Chapter6-Three phase Circuits

Ex8-pg6.14

In [1]:
## Three-Phase Circuits :example 6.8 :(pg 6.14)
VL=440.;
import math
P=50*10**3;
IL=90.;
Iph=IL/math.sqrt(3);
pf=(P/(math.sqrt(3)*VL*IL));
S=math.sqrt(3)*VL*IL;
print("\nVL=440 V \nP=50kW \nIL=90 A");
print"%s %.2f %s"%("\nVL=Vph=",VL," V");##For delta-connected load
print"%s %.2f %s"%("\nIph=IL/sqrt(3)=",Iph," A");
print("\nP=sqrt(3)*VL*IL*cos(phi)");
print"%s %.2f %s"%("\ncos(phi)=",pf," (lagging)");
print"%s %.2f %s"%("\nS=sqrt(3)*VL*IL =",S," VA");

VL=440 V 
P=50kW 
IL=90 A

VL=Vph= 440.00  V

Iph=IL/sqrt(3)= 51.96  A

P=sqrt(3)*VL*IL*cos(phi)

cos(phi)= 0.73  (lagging)

S=sqrt(3)*VL*IL = 68589.21  VA

Ex9-pg6.15

In [1]:
## Three-Phase Circuits :example 6.9 :(pg 6.15)
IL=15.;
import math
P=11.*10**3;
S=15.*10**3;
VL=S/(math.sqrt(3.)*IL);
Vph=VL/math.sqrt(3.);
x=(P/S)*57.3;
phi=math.acos(P/S);
Q=math.sqrt(3.)*VL*IL*math.sin(phi/57.3);
Iph=IL;
Zph=Vph/Iph;
R=Zph*math.cos(phi/57.3);
XL=Zph*math.sin(phi/57.3);
Vph1=VL;
Iph1=(Vph1/Zph);
IL1=math.sqrt(3.)*Iph1;
P1=math.sqrt(3.)*VL*IL1*math.cos(phi/57.3);
Q1=math.sqrt(3.)*VL*IL1*math.sin(phi/57.3);
print("\nIL=15 A \nP=11kW \nS=15kVA ");
##For a star-connected load
print"%s %.2f %s"%("\nS=sqrt(3)*VL*IL \nVL=",Vph," V");
print"%s %.2f %s"%("\ncos(phi)=P/S =",x,"");
print"%s %.3f %s"%("\nphi=",phi," degrees"); 
print"%s %.2f %s"%("\nQ=sqrt(3).VL.IL.sin(phi) = ",Q," VAR");
print"%s %.2f %s"%("\nIph=IL = ",IL," A");
print"%s %.2f %s"%("\nZph=Vph/Iph = ",Zph," Ohm");
print"%s %.2f %s"%("\nR= Zph*cos(phi) =",R," Ohm");
print"%s %.2f %s"%("\nXL=Zph*sin(phi)= ",XL," Ohm");
##If these coils are connected in Delta 
print"%s %.2f %s"%("\nCph =VL =",VL," V");
print"%s %.2f %s"%("\nZph= ",Zph," Ohm");
print"%s %.2f %s"%("\nIph=Vph/Zph =",Iph1," A ");
print"%s %.2f %s"%("\nIL=sqrt(3)*Iph =",IL1," A");
print"%s %.2f %s"%("\nP=sqrt(3)*VL*IL*cos(phi) =",P1," W");
print"%s %.2f %s"%("\nQ=sqrt(3)*VL*IL*sin(phi) =",Q1," VAR");

IL=15 A 
P=11kW 
S=15kVA 

S=sqrt(3)*VL*IL 
VL= 333.33  V

cos(phi)=P/S = 42.02 

phi= 0.748  degrees

Q=sqrt(3).VL.IL.sin(phi) =  195.70  VAR

Iph=IL =  15.00  A

Zph=Vph/Iph =  22.22  Ohm

R= Zph*cos(phi) = 22.22  Ohm

XL=Zph*sin(phi)=  0.29  Ohm

Cph =VL = 577.35  V

Zph=  22.22  Ohm

Iph=Vph/Zph = 25.98  A 

IL=sqrt(3)*Iph = 45.00  A

P=sqrt(3)*VL*IL*cos(phi) = 44996.17  W

Q=sqrt(3)*VL*IL*sin(phi) = 587.09  VAR

Ex10-pg6.15

In [2]:
## Three-Phase Circuits :example 6.10 :(pg 6.16)
P=1500.*10**3;
import math
pf=0.85;
VL=2.2*10**3;
phi=math.acos(pf)*57.3;
IL=P/(math.sqrt(3.)*VL*pf);
Iph=IL/math.sqrt(3.);
AC=Iph*pf;
RC=Iph*math.sin(phi/57.3);
IAC=IL*pf;
IRC=IL*math.sin(phi/57.3);
print("\nP=1500kW \npf=0.85 (lagging) \nVL=2.2kV");
##For Delta-connected load
print"%s %.2f %s"%("\nP=sqrt(3)*VL*IL*cos(phi) \nIL=",IL," A");
print"%s %.2f %s"%("\nIph=IL/sqrt(3)= ",Iph," A");
##AC=Active Component
print"%s %.2f %s"%("\nAC=Iph*cos(phi) = ",AC," A"); ##in each phase of load
##RC=Reactive Component
print"%s %.2f %s"%("\nRC=Iph*sin(phi) = ",RC," A"); ##in each phase of load
##For star-connected source
print"%s %.2f %s"%("\nIAC = ",IAC," A"); ## current of AC in each phase of source
print"%s %.2f %s"%("\nIRC = ",IRC,"A"); ## current of RC in each phase of source

P=1500kW 
pf=0.85 (lagging) 
VL=2.2kV

P=sqrt(3)*VL*IL*cos(phi) 
IL= 463.12  A

Iph=IL/sqrt(3)=  267.38  A

AC=Iph*cos(phi) =  227.27  A

RC=Iph*sin(phi) =  140.85  A

IAC =  393.65  A

IRC =  243.96 A

Ex11-pg6.16

In [3]:
## Three-Phase Circuits :example 6.11 :(pg 6.16)
import math
VL=208.;
P=1800.;
IL=10.;
Vph=VL/math.sqrt(3.);
Zph=(Vph/IL);
pf=P/(math.sqrt(3.)*VL*IL);
phi=math.acos(pf)*57.3;
Rph=Zph*pf;
Xph=Zph*math.sin(phi/57.3);
print("\nVL=208 V \nP=1800 W \nIL= 10 A");
##For a Wye-connected load,
print"%s %.2f %s"%("\nVph = VL/sqrt(3) = ",Vph," V");
print"%s %.2f %s"%("\nIph = IL = ",IL," A");
print"%s %.2f %s"%("\nZph=Vph/Iph = ",Zph," Ohm");
print("\nP=sqrt(3)*VL*IL*cos(phi)");
print"%s %.2f %s"%("\ncos(phi)= ",pf," degrees");
print"%s %.2f %s"%("\nphi= ",phi," degrees");
print"%s %.2f %s"%("\nRph=Zph*cos(phi) = ",Rph," Ohm");
print"%s %.2f %s"%("\nXph=Zph*sin(phi) = ",Xph," Ohm");

VL=208 V 
P=1800 W 
IL= 10 A

Vph = VL/sqrt(3) =  120.09  V

Iph = IL =  10.00  A

Zph=Vph/Iph =  12.01  Ohm

P=sqrt(3)*VL*IL*cos(phi)

cos(phi)=  0.50  degrees

phi=  60.03  degrees

Rph=Zph*cos(phi) =  6.00  Ohm

Xph=Zph*sin(phi) =  10.40  Ohm

Ex12-pg6.17

In [4]:
## Three-Phase Circuits :example 6.12 :(pg 6.17)
P=100.*10**3;
import math
IL=80.;
VL=1100.;
f=50.;
Vph=(VL/math.sqrt(3.));
Iph=IL;
Zph=(Vph/Iph);
pf=(P/(math.sqrt(3.)*VL*IL));
phi=math.acos(pf)*57.3;
Rph=Zph*pf;
Xph=Zph*math.sin(phi/57.3);
C=(1./(2.*math.pi*f*Xph));
print("\nP=100kW \nIL=80 A \nVL=1100 V \nf=50 Hz");
##For a star-connected load

print"%s %.2f %s"%("\nIph=IL  = ",Iph," A");



## as current is leading,reactance will be capacitive in nature
print("\nXC=(1/2*pi*C)");
print"%s %.2e %s"%("\nC= ",C," F");

print"%s %.2f %s"%("\nVph = VL/sqrt(3) = ",Vph," V");

print"%s %.2f %s"%("\nZph=Vph/Iph = ",Zph," Ohm");
print("\nP=sqrt(3)*VL*IL*cos(phi)");
print"%s %.2f %s"%("\ncos(phi)= ",pf," degrees");
print"%s %.2f %s"%("\nphi= ",phi," degrees");
print"%s %.2f %s"%("\nRph=Zph*cos(phi) = ",Rph," Ohm");
print"%s %.2f %s"%("\nXph=Zph*sin(phi) = ",Xph," Ohm");

P=100kW 
IL=80 A 
VL=1100 V 
f=50 Hz

Iph=IL  =  80.00  A

XC=(1/2*pi*C)

C=  5.31e-04  F

Vph = VL/sqrt(3) =  635.09  V

Zph=Vph/Iph =  7.94  Ohm

P=sqrt(3)*VL*IL*cos(phi)

cos(phi)=  0.66  degrees

phi=  49.00  degrees

Rph=Zph*cos(phi) =  5.21  Ohm

Xph=Zph*sin(phi) =  5.99  Ohm

Ex13-pg6.17

In [5]:
## Three-Phase Circuits :example 6.13 :(pg 6.17 & 6.18)

import math
VL=400.;
IL=34.65;
P=14.4*10**3;
Iph=(IL/math.sqrt(3.));
Zph=(VL/Iph);
pf=(P/(math.sqrt(3.)*VL*IL));
phi=math.acos(pf)*57.3;
Rph=(Zph*pf);
Xph=(Zph*math.sin(phi/57.3));
print("\nVL=400 V \nIL=34.65 A \nP=14.4kW");
##For a Delta-connected load
print"%s %.2f %s"%("\nVL=Vph= ",VL," V");
print"%s %.2f %s"%("\nIph=IL/sqrt(3)= ",Iph," A");


print"%s %.2f %s"%("\nZph=Vph/Iph = ",Zph," Ohm");
print("\nP=sqrt(3)*VL*IL*cos(phi)");
print"%s %.2f %s"%("\ncos(phi)= ",pf," degrees");
print"%s %.2f %s"%("\nphi= ",phi," degrees");
print"%s %.2f %s"%("\nRph=Zph*cos(phi) = ",Rph," Ohm");
print"%s %.2f %s"%("\nXph=Zph*sin(phi) = ",Xph," Ohm");

VL=400 V 
IL=34.65 A 
P=14.4kW

VL=Vph=  400.00  V

Iph=IL/sqrt(3)=  20.01  A

Zph=Vph/Iph =  19.99  Ohm

P=sqrt(3)*VL*IL*cos(phi)

cos(phi)=  0.60  degrees

phi=  53.15  degrees

Rph=Zph*cos(phi) =  11.99  Ohm

Xph=Zph*sin(phi) =  16.00  Ohm

Ex14-pg6.18

In [6]:
## Three-Phase Circuits :example 6.14 :(pg 6.18)
P=10.44*10**3;
import math
VL=200.;
pf=0.5;
x=math.acos(pf)*57.3;
IL=(P/(math.sqrt(3.)*VL*pf));
Iph=(IL/math.sqrt(3.));
Zph=(VL/Iph);
Rph=(Zph*pf);
Xph=(Zph*math.sin(x/57.3));
Q=(math.sqrt(3.)*VL*IL*math.sin(x/57.3));
print("\nP=10.44kW \nVL=200 V \npf=0.5(leading)");
## For a delta-connected load,

print"%s %.2f %s"%("\nP=qrt(3)*VL*IL*cos(phi) \nIL= ",IL," A");


print"%s %.2f %s"%("\nQ=sqrt(3)*VL*IL*sin(phi) = ",Q," VAR");


print"%s %.2f %s"%("\nVL=Vph= ",VL," V");
print"%s %.2f %s"%("\nIph=IL/sqrt(3)= ",Iph," A");


print"%s %.2f %s"%("\nZph=Vph/Iph = ",Zph," Ohm");

print"%s %.2f %s"%("\nRph=Zph*cos(phi) = ",Rph," Ohm");
print"%s %.2f %s"%("\nXph=Zph*sin(phi) = ",Xph," Ohm");

P=10.44kW 
VL=200 V 
pf=0.5(leading)

P=qrt(3)*VL*IL*cos(phi) 
IL=  60.28  A

Q=sqrt(3)*VL*IL*sin(phi) =  18082.61  VAR

VL=Vph=  200.00  V

Iph=IL/sqrt(3)=  34.80  A

Zph=Vph/Iph =  5.75  Ohm

Rph=Zph*cos(phi) =  2.87  Ohm

Xph=Zph*sin(phi) =  4.98  Ohm

Ex17-pg6.20

In [7]:
## Three-Phase Circuits :example 6.17 :(pg 6.20)
import math
Po=200.*10**3;
f=50.;
VL=440.;
N=0.91;
pf=0.86;
phi=math.acos(pf)*57.3;
Pi=(Po/N);
IL=(Pi/(math.sqrt(3.)*VL*pf));
Iph=(IL/math.sqrt(3.));
AC=(Iph*pf);
RC=(Iph*math.sin(phi/57.3));
print("\nPo=200 kW \nf=50Hz \nVL= 440 V \nN=0.91 \npf=0.86");
##For a delta connected load (induction motor)
print"%s %.2f %s"%("\nVph =VL =  ",VL,"");
print("\nN=(Po/Pi)");##efficiency
print"%s %.2f %s"%("\nPi= ",Pi," W");##Input power
print"%s %.2f %s"%("\nPi=sqrt(3)*VL*IL*cos(phi) \nIL= ",IL," A");
print"%s %.2f %s"%("\nAC = (Iph*cos(phi))= ",AC," A");##Active component of phase current
print"%s %.2f %s"%("\nRC=(Iph*sin(phi)) = ",RC," A");##Reactive component of phase current

Po=200 kW 
f=50Hz 
VL= 440 V 
N=0.91 
pf=0.86

Vph =VL =   440.00 

N=(Po/Pi)

Pi=  219780.22  W

Pi=sqrt(3)*VL*IL*cos(phi) 
IL=  335.33  A

AC = (Iph*cos(phi))=  166.50  A

RC=(Iph*sin(phi)) =  98.80  A

Ex18-pg6.21

In [8]:
## Three-Phase Circuits :example 6.18 :(pg 6.20)
VL=400.;
import math
Po=112.*10**3;
pf=0.86;
phi=(math.acos(pf)*57.3);
N=0.88; ##Efficiency
Pi=(Po/N);
IL=(Pi/(math.sqrt(3.)*VL*pf));
Iph=(IL/math.sqrt(3.));
AC=(Iph*pf);
RC=(Iph*math.sin(phi/57.3));
Aac=(IL*pf);
Arc=(IL*math.sin(phi/57.3));
print("\nVL=400 V \nPo=112kW \npf=0.86 \nN=0.88");
##For a mesh-connected load (induction motor)
print"%s %.2f %s"%("\nVph=VL= ",VL," V");
print"%s %.2f %s"%("\nN=Po/Pi  \nPi= ",Pi," W");##Input power
print"%s %.2f %s"%("\nPi=sqrt(3)*VL*IL*cos(phi) \nIL= ",IL," A");
print"%s %.2f %s"%("\nIph=IL/sqrt(3) = ",Iph," A");
##current in star-connected load=line current drawn by motor
print"%s %.2f %s"%("\nIA= ",IL," A");##current in alternate phase
print"%s %.2f %s"%("\nAC=Iph*cos(phi) = ",AC," A");##active component in each phase of motor
print"%s %.2f %s"%("\nRC=Iph*sin(phi) = ",RC," A");##Reactive component in each phase of motor
print"%s %.2f %s"%("\nAac= ",Aac," A");##active component in each alternate phase
print"%s %.2f %s"%("\nArc= ",Arc," A");##reactive component in each alternate phase

VL=400 V 
Po=112kW 
pf=0.86 
N=0.88

Vph=VL=  400.00  V

N=Po/Pi  
Pi=  127272.73  W

Pi=sqrt(3)*VL*IL*cos(phi) 
IL=  213.61  A

Iph=IL/sqrt(3) =  123.33  A

IA=  213.61  A

AC=Iph*cos(phi) =  106.06  A

RC=Iph*sin(phi) =  62.93  A

Aac=  183.70  A

Arc=  109.00  A

Ex19-pg6.21

In [9]:
## Three-Phase Circuits :example 6.19 :(pg 6.21 & 6.22)

import math
VL=400.;
IL=5.;
Vph=(VL/math.sqrt(3.));
Zph=(Vph/IL);
Iph=(IL/math.sqrt(3));
Vph1=(Iph*Zph);
print("\nVl=400 V \nIL=5 A");
##For a star-connected load
print"%s %.2f %s"%("\nVph=VL/sqrt(3) = ",Vph," V");
print"%s %.2f %s"%("\nIph=IL= ",IL," A");
print"%s %.2f %s"%("\nZph=Rph=Vph/Iph = ",Zph," Ohm");
##For a delta connected load
print"%s %.2f %s"%("\nIL=5 A \nRph= ",Zph," Ohm");
print"%s %.2f %s"%("\nIph=IL/sqrt(3)= ",Iph," A");
print"%s %.2f %s"%("\nVph=Iph*Rph \n= ",Vph1," V");
##Voltage needed is 1/3 of the star value

Vl=400 V 
IL=5 A

Vph=VL/sqrt(3) =  230.94  V

Iph=IL=  5.00  A

Zph=Rph=Vph/Iph =  46.19  Ohm

IL=5 A 
Rph=  46.19  Ohm

Iph=IL/sqrt(3)=  2.89  A

Vph=Iph*Rph 
=  133.33  V

Ex20-pg6.22

In [10]:
## Three-Phase Circuits :example 6.20 :(pg 6.22 & 6.23)
VL=400;
import math
Zph=100.;
Vph=(VL/math.sqrt(3.));
Iph=(Vph/Zph);
pf=1.;
P=(math.sqrt(3.)*VL*Iph*pf);
Iph1=(VL/Zph);
IL1=(math.sqrt(3.)*Iph1);
P1=(math.sqrt(3.)*VL*IL1*pf);
I1=(VL/200.);
Pa=(VL*I1);
I2=(VL/100.);
Pb=(VL*I1*I2);
print("\nVL=400 V \nZph = 100 Ohm");
##For a star connected load
print"%s %.2f %s"%("\nVph=VL/sqrt(3) = ",Vph," V");
print"%s %.2f %s"%("\nIph = VL/Zph = ",Iph," A");
print"%s %.2f %s"%("\nIL=Iph = ",Iph," A");
print"%s %.2f %s"%("\ncos(phi)=1 \nP=sqrt(3).VL.IL.cos(phi) = ",P," W");
##For a delta connected load
print"%s %.2f %s"%("\nVph=VL= ",VL," V");
print"%s %.2f %s"%("\nIph=Vph/Zph = ",Iph1," A");
print"%s %.2f %s"%("\nIL=sqrt(3)*Iph = ",IL1," A");
print"%s %.2f %s"%("\nP=sqrt(3)*VL*IL*cos(phi) =  ",P1," W");
##When resistors are open circuited
##(i)Star connection
print"%s %.2f %s"%("\nI= ",I1," A");##Current in lines
print"%s %.2f %s"%("\nP= ",Pa," W");##Power taken from mains
##(ii)Delta connection
print"%s %.2f %s"%("\nI= ",I2,"A");##Current in each phase
print"%s %.2f %s"%("\nP= ",Pb," W");##Power taken from mains

VL=400 V 
Zph = 100 Ohm

Vph=VL/sqrt(3) =  230.94  V

Iph = VL/Zph =  2.31  A

IL=Iph =  2.31  A

cos(phi)=1 
P=sqrt(3).VL.IL.cos(phi) =  1600.00  W

Vph=VL=  400.00  V

Iph=Vph/Zph =  4.00  A

IL=sqrt(3)*Iph =  6.93  A

P=sqrt(3)*VL*IL*cos(phi) =   4800.00  W

I=  2.00  A

P=  800.00  W

I=  4.00 A

P=  3200.00  W

Ex27-pg6.30

In [11]:
## Three-Phase Circuits :example 6.27 :(pg 6.30 & 6.31)
import math
W1=2000.;
W2=500.;
W3=-500.;
x=(math.sqrt(3.)*((W1-W2)/(W1+W2)));
phi=math.atan(x)*57.3;
pf=math.cos(phi/57.3);
y=(math.sqrt(3.)*((W1-W3)/(W1+W3)));
phi1=math.atan(y)*57.3;
pf1=math.cos(phi1/57.3);
print("\nW1 = 2000W \nW2 = 500 W");
##(i) When both readings are same
print("\nWhen W1 &W2 are same \nW1 = 2000W \nW2 = 500 W");
print"%s %.2f %s"%("\ntan(phi)= sqrt(3).(W1-W2/W1+W2) = ",x,"");
print"%s %.2f %s"%("\nphi= ",phi," degrees");
print"%s %.2f %s"%("\npf=cos(phi)=",pf,"");##Power factor
##(ii) When the latter reading is obtained after reversing the connection to the current coil of 1 instrument
print("\nWhen W2 is reversed \nW1= 2000 W \nW2= -500 W");
print"%s %.2f %s"%("\ntan(phi)= sqrt(3).(W1-W2/W1+W2) =",y,"");
print"%s %.2f %s"%("\nphi= ",phi1," degrees");
print"%s %.2f %s"%("\npf=cos(phi)= ",pf1,"");##Power factor

W1 = 2000W 
W2 = 500 W

When W1 &W2 are same 
W1 = 2000W 
W2 = 500 W

tan(phi)= sqrt(3).(W1-W2/W1+W2) =  1.04 

phi=  46.11  degrees

pf=cos(phi)= 0.69 

When W2 is reversed 
W1= 2000 W 
W2= -500 W

tan(phi)= sqrt(3).(W1-W2/W1+W2) = 2.89 

phi=  70.90  degrees

pf=cos(phi)=  0.33

Ex28-pg6.31

In [12]:
## Three-Phase Circuits :example 6.28 :(pg 6.31)
W1=5.*10**3;
import math
W2=-(0.5*10**3);
P=(W1+W2);
x=(math.sqrt(3.)*((W1-W2)/(W1+W2)));
phi=math.atan(x)*57.3;
pf=math.cos(phi/57.3);
print("\nW1=5kW \W2=0.5kW");
## When the latter readings are obtained after the reversal of the current coil terminals of the wattmeter
print("\nWhen W2 is reversed \nW1=5kW \nW2=-0.5kW");
print"%s %.2f %s"%("\nP=W1+W2 =  ",P," W");##Power
print"%s %.2f %s"%("\ntan(phi)=sqrt(3)*(W1-W2/W1+W2) =",x,"");
print"%s %.2f %s"%("\nphi= ",phi," degrees ");
print"%s %.2f %s"%("\npf=cos(phi) =",pf,"");##Power factor

W1=5kW \W2=0.5kW

When W2 is reversed 
W1=5kW 
W2=-0.5kW

P=W1+W2 =   4500.00  W

tan(phi)=sqrt(3)*(W1-W2/W1+W2) = 2.12 

phi=  64.72  degrees 

pf=cos(phi) = 0.43

Ex29-pg6.31

In [13]:
## Three-Phase Circuits :example 6.29 :(pg 6.31)
import math
S=10*10**3;
pf=0.342;
x=(S/math.sqrt(3.));
phi=math.acos(pf)*57.3;
W1=x*math.cos(30+phi)/(57.3);
W2=x*math.cos(30-phi)/(57.3);
print("\nS=10kVA \npf=0.342 \nS=sqrt(3)*VL*IL");
print"%s %.2f %s"%("\nVL*IL= ",x,"VA");
print"%s %.2f %s"%("\ncos(phi)=",pf,"");
print"%s %.2f %s"%("\nphi= ",phi," degrees");
##(i)when power factor is leading
print"%s %.2f %s"%("\npf leading \nW1=VL.IL.cos(30+phi)=  ",W1," W");
print"%s %.2f %s"%("\n \nW2=VL.IL.cos(30-phi)= ",W2," W");
##(i)when power factor is lagging
print"%s %.2f %s"%("\npf lagging \nW1=VL.IL.cos(30-phi)= ",W2," W");
print"%s %.2f %s"%("\n \nW2=VL.IL.cos(30+phi)=",W1," W");

S=10kVA 
pf=0.342 
S=sqrt(3)*VL*IL

VL*IL=  5773.50 VA

cos(phi)= 0.34 

phi=  70.01  degrees

pf leading 
W1=VL.IL.cos(30+phi)=   87.21  W

 
W2=VL.IL.cos(30-phi)=  -67.68  W

pf lagging 
W1=VL.IL.cos(30-phi)=  -67.68  W

 
W2=VL.IL.cos(30+phi)= 87.21  W

Ex30-pg6.31

In [14]:
## Three-Phase Circuits :example 6.30 :(pg 6.31 & 6.32)
VL=2000.;
import math
N=0.9;##efficiency
W1=300.*10**3;
W2=100.*10**3;
P=W1+W2;
x=(math.sqrt(3.)*((W1-W2)/(W1+W2)));
phi=math.atan(x)*57.3;
pf=math.cos(phi/57.3);
IL=(P/(math.sqrt(3.)*VL*pf));
print("\nVL=2000 V \nN=0.9 \nW1=300kW \nW2=100kW");
print"%s %.2f %s"%("\nP=W1+W2 = ",P," W");##Input Power
print"%s %.2f %s"%("\ntan(phi)=(sqrt(3)*(W1-W2/W1+W2)) =",x,"");
print"%s %.2f %s"%("\nphi= ",phi," degrees ");
print"%s %.2f %s"%("\ncos(phi)=",pf,"");##Power factor
print"%s %.2f %s"%("\nP=sqrt(3)*VL*IL*cos(phi) \nIL= ",IL," A");

VL=2000 V 
N=0.9 
W1=300kW 
W2=100kW

P=W1+W2 =  400000.00  W

tan(phi)=(sqrt(3)*(W1-W2/W1+W2)) = 0.87 

phi=  40.90  degrees 

cos(phi)= 0.76 

P=sqrt(3)*VL*IL*cos(phi) 
IL=  152.75  A

Ex31-pg6.32

In [15]:
## Three-Phase Circuits :example 6.31 :(pg 6.32)
import math
VL=220.;
Po=11.2*10**3;
N=0.88;##efficiency
IL=38.;
Pi=(Po/N);
x=(Pi/(math.sqrt(3.)*VL*IL));
phi=math.acos(x)*57.3;
W1=(VL*IL*math.cos(30-phi)/57.3);
W2=(VL*IL*math.cos(30+phi)/57.3);
print"%s %.2f %s"%("\nVL=220 V \nPo=11.2kW \nN=0.88 \nIL=38A \N=(Po/Pi)= ",Pi," W");
print"%s %.2f %s"%("\nPi=sqrt(3)*VL*IL*cos(phi) \ncos(phi)= ",x," lagging");
print"%s %.2f %s"%("\nphi=",phi," degrees");
print"%s %.2f %s"%("\nW1 =VL*IL*cos(30-phi) = ",W1," W");
print"%s %.2f %s"%("\nW2 =VL*IL*cos(30+phi) = ",W2," W");

VL=220 V 
Po=11.2kW 
N=0.88 
IL=38A \N=(Po/Pi)=  12727.27  W

Pi=sqrt(3)*VL*IL*cos(phi) 
cos(phi)=  0.88  lagging

phi= 28.49  degrees

W1 =VL*IL*cos(30-phi) =  8.15  W

W2 =VL*IL*cos(30+phi) =  -52.16  W