# Chapter 6 : Rotating electrical machine¶

## Example 1 : pg 105¶

In :
#Example  6.1# Terminal voltage
#calculate the terminal voltage
#given data :
Z=440.;# number of lap
N=900.;# revolutions in rpm
fi=0.07;#fluxin Wb
P=4.;# number of pole
A=4.;#constant
Ia=50.;# armature current in Amperes
E=462.;#voltage in V
#calculations
E=(P*fi*Z*N)/(60*A);#general voltage in volts
R=0.002;# resistance in ohm
C=110.;# conductors
Re=C*R;#resistance of each path in ohm
Ra=Re/A;#armature resistance in ohm
V=E-(Ia*Ra);#terminal voltage in volts
#results
print "Terminal voltage,(V) = ",V

Terminal voltage,(V) =  459.25


## Example 2 : pg 105¶

In :
#Example  6.2# e.m.f
#calculate the emf in all cases
#given data :
V=200.;#voltage
Ra=0.1;#resistance in ohm
Ia=50.;#armature current in Amperes
#calculations
E=V+(Ia*Ra);#generator voltage in volts
Eb=V-(Ia*Ra);#motor voltage in volts
#results
print "emf when machine acts as generator,(V) = ",E
print "emf when machine acts as motor,(V) = ",Eb

emf when machine acts as generator,(V) =  205.0
emf when machine acts as motor,(V) =  195.0


## Example 3 : pg 106¶

In :
#Example  6.3
#calculate the speed ,torque and efficiency
v=200.;#voltage in volts
r=100.;#resistance in ohms
#calculations
ish=v/r;#shunt current in amperes
i=4;#current in amperes
nla=i-ish;#no load armature current in amperes
w=8.;#powerin kW
ifl=(w*10**3)/v;#full load current in amperes
fla=ifl-ish;#full load armature current in amperes
r1=0.6;#internal resistance in ohms
ebo=(v-(ish*r1));#voltage in volts
eb=(v-(fla*r1));#voltage in volts
no=700.;#number of rpm
n=no*(eb/ebo);#number of rpm
ta=((eb*fla*60)/(2*n));#armature torque in N-m
nlpi=v*i;#no load power input in watts
cl=(ish**2*r1);#copper losses in watts
cl=nlpi-cl;#total copper lossses in Watts
flacl=(fla**2*r1);#full load armmature copper losses in Watts
tfll=flacl+cl;#total full load losses in Watts
flo=(w*10**3)-tfll;#full load output in Watts
ef=((flo)/(w*10**3))*100;#efficiency
#results
print "speed  is,(rpm)=",round(n,3)
print "armature torque is, (N-m)=",ta
print "full load motor efficiency is ,(%)=",ef
#armature torque is calculated wrong in the textbook

speed  is,(rpm)= 623.944
armature torque is, (N-m)= 323.76
full load motor efficiency is ,(%)= 79.2


## Example 4 : pg 108¶

In :
#Example  6.4#  speed
#calculate the speed of the machine
#given data :
fi=0.02# flux in Wb
P=4.;# number of poles
A=2.;#constant
Z=151.*A;#turns
V=200.;# in volts
Rsh=50.;#shunt resistance in ohm
Ra=0.01;# armature resistance in ohm
Pr=40000.;#power required  in Watts
#calculations
Il=Pr/V;#load current in amperes
Ish=V/Rsh;#shunt current in amperes
Ia=Il+Ish;#armature current in amperes
E=V+(Ia*Ra);#generated voltage
N=(60*A*E)/(fi*P*Z);#rpm
#results
print "The speed of the machine,(rpm) = ",round(N,3)
#answer is wrong in the textbook

The speed of the machine,(rpm) =  1003.51


## Example 5 : pg 112¶

In :
#Example  6.5#  Power
#calculate the power consumed
#given data :
fp=0.024;# flux per pole
lf=1.2;# leakage factor
fi=fp/lf;# in Wb
Z=756;#turns
P=4;# number of pole
N=1000;# in rpm
A=4;#constant
#calculations
E=(fi*Z*N*P)/(60*A);#generated voltage
il=1/10.;#load current in amperes
ish=1/100.;#shunt current in amperes
ra=1;#armature resistance in ohms
isa=il+ish;#current in amperes
v=((E)/(1+(ra*isa)));#volts
r2=10;#ohms
il=v/r2;#amperes
pc=il*v;#Watts
#results
print "Power consumed is,(W)=",round(pc,3)
#answer is wrong in the textbook

Power consumed is,(W)= 5154.127


## Example 6 : pg 115¶

In :
#Example  6.6:
#calculate the e.m.f ,copper losses ,output of the prime mover ,commercial, mechanical and electrical efficiencies
#given data :
Il=190;#load current in Amperes
V=250;# voltage in volts
Ra=0.02;#armature resistance in ohm
Rsh=25.;#shunt resistance in ohm
#calculations and results
Ish=V/Rsh;#shunt current in amperes
Ia=Ish+Il;#armature current in amperes
E=V+(Ia*Ra);#generated voltage
print "part (a)"
print "emf genereted,(V) = ",E
Cl=(Ia**2*Ra);# armeture copper losses
Sl=Ish*V;# shunt copper losses
T=(Cl+Sl)*10**-3;#copper losses in k-Watt
print "part (b)"
print "Total copper losses,(kW) = ",T
Eo=V*Il;#output voltage in volts
I_l=950.;#iron loss in watt
O=Eo+I_l+(T*10**3);#output in watt
print "Output of the prime mover,(W) = ",O
Ep=O-I_l;# electrical power in W
Me=(Ep/O)*100;#Mechanical efficiency
print "part (c)"
print "Mechanical efficiency,(%) = ",round(Me,3)
Ee=(Eo/Ep)*100;#Electrical efficiency
print "Electrical efficiency,(%) = ",round(Ee,3)
Ce=(Eo/O)*100;#Commercial efficiency
print "Commercial efficiency,(%) = ",round(Ce,3)

part (a)
emf genereted,(V) =  254.0
part (b)
Total copper losses,(kW) =  3.3
Output of the prime mover,(W) =  51750.0
part (c)
Mechanical efficiency,(%) =  98.164
Electrical efficiency,(%) =  93.504
Commercial efficiency,(%) =  91.787


## Example 7 : pg 117¶

In :
#Example  6.7# resistance
#calculate the resistance
#given:
n=1000;#turns in rpm
ra=0.3;#armature resistance in ohms
rf=40;#field resistance in ohms
it=5;#field current in amperes
if1=4;#field current in amperes
e1=220.;#emf in volts
e2=200.;#emf in volts
ia=35.;#armature current in amperes
#calculations
eb=(e1-(ia*ra));#emf in volts
x=((eb-e2)/(it*if1));#additional field current in amperes
ce=e1-e2;#change in emf in volts
ix=if1+x;#total current in amperes
rt=(e1/ix);#total resistance in ohms
adr=rt-rf;#additional resistance required in ohms
#results
print "additional resistance required is,(Ohm)=",round(adr,3)

additional resistance required is,(Ohm)= 9.162


## Example 8 : pg 120¶

In :
#Example  6.8# resistance and speed
#calculate the resistance and speed
from math import ceil
#given:
v1=240.;#primary voltage
r1=0.2;#primary resistance in ohm
i1=40.;#primary current in volts
#calculations and results
eb1=(v1-i1*r1);#primary emf
n11=1800.;#number of turns on primary side in rpm
n21=1600.;#number of turns on secondary side in rpm
i2=10.;#secondary current in amperes
x=((n21/n11)*(i2/i1)*eb1);#variable
r=((v1-(i2*r1))-x)/i2;#resistance in ohm
print "part (a)"
print "resistance to be added is,(Ohm)=",round(r,3)
print "part (b)"
n11=1800.;#number of turns on primary side
n21=900.;#number of turns on secondary side in rpm
i2=60.;#secondary current in amperes
x=((n21/n11)*(1.18)*eb1);#variable
r=((v1-(i2*r1))-x)/i2;#resistance in ohms
print "resistance to be added is,(Ohm)=",round(r,3)
eb2=228.;#secondary emf in volts
eb1=232.;#primary emf in volts
p1=100.;#primary power in watt
p2=118.;#secondary power in watt
n2=((eb2/eb1)*(p1/p2)*n11);#speed in rpm
print "speed is,(rpm)=",ceil(n2)

part (a)
resistance to be added is,(Ohm)= 18.644
part (b)
resistance to be added is,(Ohm)= 1.519
speed is,(rpm)= 1500.0


## Example 9 : pg 121¶

In :
#Example  6.9# speed
#calculate the speed
from math import sqrt
#given:
i1=50.;#primary current in amperes
i2=i1/(sqrt(2));#secondary current in amperes
r1=0.2;#primary resistance in ohms
v1=220.;#primary voltage in volts
#calculations
eb1=((v1-(i1*r1)));#primary emf in volts
eb2=((v1-(i2*r1)));#secondary emf in volts
n1=1000#primary speed in rpm
n2=(n1*(eb2/eb1)*(i1/i2));#seconadry speed in rpm
#results
print "speed is,(rpm)=",round(n2,3)

speed is,(rpm)= 1433.938


## Example 10 : pg 124¶

In :
#Example 6.10#
#calculate the Speed ,motor speed,and frequency
#given data :
print "part (a)"
f=50.;#frquency  in Hz
P=4;# number of pole
#calculations and results
Ns=(120*f)/P;#speed in rom
print " The speed of rotating magnetic field,(rpm) = ",Ns
print "part (b)"
S=0.035;# slip
N=Ns*(1-S);#motor speed in rpm
print "Motor speed,(rpm) = ",N
print "part (c)"
S=0.04;# slip
F=S*f;#frequency in Hz
print "Frequency ",F," Hz or ",120," rpm "
print "part (d)"
f=50.;# in Hz
F=f;#frequency in Hz
print "Frequency of rotor current,(Hz) = ",F

part (a)
The speed of rotating magnetic field,(rpm) =  1500.0
part (b)
Motor speed,(rpm) =  1447.5
part (c)
Frequency  2.0  Hz or  120  rpm
part (d)
Frequency of rotor current,(Hz) =  50.0


## Example 11 : pg 125¶

In :
#Example 6.11#
#calculate the current per phase and power factor
from math import sqrt
#given:
v1=100.;#emf in volts
vi=v1/sqrt(3);#induced emf in volts
r1=1.;#rotor resistance ohms per phase
r2=4.;#rotor reactance ohms per phase
#calculations and results
r=sqrt(r1**2+r2**2);#rotor impedence per phase
rcp=(vi/r);#rotor current per phase
pf=(1./r);#power factor
print "part (a)"
print "rotor current per phase is,(A)=",round(rcp,3)
print "power factor is,=",round(pf,3)
r3=3.;#ohms
r4=r1+r3;#rotor resistance ohms per phase
r2=4.;#rotor reactance ohms per phase
r=sqrt(r4**2+r2**2);#rotor impedence per phase
rcp=(vi/r);#rotor current per phase
pf=(r4/r);#power factor
print "part (b)"
print "rotor current per phase is,(A)=",round(rcp,3)
print "power factor is,=",round(pf,3)

part (a)
rotor current per phase is,(A)= 14.003
power factor is,= 0.243
part (b)
rotor current per phase is,(A)= 10.206
power factor is,= 0.707


## Example 12 : pg 127¶

In :
#Example 6.12# emf
#calculate the emf
from math import sqrt, pi
#given:
print "part (a) generator "
kva=4.;#kVA
v=110.;#volts
re=3.;#syncronous reacrance in ohms
#calculations and results
ip=((kva*10**3)/(sqrt(3)*v));#phase current in Amperes
ep=v/(sqrt(3));#phase voltage in volts
e1=ep+1j*(ip*3);#line voltage in volts
e11=sqrt((e1.real**2)+e1.imag**2);#line voltage per phase in volts
pf=0.8;#power factor
e12=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))+e1.imag))**2));#
e13=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))-e1.imag))**2));#
print "emf  when the armature current is full load unit pf is,(V)=",round(e11,3)
print "emf  when the armature current is full load 0.8 pf (lag) is,(V)=",round(e12,3)
print "emf  when the armature current is full load 0.8 pf (lead) is,(V)=",round(e13,3)
print "part (b) motor"
kva=4;#kVa
v=110;#volts
re=3;#syncronous reacrance in ohms
ip=((kva*10**3)/(sqrt(3)*v));#phase current in Amperes
ep=v/(sqrt(3));#phase voltage in volts
e1=ep-1j*(ip*3);#line voltage in volts
e11=sqrt((e1.real**2)+e1.imag**2);#line voltage per phase in volts
pf=0.8;#power factor
e12=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))-e1.imag))**2));#
e13=(sqrt((e1.real*pf)**2+(((e1.imag*sqrt(1-pf**2))+e1.imag))**2));#
print "emf  when the armature current is full load unit pf is,(V)=",round(e11,3)
print "emf  when the armature current is full load 0.8 pf (lag) is,(V)=",round(e12,3)
print "emf  when the armature current is full load 0.8 pf (lead) is,(V)=",round(e13,3)

part (a) generator
emf  when the armature current is full load unit pf is,(V)= 89.444
emf  when the armature current is full load 0.8 pf (lag) is,(V)= 112.857
emf  when the armature current is full load 0.8 pf (lead) is,(V)= 56.71
part (b) motor
emf  when the armature current is full load unit pf is,(V)= 89.444
emf  when the armature current is full load 0.8 pf (lag) is,(V)= 56.71
emf  when the armature current is full load 0.8 pf (lead) is,(V)= 112.857