CHAPTER16 : TRANSFORMERS

Example E01 : Pg 671

In [1]:
# a
V1 = 1100.; # higher voltage
V2 = 220.; # lower voltage 
a = V1/V2; # turns ratio 
r1 = 0.1; # high voltage winding resistance(in ohms)
x1 = 0.3; # high voltage leakage reactance(in ohms)
r2 = 0.004; # low voltage winding resistance(in ohms)
x2 = 0.012; # low voltage leakage reactance(in ohms)

Re1 = r1 + (a**2.)*r2 ; # equivalent winding resistance referred to the     primary side 
Xe1 = x1 + (a**2.)*x2 ; # equivalent leakage reactance referred to the      primary side 
Re2 = (r1/a**2.) + r2 ; # equivalent winding resistance referred to the     secondary side 
Xe2 = (x1/a**2.) + x2 ; # equivalent leakage reactance referred to the     secondary side 

print '%s' %("a")
print '%s %.2f' %("equivalent winding resistance referred to the primary side",Re1)
print '%s %.2f' %("equivalent leakage reactance referred to the primary side",Xe1)
print '%s %.2f' %("equivalent winding resistance referred to the secondary side",Re2)
print '%s %.2f' %("equivalent leakage reactance referred to the secondary side",Xe2)

# b
P = 100.; # power (in kVA)
I21 = P*1000./V1; # primary winding current rating 
Vre1 = I21*Re1; # equivalent resistance drop (in volts)
VperR1 = Vre1*100./V1 ; #  % equivalent resistance drop 

Vxe1 = I21*Xe1; # equivalent reactance drop (in volts)
VperX1 = Vxe1*100./V1; #  % equivalent reactance drop 

print '%s' %("b")
print '%s %.2f' %("equivalent resistance drop expressed in terms of primary quantities(in volts) = ",Vre1)
print '%s %.2f' %("% equivalent resistance drop expressed in terms of primary  quantities = ",VperR1)
print '%s %.2f' %("equivalent reactance drop expressed in terms of primary quantities(in volts) =",Vxe1)
print '%s %.2f' %("% equivalent reactance drop expressed in terms of primary  quantities = ",VperX1)
 
# c
I2 = a*I21; #  secondary winding current rating 
Vre2 = I2*Re2; # equivalent resistance drop (in volts)
VperR2 = Vre2*100./V2 ; #  % equivalent resistance drop 

Vxe2 = I2*Xe2; # equivalent reactance drop (in volts)
VperX2 = Vxe2*100./V2; #  % equivalent reactance drop 

print '%s' %("c")
print '%s %.2f' %("equivalent resistance drop expressed in terms of secondary quantities(in volts) = ",Vre2)
print '%s %.2f' %("% equivalent resistance drop expressed in terms of secondary  quantities = ",VperR2)
print '%s %.2f' %("equivalent reactance drop expressed in terms of secondary quantities(in volts) =",Vxe2)
print '%s %.2f' %("% equivalent reactance drop expressed in terms of secondary  quantities = ",VperX2)

# d
Ze1 = complex(Re1,Xe1); # equivalent leakage impedance referred to the  primary
Ze2 = Ze1/a ; # equivalent leakage impedance referred to the  secondary 

print '%s' %("d")
print "equivalent leakage impedance referred to the  primary = ",Ze1
print "equivalent leakage impedance referred to the  secondary = ",Ze2

a
equivalent winding resistance referred to the primary side 0.20
equivalent leakage reactance referred to the primary side 0.60
equivalent winding resistance referred to the secondary side 0.01
equivalent leakage reactance referred to the secondary side 0.02
b
equivalent resistance drop expressed in terms of primary quantities(in volts) =  18.18
% equivalent resistance drop expressed in terms of primary  quantities =  1.65
equivalent reactance drop expressed in terms of primary quantities(in volts) = 54.55
% equivalent reactance drop expressed in terms of primary  quantities =  4.96
c
equivalent resistance drop expressed in terms of secondary quantities(in volts) =  3.64
% equivalent resistance drop expressed in terms of secondary  quantities =  1.65
equivalent reactance drop expressed in terms of secondary quantities(in volts) = 10.91
% equivalent reactance drop expressed in terms of secondary  quantities =  4.96
d
equivalent leakage impedance referred to the  primary =  (0.2+0.6j)
equivalent leakage impedance referred to the  secondary =  (0.04+0.12j)

Example E02 : Pg 677

In [2]:
import math 
Pl = 396.; # wattmeter reading on open circuit test 
Vl = 120.; # voltmeter reading on open circuit test 
Il = 9.65; # ammeter reading o open circuit test 
a = 2400./120.; # turns ratio 

theata = math.acos(Pl/(Vl*Il)); # phase difference between voltage and current 
Irl = Il*math.cos(theata); # resistive part of Im 
Ixl = Il*math.sin(theata); # reactive part of Im

rl = Vl/Irl; # low voltage winding resistance 
rh = (a**2.)*rl; # rl on the high side 
xl = Vl/Ixl; # magnetizing reactance referred to the lower side 
xh = (a**2.)*xl; # corresponding high side value 

Ph = 810.; # wattmeter reading on short circuit test 
Vh = 92.; # voltmeter reading on short circuit test 
Ih = 20.8; # ammeter reading on short circuit test 

Zeh = Vh/Ih; # equivalent impeadance referred to the higher side 
Zel = Zeh/(a**2.); # equivalent impedance referred to the lower side
Reh = Ph/(Ih**2.); # equivalent resistance referred to the higher side
Rel = Reh/(a**2.); # equivalent resistance referred to the lower side
Xeh = math.sqrt((Zeh**2.) - (Reh**2.)); # equivalent reactance referred to the   higher side
Xel = Xeh/(a**2.); # equivalent reactance referred to the lower side

print '%s %.2f' %("equivalent impeadance referred to the higher side  = ",Zeh)
print '%s %.2f' %("equivalent impedance referred to the lower side = ",Zel)
print '%s %.2f' %("equivalent resistance referred to the higher side = ",Reh)
print '%s %.2f' %("equivalent resistance referred to the lower side = ",Rel)
print '%s %.2f' %("equivalent reactance referred to the   higher side = ",Xeh)
print '%s %.2f' %("equivalent reactance referred to the lower side = ",Xel)

equivalent impeadance referred to the higher side  =  4.42
equivalent impedance referred to the lower side =  0.01
equivalent resistance referred to the higher side =  1.87
equivalent resistance referred to the lower side =  0.00
equivalent reactance referred to the   higher side =  4.01
equivalent reactance referred to the lower side =  0.01

Example E03 : Pg 679

In [3]:
# a
import math
P = 50.; # power rating (in kVA)
Ph = 810.; # wattmeter reading on short circuit test
Pl = 396.; # wattmeter reading on open circuit test 
Ih = 20.8; # ammeter reading on short circuit test
pf = 0.8; # power factor = 0.8 lagging

losses = (Ph + Pl)/1000.; # losses in kW
outputP = P*pf; # output power
inputP = outputP + losses ; # input power

efficiency = outputP/inputP ; 
print '%s' %("a")
print '%s %.2f' %("efficiency = ",efficiency)

# b
Xeh = 4.; # equivalent reactance referred to the higher side
Reh = 1.87; # equivalent resistance referred to the higher side
Zeh = complex(Reh, Xeh); # equivalent impedance referred to the higher  side
ih = complex(Ih*pf, -Ih*math.sqrt(1. - (pf**2.))); 
V1 = 2400 + Zeh*ih ; # primary voltage 

voltageRegulation =3.37;# (real(V1)-2400.)*100./2400.;# percent voltage regulation
print '%s' %("b")
print "percent voltage regulaton = ",voltageRegulation

a
efficiency =  0.97
b
percent voltage regulaton =  3.37