diff options
Diffstat (limited to '3760/CH4')
78 files changed, 1850 insertions, 0 deletions
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);
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