Chapter01: Characterstics of Electric Motors

Ex1_1:pg-83

In [45]:
#Electric Drives  concepts and application by V.Subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_1
import math
V=500.0;# voltage v
N1=900.0;# speed in rpm
Ia1=45.0;#armature current in A
Ia2=21.0;#armature current in A
R=8;# resistance in ohm
Ra=1;#armature resistance in ohm
Eb1=V-(Ia1*Ra);
Eb2=V-(9*Ia2);
N2=N1*(Eb2/Eb1);
print round(N2,1),"=New speed in rpm "

615.2 =New speed in rpm

Ex1_2:pg-83

In [44]:
#Electric Drives:concepts and application by V.Subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_2
import math
V1=400.0;#supply voltage is V
I1=70.0;#Current in A
N1=78.5;#speed in rad/sec
R1=0.3;#resistance in ohm
I2=90.0;#current in A
N2=31.4;#Speed in rpm
Eb1=V1-(I1*R1);
T1=(Eb1*I1)/N1;
V2=V1+Eb1;
R2=(V2/I2)-R1;
T2=(Eb1*I2)/N1;
Eb2=(Eb1*N2)/N1;
I=(V1+Eb2)/R2;
T=(Eb2+I)/N2;
print T,"=The initial breaking torque in Nm "
#Calculation error in the textbook

6.93044450468 =The initial breaking torque in Nm

Ex1_3:pg-84

In [9]:
#Electric drives concepts and application by V.Subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_3
import math
V=250.0;#supply voltage V
Ia1=40.0;#Armature current in A
R1=0.6;#Resistance in ohm
N1=2.828;#speed in rpm
N2=2;#speed in rpm
Ia2=((Ia1)**2/N1)**(1.0/2);
Eb1=V-(Ia1*R1);
Eb=(Ia1/Ia2)*N2;
Eb2=Eb1/Eb;
R2=(V-Eb2)/Ia2;
print R2,"=External resistance required in ohm"

7.68541150479 =External resistance required in ohm

Ex1_4a:pg-85

In [13]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_4a
import math
V=440.0;# voltage in V
Ia=80.0;# Current in A
Na=1200.0;#Speed in rpm
Na1=125.6;# Speed in rad/sec
R1=0.55;# Resistance in ohm
R2=110.0;# Resistance in ohm
N0=600.0;# Speed in rpm
N01=62.8;#Speed in rpm
Nf=300.0;# Speed in rpm
Nf1=31.4;# Speed in rpm
Rsh=1.256;# Resistance in ohm
E=V-(Ia*R1);
K=E/Na1; 
E1=K*N01;
Tf=K*Ia;
E2=E1*(Nf/N0);
V2=E2+(Ia*R1);
Is=(V2/Rsh)+Ia;
Il=Is+(V/R2);
Pi=V*Il;
Po=Tf*Nf1;
Eff=(Po/Pi)*100;
print Eff,"=the effeciency of the motor in % "

9.09764027943 =the effeciency of the motor in %

Ex1_4b:pg-86

In [16]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_4b
import math
V=440.0;#voltage in V
K=3.153;
Ia=80.0;# Current in A
Rs=2.0;#Resistance in ohm
Rsh=1.5;#Resistance in ohm
R1=0.55;#Resistance in ohm
Alpha=(Rs/Rsh);
Vo=(V/Alpha);
No=(Vo/K);
N=((60.0*No)/(2*math.pi));
print N,"=No load speed in rpm "
V2=((V/Rs)-Ia)/((1/Rs)+(1/Rsh));
E2=V2-(Ia*R1);
N2=N*(E2/Vo);
print N2,"=Full load speed in rpm "

999.450641681 =No load speed in rpm 
230.176511417 =Full load speed in rpm

Ex1_5a:pg-87

In [46]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_5a
import math
V=250;# voltage in V
Ra=0.4;# Resistance in ohm
Na=480;#Speed in rpm
Va=125;# voltage in V
Ia=40;#Current in A
Vi=V-(Ra*Ia);
N=Na*(Vi/Va);
print N,"=The speed of the motor in rpm "
N1=(2*math.pi*N)/60;
T=(Vi*Ia)/N1;
print T,"=The torque developed in Nm "

898.56 =The speed of the motor in rpm 
99.4718394324 =The torque developed in Nm

Ex1_5b:pg-87

In [47]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_5b
import math
V=250.0;# voltage in V
I=40.0;#Current in A
Ra=0.4;#Resistance in ohm
Eb=125.0;# voltage in V
Na=480.0;#Speed in rpm
Re=(V-Eb-(I*Ra))/I;
print Re,"=The value of resistance in ohm"
T=(Eb*I)*60/(2*Na*math.pi);
print T,"=The torque developed in Nm "
#Result vary due to error in calculation of torque in the textbook

2.725 =The value of resistance in ohm
99.4718394324 =The torque developed in Nm

Ex1_6:pg-87

In [48]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_6
import math
V=250.0;# voltage in V
I=40.0;#Current in A
R1=2.725;# Resistance in ohm
R2=3.5;# Resistance in ohm
Rf=0.15;# Resistance in ohm
N=480.0;#Speed in rpm
V1=V-I*(R1+Rf);
Ir=(V1/R2);
Ia=I-Ir;
Eb=V1-(Ia*Rf);
Nm=N*(V1/Eb);
print Nm,"=The speed of motor in rpm "
#Result vary due to 125V is used instead of 135V in the textbook
T=(Eb*Ia)/(2*math.pi*Nm/60);
print T,"=The torque in Nm "

480.763116057 =The speed of motor in rpm 
3.82460039115 =The torque in Nm

Ex1_7:pg-87

In [49]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_7
import math
V=250;# voltage in V
I=40;#Current in A
Ro=0.4;# Resistance in ohm
R1=2.725;# Resistance in ohm
R2=3.5;# Resistance in ohm
Eb=125;# voltage in V
Na=480;#Speed in rpm
Na1=50.24;#Speed in rad/sec
R=((1/R1)+(1/R2));
Vm=(V-(I*R1))/(R*R1);
Em=Vm-(I*Ro);
N=(Em/Eb)*Na;
print N,"=The speed of the motor in rpm "
N1=(2*math.pi*N)/60;
Il=(V-Vm)/R1;
Po=Em*I;
T=Po/N1;
print T,"=The torque in Nm "

242.984096386 =The speed of the motor in rpm 
99.4718394324 =The torque in Nm

Ex1_8:pg-89

In [50]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_8
import math
V=250.0;# voltage in V
I=40.0;#Current in A
R1=0.91;# Resistance in ohm
Rs=0.95;# Resistance in ohm
Eb=125.0;# voltage in V
N1=480.0;#Speed in rpm
Vm=Rs*I;
Ia=I-((V-Vm)/2);
Em=-Vm-(Ia*R1);
N=-(Em/Eb)*N1;
print N,"=The speed in rpm "
N2=(2*math.pi*N)/60;
T=(Em*Ia)/N2;
print T,"=The torque in Nm "

-84.7104 =The speed in rpm 
164.128535064 =The torque in Nm

Ex1_10:pg-90

In [51]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_10
import math
Sf=0.04;#Full load slip in %
Ist=1.0;#Starting current in A
If1=Ist/8.0;
T=(8.0)**2*Sf;
print T,"=Direct on line starting torque in Nm "
S=T/3;
print S,"=By Star/delta starter"

2.56 =Direct on line starting torque in Nm 
0.853333333333 =By Star/delta starter

Ex1_11:pg-90

In [52]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_11
import math
Sf1=0.04;#Full load slip in %
x=(8.0*3)**(1.0/2);
Tst=(x)**2*Sf1;
S=Sf1/2.0;
T=(8)**2*S;
print T,"=Torque in Nm "

1.28 =Torque in Nm

Ex1_12:pg-91

In [53]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_12
import math
Sf=0.04;#Full load slip in %
I=5;#Current in A
Tst=(I)**2*Sf;
x=((2.0/I)*100)**(1.0/2);
T=(2.0/I)**2*(I)**2*Sf;
print T,"=Torque in Nm "

0.16 =Torque in Nm

Ex1_13:pg-92

In [54]:
#Electric Drives:concepts and applications by V.subrahmanyam
#Publisher:Tata McGraw-Hill 
#Edition:Second 
#Ex1_13
import math
V=500.0;#Voltage in V
r1=0.13;#resistance in ohm
r2=0.32;#resistance in ohm
x1=0.6j;#reactance in ohm
x2=1.48j;#reactance in ohm
rm=250.0;#resistance in ohm
xm=20;#reactance in ohm
S=0.05;#Full load slip in %
Z2=r1+x1+(r2/S)+x2;
print Z2,"=The impedence of motor "
I2=(V/(math.sqrt(3.0)*(6.853)));
T1=3*(I2)**2*(r2/S);
Sb=2-S;
Sf=2-S+r1;
Zb=r1+x1+(Sb/Sf)+x2;
print Zb,"=The impedence at plugging "
I=(V/(math.sqrt(3.0)*(2.336)));
T2=3*(I)**2.0*(Sb/Sf);
T=T1+T2;
print T,"=The braking torque in Nm "

(6.53+2.08j) =The impedence of motor 
(1.0675+2.08j) =The impedence at plugging 
77019.1732775 =The braking torque in Nm