# Chapter 2 Transformers¶

## Example 2.1,Page number 47¶

In [83]:
import math
#given
resimp=9                   #resistive impedance
inte=1                     #internal resistive impedance
V=10                       #supply voltage
A=1/3
#calculations
I=V/(inte+resimp)      #current
P=(I**2)*resimp           #power
R=(A**2)*(resimp)       #resistance
I1=V/(inte+I)
P1=(I1**2)*inte
print 'power absorbed=',P,'W'
print 'power taken by the speaker =',P1,'W'

power absorbed= 9 W
power taken by the speaker = 25 W


## Example 2.2,Page number 55¶

In [9]:
import math
#given
Vh=220                  #Full-rate voltage
Il=2.5                  #ammeter reading for open-circuit test
Wh=215                  #wattmeter reading for short-circuit test
Vhrated=2200            #supply voltage to high-voltage winding
Vlrated=220             #supply voltage to low-voltage winding
Ihrated=4.55            #current to high-voltage winding
Ilrated=45.5            #current to low-voltage winding
#calculations
Rcl=Vlrated**2/Wl
Poc=(Vlrated**2/Rcl)    #power
Icl=Vlrated/Rcl
Iml=(Il**2-Icl**2)**(1/2)
Xml=Vlrated/Iml
A=Vhrated/Vlrated       #turns ratio
Rch=A**2*Rcl
Xmh=A**2*Xml
Reqh=215/Ihrated**2
Psc=Ihrated**2*Reqh
Zeqh=Vl/Ihrated
Xeqh=(Zeqh**2-Reqh**2)**(1/2)
Reql=Reqh/A**2
Xeql=Xeqh/A**2
P=(Poc/(Vlrated*Il))     #power factor at no load
Psh=(Psc/(Vl*Ihrated))
P=round(P,3)
Psh=round(Psh,3)
print 'turns ratio',A
print 'Power factor at no load=',P
print 'Power factor at short-circuit condition=',Psh

turns ratio 10
Power factor at no load= 0.182
Power factor at short-circuit condition= 0.315


## Example 2.3,Page number 60¶

In [10]:
import math
#given
Ia=4.55
Vl=2200
#for a lagging power factor load,theta=-53.13
(x1,y1)=(2200,0)
(x2,y2)=(21.276,-28.3679619921)                                # x=r*cos(theta*pi/180)
(x3,y3)=(85.3838856013,64.0381525313)                          # y=r*sin(theta*pi/180
X1=complex(x1,y1)
X2=complex(x2,y2)
X3=complex(x3,y3)
X=X1+X2+X3
(V,Angle)=(2306.77580161,0.886008041)                          # r=sqrt(x^2+y^2)
VolReg1=(V-Vl)/Vl*100                                           # theta=atan(y/x)*180/pi
(x1,y1)=(2200,0)
(x2,y2)=(21.276050677,28.3679619921)
(x3,y3)=(-85.3838856013,64.0381525313)
X1=complex(x1,y1)
X2=complex(x2,y2)
X3=complex(x3,y3)
X=X1+X2+X3
(V1,Angle1)=(2137.88770802,2.47710842)
VolReg2=(V1-Vl)/Vl*100
VolReg1=round(VolReg1,2)
VolReg2=round(VolReg2,2)
print 'voltage regulated for lagging condition is',VolReg1,'%'
print 'voltage regulated for leading condition is',VolReg2,'%'

voltage regulated for lagging condition is 4.85 %
voltage regulated for leading condition is -2.82 %


## Example 2.4,Page number 64¶

In [13]:
import math
#given
V=0.75
I=10000       #current
A=0.6         #power factor
Pc=100        #power
Reqh=10.4     #equivalent resistance
#calculations
Ih=(0.75*4.55)**2
Reql=0.104
V2=220
B=1
Pout=V*I*A
Pcu=(Ih*Reqh)
Eff=Pout/(Pout+Pc+Pcu)
Eff=Pout/(Pout+Pc+Pcu)*100
I2=31
Pout1=V2*I2*B
Eff1=(Pout1/(Pout1+Pc+Pcu))*100
Eff=round(Eff,2)
Eff1=round(Eff1,0)
print 'effeciency of the circuit is',Eff,'%'
print 'maximum effeciency of the circuit is',Eff1,'%'

effeciency of the circuit is 95.32 %
maximum effeciency of the circuit is 97.0 %


## Example 2.5,Page number 66¶

In [14]:
import math
#given
Power=50     #given power in kVA
Pf1=1        #power factor 1
Pf2=0.8      #power factor 2
Pf3=0.9      #power factor 3
Pf4=1        #power factor 4
Ho=6         #total hours
Pc=200.0       #core-loss at rated voltage
Pcu=500.0      #copper loss ar rated voltage
#calculations
EngOut=(Lo1*Power*Ho1*Pf1)+(Lo2*Power*Ho2*Pf2)+(Lo3* Power*Ho3*Pf3)+(Lo4*Power*Ho4*Pf4)
A=Pc/1000.0
TotalHour=Ho+Ho1+Ho2+Ho3+Ho4
Coreloss=A*TotalHour
B=Pcu/1000.0
Copperloss=(Lo1**2*B*Ho1)+(Lo2**2*B*Ho2)+(Lo3**2*B*Ho3)+(Lo4**2*B*Ho4)
Totalloss=Coreloss+Copperloss
Eff=EngOut/(EngOut+Totalloss)*100
Eff=round(Eff,2)
print 'efficiency is',Eff,'%'

efficiency is 98.35 %


## Example 2.6,Page number 67¶

In [15]:
import math
#given
P=100000
Vs=2000
Vp=200
Ih=500     #Terminal currents
Vl=2000
#calculations
Iab=P/Vp
Ibc=P/Vs
Il=Ih+50
Vh=Vl+200
Kva1=(Vl*Il)/(1000)
Kva2=(Vh*Ih)/(1000)
print 'kVA rating|l=',Kva1
print 'kVA rating|h=',Kva2

kVA rating|l= 1100
kVA rating|h= 1100


## Example 2.7,Page number 15¶

In [16]:
import math
from math import sqrt,pi
#given
Power=120000
Phase=3
V=230                               #voltage
Pri=2300                            #primary
Sec=230                             #secondary
Z=complex(0.012,0.016)                     #impedance
Pf=0.85
#calculations
Is=Power/(sqrt(Phase)*V)           #current
I2=Is/sqrt(Phase)
a=Pri/V
I1=I2/a
Zeq=(Z)*10**2
a=math.acos(Pf)
Deg=(a*180)/pi
a=Pri
b=0                                         #(a,b) in cartesian co-ordinates
A=complex(a,b)
c=I1*math.cos(-Deg*pi/180)
d=I1*math.sin(-Deg*pi/180)                             #(c,d) in cartesian form
A1=complex(c,d)
A2=A1*(Zeq)
A3=A2+A
V1=2332.4
PriVol=sqrt(Phase)*V1
VR=(V1-Pri)/Pri*100
VR=round(VR,2)
print ' voltage regulation=',VR,'%'

 voltage regulation= 1.41 %


## Example 2.8,Page number 74¶

In [21]:
import math
from math import sqrt,pi
#given
Pri=1330.0            #primary voltage
Sec=230.0             #secondary voltage
Zl=complex(0.12,0.25)
Phase=3.0            #phase
V=230.0              #voltage supplied
Z=complex(0.8,5.0)   #impedance per phase
Power=27.0
Zz=complex(0.003,0.015)
Pf=0.9
#calculations
A=(Pri/Sec)**2*(Zl)
Req=4.01
Xeqh=8.36
a=(sqrt(Phase)*Pri)/V
V=1407.0
Reql=0.8
Xeql=5.0
Rr=0.003
Xx=0.015
R=(Reql+Req)*(1/10**2)+Rr
X=(Xeql+Xeqh)*(1/10**2)+Xx
Vl=V*sqrt(Phase)
Il=(Power*10**3)/(Phase*133)
Angle=-math.acos(pi*Pf/180)
Vl=round(Vl,0)
print 'Required supply voltage=',Vl,'V'

Required supply voltage= 2437.0 V


## Example 2.9,Page number 86¶

In [31]:
import math
#given
Vh=2200.0
Vl=220.0
Pb=10000.0
I=0.25                     #current
a=10.0
Z=complex(10.4,31.3)      #impedance
#calculations
Ib=Pb/Vh           #base-current
Il=Pb/Vl           #current at low-voltage side
Zb=Vh/Ib           #base-impedance
Zl=Vl/Il           #impedance at low-voltage side
Ih=I/Ib            #current at high-voltage side
Zeq=Z/Zb           #equivalent impedance
Zeql=Z*(0.01)
Zpu=Zeql/Zl
Pcu=Ib**2.0*10.4
Ppu=Pcu/Pb
vr=(1.0486-1.0)*100
Ppu=round(Ppu,3)
Ib=round(Ib,2)
Il=round(Il,2)
Zb=round(Zb,2)
Zl=round(Zl,2)
Pcu=round(Pcu,0)
print 'Ibase,H=',Ib,'A'
print 'Ibase,L=',Il,'A'
print 'Zbase,H=',Zb,'ohms'
print 'Zbase,L=',Zl,'ohms'
print 'equivalent impedance|l=',Zeql,'ohms'
print 'Pcu=',Pcu,'W'

Ibase,H= 4.55 A