Chapter10 - Power factor improvement¶

Exa 10.1 - page 268¶

In [5]:
import numpy as np
#Given Data :
cosfi_1=0.75 #powerfactor
x=40 #in Rs/year/KVA
x1=60 #cost of PF improvement equipment in Rs./KVAR
i=12 #in % per annum
y=x1*i/100 #in Rs.
cosfi_2=0.98 #unitless
AnnualSaving=x*(KVA1-KVA2) #in Rs.
fi_1=np.arccos(cosfi_1)*180/np.pi #in degree
tanfi_1=np.tan(fi_1*np.pi/180) #unitless
fi_2=np.arccos(cosfi_2)*180/np.pi #in degree
tanfi_2=np.tan(fi_2*np.pi/180) #unitless
Rating=Pr1-Pr2 #in KVAR
AnnualExpenditure=y*Rating #in Rs.
NetSaving=AnnualSaving-AnnualExpenditure #in Rs./year
print "Net saving per year = %0.2f Rs." %NetSaving
# Answer in the textbook is not accurate.

Net saving per year = 3882.50 Rs.


Exa 10.2 - page 270¶

In [8]:
import numpy as np
#Given Data :
Eta=85 #in %
P=30 #in HP
P1=P*0.7355*Eta/100 #in KW
cosfi_1=0.8 #powerfactor
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Pr=P1*tanfi_1 #in KVAR
#Let active power P2 : Total Active power = P1+P2
cosfi=0.9 #overall powerfactor
tanfi=np.tan(np.arccos(cosfi)) #unitless
#Pr1=tanfi*(P1+P2) #in KVAR
#Putting Pr=Pr1
P2=(Pr-P1*tanfi)/tanfi #in KW
print "Rating of the heater = %0.2f KW" %P2

Rating of the heater = 10.29 KW


Exa 10.3 - page 270¶

In [11]:
import numpy as np
#Given Data :
Im=50 #in Ampere
f=50 #in Hz
V=400 #in volts
cosfi_1=0.6 #powerfactor
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Ia=Im*cosfi_1 #in Ampere
Ir1=Ia*tanfi_1 #in Ampere
#Let the capaitor of C farads be connected to improve pf i.e., 0.9(lag)
cosfi_2=0.9 #powerfactor
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Ir2=Ia*tanfi_2 #in Ampere
Ic=Ir1-Ir2 #in Ampere
print "Capacity of condenser = %0.1f uF" %(C*10**6)

Capacity of condenser = 202.7 uF


Exa 10.4 - page 271¶

In [12]:
import numpy as np
#Given Data :
Im=10 #in Ampere
f=50 #in Hz
V=240 #in volts
cosfi_1=0.707 #powerfactor
sinfi_1=np.sin(np.arccos(cosfi_1)) #unitless
Ir1=Im*sinfi_1 #in Ampere
cosfi_2=1 #powerfactor
Ir2=0 #in A(as cosfi_2=1)
Ic=Ir1-Ir2 #in Ampere
print "Capacity of condenser = %0.2f uF" %(C*10**6)

Capacity of condenser = 93.80 uF


Exa 10.5 - page 272¶

In [14]:
import numpy as np
#Given Data :
Im=30 #in Ampere
f=50 #in Hz
V=200 #in volts
cosfi_1=0.8 #powerfactor
Ia=Im*cosfi_1 #in Ampere
cosfi_2=1 #powerfactor
Ir2=0 #in A(as cosfi_2=1)
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Ir1=Ia*tanfi_1 #in Ampere
Ic=Ir1-Ir2 #in Ampere
print "Capacity of condenser = %0.1f uF" %(C*10**6)

Capacity of condenser = 286.5 uF


Exa 10.6 - page 272¶

In [15]:
import numpy as np
#Given Data :
Im=30 #in Ampere
f=50 #in Hz
V=200 #in volts
cosfi_1=0.7 #powerfactor
Ia=Im*cosfi_1 #in Ampere
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Ir1=Ia*tanfi_1 #in Ampere
cosfi_2=0.85 #powerfactor
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Ir2=Ia*tanfi_2 #in Ampere
Ic=Ir1-Ir2 #in Ampere
print "Capacity of condenser = %0.2f uF" %(C*10**6)

Capacity of condenser = 133.84 uF


Exa 10.7 - page 273¶

In [20]:
from __future__ import division
import numpy as np
#Given Data :
#(i)
IMO=200 #in HP(Induction Motor output)
IMO=IMO*0.7355 #in KW(Induction Motor output)
LagEff=90 #in %
LagEff=90/100 #in fraction
MotorIn=IMO/(LagEff) #in KW
cosfi_1=0.75 #powerfactor
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Pr1=MotorIn*tanfi_1 #in KVAR
#(ii)
P2=300 #in KW
cosfi_2=0.5 #unitless
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Pr2=P2*tanfi_2 #in KVAR
#(iii)
P3=200 #in KW
cosfi_3=1 #unitless
tanfi_3=0 #unitless
Pr3=0 #in KVAR
#(iv)
PsynMotor=500 #in KW
Eff=93 #in %
Eff=93/100 #in fration
Input=PsynMotor/Eff #in KW
Pa=MotorIn+P2+P3+PsynMotor #in KW
P1=Pr1+Pr2+Pr3 #in KVAR
cosfi=1 #unitless
tanfi=0 #unitless
Pr=Pa*tanfi #in KVAR
Prm=Pr-P1 #in KVAR
tanfi_m=Prm/Input
cosfi_m=np.cos(np.arctan(tanfi_m)) #unitless
print "P.F. of the motor = %0.4f lead" %cosfi_m
#Note : Answer in the book is wrong

P.F. of the motor = 0.6294 lead


Exa 10.8 - page 274¶

In [21]:
from __future__ import division
import numpy as np
#Given Data :
f=50 #in Hz
V=400 #in volts
MotorOut=20 #in HP(Motor output)
MotorOut=MotorOut*735.5 #in Watts(Induction Motor output)
CorrectPF=0.85 #in fraction
MotorIn=MotorOut/(CorrectPF*1000) #in KW
cosfi_1=0.7071 #powerfactor
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Pr1=MotorIn*tanfi_1 #in KVAR
cosfi_2=0.85 #unitless
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Pr2=Pr1*tanfi_2 #in KVAR
Prc=Pr1-Pr2 #in KVAR
Prc_ph=Prc/3 #in KVAR
C=Prc_ph*10**3/(2*np.pi*f*V**2)
print "Rating of each capacitor per phase = %0.2f uF" %(C*10**6)

Rating of each capacitor per phase = 43.64 uF


Exa 10.9 - page 275¶

In [28]:
from __future__ import division
import numpy as np
#Given Data :
Pa=500 #in KW
cosfi_1=0.7071 #powerfactor
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Pr1=Pa*tanfi_1 #in KVAR
Pm=100 #in KW
P=Pa+Pm #in KW
cosfi_2=0.95 #unitless
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Pr=P*tanfi_2 #in KVAR
Prm=Pr-Pr1 #in KVAR
Pam=np.sqrt(Pm**2+Prm**2)
print "P.F. of synchronous motor = %0.4f lead" %(PFsynMotor)

P.F. of synchronous motor = 0.3136 lead


Exa 10.10 - page 275¶

In [27]:
from __future__ import division
import numpy as np
#Given Data :
P=1500 #in KW
cosfi_1=0.75 #powerfactor
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Pr1=P*tanfi_1 #in KVAR
Pm=150 #in KW
P=P+Pm #in KW
cosfi_2=0.9 #unitless
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Pr=P*tanfi_2 #in KVAR
Prm=Pr-Pr1 #in KVAR
Pam=np.sqrt(Pm**2+Prm**2)
print "P.F. of synchronous motor = %0.4f lead" %cosfi

P.F. of synchronous motor = 0.2753 lead


Exa 10.11 - page 276¶

In [30]:
from __future__ import division
import numpy as np
#Given Data :
x=100 #in Rs/KVA
y=600*(10/100) #in Rs.
cosfi_2=np.sqrt(1-(y/x)**2)
print "P.F. = %0.1f lag" %(cosfi_2)
MaxDemand2=Load/cosfi_2 #in KW(at cosfi_2 power factor)
AnnSaving=(MaxDemand1-MaxDemand2)*x #in Rs.
cosfi_1=0.75 #powerfactor
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Rating=KVAR1-KVAR2 #in KVAR
AnnualExpenditure=y*Rating #in Rs.
AnnualSaving=AnnSaving-AnnualExpenditure #in Rs.
print "Annual Savings = %0.1f Rs." %AnnualSaving

P.F. = 0.8 lag
Annual Savings = 341.8 Rs.


Exa 10.12 - page 277¶

In [36]:
from __future__ import division
import numpy as np
#Given Data :
#(i)
PHeater=50 #in KW
cosfi_1=1 #unitless
tanfi_1=np.tan(np.arccos(cosfi_1)) #unitless
Pr1=PHeater*tanfi_1 #in KVAR
#(ii)
cosfi_2=0.7 #unitless
P2=200*735.5/(1000*0.8) #in KW
tanfi_2=np.tan(np.arccos(cosfi_2)) #unitless
Pr2=P2*tanfi_2 #in KVAR
#(iii)
cosfi=0.9 #unitless New PF
P3=200*735.5/(1000*cosfi) #in KW
TotalActivePower=PHeater+P2+P3 #in KW
TotalReactivePower=Pr1+Pr2 #in KW
tanfi=np.tan(np.arccos(cosfi)) #unitless
TotalPr=TotalActivePower*tanfi #in KVAR
Pnn=TotalPr-TotalReactivePower #in KVAR(ReactivePower of motor)
tanfi_mu=Pnn/P3 #unitless
cosfi_mu=np.cos(np.arctan(tanfi_mu))
print "PF of the synchronous motor = %0.2f" %cosfi_mu
#Note : Answer in the book is wrong due to accuracy. My ans is 0.9996 if calculate upto 4 decimal place.

PF of the synchronous motor = 1.00


Exa 10.13 - page 277¶

In [38]:
from __future__ import division
import numpy as np
#Given Data :
x=60 #in Rs./KVA
x1=100 #in Rs/KVAR(cost of phase advancing equipment)
InterestCepriciation=x1*10/100 #in Rs.
y=10 #in Rs./KVAR
cosfi_2=np.sqrt(1-(y/x)**2) #unitless
print "Most Ecomnomical PF = %0.3f lag" %cosfi_2

Most Ecomnomical PF = 0.986 lag


Exa 10.14 - page 278¶

In [40]:
from __future__ import division
import numpy as np
#Given Data :
f=50 #in Hz
V=240 #in Volts
#(i)
Imoter=20 #in Ampere
cosfi_1=0.75 #unitless
ReacComponent1=Imoter*np.sqrt(1-cosfi_1**2) #in Ampere
#(ii)
cosfi_2=0.9 #unitless
P2=200*735.5/(1000*0.8) #in KW
ReacComponent2=Imoter*np.sqrt(1-cosfi_2**2) #in Ampere
print "Capacitance of the capacitor = %0.2f uF" %(round(C*10**6))
#Power of the motor=5 KW
P=5 #in KW
tanfi_1=np.tan(np.arccos(cosfi_1))
tanfi_2=np.tan(np.arccos(cosfi_2))
print "KVAR supplied per phase = %0.2f KVAR" %(LeadingKVAR/3)
#Note : Answer in the book is wrong

Capacitance of the capacitor = 60.00 uF
Leading KVAR supplied by the capactor = 2.00 KVAR
KVAR supplied per phase = 0.66 KVAR


Exa 10.15 - page 279¶

In [42]:
from __future__ import division
import numpy as np
#Given Data :
f=50 #in Hz
V=240 #in Volts
cosfi_1=0.8 #unitless
tanfi_1=np.tan(np.arccos(cosfi_1))
cosfi_2=0.9 #unitless
tanfi_2=np.tan(np.arccos(cosfi_2))
#(i)
OA=200 #in KW
OD=280 #in KW
CM=OA*tanfi_1-OD*tanfi_2 #in KVAR
print "(i) Leading KVAR supplied by the motor = %0.1f KVAR" %CM
#(ii)
BM=80 #in KW
CM=15.6 #in KW
KVA_Rating=np.sqrt(BM**2+CM**2) #in KVA
print "(ii) KVA rating = %0.1f KVA" %(KVA_Rating)
#(iii)
BC=KVA_Rating #in KW
cosfi_m=BM/BC #unitless
print "(iii) P.F. Of the motor = %0.2f "%cosfi_m
#Note : Answer of (i) part is wrong in the book is wrong

(i) Leading KVAR supplied by the motor = 14.4 KVAR
(ii) KVA rating = 81.5 KVA
(iii) P.F. Of the motor = 0.98


Exa 10.16 - page 280¶

In [43]:
from __future__ import division
import numpy as np
#Given Data :
x=80 #in Rs./KVA
x1=100 #in Rs/KVAR(cost of phase advancing equipment)
i=12 #in %
y=(i/100)*150 #in Rs./KVAR
cosfi_2=np.sqrt(1-(y/x)**2) #unitless
print "Most Ecomnomical PF = %0.2f lag" %cosfi_2

Most Ecomnomical PF = 0.97 lag


Exa 10.17 - page 280¶

In [46]:
from __future__ import division
import numpy as np
#Given Data :
P=300 #in KW
cosfi_1=0.7 #unitless
tanfi_1=np.tan(np.arccos(cosfi_1))
y=13 #in Rs./KVAR
x=130 #in Rs./KVA
cosfi_2=np.sqrt(1-(y/x)**2) #unitless
print "(i) Most Ecomnomical PF = %0.3f"%cosfi_2
tanfi_2=np.tan(np.arccos(cosfi_2))
#(ii)

(i) Most Ecomnomical PF = 0.995