Chapter03: Converters for Feeding Electric Motors

Ex3_1:pg-273

In [1]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_1
import math
Rd=2;#Resistance in ohm
Eb=150;#Back emf in V
Vs=400;#Supply voltage in V
Alpha=0.52;#angle in radian
Vdia=((2*math.sqrt(2)*Vs*math.cos(Alpha))/math.pi);
Id=(Vdia-Eb)/Rd;
Irms=Id/math.sqrt(2);
print Id,"=Current in the load in A "

81.2623533876 =Current in the load in A

Ex3_2:pg-273

In [2]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_2
import math
Vs=400;#Supply voltage in V
Id=80.88;#Current in A
Rd=2;#Resistance in ohm
Eb=-150;#Back emf in V
Vdia=Id*Rd+Eb;
a=math.acos((Vdia*math.pi)/(2*math.sqrt(2)*Vs));
Alpha=(a*180)/math.pi;
print Alpha,"=The firing angle in degree "

88.1286627695 =The firing angle in degree

Ex3_3:pg-274

In [3]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_3
import math
Id=80.88;#Current in A
Rd=2;#Resistance in ohm
Xc=0.628;#Reactance in ohm
Vs=400;#Supply voltage in V
Eb=150;#Back emf in V
Z=Id*(Rd+(Xc/math.pi));
a=math.acos((Z-Eb)/(0.9*Vs));
Alpha=(a*180)/math.pi;
c=math.cos(Alpha);
d=-c/11;
b=(Id*Xc*2)/(math.pi*Vs);
X=d-b;
e=math.acos(X);
f=(e*180)/math.pi;
u=f-Alpha;
print u,"=The overlap angle in deg "

5.19163041855 =The overlap angle in deg

Ex3_4:pg-275

In [5]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_4
import math
Vs=200.0;#Supply voltage in V
Rd=12.5;#Resistance in ohm
Xc=0.5;#Reactance in ohm
pf=0.5;#Powerfactor
Vdia=0.9*Vs*pf;
Id=Vdia/(Rd+(Xc/math.pi));
print Id,"=The average value of dc current in A "
Vd=Id*Rd;
print Vd,"=The average value of converter voltage in V "
Vc=Vdia-Vd;
X=pf-((Vc*2.0)/Vs);
c=math.acos(X);
d=(c*180.0)/math.pi;
u=d-60;
print u,"=The overlap angle in deg "
#Result vary due to error in calculation of overlap angle in the textbook

7.10947929815 =The average value of dc current in A 
88.8684912269 =The average value of converter voltage in V 
0.745818730364 =The overlap angle in deg

Ex3_5:pg-276

In [7]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_5
import math
f=50.0;#Frequency in Hz
Rd=2.5;#Resistance in ohm
Lc=0.005;#Inductance in mH
Vs=220.0;#Supply voltage in V
pf=1;#Powerfactor
pf1=0.866;#Powerfactor
Xc=2*math.pi*f*Lc;
Z=Rd+((2*Xc)/math.pi);
Vdia=0.9*Vs*pf;
Id=Vdia/Z;
print Id,"=The average value of load current in A "
Vd=Id*Rd;
Vdc=Vdia-Vd;
a=(1-((Vdc*2)/Vdia));
b=math.acos(a);
u=(b*180.0)/math.pi;
print u,"=The overlap angle u in deg "
Vdia1=0.9*Vs*pf1;
Id1=Vdia1/Z;
Vd1=Id1*Rd;
Vdc1=Vdia1-Vd1;
V=pf1-((Vdc1*2)/Vs);
c=math.acos(V);
d=(c*180.0)/math.pi;
u1=d-30;
print u1,"=The overlap angle u1 in deg "
#Result vary due to error in calculation of overlap angle in the textbook

56.5714285714 =The average value of load current in A 
64.6230664748 =The overlap angle u in deg 
35.1257218105 =The overlap angle u1 in deg

Ex3_6:pg-277

In [9]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_6
import math
Vs=220.0;#Supply voltage in V
f=50.0;#Frequency in Hz
Eb=-200.0;#Back emf in V
Rd=3.0;#Resistance in ohm
Vdc=200.0;# voltage in V
Xc=0.314;#Reactance in ohm
L=0.001;#Inductance in mH
pf=-0.5;#Powerfactor
Vdia=0.9*Vs*pf;
Id=(Vdia-Eb)/(Rd+((2*Xc)/math.pi));
Vd=Id*Rd+Eb;
a=-pf+((Vd*2)/Vdc);
b=math.acos(a);
c=(b*180.0)/math.pi;
u=c-120;
print u,"=The overlap angle in deg "
#Result vary due to error in calculation of overlap angle in the textbook

3.57960292596 =The overlap angle in deg

Ex3_7:pg-278

In [10]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_7
import math
Id=50.0;#Current in A
Vs=220.0;#Supply voltage in V
Vdio=257.4;# voltage in V
f=50.0;#Frequency in Hz
L=0.0015;#Inductance in mH
pf=0.866;#Powerfactor 
Xc=2*math.pi*f*L;
Vdia=1.17*Vs*pf;
Vd=Vdia-((3*Id*Xc)/(2*math.pi));
Vc=Vdia-Vd;
a=pf-((Vc*2)/Vdio);
b=math.acos(a);
c=(b*180.0)/math.pi;
u=c-30;
print u,"=the overlap angle in deg "

8.86857843179 =the overlap angle in deg

Ex3_8:pg-280

In [11]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_8
import math
Rd=2.5;#Resistance in ohm
V=250;# voltage in V
f=50;#Frequency in Hz
Vs=150;#Supply voltage in V
pf=-0.5;#Powerfactor
Eb=-250;#Back emf in V
Xc=0.636;#Reactance in ohm
Vdia=1.17*Vs*pf;
Id=(Vdia-Eb)/Rd;
print Id,"=load current in A "
Ith=(Id*Xc)/2;	
print Ith,"=Average value of load current in A "
Irms=math.sqrt(3)*Ith;
print Irms,"=Rms value of load current in A "
#Result vary due to error in calculation of current in the textbook

64.9 =load current in A 
20.6382 =Average value of load current in A 
35.7464109768 =Rms value of load current in A

Ex3_9:pg-280

In [12]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_9
import math
L=0.003;#Inductance in mH
Id=64.9;#Current in A
V=162.25;#voltage in V
Vs=150;#Supply voltage in V
f=50;#Frequency in Hz
Rd=2.5;#Resistance in ohm
Eb=-250;#Back emf in V
pf=-0.5;#Powerfactor
Xc=2*math.pi*f*L;
Vdia=(Id*(Rd+((3*Xc)/(2*math.pi))))+Eb;
a=Vdia/(1.17*Vs);
b=math.acos(a);
c=(b*180)/math.pi;
Alpha=-0.3338;#angle in radian
X=(3*Id*Xc)/(math.pi*Vs);
d=math.acos(Alpha-X);
e=(d*180)/math.pi;
u=e-c;
print u,"=The overlap angle in deg "
#Result vary due to error in calculation of overlap angle in the textbook

26.8325105187 =The overlap angle in deg

Ex3_10:pg-280

In [13]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_10
import math
Vs=400;#Supply voltage in V
f=50;#Frequency in Hz
Rd=15;#Resistance in ohm
pf=0.2588;#Powerfactor
Vdia=1.35*Vs*pf;
print Vdia,"=Average value of load voltage in V "
Id=Vdia/Rd;
print Id,"=Average value of load current in A "
P=Vdia*Id;	
print P,"=Power dissipation in W "

139.752 =Average value of load voltage in V 
9.3168 =Average value of load current in A 
1302.0414336 =Power dissipation in W

Ex3_11:pg-281

In [14]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_11
import math
Alpha=75;#angle in degree
a=math.cos(Alpha);
b=a/3.6;
pf=(3*b)/math.pi;
print pf,"=The power factor "

0.24450211813 =The power factor

Ex3_12:pg-281

In [16]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_12
import math
Vs=400;#Supply voltage in V
Id=9.317;#Current in A
pf=0.2588;#Powerfactor
Vth=math.sqrt(2)*Vs;
Ia=math.sqrt(2/3.0)*Id;
Ith=Ia/math.sqrt(2);
Imax=Ith/pf;
print Imax,"=The max current in A "

20.7850558657 =The max current in A

Ex3_14:pg-282

In [18]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_14
import math
t0=1.5;#Time in ms
t1=3;#Time in ms
Vs=200.0;#Supply voltage in V
gama=t0/t1;
Vl=gama*Vs;
Vrms=math.sqrt(gama)*Vs;
Rf=(math.sqrt(1-gama))/(math.sqrt(gama));
print Rf,"=Ripple factor "

1.0 =Ripple factor

Ex3_14:pg-283

In [24]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_14
import math
t0=1.5;#Time in ms
t1=3;#Time in ms
Vs=200.0;#Supply voltage in V
gama=t0/t1;
Vl=gama*Vs;
Vrms=math.sqrt(gama)*Vs;
Rf=(math.sqrt(1-gama))/(math.sqrt(gama));
print Rf,"=Ripple factor "

1.0 =Ripple factor

Ex3_15:pg-284

In [22]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex3_15
import math
R=1.5;#Resistance in ohm
L=3;#Inductance in H
Ton=2;#Time in ms
T=6;#Time in ms
Vs=150.0;#Supply voltage in V
t=Ton/T;
tON=L/R;
Vavg=T*Vs;
Iavg=Vavg/R;
P=(Iavg)**2*R;
Io=23.032;
I=1-math.exp(-t);
I1=Io*math.exp(-t);
Imax=(Vs/R)*I+I1;
print Imax,"=Maximum current in A "
Imin=Imax*math.exp(-2*t);
print Imin,"=Minimum current in A "

23.032 =Maximum current in A 
23.032 =Minimum current in A