# Chapter 15 The AC motor control¶

## Example 15.1,Pg.no.48¶

In [17]:
import math
from math import sqrt
S1=2.0            #value of slip in percentage of slip ring induction motor
Ns=1000.0         #value of stator speed in rpm
Nr=500.0          #value of rotor speed in rpm
S2=(Ns-Nr)*100/Ns        #valu of slip in percentage of motor
print 'value of slip of motor=S2=',S2,'percentage'
I1=50.0                  #stator current in amps
I2=I1*sqrt(S2/S1)
print 'value of new stator current=I2=',I2,'Amp'

value of slip of motor=S2= 50.0 percentage
value of new stator current=I2= 250.0 Amp


## Example 15.2,Pg.no.48¶

In [18]:
import math
Imr=50.0       #motor field rating in amp//
Icr=1.5*Imr    #converter rated current in amp
print 'value of converter rated current=Icr=',Icr,'amp'
Vdc=100.0       #converter dc rating in volts
Vac=Vdc/1.35    #converter ac rating voltage required
Vac=round(Vac,2)
print 'value of converter rated ac voltage=Vac=',Vac,'volts'
Pkva=(1.05*100*75)/1000          #KVA rating of the transformer
print 'KVA rating of transformer=Pkva=',Pkva,'KVA'

value of converter rated current=Icr= 75.0 amp
value of converter rated ac voltage=Vac= 74.07 volts
KVA rating of transformer=Pkva= 7.875 KVA


## Example 15.3,Pg.no.49¶

In [19]:
import math
S1=0.04        #value of slip in of induction motor
Ns=1500.0        #value of initial speed in rpm
N2=1300.0      #value of speed reduced to in rpm
N1=Ns*(1-S1)   #value of speed N1 in rpm
print 'value of speed N1=',N1,'rpm'
f=(Ns-N1)/(Ns-N2)
print 'value of f=',f
T1=2000.0         #developing torque in induction motor in watts
T2=T1/f        #new value of torque developed by the motor in watts
T2=round(T2,1)
print 'value of new torque developed=T2=',T2,'Watts'

value of speed N1= 1440.0 rpm
value of f= 0.3
value of new torque developed=T2= 6666.7 Watts


## Example 15.4,Pg.no.49¶

In [20]:
import math
f1a=50.0         #initial frequency in hertz
f1b=75.0         #value of frequency increased to in hertz
Ta=1500.0        #developing torque in induction motor in watts
Tb=Ta*f1a/f1b    #new value of torque developed by the motor in watts
print 'value of new torque developed=Tb=',Tb,'Watts'

value of new torque developed=Tb= 1000.0 Watts


## Example 15.5,Pg.no.50¶

In [21]:
import math
V=415.0         #operating input voltage of induction motor in volts
S=0.04          #input slip
r2=1.0          #rotor resistance referred to stator in ohms
T=(S*V**2)/r2   #torque developed by motor in watts
print 'torque developed by motor=T=',T,'watts'
f1=75.0         #input stator frequency in hertz
f2=S*f1         #rotor frequency in hertz
print 'value of rotor frequency=f2=',f2,'hertz'

torque developed by motor=T= 6889.0 watts
value of rotor frequency=f2= 3.0 hertz


## Example 15.6,Pg.no.50¶

In [22]:
import math
f1a=50.0       #intial frequency in hertz
f1b=30.0       #value of frequency reduced to in hertz
Va=415.0       #operating voltage of induction motor in volts
Vb=Va*f1b/f1a  #input voltage to the motor in volts
print 'value of input voltage to the motor=Vb=',Vb,'volts'
Pa=100.0       #operating power of induction motor in KVA
Pb=Pa*f1b/f1a  #input power to the motor in KVA
print 'value of input power to the motor=Pb=',Pb,'KVA'

value of input voltage to the motor=Vb= 249.0 volts
value of input power to the motor=Pb= 60.0 KVA


## Example 15.7,Pg.no.51¶

In [23]:
import math
f1a=40.0     #intial frequency in hertz
Pa=200.0     #input power of squirrel cage motor in KVA
Pb=150.0     #input power to the motor after change in speed in KVA
f1b=f1a*Pb/Pa      #frequency changed to in hertz
print 'value of frequency changed to f1b=',f1b,'hz'
Nsa=1200.0         #motor initial syncronous speed in rpm
Nsb=Nsa*f1b/f1a
Sb=0.04
Nb=Nsb*(1-Sb)      #speed in rpm at 4% slip
print 'speed at 4 percent slip=Nb=',Nb,'rpm'
Va=325            #operating voltage of induction motor in volts
Vb=Va*f1b/f1a     #stator voltage to the motor in volts
print 'value of stator voltage to the motor=Vb=',Vb,'volts'
Pag=150.0         #power transferred from stator to rotor at 30 hz in KVA
Ws=2*3.14*Nsb/60
T=Pag*1000/Ws     #torque if stator drop is negligible in watts
T=round(T,2)
print 'torque if stator drop is negligible=T=',T,'watts'
P2=Sb*Pag         #rotor copper loss in KVA
print 'rotor copper loss=P2=',P2,'KVA'

value of frequency changed to f1b= 30.0 hz
speed at 4 percent slip=Nb= 864.0 rpm
value of stator voltage to the motor=Vb= 243.75 volts
torque if stator drop is negligible=T= 1592.36 watts
rotor copper loss=P2= 6.0 KVA


## Example 15.8,Pg.no.52¶

In [24]:
import math
from math import sqrt
f1a=50.0       #i n t i a l input frequency in hertz
Ta=2000.0      #developing torque in induction motor in watts
Tb=1500.0      #new value of torque reduced to in watts
f1b=f1a*sqrt(Ta/Tb)         #value of stator frequency increased to in hertz
f1b=round(f1b,2)
print 'value of stator frequency increased to f1b=',f1b,'hertz'

value of stator frequency increased to f1b= 57.74 hertz


## Example 15.9,Pg.no.52¶

In [25]:
import math
from math import pi,sqrt
Vom1=sqrt(2)*41.5            #starting rms value of output voltage
Vom2=sqrt(2)*166             #ending rms value of output voltage
V=415.0                      #operating voltage of cyclo converter
A1=(math.acos(Vom1/(1.35*V)))*180/pi           #firing angle starts from
A1=round(A1,1)
print 'firing angle starts from A1=',A1,'degrees'
A2=(math.acos(Vom2/(1.35*V)))*180/pi         #f i r i n g angle ends at
A2=round(A2,1)
print 'firing angle ends at A2=',A2,'degrees'
IPF=math.cos(pi*7/15)*PFl/sqrt(2)      #input power factor
DF=0.7                                 #input displacement factor
IPF=round(IPF,4)
print 'input power factor=IPF=',IPF
Mh=math.cos(pi*0.3627)*PFl/(sqrt(2)*DF)
Mh=round(Mh,4)
print 'distortion factor=Mh=',Mh

firing angle starts from A1= 84.0 degrees
firing angle ends at A2= 65.2 degrees
input power factor=IPF= 0.0591
distortion factor=Mh= 0.3379


## Example 15.10,Pg.no.53¶

In [26]:
import math
from math import sqrt,pi
Vo5m=sqrt(2)*41.5          #rms value of output voltage
V=415.0                    #operating voltage of cyclo converter
A5=(math.acos(Vo5m/(1.35*V)))*180/pi          #trigger angle ranges from
A5=round(A5,2)
print 'trigger angle ranges fromA5=',A5,'degrees'
A51=180.0-A5                #trigger angle ranges upto
A51=round(A51,2)
print 'trigger angle ranges upto A51=',A51,'degrees'
CA15=0.3132                 #maximum cosine value corresponding to operating frequency 15hz
HIPF=CA15*LPF/sqrt(2)       #highest value of input power factor
HIPF=round(HIPF,2)
print 'highest value of input power factor=HIPF=',HIPF
LIPF=math.cos(A5*pi/180)*LPF/sqrt(2)         #lowest value of input power factor
LIPF=round(LIPF,2)
print 'lowest value of input power factor=LIPF=',LIPF
IDF=0.75                                     #input displacement factor
HDF=CA15*LPF/(sqrt(2)*IDF)                   #highest value of distortion factor
HDF=round(HDF,2)
print 'highest value of distortion factor=HDF=',HDF
LDF=HDF*math.cos(A5*pi/180)/CA15             #lowest value of distortion factor
LDF=round(LDF,2)
print 'lowest value of distortion factor=LDF=',LDF

trigger angle ranges fromA5= 83.99 degrees
trigger angle ranges upto A51= 96.01 degrees
highest value of input power factor=HIPF= 0.2
lowest value of input power factor=LIPF= 0.07
highest value of distortion factor=HDF= 0.27
lowest value of distortion factor=LDF= 0.09


## Example 15.11,Pg.no.54¶

In [27]:
import math
from math import sqrt
PFm=0.5              #highest value of input factor
Am=3.14/6            #highest value of input powerfactor occurs at 30 degrees
A=math.cos(Am)       #highest value of cosAm if firingangle ranging from 30 to 150
A=round(A,3)
print 'highest value of cosAm=',A
PFl=(sqrt(2)*PFm)/A
PFl=round(PFl,3)
print 'laod power factor of cyclo converter=',PFl

highest value of cosAm= 0.866
laod power factor of cyclo converter= 0.817


## Example 15.12,Pg.no.54¶

In [28]:
import math
PFi=0.6         #input powerfactor
DF=0.7          #distortion factor
IDF=PFi/DF      #input displacement factor
IDF=round(IDF,3)
print 'input displacement factor=',IDF

input displacement factor= 0.857


## Example 15.13,Pg.no.54¶

In [29]:
import math
from math import sqrt
PFi=0.1         #input powerfactor
A=(math.acos(sqrt(2)*PFi/PFl))*180/3.14         #firing angle indegrees
A=round(A,2)
print 'firing angle of cyclo converter drive=A=',A,'degrees'
DF=PFi/IDF      #distortion factor
DF=round(DF,3)
print 'distortion factor=DF=',DF

firing angle of cyclo converter drive=A= 81.0 degrees
distortion factor=DF= 0.143


## Example 15.14,Pg.no.55¶

In [30]:
import math
Ap=30.0      #triggering angle of positive group in degrees
An=180-Ap    #triggering angle of negative group in degrees
print 'triggering angle of negative group=An=',An,'degrees'

triggering angle of negative group=An= 150.0 degrees


## Example 15.15,Pg.no.55¶

In [31]:
import math
from math import pi,sqrt
V=415.0         #input operating voltage of cycloconverter in volts
Pi=50.0         #input power of the cycloconverter in KVA
PF=0.8          #input power factor
I=(Pi*1000*sqrt(2))/(3*V*PF*math.cos(A))      #input current to the converter in amp
I=round(I,3)
print 'input current to the converter=I=',I,'amp'

input current to the converter=I= 100.362 amp


## Example 15.16,Pg.no.56¶

In [32]:
import math
Vo=200.0          #input operating voltage of cycloconverter in volts
Po=50*10**3       #input power of the cycloconverter in VA
Io=100.0          #drawing current from motor in amp

load power factor of motor=PF= 0.83