diff options
Diffstat (limited to '3760/CH1')
74 files changed, 1682 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)
+
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