Chapter3:THREE PHASE CIRCUITS

Ex3.1:pg-286

In [5]:
import cmath
f=50.0; #Assigning values to parameters
Vl=400.0;
Rph=20.0;
L=0.5;
Xl=2*math.pi*f*L;
Zph=20+1j*157;
[r,t]=cmath.polar(Zph);
Vph=Vl/sqrt(3); #Star connection
Iph=Vph/r;
Il=Iph;
P=sqrt(3)*Vl*Il*cos(t);
print"The line current for Star connection is Il=",round(Il,2),"Amperes"
print"The total power absorbed in Star connection is P=",round(P,3),"Watts"
Vph=Vl;  #Delta connection
Iph=Vph/r;
Il=sqrt(3)*Iph;
P=sqrt(3)*Vl*Il*cos(t);
print"The line current for Delta connection is Il=",round(Il,2),"Amperes"
print"The total power absorbed in Delta connection is P=",round(P,2),"Watts"

The line current for Star connection is Il= 1.46 Amperes
The total power absorbed in Star connection is P= 127.75 Watts
The line current for Delta connection is Il= 4.38 Amperes
The total power absorbed in Delta connection is P= 383.25 Watts

Ex3.2:pg-288

In [6]:
import cmath
f=50 #Assigning values to parameters
rph=8
l=0.02
xl=2*math.pi*f*l
vl=230
f=50
vph=vl/sqrt(3)
zph=8+1j*6.28
[r,t]=cmath.polar(zph)
iph=vph/r
il=iph
p=sqrt(3)*vl*il*cos(t)
q=sqrt(3)*vl*il*sin(t)
s=sqrt(3)*vl*il
print"The line current is il=",round(il,2),"Amperes"
print"The total Power absorbed is P=",round(P,2),"Watts"
print"The reactive volt amperes is q=",round(q,2),"VAR"
print"The Volt amperes is s=",round(s,2),"Volt Ampere"

The line current is il= 13.06 Amperes
The total Power absorbed is P= 383.25 Watts
The reactive volt amperes is q= 3211.69 VAR
The Volt amperes is s= 5201.33 Volt Ampere

Ex3.3:pg-289

In [22]:
import cmath
Vl=230;       #Assigning values to parameters
f=50;
Rph=15;
L=0.03;
Xl=2*math.pi*f*L;
Zph=15+1j*9.42;
[r,t]=cmath.polar(Zph)
Vph=Vl;
Iph=Vph/r;
Il=sqrt(3)*Iph;
P=sqrt(3)*Vl*Il*cos(t);
print"Phase current is Iph=",round(Iph,2),"Amperes"
print"Line current is Il=",round(Il,1),"Amperes"
print"Power absorbed is=",round(P/1000,2),"KW"

Phase current is Iph= 12.99 Amperes
Line current is Il= 22.5 Amperes
Power absorbed is= 7.59 KW

Ex3.4:pg-290

In [29]:
import cmath
f=50#assigning values to the parameters
xc=200
vph=400
vl=vph
zph=14.151-1j*200
[r,t]=cmath.polar(zph)
iph=vph/r
il=sqrt(3)*iph
p=sqrt(3)*vl*il*cos(t)
pwr=vph*iph*cos(t)
c=1.0/(2*math.pi*f*xc)
print"power consumed in each branch of delta is pwr=",round(pwr,2),"Watts"
print"capacitive reactance is c=""{:.2e}".format(c),"Farads"

power consumed in each branch of delta is pwr= 56.32 Watts
capacitive reactance is c=1.59e-05 Farads

Ex3.5:pg-290

In [39]:
import cmath
l=50                    #Assigning values to parameters
w=800
c=50
xl=w*l
xc=1/(w*c)
z1=0+1j*40
z2=50
z3=0-1j*25
zph=z1+z2*z3/(z2+z3)
[r,t]=cmath.polar(zph)
vl=550
vph=vl
iph=vph/r
il=sqrt(3)*iph
p=sqrt(3)*vl*il*cos(t)
pf=cos(t)
q=sqrt(3)*vl*il*sin(t)
s=sqrt(3)*vl*il
print"The phase current is",round(iph,2),"Amperes"
print"The line current is",round(il,2),"Amperes"
print"The power drawn is",round(p/1000,2),"kw"
print"The power factor is",round(pf,2)
print"The reactive power is",round(q/1000,2),"kw"
print"The kva rating of load is",round(s/1000,2),"KVA"

The phase current is 24.6 Amperes
The line current is 42.6 Amperes
The power drawn is 18.15 kw
The power factor is 0.45
The reactive power is 36.3 kw
The kva rating of load is 40.58 KVA

Ex3.7:pg-294

In [50]:
import cmath
p=10000                      #Assigning values to parameters
t=math.acos(0.6)
vl=440
vph=vl
il=p/(sqrt(3)*vl*cos(t))
iph=il/sqrt(3)
zph=vph/iph
zph1=20.9-1j*27.87
res=zph1.real
xc=zph1.imag
q=sqrt(3)*vl*il*sin(t)
print"The resistance value of circuit element is",round(res,2),"ohms"
print"The capacitive value of circuit element is",round(-xc,2),"ohms"
print"The reactive volt-ampere",round(-q/1000,2),"KVAR"

The resistance value of circuit element is 20.9 ohms
The capacitive value of circuit element is 27.87 ohms
The reactive volt-ampere -13.33 KVAR

Ex3.8:pg-295

In [52]:
import cmath
f=50                     #Assigning values to parameters
vl=440
p=1500
t=math.acos(0.2)
vph=vl/sqrt(3)
il=p/(sqrt(3)*vl*p*cos(t))
iph=il
zph=vph/iph
zph1=5.17+1j*25.3
res=zph1.real
xl=zph1.imag
l=xl/(2*math.pi*f)
print"The resistive circuit constant is",round(res,2),"ohms"
print"The inductive  circuit constant is",round(l,2),"H"

The resistive circuit constant is 5.17 ohms
The inductive  circuit constant is 0.08 H

Ex3.9:pg-296

In [58]:
import cmath
p=100000                   #Assigning values to parameters
il=80
vl=1100
f=50
vph=vl/sqrt(3)
iph=il
zph=vph/iph
t=math.acos(p/(sqrt(3)*vl*il))
zph1=5.21-1j*6
r=zph1.real
xc=zph1.imag
c=1/(2*math.pi*f*xc)
print"The resistive circuit constant is",round(r,2),"ohms"
print"The capacitive circuit constant is",round(-xc,2),"ohms"
print"The capacitance is","{:.2e}".format(-c),"farads"

The resistive circuit constant is 5.21 ohms
The capacitive circuit constant is 6.0 ohms
The capacitance is 5.31e-04 farads

Ex3.10:pg-296

In [79]:
Vl=400;              #Assigning values to parameters
Il=34.65;
P=14.4*10**3;
Vph=Vl;
Iph=Il/sqrt(3);
Zph=Vph/Iph;
t=math.acos(P/(sqrt(3)*Vl*Il))
Z=complex(Zph,t);
a=cmath.rect(Zph,t)
print"Impedance",a,"ohms"
print "Resistance",round(a.real),"ohms"
print "Reactance",round(a.imag),"ohms"

Impedance (11.9937782275+15.9981840036j) ohms
Resistance 12.0 ohms
Reactance 16.0 ohms

Ex3.11:pg-297

In [102]:
import cmath
vl=415           #assigning values to the parameters
r=15
l=0.1
c=177*10**-6
f=50
vph=vl/sqrt(3)
xl=2*math.pi*f*l
xc=1.0/(2*math.pi*f*c)
a=xl-xc
zph=r+1j*a
[r1,t]=cmath.polar(zph)
iph=vph/r1
il=iph
p=sqrt(3)*vl*il*cos(t)
q=sqrt(3)*vl*il*sin(t)
s=sqrt(3)*vl*il
print"The phase current is",round(iph,1),"Amperes"
print"The line current is",round(il,2),"Amperes"
print"The power drawn is",round(p/1000,2),"KW"
print"The reactive power is",round(q/1000,2),"KVAR"
print"The total kVA is",round(s/1000,2),"KVA"

The phase current is 11.9 Amperes
The line current is 11.9 Amperes
The power drawn is 6.37 KW
The reactive power is 5.71 KVAR
The total kVA is 8.55 KVA

Ex3.12:pg-299

In [103]:
vl=400                #assigning values to the parameters
t=0
zph=50
vph=vl/sqrt(3)
iph=vph/zph
il=iph
p=sqrt(3)*vl*il*cos(t)
print"Power taken is",round(p,2),"Watts"
iph=4
il=iph
p=vl*il*cos(t)
print"Power taken after disconecting one of the resistor is",round(p,2),"Watts"

Power taken is 3200.0 Watts
Power taken after disconecting one of the resistor is 1600.0 Watts

Ex3.13:pg-300

In [104]:
vl=400                  #Assigning values to parameters
vph=vl
r=40
t=0
iph=vph/r
il=sqrt(3)*iph
p=sqrt(3)*vl*il*cos(t)
print"Power taken is",round(p,2),"Watts"
i=10
p=2*i*i*r
print"Power taken after diconnecting one resistor is",round(p,2),"Watts"

Power taken is 12000.0 Watts
Power taken after diconnecting one resistor is 8000.0 Watts

Ex3.16:pg-310

In [117]:
import math
w1=500       #Assigning values to parameters
w2=2500
p=w1+w2
t=math.atan(sqrt(3)*(w2-w1)/(w1+w2))
pf=cos(t)
print"Total Power supplied is",round(p,2),"Watts"
print"Power factor is",round(pf,3)
w2=2500
w1=-500
p=w1+w2
t=math.atan(sqrt(3)*(w2-w1)/(w1+w2))
pf=cos(t)
print"Total Power supplied after reversing the connections to the current coil is",round(p,2),"Watts"
print"Power factor after reversing the connections to the current coil is",round(pf,3)

Total Power supplied is 3000.0 Watts
Power factor is 0.655
Total Power supplied after reversing the connections to the current coil is 2000.0 Watts
Power factor after reversing the connections to the current coil is 0.359

Ex3.17:pg-311

In [112]:
import math
w1=3000        #Assigning values to parameters
w2=5000
t=math.atan(sqrt(3)*(w2-w1)/(w1+w2))
pf=cos(t)
p=w1+w2
il=p/(sqrt(3)*vl*cos(t))
print"Watts",p,"Total Power supplied is",round(p,2),"Watts"
print"Power factor is",round(pf,2)
print"The line current is",round(il,2),"Amperes"

Watts 8000 Total Power supplied is 8000.0 Watts
Power factor is 0.92
The line current is 12.58 Amperes

Ex3.18:pg-311

In [119]:
import math
w1=-1000        #Assigning values to parameters
w2=3000
vl=400
t=math.atan(sqrt(3)*(w2-w1)/(w1+w2))
pf=cos(t)
p=w1+w2
il=p/(sqrt(3)*vl*cos(t))
print"Total Power supplied is",round(p,2),"Watts"
print"Power factor is",round(pf,3)
print"The line current is",round(il,2),"Amperes"

Total Power supplied is 2000.0 Watts
Power factor is 0.277
The line current is 10.41 Amperes

Ex3.19:pg-312

In [121]:
import math
w1=100000        #Assigning values to parameters
w2=300000
vl=2000
n=0.9
t=math.atan(sqrt(3)*(w2-w1)/(w1+w2))
pf=cos(t)
p=w1+w2
il=p/(sqrt(3)*vl*cos(t))
print"Total Power supplied is",round(p,2),"Watts"
print"Power factor is",round(pf,2)
print"The line current is",round(il,2),"Amperes"

Total Power supplied is 400000.0 Watts
Power factor is 0.76
The line current is 152.75 Amperes

Ex3.20:pg-312

In [138]:
vl=220        #Assigning values to parameters
il=38
n=0.88
p=11200
ip=p/n
t=math.acos(ip/(sqrt(3)*vl*il))
a=math.degrees(t)
w2=vl*il*cos(30-a)
w1=vl*il*cos(30+a)
print"The wattmeter reading is w2=",round(w2,2),"Watts"
print"The wattmeter reading is w1=",round(w1,2),"Watts"
# the answer of w2,w1 are wrong in the book

The wattmeter reading is w2= 449.52 Watts
The wattmeter reading is w1= -2972.66 Watts

Ex3.21:pg-313

In [127]:
import math
w1=1        #Assigning values to parameters
w2=2*w1
t=math.atan(sqrt(3)*(w2-w1)/(w1+w2))
pf=cos(t)
print"Power factor is",round(pf,3)

Power factor is 0.866