# 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