# Chapter 5 - REPRESENTATION AND PERFORMANCE OF SHORT AND MEDIUM TRANSMISSION LINES¶

## Example E1 - Pg 128¶

In [3]:
#calculate Voltage at sending end,Regulation,Transmission Efficiency
import math
#Given data :
P=1100.##kW
VR=11.*1000.##V
pf=0.8##power factor
R=2.##ohm
X=3.##ohm
I=P*1000./VR/pf##A
cos_fi_r=pf#
sin_fi_r=math.sqrt(1.-cos_fi_r**2)#
VS=math.sqrt((VR*cos_fi_r+I*R)**2.+(VR*sin_fi_r+I*X)**2.)##V
print '%s %.f' %("Voltage at sending end(V)",VS)#
Reg=(VS-VR)/VR*100.##%
print '%s %.3f' %("Regulation",Reg)#
LineLoss=I**2.*R/1000.##kW
Eta_T=P*100./(P+LineLoss)##%
print '%s %.2f' %("Transmission Efficiency(%)",Eta_T)#

Voltage at sending end(V) 11426
Regulation 3.873
Transmission Efficiency(%) 97.24


## Example E2 - Pg 128¶

In [4]:
#calculate Transmission Efficiency(%)
import math
#Given data :
R=0.4##ohm
X=0.4##ohm
P=2000.##kVA
pf=0.8##power factor
VL=3000.##V
VR=VL/math.sqrt(3.)##V
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2.)#
I=P*1000./3./VR##A
VS=VR+I*(R*cos_fi_r+X*sin_fi_r)##V
Reg=(VS-VR)/VR*100.##%
print '%s %.2f' %("% Regulation",Reg)#
LineLoss=3.*I**2.*R/1000.##kW
Pout=P*cos_fi_r##kW
Eta_T=Pout*100./(Pout+LineLoss)##%
print '%s %.f' %("Transmission Efficiency(%)",Eta_T)#

% Regulation 12.44
Transmission Efficiency(%) 90


## Example E3 - Pg 129¶

In [22]:
#calculate
import math
#Given data :
l=15.##km
P=5.##MW
V=11.##kV
f=50.##Hz
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
L=1.1##mH/Km
VR=V*1000./math.sqrt(3.)##V
I=P*1000./math.sqrt(3.)/V/cos_fi_r##A
LineLoss=12./100.*P*10**6##W
R=LineLoss/3./I**2##ohm
X=2.*math.pi*f*L*10**-3*l##ohm/phase
VS=VR+I*(R*cos_fi_r+X*sin_fi_r)##V
VSL=math.sqrt(3.)*VS/1000.##KV
print '%s %.3f' %("Line voltage at sending end(kV)",VSL)#
Reg=(VSL-V)/V*100.##%
print '%s %.3f' %("% Regulation",Reg)#

Line voltage at sending end(kV) 13.612
% Regulation 23.745


## Example E4 - Pg 130¶

In [23]:
#calculate Line voltage at sending end(kV),Sending end pf(lagging),Transmission Efficiency(%),Regulation
import math
#Given data :
l=50.##km
S=10000.##kVA
pf=0.8##power factor
d=1.2*100.##cm
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
V=33000.##Volts
VR=V/math.sqrt(3.)##V
f=50.##Hz
I=S*1000./math.sqrt(3.)/V##A
LineLoss=10./100.*S*10.**3*pf##W
R=LineLoss/3./I**2##ohm
rho=1.73*10**-6##kg/m**3
a=rho*l*1000.*100./R##cm**2
r=math.sqrt(a/math.pi)##cm
L=0.2*math.log(d/r/0.7788)*l##mH
X=2*math.pi*f*L*10**-3##ohm
VS=VR+I*(R*cos_fi_r+X*sin_fi_r)##V
VSL=math.sqrt(3.)*VS/1000.##kV
print '%s %.2f' %("Line voltage at sending end(kV)",VSL)#
pf_s=(VR*cos_fi_r+I*R)/VS##lagging(sendinf end pf)
print '%s %.4f' %("Sending end pf(lagging) ",pf_s)#
Eta_T=S*pf/(S*pf+LineLoss/1000.)*100.#
print '%s %.2f' %("Transmission Efficiency(%)",Eta_T)#
Reg=(VSL-V/1000.)/(V/1000.)*100.##%
print '%s %.2f' %("% Regulation",Reg)#

Line voltage at sending end(kV) 38.32
Sending end pf(lagging)  0.7579
Transmission Efficiency(%) 90.91
% Regulation 16.12


## Example E5 - Pg 130¶

In [7]:
#calculate Resistance per phase(ohm/phase),Inductance per phase(mH/phase)
import math
#Given data :
VRL=30000.##Volts
VSL=33000.##Volts
f=50.##Hz
P=10.*10.**6##W
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
VR=VRL/math.sqrt(3.)##V
I=P/math.sqrt(3.)/VRL/pf##A
Eta_T=0.96##Efficiency
LineLoss=P*(1/Eta_T-1)##W
R=LineLoss/3/I**2##ohm/phase
print '%s %.1f' %("Resistance per phase(ohm/phase)",R)#
VS=VSL/math.sqrt(3.)##V
X=(VS-VR-I*R*cos_fi_r)/I/sin_fi_r##V
L=X/2./math.pi/f##H/phase
print '%s %.f' %("Inductance per phase(mH/phase)",L*1000)#

Resistance per phase(ohm/phase) 2.4
Inductance per phase(mH/phase) 28


## Example E6 - Pg 131¶

In [24]:
#calculate Line voltage at load end(volt),Transmission Efficiency(%)
import math
import numpy
from numpy import roots
#Given data :
l=3.##km
P=3000.##KW
VSL=11.*10**3##volt
R=l*0.4##ohm
X=l*0.8##ohm
VS=VSL/math.sqrt(3.)##Volts
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
#VS=VR+I*(R*cos_fi_r+X*sin_fi_r)##V
I_into_VR=P*1000./3./cos_fi_r##VA
#VR**2-VS*VR+I_into_VR*(R*cos_fi_r+X*sin_fi_r)#
p=([1, -VS, I_into_VR*(R*cos_fi_r+X*sin_fi_r)])#
VR=numpy.roots(p)#
VR=VR[0]##taking greater value
I=I_into_VR/VR##A
VRL=math.sqrt(3.)*VR##volt
print '%s %.f' %("Line voltage at load end(volt) : ",VRL)#
Eta_T=P*1000/(P*1000+3*I**2*R)*100##%
print '%s %.1f' %("Transmission Efficiency(%) : ",Eta_T)#

Line voltage at load end(volt) :  10110
Transmission Efficiency(%) :  94.8


## Example E7 - Pg 131¶

In [9]:
#calculate Power output(kW),Power factor at sending end(lagging)
import math
#Given data :
R=5.##ohm/phase
X=20.##ohm/phase
VSL=46.85##kV
VRL=33.##kV
VRL=VRL*1000.##v
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
VR=VRL/math.sqrt(3.)##V
I=(VSL*1000./math.sqrt(3.)-VR)/(R*cos_fi_r+X*sin_fi_r)##A
Pout=math.sqrt(3.)*VRL*I*pf/1000.##kW
print '%s %.f' %("Power output(kW)",Pout)#
cosfi_s=(VR*pf+I*R)/(VSL*1000/math.sqrt(3.))##power factor
print '%s %.3f' %("Power factor at sending end(lagging)",cosfi_s)#

Power output(kW) 22853
Power factor at sending end(lagging) 0.656


## Example E8 - Pg 136¶

In [67]:
#calculate Sending end power factor(lag),Regulation(%),Transmission Efficiency(%)
import math
import cmath
#Given data :
l=80.##km
P=15.##MW
VR=66.*10**3##Volt
R=l*0.3125##ohm
X=l*1.##ohm
Y=l*17.5*10**-6##S
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
IR=P*10**6/(VR*pf)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
IC=1j*Y*VR##A
IS=IR+IC##A
print '%s %.1f %s %.2f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
VS=VR+IS*(R+1j*X)##volt
print '%s %.f %s %.2f' %("Sending end voltage(V), magnitude is ",abs(VS)," and angle in degree is ",cmath.phase(VS)*180/math.pi)#
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fis=math.cos(fi_s)##sending end pf
print '%s %.2f' %("Sending end power factor(lag) : ",cos_fis)#
Reg=(abs(VS)-VR)/VR*100##%
print '%s %.1f' %("Regulation(%) :  ",Reg)#
LineLoss=abs(IS)**2*R/1000.##kW
print '%s %.1f' %("Line Losses in kW : ",LineLoss)#
Eta_T=P*1000/(P*1000+LineLoss)*100##%
print '%s %.2f' %("Transmission Efficiency(%) : ",Eta_T)#

Sending end current(A), magnitude is  240.3  and angle in degree is  -18.95
Sending end voltage(V), magnitude is  79598  and angle in degree is  11.77
Sending end power factor(lag) :  0.86
Regulation(%) :   20.6
Line Losses in kW :  1443.6
Transmission Efficiency(%) :  91.22


## Example E9 - Pg 137¶

In [27]:
#calculate Sending end line voltage(Volt) ,Regulation(%),Transmission Efficiency(%)
import math
import cmath
#Given data :
l=100.##km
P=20.##MW
VRL=66.*10**3##volt
f=50.##Hz
R=10.##ohm
L=111.7*10**-3##H
C=0.9954*10**-6##F
pf=0.8##power factor
X=2.*math.pi*f*L##ohm
Y=2.*math.pi*f*C##S
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
VR=VRL/math.sqrt(3.)##volt
IR=P*10**6/(math.sqrt(3.)*VRL*pf)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
Z=R+1j*X##ohm
Vdash=VR+1./2.*IR*Z##Volt
IC=Vdash*1j*Y##A
IS=IR+IC##A
VS=Vdash+1./2.*IS*Z##Volt
VSL=abs(VS)*math.sqrt(3.)##Volt
print '%s %.f' %("Sending end line voltage(Volt) :",VSL)#
Reg=(VSL-VRL)/VRL*100.##%
print '%s %.2f' %("Regulation(%) :  ",Reg)#
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fi_s=math.cos(fi_s)##sending end pf
Eta_T=math.sqrt(3.)*VRL*abs(IR)*cos_fi_r/(math.sqrt(3)*VSL*abs(IS)*cos_fi_s)*100##%
print '%s %.1f' %("Transmission Efficiency(%) : ",Eta_T)#
#Ans is not accurate in the book.

Sending end line voltage(Volt) : 77071
Regulation(%) :   16.77
Transmission Efficiency(%) :  93.5


## Example E10 - Pg 138¶

In [65]:
#calculate Sending end line voltage(kV),Regulation(%),Transmission Efficiency(%)
import math
import cmath
#Given data :
l=200.##km
P=50.##MVA
VRL=132.*10**3.##Volt
f=50.##Hz
R=l*0.15##ohm
X=l*0.50##ohm
Y=l*2.*10**-6##mho
pf=0.85##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
VR=VRL/math.sqrt(3.)##Volt
IR=P*10**6/(math.sqrt(3.)*VRL)##A
Z=R+1j*X##ohm
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
Vdash=VR+1/2*IR*Z##Volt
IC=Vdash*1j*Y##A
IS=IR+IC##A
print '%s %.2f %s %.2f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
VS=Vdash+1/2*IS*Z##Volt
VSL=abs(VS)*math.sqrt(3)##Volt
print '%s %.2f' %("Sending end line voltage(kV) :",VSL/1000)#
Reg=(VSL-VRL)/VRL*100##%
print '%s %.2f' %("Regulation(%) :  ",Reg)#
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fi_s=math.cos(fi_s)##sending end pf
Eta_T=math.sqrt(3.)*VRL*abs(IR)*cos_fi_r/(math.sqrt(3)*VSL*abs(IS)*cos_fi_s)*100##%
print '%s %.2f' %("Transmission Efficiency(%) : ",Eta_T)#
#Ans is wrong in the book.Angle of VS is calculated wrong leads to wrong answers.

Sending end current(A), magnitude is  204.28  and angle in degree is  -24.50
Sending end line voltage(kV) : 132.00
Regulation(%) :   0.00
Transmission Efficiency(%) :  100.00


## Example E11 - Pg 139¶

In [31]:
#calculate Sending end power factor(lag)
import math
import cmath
#Given data :
S=1.*10**3##kVA
pf=0.71##power factor
VRL=22.*10**3##Volt
f=50.##Hz
R=15.##ohm
L=0.2##H
C=0.5*10**-6##F
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
IR=S*10.**3/VRL##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
X=2.*math.pi*f*L##ohm
#Z=sqrt(R**2+X**2)##ohm
Z=R+1j*X##ohm
Y=2.*math.pi*f*C##S
ICR=1./2.*1j*Y*VRL##A
IL=IR+ICR##A
VS=VRL+IL*Z##Volt
print '%s %.f %s %.2f' %("Sending end voltage(Volt), magnitude is ",abs(VS)," and angle in degree is ",cmath.phase(VS))#
ICS=1./2.*1j*Y*VS##A
IS=IL+ICS##A
print '%s %.3f %s %.2f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS))#
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fi_s=math.cos(fi_s)##sending end pf
print '%s %.3f' %("Sending end power factor(lag) : ",cos_fi_s)#

Sending end voltage(Volt), magnitude is  24437  and angle in degree is  0.06
Sending end current(A), magnitude is  42.874  and angle in degree is  -0.72
Sending end power factor(lag) :  0.706


## Example E12 - Pg 139¶

In [32]:
#calculate Sending end line to line voltage(kV)
import math
#Given data :
P=50.*10**6##W
f=50.##Hz
l=150.##km
pf=0.8##power factor
VRL=110.*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
R=0.1*l##ohm
XL=0.5*l##ohm
Z=R+1j*XL##ohm
IR=P/(math.sqrt(3)*VRL*pf)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
Y=3.*10**-6*l##S
ICR=1./2.*1j*Y*VR##A
IL=IR+ICR##A
VS=VR+IL*Z##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.3f' %("Sending end line to line voltage(kV) :",VSL/1000.)#

Sending end line to line voltage(kV) : 143.562


## Example E13 - Pg 140¶

In [63]:
#calculate Sending end line to line voltage(kV),Sending end power factor(lag)
import math
import cmath
#Given data :
f=50.##Hz
l=30.##km
Z=40.+1j*125##ohm
Y=10**-3##mho
P=50.*10**6##W
VRL=220.*10**3##Volt
VR=VRL/math.sqrt(3)##Volt
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
IR=P/(math.sqrt(3.)*VRL*pf)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
ICR=1./2.*1j*Y*VR##A
IL=IR+ICR##A
VS=VR+IL*Z##Volt
VSL=math.sqrt(3)*abs(VS)##Volt
print '%s %.2f ' %("Sending end line to line voltage(kV) :",VSL/1000)#
IS=IL+1./2.*1j*Y*VS##A
print '%s %.2f %s %.1f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fis=math.cos(fi_s)##sending end pf
print '%s %.3f' %("Sending end power factor(lag) : ",cos_fis)#

Sending end line to line voltage(kV) : 238.07
Sending end current(A), magnitude is  128.15  and angle in degree is  15.1
Sending end power factor(lag) :  0.988


## Example E14 - Pg 141¶

In [16]:
#calculate Sending end line to line voltage(kV)
import math
#Given data :
f=50.##Hz
l=30.##km
Z=40.+1j*125.##ohm
Y=10**-3##mho
P=50.*10**6##W
VRL=220.*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
IR=P/(math.sqrt(3.)*VRL*pf)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
ICR=1./2.*1j*Y*VR##A
IL=IR+ICR##A
VS=VR+IL*Z##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.2f' %("Sending end line to line voltage(kV) :",VSL/1000.)#

Sending end line to line voltage(kV) : 238.07


## Example E15 - Pg 141¶

In [61]:
#calculate Sending end line voltage(kV),Sending end power factor(lag),Transmission Efficiency(%)
import math
import cmath
#Given data :
f=50.##Hz
l=100.##km
P=50.*10**6##W
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
VRL=132.*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
R=0.1*l##ohm
XL=0.3*l##ohm
Z=R+1j*XL##ohm
Y=3.*10**-6*l##S
IR=P/(math.sqrt(3)*VRL*pf)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
ICR=1/2*1j*Y*VR##A
IL=IR+ICR##A
VS=VR+IL*Z##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.2f' %("Sending end line voltage(kV) :",VSL/1000)#
ICS=1./2.*1j*Y*VS##A
IS=IL+ICS##A
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fi_s=math.cos(fi_s)##sending end pf
print '%s %.2f' %("Sending end power factor(lag) : ",cos_fi_s*180/math.pi)#
Eta_T=math.sqrt(3)*VRL*abs(IR)*cos_fi_r/(math.sqrt(3)*VSL*abs(IS)*cos_fi_s)*100##%
print '%s %.3f' %("Transmission Efficiency(%) : ",Eta_T)#

Sending end line voltage(kV) : 144.56
Sending end power factor(lag) :  45.03
Transmission Efficiency(%) :  95.709


## Example E16 - Pg 142¶

In [34]:
#calculate Line voltage at mid point(kV),Sending end line voltage(kV)
import math
import cmath
#Given data :
f=50.##Hz
l=10.##km
S1=5000.*10**3##VA
S2=10000.*10**3##VA
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
pf2=0.7071##power factor
cos_fi_r2=pf2#
sin_fi_r2=math.sqrt(1-cos_fi_r2**2)#
R=0.6*l##ohm
XL=1.5*l##ohm
VRL=33*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
I1=S1/(math.sqrt(3.)*VRL)##A
I1=I1*(cos_fi_r-1j*sin_fi_r)##A
Z1=R+1j*XL##ohm
VB=VR+I1*Z1##Volt
VBL=math.sqrt(3)*abs(VB)##Volt
print '%s %.3f' %("Line voltage at mid point(kV) : ",VBL/1000)#
I2=S2/(math.sqrt(3.)*VBL)##A
I2=I2*(cos_fi_r2-1j*sin_fi_r2)##A
I=I1+I2##A
print '%s %.2f %s %.2f' %("Total current(A), magnitude is ",abs(I)," and angle in degree is ",cmath.phase(I))#
Z2=R+1j*XL##ohm
VS=VB+I*Z2##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.2f' %("Sending end line voltage(kV) :",VSL/1000)#

Line voltage at mid point(kV) :  35.114
Total current(A), magnitude is  251.32  and angle in degree is  -0.74
Sending end line voltage(kV) : 41.64


## Example E17 - Pg 143¶

In [36]:
#calculate Power supplied by line A(kW),B(kW)
import cmath
import math
#Given data :
P=10.##MWatt
pf=0.8##power factor
VRL=30.*10**3##Volt
R1=5.5##ohm
XL1=13.5##ohm
R2=6.##ohm
XL2=11.##ohm
ZA=R1+1j*XL1##ohm
ZB=R2+1j*XL2##ohm
S=P*10.**3./pf*(math.cos(-36.52*math.pi/180.) + 1j*math.sin(-36.52*math.pi/180.))##kVA
SA=S*ZB/(ZA+ZB)##kVA
print '%s %.f %s %.3f' %("Load supply by line A(kVA), magnitude is ",abs(SA)," at pf ",cmath.phase(SA))#
SB=S*ZA/(ZA+ZB)##kVA
print '%s %.f %s %.2f' %("Load supply by line B(kVA), magnitude is ",abs(SB)," and angle in degree is ",cmath.phase(SA))#
PA=abs(SA)*(math.cos(cmath.phase(SA)*180/math.pi))##kW
print '%s %.2f' %("Power supplied by line A(kW) : ",PA)#
PB=abs(SB)*(math.cos(cmath.phase(SB)*180/math.pi))##kW
print '%s %.2f' %("Power supplied by line B(kW) : ",PB)#
#Answer is not accurate in the book.

Load supply by line A(kVA), magnitude is  5787  at pf  -0.698
Load supply by line B(kVA), magnitude is  6733  and angle in degree is  -0.70
Power supplied by line A(kW) :  -3797.43
Power supplied by line B(kW) :  -3546.79


## Example E18 - Pg 145¶

In [20]:
#calculate Percentage rise in voltage
import math
#Given data :
L=200.##km
f=50.##Hz
Rise=omega**2.*L**2.*10.**-8./18.##%
print '%s %.2f' %("Percentage rise in voltage : ",Rise)#

Percentage rise in voltage :  2.19


## Example E19 - Pg 151¶

In [47]:
#calculate Parameter A,B,C,D
import math
import cmath
#Given data :
L=80.##km
f=50.##Hz
Z=(0.15+1j*0.78)*L##ohm
Y=(1j*5.*10.**-6)*L##mho
A=1.+1./2.*Y*Z##parameter of 3-phase line
D=A##parameter of 3-phase line
B=Z*(1.+1./4.*Y*Z)##parameter of 3-phase line
C=Y##parameter of 3-phase line
print ("Parameter A : ",A)#
print ("Parameter B : ",B)#
print ("Parameter C : ",C)#
print ("Parameter D : ",D)#
#Answer of B is wrong in the book.

('Parameter A : ', (0.98752+0.0024j))
('Parameter B : ', (11.85024+62.02502400000001j))
('Parameter C : ', 0.00039999999999999996j)
('Parameter D : ', (0.98752+0.0024j))


## Example E20 - Pg 151¶

In [69]:
#calculate Power Input(MW),Transmission Efficiency(%),Sending end power factor(lag)
import math
import cmath
#Given data :
Z=200*math.cos(80.*math.pi/180.) + 1j*math.sin(80.*math.pi/180.)##ohm
Y=0.0013*math.cos(90.*math.pi/180.) + 1j*math.sin(90.*math.pi/180.)##mho/phase
P=80*10**6##W
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
VRL=220.*10**3##Volt
VR=VRL/math.sqrt(3)##Volt
f=50##Hz
IR=P/(math.sqrt(3.)*VRL*pf)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
A=1.+1./2.*Y*Z##parameter of 3-phase line
D=A##parameter of 3-phase line
B=Z*(1.+1./4.*Y*Z)##parameter of 3-phase line
C=Y##parameter of 3-phase line
print '%s %.2f %s %.2f' %("Parameter A, magnitude is ",abs(A)," and angle in degree is ",cmath.phase(A)*180/math.pi)#
print '%s %.2f %s %.2f' %("Parameter B, magnitude is ",abs(B)," and angle in degree is ",cmath.phase(B)*180/math.pi)#
print '%s %.2f %s %.2f' %("Parameter C, magnitude is ",abs(C)," and angle in degree is ",cmath.phase(C)*180/math.pi)#
print '%s %.2f %s %.2f' %("Parameter D, magnitude is ",abs(D)," and angle in degree is ",cmath.phase(D)*180/math.pi)#
VS=A*VR+B*IR##Volt
VSL=math.sqrt(3)*abs(VS)##Volt
print '%s %.2f' %("Sending end Line voltage(kV) : ",VSL/1000.)#
IS=C*VR+D*IR##A
print '%s %.2f %s %.2f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fis=math.cos(fi_s)##sending end pf
print '%s %.2f' %("Sending end power factor(lag) : ",cos_fis)#
Pin=math.sqrt(3.)*VSL*abs(IS)*cos_fis*10**-6##MW
print '%s %.2f' %("Power Input(MW) : ",Pin)#
Eta=P/(Pin*10**6)*100.##%
print '%s %.2f' %("Transmission Efficiency(%) : ",Eta)#

Parameter A, magnitude is  17.37  and angle in degree is  88.33
Parameter B, magnitude is  302.79  and angle in degree is  86.66
Parameter C, magnitude is  1.00  and angle in degree is  90.00
Parameter D, magnitude is  17.37  and angle in degree is  88.33
Sending end Line voltage(kV) :  3930.49
Sending end current(A), magnitude is  130613.70  and angle in degree is  88.75
Sending end power factor(lag) :  1.00
Power Input(MW) :  888811.72
Transmission Efficiency(%) :  0.01


## Example E21 - Pg 152¶

In [68]:
#calculate Sending end power factor(lag),Power Input(MW),Transmission Efficiency(%)
import math
import cmath
#Given data :
P=50.*10**6##VA
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
A=0.98*math.cos(3.*math.pi/180.) + 1j*math.sin(3.*math.pi/180.)##parameter of 3-phase line
D=0.98*math.cos(3.*math.pi/180.) + 1j*math.sin(3.*math.pi/180.)##parameter of 3-phase line
B=110*math.cos(75.*math.pi/180.) + 1j*math.sin(75.*math.pi/180.)##parameter of 3-phase line
C=0.0005*math.cos(80.*math.pi/180.) + 1j*math.sin(80.*math.pi/180.)##parameter of 3-phase line
VRL=110.*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
IR=P/(math.sqrt(3.)*VRL)##A
IR=IR*(cos_fi_r-1j*sin_fi_r)##A
VS=A*VR+B*IR##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.2f' %("Sending end Line voltage(kV) : ",VSL/1000.)#
IS=C*VR+D*IR##A
print '%s %.2f %s %.2f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
fi_s=cmath.phase(VS)-cmath.phase(IS)##
cos_fis=math.cos(fi_s)##sending end pf
print '%s %.2f' %("Sending end power factor(lag) : ",cos_fis)#
Pin=math.sqrt(3.)*VSL*abs(IS)*cos_fis*10**-6##MW
print '%s %.2f' %("Power Input(MW) : ",Pin)#
Eta=P*pf/(Pin*10**6)*100.##%
print '%s %.2f' %("Transmission Efficiency(%) : ",Eta)#

Sending end Line voltage(kV) :  118.28
Sending end current(A), magnitude is  62400.97  and angle in degree is  89.80
Sending end power factor(lag) :  -0.01
Power Input(MW) :  -134.12
Transmission Efficiency(%) :  -29.82


## Example E22 - Pg 153¶

In [59]:
#calculate
import math
import cmath
import numpy
from numpy import roots
#Given data :
f=50##Hz
L=300##km
r=0.15##ohm/km
x=0.5##ohm/km
y=3*10**-6##mho/km
VRL=220*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
P=200*10**6##W
pf=0.85##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
R=r*L##ohm
X=x*L##ohm
Y=y*L##mho
Z=R+1j*X##ohm
#part (i)
A=1+1/2.*1j*Y*Z##parameter of 3-phase line
D=A##parameter of 3-phase line
B=Z##parameter of 3-phase line
C=1j*Y*(1.+1./4.*1j*Y*Z)##parameter of 3-phase line
print '%s %.4f %s %.2f' %("Parameter A, magnitude is ",abs(A)," and angle in degree is ",cmath.phase(A)*180/math.pi)#
print '%s %.1f %s %.1f' %("Parameter B, magnitude is ",abs(B)," and angle in degree is ",cmath.phase(B)*180/math.pi)#
print '%s %.2e %s %.2f' %("Parameter C, magnitude is ",abs(C)," and angle in degree is ",cmath.phase(C)*180/math.pi)#
print '%s %.2f %s %.2f' %("Parameter D, magnitude is ",abs(D)," and angle in degree is ",cmath.phase(D)*180/math.pi)#
#part (ii)
p=([0.024525, 11.427, -2102])##from VS=A*VR+B*IR##Volt
IR=roots(p)#
IR=IR[1]##taking +ve value
P=math.sqrt(3.)*VRL*IR*10**-6##MW
print '%s %.1f' %("Power received in MW : ",P)#
#/part (iii)
P=200.*10.**6##W
IR=P/math.sqrt(3.)/VRL/pf##A
fi=math.acos(pf) *180./math.pi##degree
IR=IR*math.cos(-fi*math.pi/180.) + 1j*math.sin(-fi*math.pi/180.)#
VS=A*VR+B*IR##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.2f' %("Sending end Line voltage(kV) : ",VSL/1000.)#

Parameter A, magnitude is  0.9327  and angle in degree is  1.24
Parameter B, magnitude is  156.6  and angle in degree is  73.3
Parameter C, magnitude is  8.70e-04  and angle in degree is  90.60
Parameter D, magnitude is  0.93  and angle in degree is  1.24
Power received in MW :  53.8
Sending end Line voltage(kV) :  283.60


## Example E23 - Pg 154¶

In [54]:
#Exa 5.23
import math
import cmath
#Given data :
A=0.936+1j*0.016##parameter of 3-phase line
D=A##parameter of 3-phase line
B=33.5+1j*138##parameter of 3-phase line
C=(-0.9280+1j*901.223)*10**-6##parameter of 3-phase line
VRL=200.*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
P=40*10**6##W
pf=0.86##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
IR=P/math.sqrt(3.)/VRL/pf##A
fi=math.acos(pf) *180/math.pi##degree
IR=IR*(math.cos(-fi*math.pi/180.) + 1j*math.sin(-fi*math.pi/180.))#
VS=A*VR+B*IR##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.2f' %("Sending end Line voltage(kV) : ",VSL/1000.)#
IS=C*VR+D*IR##A
print '%s %.1f %s %.2f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
fi_s=cmath.phase(VS)-cmath.phase(IS)##degree
print '%s %.4f' %("Sending end phase angle(degree): ",math.cos(fi_s))#
Ps=math.sqrt(3.)*abs(VSL)*abs(IS)*math.cos(fi_s)*10**-6##MW
print '%s %.3f' %("Sending end power(MW) : ",Ps)#
Vreg=(VSL-VRL)*100./VRL##%
print '%s %.2f' %("Voltage regulation in % : ",Vreg)#

Sending end Line voltage(kV) :  211.98
Sending end current(A), magnitude is  116.8  and angle in degree is  20.96
Sending end phase angle(degree):  0.9716
Sending end power(MW) :  41.665
Voltage regulation in % :  5.99


## Example E24 - Pg 155¶

In [51]:
#calculate Sending end Line voltage(kV)
import cmath
import math
#Given data :
A1=0.98*(math.cos(2.*math.pi/180.) + 1j*math.sin(2.*math.pi/180.))##parameter of 3-phase line
D1=A1##parameter of 3-phase line
B1=28.*(math.cos(69.*math.pi/180.) + 1j*math.sin(69.*math.pi/180.))##parameter of 3-phase line
C1=0.0002*(math.cos(88.*math.pi/180.) + 1j*math.sin(88.*math.pi/180.))##parameter of 3-phase line
A2=0.95*(math.cos(3.*math.pi/180.) + 1j*math.sin(3.*math.pi/180.))##parameter of 3-phase line
D2=A2##parameter of 3-phase line
B2=40.*(math.cos(85.*math.pi/180.) + 1j*math.sin(85.*math.pi/180.))##parameter of 3-phase line
C2=0.0004*(math.cos(90.*math.pi/180.) + 1j*math.sin(90.*math.pi/180.))##parameter of 3-phase line
VRL=110.*10**3##Volt
VR=VRL/math.sqrt(3.)##Volt
IR=200.##A
pf=0.95##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
fi=math.cos(pf)##degree
A=A1*A2+B1*C2##generalized parameter of 2 line
B=A1*B2+B1*D2##generalized parameter of 2 line
C=C1*A2+D1*C2##generalized parameter of 2 line
D=C1*B2+D1*D2##generalized parameter of 2 line
IR=IR*(math.cos(-fi*math.pi/180.) + 1j*math.sin(-fi*math.pi/180.))#
VS=A*VR+B*IR##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
print '%s %.2f' %("Sending end Line voltage(kV) : ",VSL/1000)#
IS=C*VR+D*IR##A
print '%s %.2f %s %.2f' %("Sending end current(A), magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
#Answer for VSL is wrong in the book.

Sending end Line voltage(kV) :  109.34
Sending end current(A), magnitude is  190.09  and angle in degree is  15.72


## Example E25 - Pg 156¶

In [50]:
#calculate Sending end power factor(lagging)
import cmath
import math
#Given data :
A1=0.98*(math.cos(1.*math.pi/180.) + 1j*math.sin(1.*math.pi/180.))##parameter of 3-phase line
D1=A1##parameter of 3-phase line
B1=100*(math.cos(75.*math.pi/180.) + 1j*math.sin(75.*math.pi/180.))##parameter of 3-phase line
C1=0.0005*(math.cos(90.*math.pi/180.) + 1j*math.sin(90.*math.pi/180.))##parameter of 3-phase line
A2=0.98*(math.cos(1.*math.pi/180.) + 1j*math.sin(1.*math.pi/180.))##parameter of 3-phase line
D2=A2##parameter of 3-phase line
B2=100*(math.cos(75.*math.pi/180.) + 1j*math.sin(75.*math.pi/180.))##parameter of 3-phase line
C2=0.0005*(math.cos(90.*math.pi/180.) + 1j*math.sin(90.*math.pi/180.))##parameter of 3-phase line
P=100*10**6##W
VRL=132*10**3##Volt
VR=VRL/math.sqrt(3)##Volt
pf=0.8##power factor
cos_fi_r=pf#
sin_fi_r=math.sqrt(1-cos_fi_r**2)#
fi=math.acos(pf)##degree
A=(A1*B2+A2*B1)/(B1+B2)##generalized parameter of 2 line
B=B1*B2/(B1+B2)##generalized parameter of 2 line
C=C1+C2-(A1-A2)*(D1-D2)/(B1+B2)##generalized parameter of 2 line
D=(B1*D2+B2*D1)/(B1+B2)##generalized parameter of 2 line
print '%s' %("Generalised constants ot two lines combined are : ")#
print '%s %.2f %s %.f' %("Parameter A, magnitude is ",abs(A)," and angle in degree is ",cmath.phase(A)*180/math.pi)#
print '%s %.f %s %.2f' %("Parameter B, magnitude is ",abs(B)," and angle in degree is ",cmath.phase(B)*180/math.pi)#
print '%s %.3f %s %.2f' %("Parameter C, magnitude is ",abs(C)," and angle in degree is ",cmath.phase(C)*180/math.pi)#
print '%s %.2f %s %.2f' %("Parameter D, magnitude is ",abs(D)," and angle in degree is ",cmath.phase(D)*180/math.pi)#
IR=P/math.sqrt(3.)/VRL/pf##A
IR=IR*(math.cos(-fi*math.pi/180.) + 1j*math.sin(-fi*math.pi/180.))#
VS=A*VR+B*IR##Volt
VSL=math.sqrt(3.)*abs(VS)##Volt
IS=C*VR+D*IR##A
fi_s=cmath.phase(VS)-cmath.phase(IS)#
print '%s %.4f' %("Sending end power factor(lagging) : ",math.cos(fi_s))#

Generalised constants ot two lines combined are :
Parameter A, magnitude is  0.98  and angle in degree is  1
Parameter B, magnitude is  50  and angle in degree is  75.00
Parameter C, magnitude is  0.001  and angle in degree is  90.00
Parameter D, magnitude is  0.98  and angle in degree is  1.00
Sending end power factor(lagging) :  0.9843