73fecad5 --- /dev/null +++ b/3760/CH6/EX6.44/Ex6_44.sce @@ -0,0 +1,23 @@ +clc;
+p=6; // number of poles
+m=3; // number of phases
+f=50; // frequency of motor
+P=40000; // rated power of induction motor
+v=400; // rated voltage of induction motor
+// results of blocked rotor test
+vb=200; // applied voltage
+ib=110; // applied current
+pf=0.4; // power factor
+f1=45; // frequency at starting torque is to be determined
+e=380; // voltage at starting torque is to be determined
+vbp=vb/sqrt(3); // per phase voltage during blocked rotor test
+zb=vbp/ib; // total impedance referred to stator
+R=zb*pf; // net resistance referred to stator
+X=zb*(sqrt(1-pf^2)); // net reactance referred to stator
+X=X*(f1/f); // net reactance at frequency=45
+Z=R+X*%i; // impedance at frequency=45
+v1=e/sqrt(3); // per phase stator
+is=v1/(Z); // starting current
+ws=(4*%pi*f)/p; // synchronous speed
+T=(3/ws)*abs(is)^2*(R/2);
+printf('Starting torque is %f Nm',T);
diff --git a/3760/CH6/EX6.45/Ex6_45.sce b/3760/CH6/EX6.45/Ex6_45.sce new file mode 100644 index 000000000..168f5d7eb --- /dev/null +++ b/3760/CH6/EX6.45/Ex6_45.sce @@ -0,0 +1,46 @@ +clc;
+v=400; // rated voltage of motor
+m=3; // number of phases
+r=2; // ratio of leakage reactance of stator to leakage reactance of rotor
+ns=1000; // synchronous speed
+n=960; // speed of motor
+f=50; // frequency
+// no load test results
+Vo=400; // applied voltage
+io=7.5; // no load current
+pfo=0.135; // power factor
+// blocked rotor test
+vb=150; // applied voltage
+ib=35; // current
+pfb=0.44; // power factor
+znl=Vo/(io*sqrt(3)); // no load impedance
+rnl=znl*pfo; // no load resistance
+xnl=sqrt(znl^2-rnl^2); // no load reactance
+zbr=vb/(ib*sqrt(3)); // block rotor test impedance
+Rbr=zbr*pfb; // block rotor resistance
+xbr=sqrt(zbr^2-Rbr^2); // block rotor reactance
+x2=xbr/3; // leakage reactance of rotor
+x1=x2*2; // leakage reactance of stator
+xm=xnl-x1; // magnetising reactance
+r1=Rbr/2; // stator resistance/rotor resistance
+V1=v/sqrt(3); // per phase stator voltage
+Ve=(V1*xm)/(x1+xm); // thevenin voltage
+Re=(r1*xm)/(x1+xm); // thevenin resistance
+Xe=(x1*xm)/(x1+xm); // thevenin resistance
+lr=sqrt(3)*v*io*pfo-m*io^2*r1; // rotational losses
+s=(ns-n)/ns; // slip
+ir=Ve/(Re+(r1/s)+%i*(Xe+x2)); // rotor current at slip
+Pm=m*abs(ir)^2*r1*((1-s)/s);
+disp('case a');
+Psh=Pm-lr;
+printf('Mechanical power output is %f KW\n',Psh/1000);
+disp('case b');
+wr=((2*%pi*f)*(1-s))/m; // speed at which motor is running
+T=Psh/wr;
+printf('Net torque is %f Nm\n',T);
+disp('case c');
+lor=(Pm*s)/(1-s); // rotor/stator ohmic losses
+Tl=lor*2+lr; // total losses
+pi=Tl+Psh; // input power
+ne=Psh/pi;
+printf('Efficiency of motor is %f percent',ne*100);
diff --git a/3760/CH6/EX6.46/Ex6_46.sce b/3760/CH6/EX6.46/Ex6_46.sce new file mode 100644 index 000000000..ca77363ab --- /dev/null +++ b/3760/CH6/EX6.46/Ex6_46.sce @@ -0,0 +1,11 @@ +clc;
+f=60; // frequency
+p=6; // number of poles
+n=1175; // speed of induction motor
+re=0.06; // reduction in frequency
+dv=0.1; // reduction in voltage
+ws1=(120*f)/p; // synchronous speed
+s1=(ws1-n)/ws1; // slip
+s2=((1-re)/((1-dv)^2))*s1; // new slip
+ws2=ws1*(1-s2)*(1-re);
+printf('New operating speed is %f rpm',ws2);
diff --git a/3760/CH6/EX6.47/Ex6_47.sce b/3760/CH6/EX6.47/Ex6_47.sce new file mode 100644 index 000000000..4c12aa0ae --- /dev/null +++ b/3760/CH6/EX6.47/Ex6_47.sce @@ -0,0 +1,60 @@ +clc;
+P=15000; // rated power of induction motor
+V=400; // rated voltage of motor
+f=50; // frequency
+m=3; // number of phases
+po=4; // number of poles
+// no load test results
+Vo=400; // applied line voltage
+io=9; // no load line current
+Po=1310; // power input
+// blocked rotor test
+vb=200; // line voltage
+ib=50; // line current
+pb=7100; // input power
+pfo=po/(sqrt(3)*io*Vo); // no load power factor
+pfb=pb/(sqrt(3)*ib*vb); // short circuit power factor
+isc=(V/vb)*ib; // short circuit current
+printf('Short circuit current is %d A\n',isc);
+// circle diagram is drawn in fig 6.37 with scale 6 A= 1 cm
+disp('case a');
+x=6; // scale
+pps=(V/sqrt(3))*x; // per phase power scale
+fp=P/3; // full load power per phase
+// as per the construction we obtain OP=6.05 which corresponds to full load current
+ifl=x*6.05;
+printf('Full load line current is %f A\n',ifl);
+// from fig angle POV1=29.5;
+fpf=cosd(29.5);
+printf('Full load power factor is %f lagging\n',fpf);
+// full load slip is given by ratio ba/bP where ba=2.5, bP=38.5
+fs=2.5/38.5;
+printf('Full load slip is %f \n',fs);
+ws=(2*%pi*f*120)/(po*60); // synchronous speed
+Ft=(3.85*pps*m)/ws;
+printf('Full load torque is %f Nm\n',Ft);
+// efficiency is given by ratio aP/dP where aP=3.6, dP=4.45
+ne=3.6/4.45;
+printf('Full load efficiency is %f percent\n',ne*100);
+disp('case b');
+// OP turns out to be tangent to circular locus, therefore
+disp('Maximum power factor is 0.87 lagging');
+disp('Maximum line current is 36.3 A');
+disp('case c');
+// according to constructions given in solution we obtain AA'=5.3 from which maximum power output can be calculated
+mpo=5.3*m*pps;
+printf('Maximum output power is %f KW\n',mpo/1000);
+// according to constructions given in solution we obtain CC'=8.45=radius of circle from which maximum power input can be calculated
+mpi=8.45*m*pps+po;
+printf('Maximum input power is %f KW\n',mpi/1000);
+disp('case d');
+// according to constructions given in solution we obtain BB'=6.65 from which maximum torque can be calculated
+Mt=(6.65*m*pps)/ws;
+printf('Maximum torque is %f Nm\n',Mt);
+// maximum slip is given by ratio fb'/BB' where fb'=1.58, BB'=6.65
+s=1.58/6.65;
+printf('Maximum slip is %f \n',s);
+disp('case e');
+// according to constructions given in solution we obtain DG=3.3 from which starting torque can be calculated
+St=(3.3*m*pps)/ws;
+printf('Starting torque is %f Nm\n',St);
diff --git a/3760/CH6/EX6.48/Ex6_48.sce b/3760/CH6/EX6.48/Ex6_48.sce new file mode 100644 index 000000000..1c9688d8f --- /dev/null +++ b/3760/CH6/EX6.48/Ex6_48.sce @@ -0,0 +1,55 @@ +clc;
+P=4500; // rated power of induction motor
+V=400; // rated voltage of motor
+f=50; // frequency
+m=3; // number of phases
+// no load test results
+Vo=400; // applied line voltage
+io=4.2; // no load line current
+Po=480; // power input
+// blocked rotor test
+vb=215; // line voltage
+ib=15; // line current
+pb=1080; // input power
+rs=1.2; // rotor resistance referred to stator per phase
+nt=2; // stator to rotor turns ratio
+pfo=Po/(sqrt(3)*io*Vo); // no load power factor
+pfb=pb/(sqrt(3)*ib*vb); // short circuit power factor
+isc=(V/vb)*(ib*sqrt(3)); // per phase short circuit current
+iop=io/sqrt(3); // per phase no load current
+x=1; // scale 1 A= 1 cm
+// circle diagram is drawn in fig 6.38
+disp('case a');
+// value of maximum torque at starting is not given
+// now we note Bf=4.6 and B'f=1.25 using these values external resistance to be inserted is calculated
+re=(4.6/1.25)*1.2; // external resistance
+printf('External resistance referred to rotor is %f ohms\n',re/nt^2);
+// as per the construction we obtain OB=11.24 which is needed to calculate starting line current
+is=11.24*sqrt(3);
+printf('Starting current is %f A\n',is);
+// angle OBB'=45.5 which is needed to calculate power factor
+pf=cosd(45.5);
+printf('power factor is %f lagging\n',pf);
+pps=x*V; // per phase power scale
+fp=P/m; // full load power per phase
+disp('case b');
+// now torque is 1.25 times full load torque
+// now we note NK=2.9 and N'K=2.1 using these values external resistance to be inserted is calculated
+re=(2.9/2.1)*1.2; // external resistance
+printf('External resistance referred to rotor is %f ohms\n',re/nt^2);
+// as per the construction we obtain ON=14.35 which is needed to calculate starting line current
+is=14.35*sqrt(3);
+printf('Starting current is %f A\n',is);
+// angle ONN'=58.3 which is needed to calculate power factor
+pf=cosd(58.3);
+printf('power factor is %f lagging\n',pf);
+disp('case c');
+// we obtain OH=5.35 which is per phase output current
+// thetag=41.3
+opf=cosd(41.3);
+printf('Operating power factor is %f leading\n',opf);
+po=m*5.35*V*opf;
+printf('Output power is %f KW\n',po/1000);
+// we note HL=3.95 and Ha=4.90 which is needed for efficiency
+ne=3.95/4.9;
+printf('Induction generator efficiency is %f percent',ne*100);
diff --git a/3760/CH6/EX6.49/Ex6_49.sce b/3760/CH6/EX6.49/Ex6_49.sce new file mode 100644 index 000000000..9a4b8a793 --- /dev/null +++ b/3760/CH6/EX6.49/Ex6_49.sce @@ -0,0 +1,37 @@ +clc;
+p=150000; // rated power of induction motor
+v=400; // rated voltage of induction motor
+m=3; // number of phases
+r1=0.02; // stator resistance
+r2=0.04; // rotor resistance
+xm=9.8; // magnetising reactance
+x1=0.2; // leakage reactance of stator or rotor
+s=0.04; // slip
+n=0.93; // efficiency
+disp('case a');
+Zf=(((r2/s)+%i*x1)*%i*xm)/((r2/s)+%i*(xm+x1)); // per phase impedance offered to stator by rorating air gap field
+z=r1+%i*x1; // impedance of stator
+Z=Zf+z; // total impedance
+is=v/(sqrt(3)*abs(Z)); // stator current
+pg=m*is^2*real(Zf); // air gap power
+l1=m*is^2*r1; // stator copper loss
+l2=s*pg; // rotor copper loss
+Tl=((1/n)-1)*p; // total losses
+lr=Tl-(l1+l2); // rotational and core losses
+printf('Rotational and core losses are %f W\n',lr);
+disp('case b');
+s=-0.04; // slip
+Zf=(((r2/s)+%i*x1)*%i*xm)/((r2/s)+%i*(xm+x1)); // per phase impedance offered to stator by rorating air gap field
+Z=Zf+z; // total impedance
+is=v/(sqrt(3)*abs(Z)); // stator current
+pf=cosd(180-atand(imag(Z),real(Z))); // power factor
+printf('Power factor at the generator terminal is %f leading\n',pf);
+po=sqrt(3)*is*v*pf; // electrical output
+printf('Electrical output is %f KW\n',po/1000);
+pg=-m*is^2*real(Zf); // air gap power
+l1=m*is^2*r1; // stator copper loss
+l2=-s*pg; // rotor copper loss
+Tl=l1+l2+lr; // total losses
+pi=Tl+po; // mechanical power input
+ne=po/pi;
+printf('Efficiency is %f percent',ne*100);
diff --git a/3760/CH6/EX6.5/Ex6_5.sce b/3760/CH6/EX6.5/Ex6_5.sce new file mode 100644 index 000000000..c00fb80ec --- /dev/null +++ b/3760/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,35 @@ +clc;
+P=4;
+N=1440;
+f=50;
+r2=0.2;
+x2=1;
+E2=120;
+
+//mistake in Te_fl
+
+
+//for part a
+disp('For part a');
+Ns=(120*f)/P;
+I2_st=120/(sqrt((r2*r2)+(x2*x2)));
+Rpf=(r2)/(sqrt((r2*r2)+(x2*x2)));
+Ws=(2*3.14*Ns)/60;
+Te_st=(3/Ws)*(I2_st)*(I2_st)*(r2/1);
+s_fl=(Ns-N)/Ns;
+I2_fl=(s_fl*E2)/(sqrt(r2*r2+(s_fl*x2*s_fl*x2)));
+Rpf_fl=(r2)/(sqrt(r2*r2+(s_fl*x2*s_fl*x2)));
+Te_fl=((3)*(I2_fl)*(I2_fl)*(r2))/(Ws*s_fl);
+RATIOst_fl=I2_st/I2_fl;
+RATIOtst_tfl=Te_st/Te_fl;
+mprintf('At starting \n the rotor current is %f amp \n Rotor power factor is %f \n Torque is %f rad/sec\n',I2_st,Rpf,Te_st);
+mprintf('At full load \n the rotor current is %f amp \n Rotor power factor is %f \n Torque is %f rad/sec\n',I2_fl,Rpf_fl,Te_fl);
+
+
+//for part b
+disp('For part b');
+r2_n=r2+1;
+I2_stn=E2/(sqrt((r2_n*r2_n)+(x2*x2)));
+Rpf_stn=(r2_n)/(sqrt(((r2_n)*(r2_n))+((x2)*(x2))));
+Te_stn=(3/Ws)*(I2_stn)*(I2_stn)*(r2_n/1);
+mprintf('At starting \n the rotor current is %f amp \n Rotor power factor is %f \n Torque is %f rad/sec\n',I2_stn,Rpf_stn,Te_stn);
diff --git a/3760/CH6/EX6.50/Ex6_50.sce b/3760/CH6/EX6.50/Ex6_50.sce new file mode 100644 index 000000000..fe99ba2f4 --- /dev/null +++ b/3760/CH6/EX6.50/Ex6_50.sce @@ -0,0 +1,43 @@ +clc;
+v=400; // balanced supply voltage
+i=10; // line current
+f=50; // frequency of supply
+m=3; // number of phases
+pf=0.8; // lagging power factor
+pfn=0.9; // improved power factor
+disp('staor in star');
+i=i*(pf-%i*sqrt(1-pf^2)); // complex form of line current
+il=real(i)/pfn; // line current at improved power factor
+il=il*(pfn-%i*sqrt(1-pfn^2)); // complex form of new line current
+//from fig. 6.39
+ic=-(imag(i)-imag(il)); // reactive component of current to be neutralised
+// capacitor bank is star connected
+xcs=v/(ic*sqrt(3)); // capacitance reactance
+Cs=1/(2*%pi*f*xcs); // capacitance
+K=m*ic*v/sqrt(3);
+printf('Per phase value of capacitance for star connected capacitor bank is %f microfarad\n',Cs*10^6);
+printf('Total KVA rating for star connected capacitor bank is %f KVA\n',K/1000);
+// delta connected capacitor bank
+// capacitor bank is delta connected, converting into equivalent star Xstar=Xdelta/3
+xcd=v/(ic*sqrt(3)); // capacitance reactance
+Cd=1/(2*%pi*f*xcd*m); // capacitance
+printf('Per phase value of capacitance for delta connected capacitor bank is %f microfarad\n',Cd*10^6);
+printf('Total KVA rating for delta connected capacitor bank is %f KVA\n',K/1000);
+disp('Stator in delta');
+i=(abs(i)/sqrt(3))*(pf-%i*sqrt(1-pf^2)); // complex form of line current
+il=real(i)/pfn; // line current at improved power factor
+il=il*(pfn-%i*sqrt(1-pfn^2)); // complex form of new line current
+//from fig. 6.39
+ic=-(imag(i)-imag(il)); // reactive component of current to be neutralised
+// capacitor bank is star connected
+// capacitor bank is star connected, converting into equivalent delta Xdelta=3*Xstar
+xcs=v/ic; // capacitance reactance
+Cs=m/(2*%pi*f*xcs); // capacitance
+K=m*ic*v;
+printf('Per phase value of capacitance for star connected capacitor bank is %f microfarad\n',Cs*10^6);
+printf('Total KVA rating for star connected capacitor bank is %f KVA\n',K/1000);
+// delta connected capacitor bank
+xcd=v/ic; // capacitance reactance
+Cd=1/(2*%pi*f*xcd); // capacitance
+printf('Per phase value of capacitance for delta connected capacitor bank is %f microfarad\n',Cd*10^6);
+printf('Total KVA rating for delta connected capacitor bank is %f KVA\n',K/1000);
diff --git a/3760/CH6/EX6.51/Ex6_51.sce b/3760/CH6/EX6.51/Ex6_51.sce new file mode 100644 index 000000000..f2edf37f2 --- /dev/null +++ b/3760/CH6/EX6.51/Ex6_51.sce @@ -0,0 +1,28 @@ +clc;
+v=3300; // balanced supply voltage
+p=500000; // rated power of induction motor
+f=50; // frequency of supply
+m=3; // number of phases
+pf=0.7; // lagging power factor
+pfn=0.9; // improved power factor
+vc=420; // rated voltage of capacitor
+n=0.86; // motor efficiency
+i=p/(sqrt(3)*v*pf*n); // line current
+i=i*(pf-%i*sqrt(1-pf^2)); // complex form of line current
+il=real(i)/pfn; // line current at improved power factor
+il=il*(pfn-%i*sqrt(1-pfn^2)); // complex form of new line current
+//from fig. 6.39
+ic=-(imag(i)-imag(il)); // reactive component of current to be neutralised
+// capacitor bank is delta connected
+// capacitor bank is delta connected, converting into equivalent star Xstar=Xdelta/3
+xcd=v/(ic*sqrt(3)); // capacitance reactance
+Cd=1/(2*%pi*f*xcd*m); // capacitance
+// now each capacitor is rated at 420 V, number of capacitor connected in series is
+n=ceil(v/vc);
+C=Cd*n;
+printf('Per phase value of each capacitance for delta connected capacitor bank is %f microfarad\n',C*10^6);
+// let R be resistance of distribution circuit
+// power lost without capacitor bank is m*abs(i)^2*R
+// power lost with capacitor bank is m*abs(il)^2*R therefore
+ps=(abs(i)^2-abs(il)^2)/abs(i)^2
+printf('Percentage saving in losses is %f percent',ps*100);
diff --git a/3760/CH6/EX6.53/Ex6_53.sce b/3760/CH6/EX6.53/Ex6_53.sce new file mode 100644 index 000000000..0ad0b362a --- /dev/null +++ b/3760/CH6/EX6.53/Ex6_53.sce @@ -0,0 +1,8 @@ +clc;
+fs=0.05; // full load slip
+ir=6; // ratio of starting current and full load current
+t=1; // ratio of starting torque to full load torque
+x=sqrt(t/((ir^2)*fs));
+printf('Tapping point is at %f percent\n',x*100);
+is=x^2*ir;
+printf('Starting current is %f times full load current\n',is);
diff --git a/3760/CH6/EX6.54/ex6_54.sce b/3760/CH6/EX6.54/ex6_54.sce new file mode 100644 index 000000000..c05ecbe28 --- /dev/null +++ b/3760/CH6/EX6.54/ex6_54.sce @@ -0,0 +1,9 @@ +clc;
+vr=0.4; // voltage applied during blocked rotor test as a fraction of rated voltage
+ir=2.5; // line current during blocked rotor test as a fraction of full load current
+tr=0.3; // starting torque as a fraction of rated torque
+is=1.5; // starting current as a fraction of full load current
+isc=ir/vr; // short circuit current at rated load
+x=sqrt(is/isc); // starting current as a fraction of short circuit current at rated load
+T=(x/vr)^2*tr;
+printf('Starting torque is %f percent of full load torque',T*100);
diff --git a/3760/CH6/EX6.55/Ex6_55.sce b/3760/CH6/EX6.55/Ex6_55.sce new file mode 100644 index 000000000..07e3fee52 --- /dev/null +++ b/3760/CH6/EX6.55/Ex6_55.sce @@ -0,0 +1,20 @@ +clc;
+v=440; // rated voltage of distribution circuit
+im=1200; // maximum current that can be supplied
+n=0.85; // efficiency of induction motor
+pf=0.8; // power factor of motor
+ir=5; // ratio of starting current to full load current
+disp('case a');
+il=im/ir; //rated line current
+p=sqrt(3)*v*il*n*pf;
+printf('Maximum KW rating is %f KW\n',p/1000);
+disp('case b');
+x=0.8; // rated of applied voltage and stepped down voltage
+il=im/(x^2*ir); //rated line current
+p=sqrt(3)*v*il*n*pf;
+printf('Maximum KW rating is %f KW\n',p/1000);
+disp('case c');
+// star-delta converter is same as autotransformer starter with 57.8 % tapping therefore
+il=im/(0.578^2*ir); //rated line current
+p=sqrt(3)*v*il*n*pf;
+printf('Maximum KW rating is %f KW\n',p/1000);
diff --git a/3760/CH6/EX6.56/Ex6_56.sce b/3760/CH6/EX6.56/Ex6_56.sce new file mode 100644 index 000000000..9a9bb42b3 --- /dev/null +++ b/3760/CH6/EX6.56/Ex6_56.sce @@ -0,0 +1,17 @@ +clc;
+p=10000; // rated power of motor
+v=400; // rated voltage of motor
+n=0.87; // full load efficiency
+pf=0.85; // power factor
+ir=5; // ratio of starting current to full load current
+tr=1.5; // ratio of starting torque to full load torque
+disp('case a');
+vt=v/sqrt(tr);
+printf('Voltage applied to motor terminal is %f V\n',vt);
+disp('case b');
+ifl=p/(sqrt(3)*v*pf*n); // full load current
+il=(ir*vt*ifl)/v;
+printf('Current drawn by motor is %f A\n',il);
+disp('case c');
+i=(vt/v)*il;
+printf('Line current drawn from supply mains is %f A',i);
diff --git a/3760/CH6/EX6.57/Ex6_57.sce b/3760/CH6/EX6.57/Ex6_57.sce new file mode 100644 index 000000000..af8f8eb2e --- /dev/null +++ b/3760/CH6/EX6.57/Ex6_57.sce @@ -0,0 +1,15 @@ +clc;
+tm=2; // ratio of maximum torque to full load torque
+r=0.2; // per phase rotor resistance referred to stator
+x=2; // per phase reactance referred to stator
+s=r/x; // slip at maximum torque
+disp('case a');
+ts1=(2*s*tm)/(s^2+1);
+printf('Ratio of starting torque to full load torque is %f\n',ts1);
+disp('case b');
+ts2=ts1/3;
+printf('Ratio of starting torque to full load torque with star-delta starter is %f\n',ts2);
+disp('case c');
+t=0.7; // tapping point
+ts3=ts1*t^2;
+printf('Ratio of starting torque to full load torque with autotransformer starter is %f\n',ts3);
diff --git a/3760/CH6/EX6.58/Ex6_58.sce b/3760/CH6/EX6.58/Ex6_58.sce new file mode 100644 index 000000000..3fb3a9549 --- /dev/null +++ b/3760/CH6/EX6.58/Ex6_58.sce @@ -0,0 +1,26 @@ +clc;
+v=400; // supply voltage
+f=50; // frequency of supply
+// results of short circuit test
+V=200; // applied voltage
+i=100; // short circuit current
+pf=0.4; // power factor
+zsc=(V*sqrt(3))/i; // short circuit impedance
+rsc=zsc*pf; // short circuit resistance
+xsc=sqrt(zsc^2-rsc^2); // short circuit reactance
+R=sqrt(((xsc^2+rsc^2)-3*((rsc/3)^2+(xsc/3)^2))/2); // resistance of feeder
+disp('with star connection');
+ts1=(3*(v/sqrt(3))^2*rsc)/((R+rsc)^2+xsc^2); // product of starting torque and synchronous speed
+// now two feeders are connected in parallel therefore net resistace of feeder is
+rp=R^2/(R+R);
+ts2=(3*(v/sqrt(3))^2*rsc)/((rp+rsc)^2+xsc^2); // product of new starting torque and synchronous speed
+pr=(ts2-ts1)/ts1;
+printf('Percentage increase in starting torque with star connection is %f percent\n',pr*100);
+disp('With delta connection');
+ts1=(3*(v/sqrt(3))^2*(rsc/3))/((R+(rsc/3))^2+(xsc/3)^2); // product of starting torque and synchronous speed
+// now two feeders are connected in parallel therefore net resistace of feeder is
+rp=R^2/(R+R);
+ts2=(3*(v/sqrt(3))^2*(rsc/3))/((rp+(rsc/3))^2+(xsc/3)^2); // product of new starting torque and synchronous speed
+pr=(ts2-ts1)/ts1;
+printf('Percentage increase in starting torque with delta connection is %f percent\n',pr*100);
+
diff --git a/3760/CH6/EX6.59/Ex6_59.sce b/3760/CH6/EX6.59/Ex6_59.sce new file mode 100644 index 000000000..7490c790b --- /dev/null +++ b/3760/CH6/EX6.59/Ex6_59.sce @@ -0,0 +1,14 @@ +clc;
+z=1.2+3*%i; // per phase standstill impedance
+v=400; // supply voltage
+l=500; // length of feeder line
+tr=30; // maximum percentage reduction possible in starting torque
+ro=0.02; // resistivity of feeder material
+// equating expression of starting torque with and without feeder we get a quadratic equation in R (feeder resistance) whose terms are
+t1=(1-(tr/100));
+t2=2*real(z)*t1;
+t3=t1*abs(z)^2-abs(z)^2;
+p=[ t1 t2 t3 ];
+R=roots(p);
+A=(ro*l)/R(2);
+printf('Minimum allowable cross section is %f mm^2',A);
diff --git a/3760/CH6/EX6.6/Ex6_6.sce b/3760/CH6/EX6.6/Ex6_6.sce new file mode 100644 index 000000000..f8f0eb3e4 --- /dev/null +++ b/3760/CH6/EX6.6/Ex6_6.sce @@ -0,0 +1,15 @@ +clc;
+P=6;
+f=50;
+N_f=960;
+Ns=(120*f)/P;
+n1=800;
+n2=400;
+
+s_fl=(Ns-N_f)/Ns;
+s_1=(Ns-n1)/Ns;
+s_2=(Ns-n2)/Ns;
+Ratio_1=s_1/s_fl;
+Ratio_2=s_2/s_fl;
+mprintf('The Ratio at %d rpm is %f \n',n1,Ratio_1);
+mprintf('The Ratio at %d rpm is %f \n',n2,Ratio_2);
diff --git a/3760/CH6/EX6.60/Ex6_60.sce b/3760/CH6/EX6.60/Ex6_60.sce new file mode 100644 index 000000000..ca1da5f26 --- /dev/null +++ b/3760/CH6/EX6.60/Ex6_60.sce @@ -0,0 +1,14 @@ +clc;
+f=50; // frequency
+p=10; // number of poles
+pb=120000; // power dissipated in block rotor test
+// stator ohmic losses = rotor ohmic losses
+pr=pb/2; // total rotor loss
+disp('case a');
+ws=(4*%pi*f)/p; // synchronous speed
+Ts=pr/ws;
+printf('Starting torque is %f Nm\n',Ts);
+disp('case b');
+pr=pr/3; // total rotor ohmic loss
+Ts=pr/ws;
+printf('Starting torque is %f Nm\n',Ts);
diff --git a/3760/CH6/EX6.62/Ex6_62.sce b/3760/CH6/EX6.62/Ex6_62.sce new file mode 100644 index 000000000..d5a1a4b77 --- /dev/null +++ b/3760/CH6/EX6.62/Ex6_62.sce @@ -0,0 +1,18 @@ +clc;
+s=0.03; // full load slip
+R=0.015; // rotor resistance per phase
+n=4; // number of step in starter
+al=s^(1/n);
+R1=R/s; // resistance of whole section
+r1=R1*(1-al);
+printf('Resistance of first element is %f ohms\n',r1);
+r2=r1*al;
+printf('Resistance of second element is %f ohms\n',r2);
+r3=r1*al^2;
+printf('Resistance of third element is %f ohms\n',r3);
+r4=r1*al^3;
+printf('Resistance of fourth element is %f ohms\n',r4);
+
+
+
+
diff --git a/3760/CH6/EX6.63/Ex6_63.sce b/3760/CH6/EX6.63/Ex6_63.sce new file mode 100644 index 000000000..a3ae926c9 --- /dev/null +++ b/3760/CH6/EX6.63/Ex6_63.sce @@ -0,0 +1,19 @@ +clc;
+fs=0.02; // full load slip
+ir=2; // ratio of starting current to full load current
+n=5; // number of section
+R=0.03; // rotor resistance
+//ir*ifl=(E2/R)*sm where ifl is full load current and E2 is induced voltage in rotor therefore
+sm=fs*ir; // maximum slip
+al=sm^(1/n);
+R1=R/sm; // resistance of whole section
+r1=R1*(1-al);
+printf('Resistance of first element is %f ohms\n',r1);
+r2=r1*al;
+printf('Resistance of second element is %f ohms\n',r2);
+r3=r1*al^2;
+printf('Resistance of third element is %f ohms\n',r3);
+r4=r1*al^3;
+printf('Resistance of fourth element is %f ohms\n',r4);
+r5=r1*al^4;
+printf('Resistance of fifth element is %f ohms\n',r5);
diff --git a/3760/CH6/EX6.64/Ex6_64.sce b/3760/CH6/EX6.64/Ex6_64.sce new file mode 100644 index 000000000..d3469b9a8 --- /dev/null +++ b/3760/CH6/EX6.64/Ex6_64.sce @@ -0,0 +1,28 @@ +clc;
+v=3300; // rated voltage of induction motor
+p=6; // number of poles
+f=50; // frequency
+t=3.2; // stator to rotor turns
+r=0.1; // rotor resistance
+x=1; // rotor leakage reactance
+R=t^2*r; // rotor resistance referred to stator
+X=t^2*x; // rotor reactance referred to stator
+ws=(4*%pi*f)/p; // synchronous speed
+disp('case a');
+is=(v/sqrt(3))/(sqrt(R^2+X^2));
+printf('Starting current at rated voltage is %f A\n',is);
+Ts=(3*is^2*R)/ws;
+printf('Starting torque at rated voltage is %f Nm\n',Ts);
+disp('case b');
+is=50; // starting current
+// is=Vp/(sqrt((R+rex)^2+X^2) where rex is external resistance and Vp is phase voltage
+// solving above equation we get a quadratic equation in rex whose terms are
+t1=1;
+t2=2*R;
+t3=(R^2+X^2)-((v/sqrt(3))/is)^2;
+p=[ t1 t2 t3 ];
+rex=roots(p);
+printf('External resistance referred to rotor is %f ohms\n',rex(2)/t^2);
+Ts=(3*is^2*(R+rex(2)))/ws;
+printf('Starting torque under new condition is %f Nm\n',Ts);
+
diff --git a/3760/CH6/EX6.65/Ex6_65.sce b/3760/CH6/EX6.65/Ex6_65.sce new file mode 100644 index 000000000..56458efde --- /dev/null +++ b/3760/CH6/EX6.65/Ex6_65.sce @@ -0,0 +1,32 @@ +clc;
+p=6; // number of poles
+v=400; // rated voltage of induction motor
+m=3; // number of phases
+f=50; // frequency
+r1=0.2; // stator resistance
+r2=0.5; // rotor resistance
+xm=48; // magnetising reactance
+x1=2; // leakage reactance of stator or rotor
+n=1050; // speed of motor
+ns=(120*f)/p; // synchronous speed
+s=(ns-n)/ns; // operating slip
+disp('case a');
+Zf=(((r2/s)+%i*x1)*%i*xm)/((r2/s)+%i*(xm+x1)); // per phase impedance offered to stator by rorating air gap field
+z=r1+%i*x1; // impedance of stator
+Z=Zf+z; // total impedance
+is=v/(sqrt(3)*abs(Z)); // stator current
+pf=cosd(atand(imag(Z),real(Z)));
+printf('Stator line current is %f A\n',is);
+disp('case b');
+Po=m*(v/sqrt(3))*is*pf;
+// negative power indicates induction machine is acting as generator
+printf('Power fed back to 3 phase supply system is %f W\n',-Po);
+disp('case c');
+lr=600; // rotational and core losses
+pg=m*is^2*real(Zf); // air gap power
+l1=m*is^2*r1; // stator copper loss
+l2=s*pg; // rotor copper loss
+Tl=lr+l1+l2; // total losses
+pi=-Po+Tl; // mechanical power input
+ne=-Po/pi;
+printf('Efficiency of induction motor is %f percent\n',ne*100);
diff --git a/3760/CH6/EX6.7/Ex6_7.sce b/3760/CH6/EX6.7/Ex6_7.sce new file mode 100644 index 000000000..5a4acb72e --- /dev/null +++ b/3760/CH6/EX6.7/Ex6_7.sce @@ -0,0 +1,47 @@ +clc;
+Psh=10000;
+P=4;
+f=50;
+Pi=660;
+Pw=420;
+I_l=8;
+rs=1.2;
+Pi_fl=11200;
+I_fl=18;
+Ns=(120*f)/P;
+Ws=(2*3.14*Ns)/60;
+
+
+//for part a
+disp('for part a ');
+
+Pstl=Pi-Pw-((3*I_l*I_l*rs)/(3));
+mprintf('The stator core loss is \n %f W \n',Pstl);
+
+//for part b
+disp('for part b ');
+
+Pg=Pi_fl-Pstl-(3*(I_fl/sqrt(3))*(I_fl/sqrt(3))*rs);
+Prl=Pg-Psh;
+mprintf('The rotor loss is %f W \n',Prl);
+
+//for part c
+disp('for part c ');
+
+Prol=Prl-Pw;
+mprintf('The rotor ohmic loss is %f W \n',Prol);
+
+//for part d
+disp('for part d ');
+
+s_fl=Prol/Pg;
+Nr=Ns*(1-s_fl);
+mprintf('Full Load speed of rotor is %f rpm \n',Nr);
+
+//for part e
+disp('for part e ');
+
+Te=Pg/Ws;
+Tsh=Psh/((Ws)*(1-s_fl));
+E=(Psh/Pi_fl)*100;
+mprintf('The internal torque is %f Nm \n The shaft torque is %f Nm \n The motor Efficiency is %f percent',Te,Tsh,E);
diff --git a/3760/CH6/EX6.8/Ex6_8.sce b/3760/CH6/EX6.8/Ex6_8.sce new file mode 100644 index 000000000..e725ae1cb --- /dev/null +++ b/3760/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,11 @@ +clc;
+E=0.9;
+L=45000;
+Tl=((1/0.9)-1)*L;
+
+Rl=(Tl*2)/7; //According to the given conditoins
+Pg=L+Rl+(Rl/2);
+
+s=Rl/Pg;
+
+mprintf('Slip is %f',s);
diff --git a/3760/CH6/EX6.9/Ex6_9.sce b/3760/CH6/EX6.9/Ex6_9.sce new file mode 100644 index 000000000..a4c56a4ec --- /dev/null +++ b/3760/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,39 @@ +
+clc;
+P=4;
+r1=0.15;
+x1=0.45;
+r2=0.12;
+x2=0.45;
+Xm=28.5;
+s=0.04;
+V=400;
+f=50;
+Pfixed=400;
+
+t1=complex((r2/s),x2);
+t2=complex(0,Xm);
+t3=complex((r2/s),(x2+Xm));
+T=(t1*t2)/t3;
+Zab=complex(r1,x1)+T;
+Rf=real(T);
+I1=V/(sqrt(3)*abs(Zab));
+ian=atand(imag(Zab),real(Zab));
+Pf=cosd(ian);
+I1_mag=sqrt(real(I1)*real(I1)+imag(I1)*imag(I1));
+Psti=sqrt(3)*I1_mag*V*Pf;
+Pg=3*I1*I1*Rf;
+ns=(2*f)/P;
+nr=(1-s)*ns;
+Ws=2*3.14*ns;
+Pm=(1-s)*Pg;
+Psh=Pm-Pfixed;
+To=(Psh)/((1-s)*Ws);
+Psto=3*I1_mag*I1_mag*r1;
+Prto=s*Pg;
+Tls=Psto+Prto+Pfixed;
+Pi=Psh+Tls;
+E=(1-(Tls/Pi))*100;
+
+mprintf('staror current = %f amp at lagging phase angle of %f w.r.t input voltage \n rotor speed = %f rps or %f rpm output torque = %f Nm \n Efficiency = %f percent',I1,ian,nr,nr*60,To,E);
+
diff --git a/3760/CH7/EX7.1/Ex7_1.sce b/3760/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..c592868ab --- /dev/null +++ b/3760/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,14 @@ +clc;
+p=6; // number of poles
+c=40; // number of coils
+w=2; // winding pitch for simplex lap winding
+printf('Number of commutator segments is equal to number of coils=%f\n ',c);
+k=1/3; // integer added(or subtracted) to calculate back pitch to make it an odd integer
+yb=((2*c)/p)-k;
+printf('Back pitch is %f \n',yb);
+yf=yb-w;
+printf('Front pitch for progressive winding is %f\n',yf);
+yf=yb+w;
+printf('Front pitch for retrogressive winding is %f\n',yf)
+yc=1;
+printf('For simplex lap winding, commutator pitch is equal to %f ',yc);
diff --git a/3760/CH7/EX7.10/Ex7_10.sce b/3760/CH7/EX7.10/Ex7_10.sce new file mode 100644 index 000000000..4aca2e29d --- /dev/null +++ b/3760/CH7/EX7.10/Ex7_10.sce @@ -0,0 +1,8 @@ +clc;
+disp('b(1)');
+c=12; // number of coils
+r=0.1; // resistance of each coil
+// any one coil connected to commutator segment is in parallel with other 11 series connected coils therefore
+R=11*r; // resistance of 11 coil
+req=(r*R)/(r+R);
+printf('Resistance measured between two adjacent commutator segments is %f ohm\n',req);
diff --git a/3760/CH7/EX7.11/Ex7_11.sce b/3760/CH7/EX7.11/Ex7_11.sce new file mode 100644 index 000000000..d36744414 --- /dev/null +++ b/3760/CH7/EX7.11/Ex7_11.sce @@ -0,0 +1,18 @@ +clc;
+disp('a');
+s=24; // total number of slots
+p=4; // number of poles
+np=3; // number of phases
+ph=60; // phase spread
+// given armature has double layer winding and full pitch coil span
+v=(p*180)/s;
+printf('Slot angular pitch is %d degrees\n',v);
+disp('Number of adjacent slots in one phase belt is');
+disp(ph/v);
+cs=s/p;
+printf('Coil span is %d slots\n',cs);
+disp('Using this data winding table for the three phases is shown in Ex7.11')
+disp('d');
+sp=s/(p*np); // slots per pole per phase
+disp('Distribution factor is');
+disp(sind(ph/2)/(sp*sind(v/2)));
diff --git a/3760/CH7/EX7.12/Ex7_12.sce b/3760/CH7/EX7.12/Ex7_12.sce new file mode 100644 index 000000000..952e75c57 --- /dev/null +++ b/3760/CH7/EX7.12/Ex7_12.sce @@ -0,0 +1,19 @@ +clc;
+disp('a');
+s=24; // total number of slots
+p=4; // number of poles
+np=3; // number of phases
+ph=120; // phase spread
+// given armature has double layer winding and full pitch coil span
+v=(p*180)/s;
+printf('Slot angular pitch is %d degrees\n',v);
+disp('Number of adjacent slots in one phase belt is');
+disp(ph/v);
+cs=s/p;
+printf('Coil span is %d slots\n',cs);
+disp('Using this data winding table for the three phases is shown in Ex7.12')
+disp('d');
+sp=s/(p*np); // slots per pole per phase
+disp('Distribution factor is');
+disp(sind(ph/2)/(sp*sind(ph/(2*sp))));
+
diff --git a/3760/CH7/EX7.13/Ex7_13.sce b/3760/CH7/EX7.13/Ex7_13.sce new file mode 100644 index 000000000..cf76204a3 --- /dev/null +++ b/3760/CH7/EX7.13/Ex7_13.sce @@ -0,0 +1,22 @@ +clc;
+np=3; // number of phase
+sp=9; // slots per pole
+zs=4; // conductors per slot
+f=0.8; // coil span as a fraction of pole pitch
+ph=60; // phase spread
+v=180/sp; // slot angular pitch
+disp('Number of adjacent slots belonging to any phase is ');
+disp(ph/v);
+printf('Pole pitch is %f slots\n',sp);
+c=floor(0.8*sp);
+printf('Coil span is of %f slots\n',c);
+disp('Using this data, winding table is shown in Ex7.13');
+t=(sp*zs*4)/2; // total turns in machine
+spp=sp/np; // slots per pole per phase
+kd=sind(ph/2)/(spp*sind(v/2)); // distribution factor
+cp=c*v; // coil span in degrees
+e=180-cp; // chording angle
+kp=cosd(e/2); // coil span factor
+kw=kd*kp; // winding factor
+tp=(t*kw)/np;
+printf('Number of effective turns per phase is %f',tp);
diff --git a/3760/CH7/EX7.15/Ex7_15.sce b/3760/CH7/EX7.15/Ex7_15.sce new file mode 100644 index 000000000..ad69787dc --- /dev/null +++ b/3760/CH7/EX7.15/Ex7_15.sce @@ -0,0 +1,9 @@ +clc;
+s=24; // number of slots
+p=4; // number of poles
+ph=60; // phase spread
+ap=(p*180)/s; // slot angular pitch
+pp=s/p; // pole pitch
+printf('Pole pitch is %d slots\n',pp);
+printf('slot angular pitch is %d degrees',ap);
+disp('using these data, half coil and whole coil single layer concentric windings diagram are drawn');
diff --git a/3760/CH7/EX7.2/Ex7_2.sce b/3760/CH7/EX7.2/Ex7_2.sce new file mode 100644 index 000000000..a1458d2ca --- /dev/null +++ b/3760/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,20 @@ +clc;
+p=4; // number of poles
+c=12; // number of coils
+// Number of commutator segments is equal to number of coils=12
+// Each coil has two coil side therefore total coil sides are 24
+s=(2*c)/2 ; // total number of slots required
+k=1; // integer added(or subtracted) to calculate back pitch to make it an odd integer
+w=2; // winding pitch
+yb1=((2*c)/p)-k; // back pitch
+// or
+yb2=((2*c)/p)+k; // back pitch
+disp('Back pitch is ');
+disp(yb1,'or',yb2);
+yf1=yb1-2; // front pitch for yb=5
+yf2=yb2-2; // front pitch for yb=7
+disp('front pitch for progressive winding is ');
+disp(yf1,'or',yf2);
+disp('It is desirable that (yb+yf)/2 should be equal to pole pitch that is 6(in terms of coil sides per pole). So choose yb=7 and yf=5');
+disp('Commutator pitch for progressive lap winding is');
+disp(1);
diff --git a/3760/CH7/EX7.3/Ex7_3.sce b/3760/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..36d579d0f --- /dev/null +++ b/3760/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,19 @@ +clc;
+p=4; // number of poles
+s=14; // number of slots
+cp=2; // coil sides per slots
+w=2; // winding pitch
+C=(s*cp)/2; // number of coils
+yb=(2*C)/p;
+disp('Back pitch is');
+disp(yb);
+yf=yb-w;
+disp('Front pitch is');
+disp(yf);
+disp('winding table for progressive lap winding is');
+disp('(1-8)-(3-10)-(5-12)-(7-14)-(9-16)-(11-18)-(13-20)-(15-22)-(17-24)-(19-26)');
+disp('-(21-28)-(23-2)-(25-4)-(27-6)');
+disp('from winding diagram')
+disp('Brush A is touching segments 1 and 2 partly');
+disp('Brush B is at segment 5');
+disp('Brush C is at segment 8');
diff --git a/3760/CH7/EX7.5/Ex7_5.sce b/3760/CH7/EX7.5/Ex7_5.sce new file mode 100644 index 000000000..e8b631ff3 --- /dev/null +++ b/3760/CH7/EX7.5/Ex7_5.sce @@ -0,0 +1,30 @@ +clc;
+disp('case a');
+s=30; // number of slots
+c=60; // number of coils
+p=4; // number of poles
+k=1; // integer added(or subtracted) to calculate back pitch to make it an odd integer
+tc=c*2; // total coil sides
+u=tc/s; // coil sides per slots
+yb1=(tc/p)+k;
+yb2=(tc/p)-k;
+disp('Back pitch is');
+disp(yb1);
+disp('or');
+disp(yb2);
+disp('for back pitch=29, top coil sides 1 and 3 in slot 1 are connected to bottom coil 30 and 32 in slot 8. Due to this arrangement split coils can be avoided. But for back pitch= 31, coil sides 34 which is in slot 9 has to be used, so split coils are needed ')
+disp('case b');
+s=20; // number of slots
+c=60; // number of coils
+p=4; // number of poles
+k=1; // integer added(or subtracted) to calculate back pitch to make it an odd integer
+tc=c*2; // total coil sides
+u=tc/s; // coil sides per slots
+yb1=(tc/p)+k;
+yb2=(tc/p)-k;
+disp('Back pitch is');
+disp(yb1);
+disp('or');
+disp(yb2);
+disp('for back pitch=29, top coil sides 1,3 and 5 are connected to bottom coil 30, 32 and 34. Due to this arrangement split coils cannot be avoided. But for back pitch= 31, coil sides 1,3 and 5 are connected to bottom coil sides 32, 34 and 36 which are in slot 6,so split coils are not needed ');
+
diff --git a/3760/CH7/EX7.6/Ex7_6.sce b/3760/CH7/EX7.6/Ex7_6.sce new file mode 100644 index 000000000..ad8ff7729 --- /dev/null +++ b/3760/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,19 @@ +clc;
+p=4; // number of poles
+s=11; // number of slots
+ts=2; // coil sides per slot
+C=(s*ts)/2; // total coils
+w=((2*C)+2)/(p/2); // winding pitch
+// since both back and front pitch should be odd choose
+Yb=7;
+Yf=5;
+disp('Back pitch is')
+disp(Yb);
+disp('Front pitch is')
+disp(Yf);
+yc=(C+1)/(p/2);
+disp('commutator pitch');
+disp(yc);
+disp('Using this data winding diagram can be drawn');
+disp('Winding table is');
+disp('(1-8)-(13-20)-(3-10)-(15-22)-(5-12)-(17-2)-(7-14)-(19-4)-(9-16)-(21-6)-(11-18)-1');
diff --git a/3760/CH7/EX7.7/Ex7_7.sce b/3760/CH7/EX7.7/Ex7_7.sce new file mode 100644 index 000000000..14c54e7fc --- /dev/null +++ b/3760/CH7/EX7.7/Ex7_7.sce @@ -0,0 +1,20 @@ +clc;
+p=6; // number of poles
+s=72; // number of slots
+ts=4; // number of coil sides per slot
+C=(s*ts)/2; // total number of coils
+// To make commutator pitch an integer one coil is made dummy coil therefore
+C=C-1;
+yc=(C+1)/(p/2);
+disp('commutator pitch');
+disp(yc);
+yw=((2*C)+2)/(p/2);
+disp('Winding pitch is');
+disp(yw);
+// since back and front pitch should be odd choose
+yb=49;
+disp('Back pitch is');
+disp(yb);
+yf=47;
+disp('Front pitch is');
+disp(yf);
diff --git a/3760/CH7/EX7.8/Ex7_8.sce b/3760/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..744df0e7e --- /dev/null +++ b/3760/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,28 @@ +clc;
+p=4; // number of poles
+z=2540; // number of conductors
+s=32; // number of slots
+c=127; // number of commutator sectors=total number of coils
+v=500; // induced voltage required
+f=5*10^-3; // field flux per pole
+a=2; // number of parallel paths
+zs=ceil(z/s); // conductors per slot
+// for zs=80
+Z=zs*s; // total conductors
+t=floor(Z/(2*c)); // turn per coil
+C=Z/(2*t); // actual number of coils
+// It is necessary that actual coils should be same as commutator segments so one coil is made dummy
+disp('commutor pitch is')
+disp((c+1)/(p/2));
+disp('or');
+disp((c-1)/(p/2));
+disp('Winding pitch is')
+disp(((2*c)+2)/(p/2));
+disp('or');
+disp(((2*c)-2)/(p/2));
+disp('For progressive winding, back pitch=65 and front pitch=63');
+disp('For retrogressive winding, back pitch=63 and front pitch=63');
+// since dumy coil is not in circuit, number of active conductor is
+Z=c*t*2;
+n=(v*a*60)/(f*Z*p);
+printf('Speed for required induced voltage is %f rpm',n);
diff --git a/3760/CH7/EX7.9/Ex7_9.sce b/3760/CH7/EX7.9/Ex7_9.sce new file mode 100644 index 000000000..e580e99b3 --- /dev/null +++ b/3760/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,9 @@ +clc;
+p=8; // number of poles
+c=240; // number of coils
+r=10; // number of equilizer ring
+Yeq=(2*c)/p;
+printf('Equipotential pitch is %f coils\n',Yeq);
+Ytp=(2*c)/(r*p);
+printf('Tapping point pitch is %f coils',Ytp);
+disp('Arrangement is shown in tabular form in example 7.9');
diff --git a/3760/CH8/EX8.1/ExA_1.sce b/3760/CH8/EX8.1/ExA_1.sce new file mode 100644 index 000000000..a478018e7 --- /dev/null +++ b/3760/CH8/EX8.1/ExA_1.sce @@ -0,0 +1,14 @@ +clc;
+// answer is given wrong in the book
+d=0.2; // mean diameter of mild steel ring
+ac=50*10^-4; // cross sectional area of core
+uo=4*%pi*10^-7; // free space permeability
+ur=800; // relative permeability
+f=1*10^-3; // required flux
+N=200; // Number of turns
+l=%pi*d // length of core
+R=l/(uo*ur*ac); // reluctance of ring
+printf('reluctance offered by ring is %f AT/Wb\n',R);
+mmf=f*R; // mmf produced in ring
+i=mmf/N;
+printf('current required to produce the desired flux is %f A',i);
diff --git a/3760/CH8/EX8.10/ExA_10.sce b/3760/CH8/EX8.10/ExA_10.sce new file mode 100644 index 000000000..6899006fd --- /dev/null +++ b/3760/CH8/EX8.10/ExA_10.sce @@ -0,0 +1,7 @@ +clc;
+l=0.5; // length of conductor lying along Y-axis
+B=1.2; // Flux density along the X-axis
+v=2; // velocity of conductor
+//e=Blv; for maximum induced emf all the three quantities should be perpendicular to each other
+e=B*l*v;
+printf('Maximum induced EMF in conductor is %f V',e);
diff --git a/3760/CH8/EX8.12/ExA_12.sce b/3760/CH8/EX8.12/ExA_12.sce new file mode 100644 index 000000000..2c6304242 --- /dev/null +++ b/3760/CH8/EX8.12/ExA_12.sce @@ -0,0 +1,22 @@ +clc;
+disp('case a');
+// as per the data taken from Ex 1_3
+rlg=24.948*10^5; // air gap reluctance for example 1_3(a)
+rlc=12.474*10^5; // iron core reluctance for example 1_3(a)
+rl=rlg+rlc; // net reluctance
+N=500; // Number of turns
+L=(N^2/rl)*1000;
+printf('Inductance for case a is %f mH\n',L);
+disp('case b');
+// as per the data taken from Ex 1_3 part(c)
+B=1.254; // calculated flux density
+H=3200; // magnetic field intensity obtained from magnetisation curve corresponding to the flux density calculated
+uo=4*%pi*10^-7; // free space permeability
+ur=B/(H*uo); // relative permeability of iron core
+d=2.85*10^-2; // diameter of cross section
+A=(%pi*d^2)/4; // area of core
+l=0.5; // core length
+rlc=l/(ur*uo*A); // reluctance of iron core for part C
+rt=rlg+rlc; // net reluctance
+L=(N^2/rt)*1000;
+printf('Inductance for case b is %f mH\n',L);
diff --git a/3760/CH8/EX8.13/ExA_13.sce b/3760/CH8/EX8.13/ExA_13.sce new file mode 100644 index 000000000..0c47fce1a --- /dev/null +++ b/3760/CH8/EX8.13/ExA_13.sce @@ -0,0 +1,14 @@ +clc;
+// data taken from Ex A.7, fig A.16
+N1=200; // number of turns in coil 1
+f1=53.97*10^-3; // flux in outer limb containing coil 1
+m1=5000; // mmf for coil 1
+I1=m1/N1; // current in coil 1
+N2=100; // number of turns in coil 2
+f2=43.97*10^-3; // flux in outer limb containing coil 2
+m2=1102; // mmf for coil 2
+I2=m2/N2; // current in coil 2
+L1=(N1*f1)/I1;
+printf('Inductance for coil 1 is %f H\n',L1);
+L2=(N2*f2)/I2;
+printf('Inductance for coil 2 is %f H\n',L2);
diff --git a/3760/CH8/EX8.2/ExA_2.sce b/3760/CH8/EX8.2/ExA_2.sce new file mode 100644 index 000000000..7055ff815 --- /dev/null +++ b/3760/CH8/EX8.2/ExA_2.sce @@ -0,0 +1,13 @@ +clc;
+ur=10000; // relative permeability of iron
+lc=0.5; // core length
+lg=4*10^-3; // air gap length
+N=600; // number of turns
+B=1.2; // desired flux density
+uo=4*%pi*10^-7; // free space permeability
+Ac=25*10^-4; // core area
+mfc=(B*lc)/(uo*ur); // mmf for core
+mfg=(B*lg)/uo; // mmf for air gap
+mft=mfc+mfg; // net mmf
+i=mft/N;
+printf('exciting current required to establish the desired flux is %f A',i);
diff --git a/3760/CH8/EX8.3/ExA_3.sce b/3760/CH8/EX8.3/ExA_3.sce new file mode 100644 index 000000000..7c06456b2 --- /dev/null +++ b/3760/CH8/EX8.3/ExA_3.sce @@ -0,0 +1,35 @@ +clc;
+lc=0.5; // core length in metre
+dc=2.85*10^-2; // diameter of cross section of core
+lg=2*10^-3; // length of air gap
+N=500; // Number oof turns of coil
+f=0.8*10^-3; // air gap flux
+uo=4*%pi*10^-7; // permeability of free space
+HATM=[1500 2210 2720 3500 4100];
+BT=[0.9 1.1 1.2 1.275 1.3];
+plot(HATM,BT);
+xlabel('magnetic field intensity');
+ylabel('flux density');
+disp('case a');
+ur=500; // relative permeability
+Ac=(%pi/4)*dc^2; // Area of core
+Rlg=lg/(uo*Ac); // reluctance of air gap
+Rlc=lc/(uo*ur*Ac); // reluctance of iron core
+Rt=Rlg+Rlc; // Total reluctance
+I=(f*Rt)/N; // Exciting current
+printf('Exciting current in coil is %f A\n',I);
+disp('case b');
+Ag=(%pi/4)*(dc+2*lg)^2; // air gap area
+Rlg=lg/(uo*Ag); // reluctance of air gap
+I=(f*(Rlc+Rlg))/N; // Exciting current
+printf('Exciting current after accounting for flux fringing is %f A\n',I);
+disp('case c');
+Bg=f/Ac; // Air gap flux density
+Atg=(Bg*lg)/uo; // air gap mmf
+// from the plot we can get the values of core flux density and magnetic field intensity
+Bc=1.245; // core flux density in Tesla
+H=3200; // magnetic field intensity in Ats/m
+Atc=H*lc; // core mmf
+mt=Atg+Atc; // total mmf
+I=mt/N; // Exciting current
+printf('Exciting current for third case is %f A',I);
diff --git a/3760/CH8/EX8.4/ExA_4.sce b/3760/CH8/EX8.4/ExA_4.sce new file mode 100644 index 000000000..3b10615de --- /dev/null +++ b/3760/CH8/EX8.4/ExA_4.sce @@ -0,0 +1,24 @@ +clc;
+N=1000; // Number of turns
+f=1*10^-3; // flux in central limb
+Ac=8*10^-4; // Area of central limb
+Ao=4*10^-4; // Area of outer limb
+lg=2*10^-3; // length of air gap
+lc=0.15; // length of central limb in metre
+lo=0.25; // length of outer limb in metre
+uo=4*%pi*10^-7; // permeability of free space
+disp('case a');
+// for ur=infinity, reluctance offered by cast steel is zero
+Rl1=lg/(uo*Ao); // reluctance offered by outer limb
+Rl2=lg/(uo*Ac); // reluctance offered by central limb
+// Assuming magnetic circuit as a close circuit, applying KVl in one of loop gives
+I=(f*(Rl2+(Rl1/2)))/N;
+printf('Coil current for first case is %f A\n',I);
+disp('case b');
+ur=6000; // relative permability
+Rlc1=(lc+lo)/(uo*ur*Ao); // reluctance of outer steel core (including the top)
+Rlc2=(lc)/(uo*ur*Ac); // reluctance offered by central steel core
+r=(Rlc1+Rl1)/2; // resultant of outer reluctance
+// By kVL we get
+I=(f*(Rlc2+Rl2+r))/N;
+printf('Coil current for second case is %f A\n',I);
diff --git a/3760/CH8/EX8.5/ExA_5.sce b/3760/CH8/EX8.5/ExA_5.sce new file mode 100644 index 000000000..4db15d1ed --- /dev/null +++ b/3760/CH8/EX8.5/ExA_5.sce @@ -0,0 +1,22 @@ +clc;
+N=500; // number of turns in central limb
+ac=600*10^-6; // cross sectional area of central limb
+ao=375*10^-6; // cross sectional area of outer limb
+f=0.9*10^-3; // required flux in Weber
+lg=0.8*10^-3; // length of air gap
+lc=180*10^-3; // length of central limb
+lo=400*10^-3; // length of outer limb
+uo=4*%pi*10^-7; // free space permeability
+Bg=f/ac; // air gap flux density
+Hg=Bg/uo; // magnetic field intensity in air gap
+mg=Hg*lg; // mmf required for air gap
+// from fig A.7,for B=1.5T, H for cast steel is 3000Ats/m
+H=3000; // magnetic field intensity for cast steel
+mc=H*lc; // mmf in central limb
+Bo=f/(2*ao); // flux density in each outer limb
+// for B=1.2, H=1400
+H=1400; // magnetic field intensity for cast steel for given flux density
+mo=H*lo; // mmf for outer limb
+// By KVL
+I=(mg+mo+mc)/N;
+printf('The exciting current required to establish the desired flux is %f A',I);
diff --git a/3760/CH8/EX8.6/ExA_6.sce b/3760/CH8/EX8.6/ExA_6.sce new file mode 100644 index 000000000..14fb9ba3e --- /dev/null +++ b/3760/CH8/EX8.6/ExA_6.sce @@ -0,0 +1,28 @@ +clc;
+N=400; // number of turns in coil
+ac=20*10^-4; // area of cemntral limb
+ao=15*10^-4; // area of outer iimb
+lg=1*10^-3; // length of air gap
+lc=40*10^-2; // length of central limb
+lo=60*10^-2; // length of each outer limb
+f=0.9*10^-3; // required flux
+uo=4*%pi*10^-7; // free space permeability
+Bg=f/ao; // air gap flux density
+mg=(Bg*lg)/uo; // mmf or air gap
+// for B=0.6,H=575 AT/m from fig A.7
+H=575; // magnetic flux intensity for given flux density
+mo=H*lo; // mmf of outer limb which contain air gap
+mt=mo+mg; // combined mmf of air gap and outer limb
+// this mmf acts across the other outer limb
+haeb=mt/lo; // magnetic field intensity in outer limb which does not contain air gap
+// for H=1370.77, B=1.19 T from fig A.7
+Bo=1.19; // flux density for given magnetic field intensity
+faeb=Bo*ao; // flux in outer limb
+fnet=f+faeb; // net flux through central limb
+Bc=fnet/ac; // flux density in central limb
+// from fig A.7
+H=1900; // magnetic field intensity for given flux density
+mc=H*lc; // mmf in central limb
+// by KVL in one of the loop
+I=(mc+mt)/N;
+printf('Exciting current required to establish the given flux is %f A',I)
diff --git a/3760/CH8/EX8.7/ExA_7.sce b/3760/CH8/EX8.7/ExA_7.sce new file mode 100644 index 000000000..78976b45f --- /dev/null +++ b/3760/CH8/EX8.7/ExA_7.sce @@ -0,0 +1,24 @@ +clc;
+a=30*10^-4; // cross sectional area of ferromagnetic core
+uo=4*%pi*10^-7; // free space permeability
+ur=4000; // relative permeability for core
+f=10*10^-3; // flux in central limb
+n1=200; // number of turns in coil 1
+m1=5000; // mmf for coil 1
+n2=100; // number of turns in coil 2
+lc=0.3; // length of central limb
+lo=0.6; // length of outer limb
+lg=1*10^-3; // length of air gap
+rc=lc/(uo*ur*a); // reluctance for central limb
+ro=lo/(uo*ur*a); // reluctance for outer limb
+rg=lg/(uo*a); // reluctance for air gap
+mc=f*(rc+rg); // mmf in central limb
+// by KML, flux in outer limb containing coil 1 is
+f1=(m1-mc)/ro;
+// By flux law at node a in fig A.17, flux in outer limb contaning coil 2 is
+f2=f1-f;
+// by mmf law , mmf in coil 2 is
+m2=mc-f2*ro;
+I2=m2/n2; // current in coil 2, upper polarity is assumed positive
+printf('Current in coil 2 is %f A',I2);
+disp('As the mmf of coil 2 is positive , assumed polarity is correct. Therefore terminal A is positive because current enters through it and terminal B is negative ');
diff --git a/3760/CH8/EX8.8/ExA_8.sce b/3760/CH8/EX8.8/ExA_8.sce new file mode 100644 index 000000000..3820eeb03 --- /dev/null +++ b/3760/CH8/EX8.8/ExA_8.sce @@ -0,0 +1,19 @@ +clc;
+l=0.8; // length of conductor
+B=1.2; // flux density of uniform magnetic field
+v=30; // speed of conductor
+disp('case a');
+// conductor motion is normal to field flux
+theta=90; // angle between direction of motion and field flux
+e=B*l*v*sin(theta*(%pi/180));
+printf('EMF induced is %f V\n',e);
+disp('case b');
+// conductor motion is at an angle of 30 degrees from direction of field
+theta=30; // angle between direction of motion and field flux
+e=B*l*v*sin(theta*(%pi/180));
+printf('EMF induced is %f V\n',e);
+disp('case c');
+// conductor motion is parllel to field flux
+theta=0; // angle between direction of motion and field flux
+e=B*l*v*sin(theta*(%pi/180));
+printf('EMF induced is %f V\n',e);
diff --git a/3760/CH8/EX8.9/ExA_9.sce b/3760/CH8/EX8.9/ExA_9.sce new file mode 100644 index 000000000..74e3923a3 --- /dev/null +++ b/3760/CH8/EX8.9/ExA_9.sce @@ -0,0 +1,21 @@ +clc;
+// After deriving the expression
+a=0.1; // side of square coil
+N=100; // number of turns
+n=1000; // speed of rotation on rpm
+B=1; // flux density of a uniform magnetic field
+disp('case a');
+theta=90; // angle of coil with the field
+w=(2*%pi*n)/60; // angular speed of coil in rad/s
+e=N*B*a^2*w*cos(theta*(%pi/180));
+printf('Emf induced in coil is %f V\n',e);
+disp('case b');
+theta=30; // angle of coil with the field
+w=(2*%pi*n)/60; // angular speed of coil in rad/s
+e=N*B*a^2*w*cos(theta*(%pi/180));
+printf('Emf induced in coil is %f V\n',e);
+disp('case c');
+theta=0; // angle of coil with the field
+w=(2*%pi*n)/60; // angular speed of coil in rad/s
+e=N*B*a^2*w*cos(theta*(%pi/180));
+printf('Emf induced in coil is %f V\n',e);
diff --git a/3760/CH9/EX9.3/ExB_3.sce b/3760/CH9/EX9.3/ExB_3.sce new file mode 100644 index 000000000..32b11be6f --- /dev/null +++ b/3760/CH9/EX9.3/ExB_3.sce @@ -0,0 +1,31 @@ +clc;
+vl=400; // line voltage
+z=10+7.5*%i; // load impedance per phase
+disp('For star connected load');
+vp=vl/sqrt(3); // phase voltage
+ip=vp/abs(z);// phase and line current are same in the case of star connected load
+an=atand(-imag(z),real(z));
+pf=cosd(an);
+P=sqrt(3)*vl*ip;
+pa=sqrt(3)*vl*ip*pf;
+pr=-sqrt(3)*vl*ip*sind(an);
+printf('Phase and line currents are %f A\n',ip);
+printf('Power factor is %f lagging \n',pf);
+printf('Total volt ampere is %f VA\n',P);
+printf('Total active power is %f W\n',pa);
+printf('Total reactive power is %f VAr\n',pr);
+disp('For delta connected load');
+vp=vl // phase voltage and line voltage are same in the case of star connected load
+ip=vp/abs(z);
+il=ip*sqrt(3);
+an=atand(-imag(z),real(z));
+pf=cosd(an);
+P=sqrt(3)*vl*il;
+pa=sqrt(3)*vl*il*pf;
+pr=-sqrt(3)*vl*il*sind(an);
+printf('Phase current is %f A\n',ip);
+printf('Line current is %f A\n',il);
+printf('Power factor is %f lagging\n',pf);
+printf('Total volt ampere is %f VA\n',P);
+printf('Total active power is %f W\n',pa);
+printf('Total reactive power is %f VAr\n',pr);
diff --git a/3760/CH9/EX9.4/ExB_4.sce b/3760/CH9/EX9.4/ExB_4.sce new file mode 100644 index 000000000..1f3ac3edd --- /dev/null +++ b/3760/CH9/EX9.4/ExB_4.sce @@ -0,0 +1,15 @@ +clc;
+il=48; // load current(leading)
+p=30; // load power in KW
+vl=500; // line voltage
+f=50; // supply frequency
+pf=(p*1000)/(sqrt(3)*vl*il);
+vp=vl/sqrt(3); // phase voltage
+zp=vp/il; // magnitude of phase impedance
+rp=zp*pf;
+// since current is leading other parameter must be a capacitor
+xc=zp*sqrt(1-pf^2); // reactance
+c=(10^6)/(2*%pi*f*xc);
+disp('circuit parameters are');
+printf('Load resistance is %f ohm\n',rp);
+printf('Load capacitance is %f micro farad',c);
diff --git a/3760/CH9/EX9.5/ExB_5.sce b/3760/CH9/EX9.5/ExB_5.sce new file mode 100644 index 000000000..0261d1582 --- /dev/null +++ b/3760/CH9/EX9.5/ExB_5.sce @@ -0,0 +1,21 @@ +clc;
+zs=10+15*%i; // star connected load per phase
+zd=12-15*%i; // delta connected load per phase
+vl=400; // supply line voltage
+disp('case a');
+// converting delta connected load to star connected load
+zd=zd/3;
+vp=vl/sqrt(3);
+i1=vp/zs; // line current in star connected load
+i2=vp/zd; // line current in delta connected load
+i=abs(i1+i2);
+printf('Total line current is %f A\n',i);
+an=atand(imag(i1+i2),real(i1+i2));
+pf=cosd(an);
+P=(sqrt(3)*vl*i*pf);
+pr=sqrt(3)*vl*i*sqrt(1-pf^2);
+printf('Power factor is %f leading\n',pf);
+printf('Total power is %f W\n',P);
+printf('Total reactve power is %f VAr',pr);
+
+
diff --git a/3760/CH9/EX9.6/ExB_6.sce b/3760/CH9/EX9.6/ExB_6.sce new file mode 100644 index 000000000..0875e2030 --- /dev/null +++ b/3760/CH9/EX9.6/ExB_6.sce @@ -0,0 +1,13 @@ +clc;
+w1=85; // reading of wattmeter 1;
+w2=35; // reading of wattmeter 2;
+P=w1+w2; // total input power
+n=0.85; // efficiency of motor
+vl=1100; // supply voltage
+pf=cosd(atand((sqrt(3)*(w1-w2))/(w1+w2)));
+il=(P*1000)/(sqrt(3)*vl*pf); // line current
+ps=n*P;
+printf('Input power is %f KW\n',P);
+printf('Line current is %f A\n',il);
+printf('power factor is %f lagging\n',pf);
+printf('shaft power is %f KW',ps);
diff --git a/3760/CH9/EX9.7/ExB_7.sce b/3760/CH9/EX9.7/ExB_7.sce new file mode 100644 index 000000000..be6d3d08d --- /dev/null +++ b/3760/CH9/EX9.7/ExB_7.sce @@ -0,0 +1,8 @@ +clc;
+w1=2000; // reading of wattmeter 1 under no load
+w2=-400; // reading of wattmeter 2 under no load, since the connections are reversed that is why negative sign
+theta=atand((sqrt(3)*(w1-w2))/(w1+w2));
+pl=w1+w2;
+pf=cosd(theta);
+printf('No load losses are %f W\n',pl);
+printf('No load power factor is %f lagging',pf);
diff --git a/3760/CH9/EX9.8/ExB_8.sce b/3760/CH9/EX9.8/ExB_8.sce new file mode 100644 index 000000000..588b823f7 --- /dev/null +++ b/3760/CH9/EX9.8/ExB_8.sce @@ -0,0 +1,14 @@ +clc;
+vl=230; // line voltage
+f=50; // frequency of supply
+c=100*10^-6; // value of capacitance in each phase
+vp=230/sqrt(3); // phase voltage
+zp=1/(2*%pi*f*c); // phase impedance
+il=vp/zp; // line current
+// value of cos(theta) is taken from figB.15
+w1=vl*il*cosd(120);
+w2=vl*il*cosd(60);
+printf('Reading of wattmeter 1 is %f W\n',w1);
+printf('Reading of wattmeter 2 is %f W\n',w2);
+p=w1+w2;
+printf('Total input power is %f W',p);
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