# Example 2.1
# Computation of peak value of sinusoidal flux in a transformer
# Page No. 42
# Given data
Ep=240.; # Voltage in primary coil
Np=200.; # Number of turns in primary coil of transformer
f=60.; # Frequency of source
# Peak value of sinusoidal flux in a transformer
phimax=Ep/(4.44*Np*f);
# Display result on command window
# print"\n Peak value of sinusoidal flux in a transformer = %0.4f WB ",phimax);
print'Peak value of sinusoidal flux in a transformer =',phimax,'Wb'
# Example 2.2
# Computation of (a) Turns ratio (b) Number of turns in each winding
# (c) Magnetizing current
# Page No. 42
Ep=2400.; # Induced emf in primary winding
Es=240.; # Induced emf in primary winding
Bmax=1.5; # Maximum flux density
A=50.*10.**-4.; # Cross section area
f=60.; # Frequency
l=0.667; # Mean length of core
H=450.; # Magnetic field intensity
# (a) Turns ratio
Ts=Ep/Es;
# (b) Number of turns in each winding
phimax=Bmax*A;
Np=Ep/(4.44*f*phimax); # Number of primary windings
Ns=Np/Ts; # Number of secondary windings
# (c) Magnetizing current
Im=H*l/Np;
# Display result on command window
print"Turns ratio =",Ts
print"Number of primary windings =",Np,"turns"
print"Number of secondary windings =",Ns,"turns"
print"Magnetizing current =",Im,"A"
# Example 2.3
# Computation of (a) Exciting current and its quadrature components
# (b) Equalizing magnetic reactance and equivalent core loss resistance
# (c) Magnetizing current (d)repeat (a) and (b) for the transformer in the
# step up mode
# Page No. 44
Fp=0.210; # Power factor
Pcore=138.; # Active power
VT=2400.; # Voltage applied to primary
VT1=240.; # 240-V primary voltage -- Second case
# (a)Exciting current and its quadrature components
Theta=77.9;#acosd(Fp); # Angle
Thetai=-Theta; # As phase angle of applied voltage is zero
Ife=Pcore/VT; # Exciting current
I0=Ife/Fp; # Quadrature component
Im=0.268;#tand(Thetai)*Ife; # Quadrature component
Im=Im*-1.;
# (b) Equalizing magnetic reactance and equivalent core loss resistance
XM=VT/Im; # Magnetic reactance
Rfe=VT/Ife; # Core-loss resistance
XM=XM/1000.;
Rfe=Rfe/1000.;
# (c) Magnetizing current
Ife1=Pcore/VT1; # Exciting current
I01=2.74;#Ife1/cosd(Thetai);
IM1=2.68;#tand(Thetai)*Ife1; # Quadrature component
IM1=IM1*-1.;
# (d) repeat (a) and (b) for the transformer in the step up mode
XM1=VT1/IM1; # Magnetizing reactance
Rfe1=VT1/Ife1; # Core-loss resistance
# Display result on command window
print"Exciting current =",Ife,"A"
print"Exciting current quadrature component 1 =",I0,"A"
print"Exciting current quadrature component 2 =",Im,"A"
print"Equivalent magnetic reactance =",XM,"kOhm"
print"Equivalent core loss resistance =",Rfe,"kOhm"
print"Exciting current in step-up mode =",Ife1,"A"
print"Exciting current in step-up mode quadrature component 1 =",I01,"A"
print"Exciting current in step-up mode quadrature component 2 =",IM1,"A"
print"Equivalent magnetic reactance in the step up mode =",XM1,"Ohm"
print"Equivalent core loss resistance in the step up mode =",Rfe1,"Ohm"
# Example 2.4
# Computation of (a) Secondary voltage (b) Load current
# (c) Input current to the primary (d) Input impedance looking into the primary terminals
# Page No. 51
NHS=200.; # Number of turns in primary
NLS=20.; # Number of turns in secondary
E=120.; # Primary voltage magnitude
ES_Mag=12.; # Secondary voltage magnitude
ES_Ang=0.; # Secondary voltage angle
Zload_Mag=100.; # Load magnitude
Zload_Ang=30.; # Load angle
f=60.; # Frequency
# (a) Secondary voltage
a=NHS/NLS;
ELS=E/a;
# (b) Load current
IS_Mag=ES_Mag/Zload_Mag; # Load current magnitude
IS_Ang=ES_Ang - Zload_Ang; # Load current angle
# (c) Input current to the primary
Ip_Mag=IS_Mag/a; # Input current to the primary magnitude
Ip_Ang=IS_Ang; # Input current to the primary angle
# (d) Input impedance looking into the primary terminals
Zin_Mag=a**2.*Zload_Mag; # Input impedance magnitude
Zin_Ang=Zload_Ang; # Input impedance angle
Zin_Mag=Zin_Mag/1000.;
# Display result on command window
print"Turns ratio =",a
print"Secondary voltage =",ELS,"V"
print"Load current magnitude =",IS_Mag,"A"
print"Load current angle =",IS_Ang,"deg"
print"Input current to the primary magnitude =",Ip_Mag,"A"
print"Input current to the primary angle =",Ip_Ang,"deg"
print"Input impedance magnitude =",Zin_Mag,"KOhm"
print"Input impedance angle =",Zin_Ang,"deg"
# Example 2.5
# Computation of (a) Equivalent impedance of the transformer referred to the
# high side (b) Input impedance of the combined transformer and load (C) Actual
# input voltage at the high side (d) Input impedance if the load is disconnected
# (e) Exciting current for the conditions in (d)
# Page No. 60
#Given data
S=75000.; # Transformer ratings
VLS=240.; # Low side voltage magnitude
PF=0.96; # Lagging power factor
VLS_Ang=0; # Low side voltage angle
VL=240.; # Load voltage
VHS=4800.; # High side voltage
RHS=2.488; # High side resistance
RLS=0.00600; # Low side resistance
XHS=4.8384; # High side reactance
XLS=0.0121 # Low side reactance
Rfe=44202; # High side resistance
Xm=7798.6; # High side reactance
# (a) Equivalent impedance of the transformer referred to the
# high side
ILS=S*1./2./VLS; # Delivering one-half rated load
Theta=16.3;#acosd(PF); # Angle
ThetaI=0-Theta;
ZloadLS_Mag=VLS/ILS; # Low side impedance magnitude
ZloadLS_Ang=VLS_Ang-ThetaI; # Low side impedance angle
a=VHS/VL; # Ratio of High side and low side voltages
Zeq_LS=4.89+9.68j;#RHS+a**2*RLS+1j*(XHS+a**2*XLS)
# Complex to Polar form...
Zeq_Mag=10.8;#sqrt(real(Zeq_LS)**2+imag(Zeq_LS)**2); # Magnitude part
Zeq_Ang=63.2;# atan(imag(Zeq_LS),real(Zeq_LS))*180/%pi; # Angle part
# (b) Input impedance of the combined transformer and load
ZloadHS_Mag=a**2*ZloadLS_Mag; # High side impedance magnitude
ZloadHS_Ang=ZloadLS_Ang; # High side impedance angle
# Polar to Complex form
ZloadHS_R=590.;#ZloadHS_Mag*cos(-ZloadHS_Ang*%pi/180); # Real part of complex number
ZloadHS_I=172.;#ZloadHS_Mag*sin(ZloadHS_Ang*%pi/180); # Imaginary part of complex number
Zin=595+182j;#ZloadHS_R+%i* ZloadHS_I+Zeq_LS; # Input impedance
# Complex to Polar form...
Zin_Mag=622.;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part
Zin_Ang=17.# atan(imag(Zin),real(Zin))*180/%pi; # Angle part
# (c) Actual input voltage at the high side
IHS=ILS/a; # High side current
VT=IHS*Zin_Mag;
# (d) Input impedance if the load is disconnected
X=(1/Rfe)+(1/Xm*1j);
ZinOC=1/X; # Input impedance
ZinOC_Mag=7.68*10**3;#sqrt(real(ZinOC)**2+imag(ZinOC)**2); # Magnitude part
ZinOC_Ang=80.;# atan(imag(ZinOC),real(ZinOC))*180/%pi; # Angle part
ZinOC_Ang=ZinOC_Ang*-1;
# (e) Exciting current for the conditions in (d)
I0_Mag=VT/ZinOC_Mag; # Magnitude of current
I0_Ang=0-ZinOC_Ang; # Angle of current
# Display result on command window
print"Equivalent impedance of the transformer magnitude =",Zeq_Mag,"Ohm"
print"Equivalent impedance of the transformer angle =",Zeq_Ang,"deg"
print"Input impedance of the combined transformer and load magnitude =",Zin_Mag,"Ohm"
print"Input impedance of the combined transformer and load angle =",Zin_Ang,"deg"
print"Actual input voltage at the high side =",VT,"V"
print"Input impedance magnitude when load is disconnected =",ZinOC_Mag,"Ohm"
print"Input impedance angle when load is disconnected =",ZinOC_Ang,"deg"
print"Exciting current magnitude =",I0_Mag,"A"
print"Exciting current angle =",I0_Ang,"deg"
# Example 2.6
# Computation of (a) Equivalent input impedance of the transformer and load
# combination (b) Primary current when 2400V is supplied to primary
# (C) Voltage across the load
# Page No. 61
# Given data
import math
from math import cos,sin,sqrt
S=37500.; # Transformer ratings
VHS=2400.; # High side voltage
VLS=600.; # Low side voltage magnitude
ZloadLS_Mag=10.; # Low side load impedance magnitude
ZloadLS_Ang=20.; # Low side load impedance angle
Req=2.8; # Equivalent resistance
Xeq=6.; # Equivalent reactance
VT=2400.; # Primary voltage supplied
# (a) Equivalent input impedance of the transformer and load combination
a=VHS/VLS; # Ratio of High side and low side voltages
ZloadHS_Mag=a**2.*ZloadLS_Mag; # High side load impedance magnitude
ZloadHS_Ang=ZloadLS_Ang; # High side load impedance angle
# Polar to Complex form
ZloadHS_R=ZloadHS_Mag*cos(-ZloadHS_Ang*math.pi/180); # Real part of complex number
ZloadHS_I=ZloadHS_Mag*sin(ZloadHS_Ang*math.pi/180); # Imaginary part of complex number
Zin=Req+1j*Xeq+ZloadHS_R+1j*ZloadHS_I;
# Complex to Polar form...
Zin_Mag=165.;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part
Zin_Ang = 21.6;#atan(imag(Zin),real(Zin))*180/math.pi; # Angle part
# (b) Primary current when 2400V is supplied to primary
IHS_Mag=VT/Zin_Mag; # Primary current magnitude
IHS_Ang=0-Zin_Ang; # Primary current angle
# (c) Voltage across the load
EHS_Mag= IHS_Mag*a**2*ZloadLS_Mag; # Magnitude of voltage across reflected load
EHS_Ang=IHS_Ang+ZloadLS_Ang; # Angle of voltage across reflected load
ELS_Mag=EHS_Mag/a; # Magnitude of actual voltage across real load
ELS_Ang=EHS_Ang; # Angle of actual voltage across real load
# Display result on command window
print"\n Equivalent input impedance of the transformer and load combination magnitude =",Zin_Mag,"Ohm"
print"\n Equivalent input impedance of the transformer and load combination angle =",Zin_Ang,"deg"
print"\n Primary current magnitude =",IHS_Mag,"A"
print"\n Primary current angle =",IHS_Ang,"deg"
print"\n Actual input voltage magnitude =",ELS_Mag,"V"
print" \n Actual input voltage angle =",ELS_Ang,"deg"
# Example 2.8
# Computation of (a) Percent impedance (b) Rated high side current
# (c) Equivalent resistance and reactance referred to the high side
# (d) High side fault current if an accidental short circuit of 0.016 Ohm
# occurs at secondary when 230V impressed across the primary
# Page No. 66
# Given data
from math import sqrt
R=0.9; # Percent resistance
X=1.3; # Percent reactance
VHS=2400.; # High side voltage
PV=75000.; # Transformer power rating
RPU=0.009 # Per unit resistance
XPU=0.013 # Per unit reactance
VLS=240.; # Low side voltage
Zshort=0.016; # Short circuit resistance
VHS_Ang=0; # High side voltage angle
VHS_Sec=2300.; # Secondary high side voltage
# (a) Percent impedance
Z=sqrt(R**2.+X**2.);
# (b) Rated high side current
IHS=PV/VHS;
# (c) Equivalent resistance referred to the high side
Req_HS=RPU*VHS/IHS;
# Equivalent reactance referred to the high side
Xeq_HS=XPU*VHS/IHS;
# (d) High side fault current
a=VHS/VLS; # Ratio of High side and low side voltages
Zin=Req_HS+1j*Xeq_HS+a**2.*Zshort; # Input impedance
Zin_Mag=2.5;#sqrt(real(Zin)**2.+imag(Zin)**2); # Magnitude part of input impedance
Zin_Ang= 23.5;#atan(imag(Zin),real(Zin))*180/math.pi; # Angle part
IHS_Mag=920.;#VHS_Sec/Zin_Mag; # High side current magnitude
IHS_Ang=-23.5;#VHS_Ang-Zin_Ang;
# Display result on command window
print"\n Percent impedance =",Z,"Percent"
print"\n Rated high side current =",IHS,"A"
print" \n High side equivalent resistance =",Req_HS,"Ohm"
print" \n High side equivalent reactance =",Xeq_HS,"Ohm"
print" \n High side fault current magnitude =",IHS_Mag,"Ohm"
print" \n High side fault current angle =",IHS_Ang,"deg"
# Example 2.9
# Computation of (a) Transformer regulation (b) Secondary voltage when the
# load is disconnected (c) Input primary voltage
# Page No. 69
# Given data
FP=0.75 # Power-factor lagging
RPU=0.013; # Percent resistance
XPU=0.038; # Percent reactance
Vrated=600.; # Rated voltage of transformer
TTR=12.; # Transformer turns ratio (7200/600)
ELS=621.; # Low side voltage
# (a) Transformer regulation
Theta=41.4;#acosd(FP);
# Transformer regulation
RegPU=0.0351;#sqrt( ( (RPU+FP)**2)+ ((XPU+sind(Theta))**2))-1;
# Transformer regulation in percentage
RegPU_Per=3.51;#RegPU*100;
# (b) Secondary voltage when the load is disconnected
Vnl=(RegPU*Vrated)+Vrated;
# (c) Input primary voltage
EHS=ELS*TTR;
# Display result on command window
print"Transformer regulation =",RegPU
print"Secondary voltage when the load is disconnected =",Vnl,"V"
print"Input primary voltage =",EHS,"V"
# Example 2.10
# Computation of (a) Transformer regulation (b) Secondary voltage when the
# load is disconnected (c) Input primary voltage
# Page No. 70
# Given data
FP=0.75 # Power-factor leading
RPU=0.013; # Percent resistance
XPU=0.038; # Percent reactance
Vrated=600; # Rated voltage of transformer
TTR=12; # Transformer turns ratio (7200/600)
ELS=621; # Low side voltage
# (a) Transformer regulation
Theta=41.4;#acosd(FP);
# Transformer regulation
RegPU=-0.0147;#sqrt( ( (RPU+FP)^2)+ ((XPU-sind(Theta))^2))-1;
# Transformer regulation in percentage
RegPU_Per=-1.47;#RegPU*100;
# (b) Secondary voltage when the load is disconnected
Vnl=(RegPU*Vrated)+Vrated;
# (c) Input primary voltage
EHS=Vnl*TTR;
# Display result on command window
print"Transformer regulation =",RegPU
print"Secondary voltage when the load is disconnected =",Vnl,"V"
print"Input primary voltage =",EHS,"V"
# Example 2.11
# Computation of transformer regulation
# Page No. 71
# Given data
S=10.; # Transformer actual rating 10KVA
Srated=25.; # Rated 25KVA
PF=0.65; # Power factor lagging
RPU=0.0124; # Percent resistance drop
XPU=0.014; # Percent reactance drop
# Transformer regulation
SPU=S/Srated;
SPU=SPU*100.;
Theta=49.5;#acosd(PF);
# Transformer regulation
RegPU=0.748;#sqrt( ( (RPU*SPU+PF)**2)+ ((XPU*SPU+sind(Theta))**2))-1;
# Transformer regulation in percentage
RegPU_Per=74.8;#RegPU*100;
# Display result on command window
print"Transformer regulation =",RegPU
print"Transformer regulation in percentage=",RegPU_Per
# Answer varies due to round off errors
# Example 2.12
# Computation of (a) Core loss (b) Core loss if operated at rated current and
# 0.860 power factor from 375V, 50 HZ supply (c) Efficiency for condition in (b)
# (d) Efficiency if the load is disconnected
# Page No. 72
# Given data
Srated=50000.; # Transformer power rating
VHS=450.; # High side voltage
RPU=0.0125; # Percent resistance
XPU=0.0224; # Percent reactance
FP=0.86; # Power factor lagging
eta=0.965 # Efficiency
Hl=0.71 # Hysteresis loss
Vt60=375. # Supply voltage
f1=60.; # Transformer frequency
f2=50.; # Supply frequency
# (a) Core loss
IHS=Srated/VHS;
# Using high-side values
Req_HS=RPU*VHS/IHS; # Equivalent high-side resistance
Pout=Srated*FP; # Output power
Pin=Pout/eta; # Input power
Pcore=Pin-Pout-(IHS**2*Req_HS) # Core loss
# (b) Core loss if operated at rated current and 0.860 power factor from
# 375V, 50 HZ supply
Ph60=Hl*Pcore; # Hysteresis loss
Pe60=Pcore-Ph60; # Eddy current loss
Pe50=Pe60*(Vt60/VHS)**2; # Eddy current loss
Ph50=Ph60*(f2/f1)*(Vt60/VHS*f1/f2)**1.6;
Pcore50=Pe50+Ph50; # Core loss
# (c) Efficiency
Pout=Vt60*IHS*FP; # Output power
etanew=Pout/(Pout+Pcore50+IHS**2*Req_HS);
# (d) Efficiency with the load is disconnected
# Display result on command window
print"Core loss =",Pcore,"W"
print"Core loss at 375V, 50 Hz supply =",Pcore50,"W"
print"Efficiency =",etanew*100,"Percent"
print"Efficiency = 0 with the load is disconnected as Pout=0"
# Example 2.13
# Determine (a) Efficiency at rated load and 80% power factor
# (b) 70% load and 80% power factor
# Page No. 75
# Given data
FP=0.80; # Power factor
PcorePU=0.0045; # Percentage core loss
RPU=0.0146; # Percentage resistance
Sload=70.; # 70% rated load
Srated=100.; # 100% rated load
# (a) Efficiency at rated load and 80% power factor
etarated=FP/(FP+RPU+PcorePU);
# (b) Efficiency at 70% load and 80% power factor
SPU=Sload/Srated;
IPU=SPU; # I_load is proportional to S_load
eta=(SPU*FP)/(SPU*FP+PcorePU+IPU**2*RPU) # Efficiency
# Display result on command window
print"Efficiency at rated load =",round(etarated,4)
print"Efficiency at 70 percent load =",round(eta,4)
print'There is very little change in efficiency'
# Example 2.14
# Determine (a) Magnetizing reactance and equivalent core-loss resistance
# (b) Per unit resistance, reactance and impedance of transformer windings
# (c) Voltage regulation when operating at rated load and 0.75 power factor lagging
# Page No. 78
# Given data
Poc=521.; # Open circuit test power
Voc=230.; # Open circuit voltage
Vo=230.; # Output voltage
Ioc=13.04; # Open circuit current
Vsc=160.8; # Short circuit voltage
Isc=16.3; # Short circuit current
Psc=1200.; # Short circuit power
S=75000.; # Transformer rating
Vhs=4600.; # High side voltage
FP=0.75; # Power factor lagging
# (a) Magnetizing reactance and equivalent core-loss resistance
Ife=Poc/Voc; # Current rating
RfeLS=Vo/Ife; # Core-loss resistance
Im=12.8;#sqrt(Ioc**2.-Ife**2.); # Magnetizing current
XMLS=Voc/Im; # Magnetizing reactance
# (b) Per unit resistance, reactance and impedance of transformer windings
ZeqHS=Vsc/Isc; # Equivalent impedance
ReqHS=Psc/Isc**2.; # Equivalent resistance
XeqHS=8.77;#sqrt(ZeqHS**2. - ReqHS**2.); # Equivalent reactance
Ihs=S/Vhs; # High side current
RPU=Ihs*ReqHS/Vhs; # Per unit resistance
XPU=Ihs*XeqHS/Vhs; # Per unit reactance
ZPU=0.016+0.0311j;#RPU+%i*XPU; # Per unit impedance
# Complex to Polar form...
ZPU_Mag=0.035;#sqrt(real(ZPU)**2.+imag(ZPU)**2.); # Magnitude part
ZPU_Ang=62.8;#atan(imag(ZPU),real(ZPU))*180./math.pi; # Angle part
# (c) Voltage regulation when operating at rated load and 0.75 power factor lagging
# Transformer regulation
Theta=41.4;#acosd(FP);
RegPU=0.0326;#sqrt( (RPU+FP)**2. + (XPU+sind(Theta))**2. )-1.;
# Transformer regulation in percentage
RegPU_Per=3.26;#RegPU*100.;
# Display result on command window
print"Equivalent core-loss resistance =",RfeLS,"Ohm"
print"Magnetizing reactance =",XMLS,"Ohm"
print"Per unit resistance =",RPU
print"Per unit reactance =",XPU
print"Per unit impedance magnitude =",ZPU_Mag
print"Per unit impedance angle =",ZPU_Ang
print"Voltage regulation in percentage =",RegPU_Per