Chapter 12: Polyphase System¶

Example 12.1: page 248:¶

In :
from __future__ import division
import math

#given data:
pf=0.8#power  factor
Vl=250#line  voltage  in  volts

#calculations:
I=((L*10**3)/(Vl*pf*math.sqrt(3)))#line  current  in  ampers
Ip1=I  #  in  star  connection
Ip2=I/(math.sqrt(3))#phase  current
Il=math.sqrt(3)*Ip2#line  current  in  amperes

#Results
print  "(a)line  current  (star  connection)  in  amperes  is",round(I,2)
print  "phase  current  (start  connection)  in  amperes  is",round(Ip1,2)
print  "(b)phase  current  in  ampere  is",round(Ip2,2)
print  "line  current  (delta  connection  )  in  amperes  is",round(Il,2)
(a)line  current  (star  connection)  in  amperes  is 86.6
phase  current  (start  connection)  in  amperes  is 86.6
(b)phase  current  in  ampere  is 50.0
line  current  (delta  connection  )  in  amperes  is 86.6

Example 12.2: page 248:¶

In :
from __future__ import division
import math

#given data:
R=11.88#coil  resistance  in  ohms
L=0.07#inductance  in  henry
f=50  #  in  hertz
pf=0.48#power  factor
Vl=433#line  voltage  in  volts

#calculations:
Vp1=  Vl/(math.sqrt(3))#phase  voltage
Xl1=(2*math.pi*f*L)#in  ohms
Zb1=math.sqrt(R**2+Xl1**2)#  in  ohms
Ie1=Vp1/Zb1#current  in  each  winding  in  amperes
Il1=Ie1#line  current  in  amperes
W1=math.sqrt(3)*Vl*Il1*pf#power  in  watts

Vp2=  Vl#phase  voltage
Xl2=(2*math.pi*f*L)#in  ohms
Zb2=math.sqrt(R**2+Xl2**2)#  in  ohms
Ie2=Vp2/Zb2#current  in  each  winding  in  amperes
Il2=math.sqrt(3)*Ie2#line  current  in  amperes
W2=math.sqrt(3)*Vl*Il2*pf#power  in  watts

#Results
print  "(a)line  current  in  ampere  is",round(Il1)
print  "power  taken  in  connection  in  kW is",round(W1*10**-3,1)
print  "(b)line  current  in  ampere  is",round(Il2)
print  "power  taken  in  connection  in  kW is",round(W2*10**-3,1)
(a)line  current  in  ampere  is 10.0
power  taken  in  connection  in  kW is 3.6
(b)line  current  in  ampere  is 30.0
power  taken  in  connection  in  kW is 10.8

Example 12.3: page 250:¶

In :
from __future__ import division

#given data:
Vl=1100#line  voltage  in  volts
n=99  #motor  efficiency  in  percentage
pf=  0.8#power  factor

#calculations:
Mo=n*735.5#output  of  the  motor
Mi=(Mo*100)/75#  INPUT  OF  THE  MOTOR  IN  WATTS
Il=(Mi)/(math.sqrt(3)*Vl*pf)#line  current  in  amperes
Ip=Il/(math.sqrt(3))#phase  current  in  amperes
Ipm=Il#phase  curent  of  the  motor
Ac1=Ip*pf#active  component  of  phase  current  in  the  motor
Rc1=Ip*(math.sqrt(1-pf**2))#reactive  component  of  phase  current  of  motor
Ac2=Ipm*pf#active  component  of  phase  current  in  the  generator
Rc2=Ipm*(math.sqrt(1-pf**2))#reactive  component  of  phase  current  of  generator
#Results
print  "(a)phase  current  of  motor  in  amperes  is",round(Ip,2)
print  "active  component  of  phase  current  in  the  motor  in  amperes",round(Ac1,2)
print  "reactive  component  of  phase  current  in  the  motor  in  amperes",round(Rc1,2)
print  "(b)phase  current  of  generator  in  amperes  is",round(Ipm,2)
print  "active  component  of  phase  current  in  the  generator  in  amperes",round(Ac2,3)
print  "reactive  component  of  phase  current  in  the  generator  in  amperes",round(Rc2,3)
(a)phase  current  of  motor  in  amperes  is 36.77
active  component  of  phase  current  in  the  motor  in  amperes 29.42
reactive  component  of  phase  current  in  the  motor  in  amperes 22.06
(b)phase  current  of  generator  in  amperes  is 63.7
active  component  of  phase  current  in  the  generator  in  amperes 50.957
reactive  component  of  phase  current  in  the  generator  in  amperes 38.218

Example 12.4: Page 253:¶

In :
from __future__ import division
import math

#given data:
ni=74.6#efficiency
Mo=40#HP  OF  MOTOR
tw=40#total  in  kW
pf=0.8#power  factor

#calculations:
mo=Mo*ni#output  of  motor  in  watts
mi=(mo*100)/(ni*1000)#input  of  motor  in  kW
theta=math.acos(pf)#in  degree
v=math.tan(theta)#
dw=(v*tw)/(3**0.5)#

#Results
print  "first  reading  in  kW is",round(w1,2)
print  "second  reading  in  kW is",round(w2,2)
first  reading  in  kW is 28.66
second  reading  in  kW is 11.34

Example 12.5: page 253:¶

In :
from __future__ import division
import math

#given data:
w2=3  #second  reading  in  kW  ,  this  value  is  given  wrong  in  question

#calculations:
tw1=w1+w2#in  kW
dw1=w1-w2#in  kW
pfa1=math.atan(math.sqrt(3)*(dw1/tw1));
pf1=math.cos(pfa1)#//power  factor  when  both  the  eadings  are  positive

tw2=w1-w2#in  kW
dw2=w1+w2#in  kW
pfa2=math.atan(math.sqrt(3)*(dw2/tw2));
pf2=math.cos(pfa2)#//power  factor  when  second  reading  is  obtained  by  reversing  the  connection
#Results
print  "(a)power  factor  when  both  the  readings  are  positive", round(pf1,3)
print  "(b)power  factor  when  second  reading  is  obtained  by  reversing  the  connections  ",round(pf2,3)
(a)power  factor  when  both  the  readings  are  positive 0.945
(b)power  factor  when  second  reading  is  obtained  by  reversing  the  connections   0.115