# Chapter 5: Three phase AC Circuits¶

## Example 1: pg 200¶

In [1]:
#pg 200
#calculate the line current, power factor and power supplied
#  Given data
from math import cos,acos,sqrt
R = 20.;#  in ohm
X_L = 15.;#  in ohm
V_L = 400.;#  in V
f = 50.;#  in Hz
#calculations
V_Ph = V_L/sqrt(3);#  in V
Z_Ph = sqrt( (R**2) + (X_L**2) );#  in ohm
I_Ph = V_Ph/Z_Ph;#  in A
I_L = I_Ph;#  in A
print "The line current in A is",round(I_L,2)
# pf = cos(phi) = R_Ph/Z_Ph;
R_Ph = R;#  in ohm
phi= acos(R_Ph/Z_Ph);
#  Power factor
pf= cos(phi);#  in radians
print "The power factor is : ",pf,"degrees lag."
P = sqrt(3)*V_L*I_L*cos(phi);#  in W
print "The power supplied in W is",P

The line current in A is 9.24
The power factor is :  0.8 degrees lag.
The power supplied in W is 5120.0


## Example 2: pg 201¶

In [2]:
#pg 201
#calculate the line and phase voltage, current and power
#  Given data
from math import sqrt,cos
import cmath
R_Ph = 16.;#  in ohm
X_L = 12.;#  in ohm
V_L = 400.;#  in V
f = 50.;#  in Hz
#calculations
V_Ph = V_L/sqrt(3);#  in V
Z_Ph = R_Ph + 1j*X_L;#  in ohm
I_Ph= V_Ph/Z_Ph;#  in A
I_L= I_Ph;#  in A
phi= cmath.phase(I_L);
cos_phi= R_Ph/abs(Z_Ph);
P= sqrt(3)*V_L*abs(I_L)*cos_phi;#  in W
#results
print "The line voltage in V is",V_L
print "The phase voltage in V is",round(V_Ph,2)
print "The line current in A is : ",round(abs(I_L),2)
print "The line current in A is : ",round(abs(I_Ph),2)
print "Power factor is : ",cos_phi," lagging"
print "The power absorbed in W is : ",P

The line voltage in V is 400.0
The phase voltage in V is 230.94
The line current in A is :  11.55
The line current in A is :  11.55
Power factor is :  0.8  lagging
The power absorbed in W is :  6400.0


## Example 3: pg 202¶

In [3]:
#pg 202
#calculate the resistance and inductance
#  Given data
from math import sqrt,cos,pi,acos
P = 1.5;#  in kW
P = P * 10**3;#  in W
pf = 0.2;#  in lag
V_L = 400;#  in V
f = 50;#  in Hz
#calculations
phi= acos(pf);
V_Ph = V_L/sqrt(3);#  in V
# P = sqrt(3)*V_L*I_L*cos(phi);
I_L = P/(sqrt(3)*V_L*cos(phi));#  in A
I_Ph = I_L;#  in A
Z_Ph = V_Ph/I_Ph;#  in ohm
R_Ph = Z_Ph*cos(phi);#  in ohm
X_Ph = sqrt( (Z_Ph**2) - (R_Ph**2) );#  in  ohm
L_Ph = X_Ph/(2*pi*f);#  in H
#results
print "The Resistance in ohm is",round(R_Ph,2)
print "The inductance in H is",round(L_Ph,4)

The Resistance in ohm is 4.27
The inductance in H is 0.0665


## Example 4: pg 203¶

In [4]:
#pg 203
#calculate the line current and total power
#  Given data
from math import sqrt,pi,cos,acos
R = 5;#  in ohm
L =0.02;#  in H
V_L = 440.;#  in V
f = 50.;#  in Hz
#calculations
X_L = 2*pi*f*L;#  in  ohm
Z_Ph = sqrt( (R**2)+(X_L**2) );#  in ohm
V_Ph = V_L;#  in V
I_Ph = V_Ph/Z_Ph;#  in A
I_L = sqrt(3)*I_Ph;#  in A
phi = acos(R/Z_Ph);#  in lag
P = sqrt(3)*V_L*I_L*cos(phi);#  in W
P= P*10**-3;#  in kW
#results
print "The line current in A is",round(I_L,2)
print "The total power absorbed in kW is",round(P,2)

print 'Note: To evaluate the value of P, the wrong value of I_L is put , so the calculated value of P in the book is not correct'

The line current in A is 94.91
The total power absorbed in kW is 45.04
Note: To evaluate the value of P, the wrong value of I_L is put , so the calculated value of P in the book is not correct


## Example 5: pg 203¶

In [5]:
#pg 203
#calculate the phase current, resistance, inductance and power
#  Given data
from math import acos,sqrt,pi,cos
V_L = 400.;#  in V
f = 50.;#  in Hz
I_L = 17.32;#  in A
pf = 0.8;# in lag
#calculations
I_Ph = I_L/sqrt(3);#  in A
print "The phase current in A is",round(I_Ph)
V_Ph = V_L;#  in V
Z_Ph = V_Ph/I_Ph;#  in ohm
phi = acos(pf)#  in lag
R_Ph = Z_Ph*cos(phi);#  in ohm
print "The resistance of coil in ohm is",round(R_Ph)
X_Ph = sqrt( (Z_Ph**2) - (R_Ph**2) );#  in ohm
#  X_Ph = 2*%pi*f*L;
L = X_Ph/(2*pi*f);#  in H
L = L * 10**3;#  in mH
print "The inductance of coil in mH is",round(L,1)
P = V_Ph*I_Ph*cos(phi);#  in W
print "The power drawn by each coil in W is",round(P)

The phase current in A is 10.0
The resistance of coil in ohm is 32.0
The inductance of coil in mH is 76.4
The power drawn by each coil in W is 3200.0


## Example 6: pg 208¶

In [6]:
#pg 208
#calculate the power factor
from math import atan,sqrt,cos
#  Given data
W1 = 1000.;#  in W
W2 = 550.;#  in W
#calculations
phi = (atan( sqrt(3)*((W1-W2)/(W1+W2)) ));# in radians
#  power factor
pf= cos(phi);#  lag
print "The power factor of the load is : ",round(pf,2)," lag."

The power factor of the load is :  0.89  lag.


## Example 7: pg 208¶

In [7]:
#pg 208
#calculate the power factor in both cases
#  Given data
from math import cos,atan,sqrt
W1 = 2000.;#  in W
W2 = 500.;#  in W
#calculations
phi = (atan( sqrt(3)*((W1-W2)/(W1+W2)) ));#  in lag
#  power factor
pf= cos(phi);#  lagging
print "Part (i) : Power factor is : ",round(pf,4)," lagging"
W2 = -W2;#  in W
phi = (atan( sqrt(3)*((W1-W2)/(W1+W2)) ));#  in lag
#  power factor
pf= cos(phi);#  lagging
print "Part (ii) : Power factor is : ",round(pf,3)," lagging"

Part (i) : Power factor is :  0.6934  lagging
Part (ii) : Power factor is :  0.327  lagging


## Example 8: pg 208¶

In [8]:
#pg 208
#calculate the power factor
#  Given data
from math import atan,sqrt,cos
W1 = 375.;#  in W
W2 = -50.;#  in W
#calculations
#  tan(phi) = sqrt(3)*((W1-W2)/(W1+W2));
phi = atan(sqrt(3)*((W1-W2)/(W1+W2)));#  in degree
#  power factor
pf= cos(phi);#  lag
#results
print "The power factor is : ",round(pf,3)," lag."

The power factor is :  0.404  lag.


## Example 9: pg 209¶

In [9]:
#pg 209
#calculate the power input,factor,output and line current
#  Given data
from math import atan,cos,sqrt
W1 = 300.;#  in kW
W2 = 100.;#  in kW
V_L= 2000.;#  in V
Eta= 90/100.;
#calculations
P = W1+W2;#  in kW
#  tan(phi) = sqrt(3)*((W1-W2)/(W1+W2));
phi = atan(sqrt(3)*((W1-W2)/(W1+W2)));
pf = cos(phi);#  power factor
#  P = sqrt(3)*V_L*I_L*cosd(phi);
I_L = (P*10**3)/(sqrt(3)*V_L*pf);#  in A
output = P*Eta;#  in kW
#results
print "The power input in kW is",P
print "The power factor is",round(pf,3)
print "The line current in A is",round(I_L,2)
print "The power output in kW is",output

The power input in kW is 400.0
The power factor is 0.756
The line current in A is 152.75
The power output in kW is 360.0


## Example 10: pg 209¶

In [10]:
#pg 209
#calculate the phase current,impedance and power factor
#  Given data
from math import sqrt,acos,cos
P = 12.;#  in kW
P = P * 10**3;#  in W
V_L = 400.;#  in V
I_L = 20.;#  in A
I_Ph = I_L;#  in A
#calculations
V_Ph = V_L/sqrt(3);#  in V
Z_Ph = V_Ph/I_Ph;#  in ohm
#  P = sqrt(3)*V_L*I_L*cos(phi);
phi= acos(P/(sqrt(3)*V_L*I_L));#  in lag
#  power factor
pf= cos(phi);#  lag
#results
print "The phase current in A is",I_Ph
print "The impedance of load in ohm is",round(Z_Ph,2)
print "The power factor is : ",round(pf,3)," lag."

The phase current in A is 20.0
The impedance of load in ohm is 11.55
The power factor is :  0.866  lag.


## Example 11: pg 210¶

In [11]:
#pg 210
#calculate the line current, power factor, three phase power and volt amperes
#  Given data
import cmath
from math import cos,sqrt
Z_Ph= 8+6*1j;#  in ohm
V_L= 400;#  in V
#calculations
V_Ph= V_L/sqrt(3);#  in V
I_Ph= V_Ph/Z_Ph;#  in A
I_L= I_Ph;#  in A
phi= cmath.phase(I_L);#  in radians
print "The line current in A is : ",round(abs(I_L),2)
#  power factor
pf= cos(phi);#  lagging
print "Power factor is : ",pf," lagging"
P= sqrt(3)*V_L*abs(I_L)*cos(phi);#  in W
print "The three phase power in W is : ",P
S= sqrt(3)*V_L*abs(I_L);#  in VA.
print "The three phase volt-amperes in VA is : ",S

The line current in A is :  23.09
Power factor is :  0.8  lagging
The three phase power in W is :  12800.0
The three phase volt-amperes in VA is :  16000.0


## Example 12: pg 211¶

In [12]:
#pg 211
#calculate the power and power factor
#  Given data
from math import atan,cos,sqrt
W1 = 20.;#  in kW
W2 = -5.;#  in kW
#calculations
P = W1+W2;#  in kW
phi = (atan( sqrt(3)*((W1-W2)/(W1+W2)) ));#  in lag
#  Power factor of the load
pf= cos(phi)
#results
print "The power in kW is : ",P
print "The power factor of the load is : ",round(pf,4)

The power in kW is :  15.0
The power factor of the load is :  0.3273


## Example 13: pg 211¶

In [13]:
#pg 211
#calculate the readings on both meters
#  Given data
from math import atan,sqrt,cos,pi
V_L = 400.;#  in V
I_L = 10.;#  in A
W2= 1.;#  assumed
#calculations
W1= 2*W2;
phi= atan(sqrt(3)*(W1-W2)/(W1+W2))*180/pi;
W1= V_L*I_L*cos(30-phi);#  in W
W2= V_L*I_L*cos(30+phi);#  in W
#results
print "The reading of first wattmeter in W is : ",W1
print "The reading of second wattmeter in W is : ",round(W2)
print 'The answer in textbook is wrong. please check using a calculator'

The reading of first wattmeter in W is :  4000.0
The reading of second wattmeter in W is :  -3810.0
The answer in textbook is wrong. please check using a calculator


## Example 14: pg 212¶

In [15]:
#pg 212
#calculate the phase current, resistance, inductance and power
#  Given data
from math import acos,pi,cos,sqrt
from cmath import phase,exp
V_L = 400;#  in V
f = 50;#  in Hz
I_L = 17.32;#  in A
#calculations
phi = acos(0.8);
I_Ph =I_L/sqrt(3);#  in A
print "The phase current in A is",round(I_Ph)
V_Ph=V_L;#  in V
Z_Ph = V_Ph/I_Ph;#  in ohm
Z_Ph= Z_Ph*exp(phi*1j);#  in ohm
R= Z_Ph.real;#  in ohm
XL= Z_Ph.imag;#  in ohm
L= XL/(2*pi*f);#  in H
L= L*10**3;#  in mH
print "The resistance of the coil in ohm is : ",round(R)
print "The inductance of the coil in mH is : ",round(L,4)
#  The power drawn by each coil
P_Ph= V_Ph*I_Ph*cos(phi);#  in W
print "The power drawn by each coil in W is : ",round(P_Ph)

The phase current in A is 10.0
The resistance of the coil in ohm is :  32.0
The inductance of the coil in mH is :  76.3966
The power drawn by each coil in W is :  3200.0


## Example 15: pg 212¶

In [16]:
#pg 212
#calculate the readings of both wattmeters
#  Given data
from math import sqrt,acos,cos,pi
P = 30;#  in kW
pf = 0.7;
#calculations
#  cosd(phi) = pf;
phi = acos(pf)*180/pi;#  in degree
#  P = sqrt(3)*V_L*I_L*cosd(phi);
theta = 30.;#  in degree
V_LI_L = P/(sqrt(3)*cos(phi*pi/180));
W1 = V_LI_L*cos((theta-phi)*pi/180);#  in kW
W2 = V_LI_L*cos((theta+phi)*pi/180);#  in kW
#results
print "The reading of first wattmeter in kW is",round(W1,4)
print "The reading of second wattmeter in kW is",round(W2,4)

The reading of first wattmeter in kW is 23.8352
The reading of second wattmeter in kW is 6.1648


## Example 16: pg 213¶

In [17]:
#pg 213
#calculate the power factor,resistance, capacitance
#  Given data
from math import cos,pi,acos,sqrt
from cmath import exp
P = 18.;#  in kW
P= P*10**3;#  in W
I_L = 60.;#  in A
V_L = 440.;#  in V
f= 50.;#  in Hz
#calculations
#  P = sqrt(3)*V_L*I_L*cosd(phi);
phi= acos(P/(sqrt(3)*V_L*I_L));#  in radians
I_L= I_L*exp(phi*1j);#  in A
I_Ph= I_L;#  in A
V_Ph= V_L/sqrt(3);#  in V
Z_Ph= V_Ph/I_Ph;#  in ohm
R= Z_Ph.real;#  in ohm
XC=abs(Z_Ph.imag);#  in ohm
C = 1/(2*pi*f*XC);#  in F
C=C*10**6;#  in muF
#  Power factor
#results
print "The power factor is : ",round(pf,4)," leading"
print "The resistance in ohm is : ",round(R,4)
print "The capacitance in muF is : ",round(C,4)
print "The load is capacitive in nature."

The power factor is :  0.3936  leading
The resistance in ohm is :  1.6667
The capacitance in muF is :  817.8438
The load is capacitive in nature.


## Example 17: pg 213¶

In [18]:
#pg 213
#calculate the power factor, line current, impedance, resistance and inductance
#  Given data
from math import cos,pi,acos,sqrt,atan
from cmath import exp
V_L = 400.;#  in V
f = 50.;#  in Hz
W1 = 8000.;#  in W
W2 = 4000.;#  in W
#calculations
W = W1+W2;#  in W
phi =(atan( sqrt(3)*((W1-W2)/(W1+W2)) ));#  in lag
P = W;#  in W
# P = sqrt(3)*V_L*I_L*cosd(phi);
I_L = P/(sqrt(3)*V_L*cos(phi));#  in A
V_Ph = V_L/sqrt(3);#  in V
I_Ph = I_L;#  in A
Z_Ph = V_Ph/I_Ph;#  in  ohm
Z_Ph= Z_Ph*exp(phi*1j);#  ohm
R_Ph= Z_Ph.real;#  in ohm
XL_Ph= Z_Ph.imag;#  in ohm
L_Ph= XL_Ph/(2*pi*f);#  in H
#  power factor
pf= cos(phi);
#results
print "The power factor is : ",round(pf,5)
print "The line current in A is",I_L
print "The impedance of each phase in ohm is : ",Z_Ph
print "The resistance of each phase in ohm is : ",R_Ph
print "The inductance of each phase in H is : ",round(L_Ph,5)

The power factor is :  0.86603
The line current in A is 20.0
The impedance of each phase in ohm is :  (10+5.7735026919j)
The resistance of each phase in ohm is :  10.0
The inductance of each phase in H is :  0.01838