Chapter 7 - CORONA

Example E1 - Pg 189

In [1]:
#calculate Line Voltage for comencing of corena(in kV)
import math
#Given data :
r=1.##cm
d=4.##meter
g0=30./math.sqrt(2.)##kV/cm
LineVoltage=math.sqrt(3.)*g0*r*math.log(d*100./r)##kV
print '%s %.2f' %("Line Voltage for comencing of corena(in kV) :",round(LineVoltage))#

Line Voltage for comencing of corena(in kV) : 220.00

Example E2 - Pg 190

In [2]:
#calculate Disruptive critical voltage from line to line(kV rms)
import math
#Given data :
Ph=3.##phase
V=220.##kV
f=50.##Hz
r=1.2##cm
d=2.##meter
mo=0.96##Irregularity factor
t=20.##degree C
T=t+273.##K
b=72.2##cm
go=21.1##kV rms/cm
dela=3.92*b/T##Air density factor
Vdo=go*dela*mo*r*math.log(d*100./r)##in kV
Vdo_line=math.sqrt(3.)*Vdo##in kV
print '%s %.2f' %("Disruptive critical voltage from line to line(kV rms) : ",round(Vdo_line))#

Disruptive critical voltage from line to line(kV rms) :  208.00

Example E3 - Pg 190

In [3]:
#calculate Spacing between conductors in meter
import math
#Given data :
V=132.##kV
r=2./2.##cm
Vexceed=210.##kV(rms)
go=30000./math.sqrt(2.)##Volts/cm
go=go/1000.##kV/cm
Vdo=Vexceed/math.sqrt(3.)##Volt
mo=1.##assumed 
dela=1.##assumed air density factor
#Formula : Vdo=go*del*mo*r*log(d*100/r)##in kV
d=math.exp(Vdo/go/dela/mo/r)*r##cm
print '%s %.2f' %("Spacing between conductors in meter : ",d*10**-2)#

Spacing between conductors in meter :  3.04

Example E4 - Pg 190

In [1]:
#calculate Minimum Diameter of conductor by Hit & Trial method(cm)
import math
import numpy
#Given data :
Ph=3.##phase
V=132.##kV
f=50.##Hz
d=3.##meter
d=d*100.##in cm
go=21.21##kV/cm : assumed
mo=0.85##assumed 
dela=0.95##assumed air density factor
Vdo=V/math.sqrt(3.)##kV
#Formula : Vdo=go*del*mo*r*log(d*100/r)##in kV
#r*log(d/r)=Vdo/go/del/mo: solving
#Implementing Hit & Trial method
w=numpy.zeros(200)

w[0]=.1
for i in range (1,200):
	w[i]=.1+w[i-1];

for r in w:
    if round(r*math.log(d/r))==round(Vdo/go/dela/mo):
        print '%s %.2f' %("Minimum Diameter of conductor by Hit & Trial method(cm) : ",2*r)#
        break

Minimum Diameter of conductor by Hit & Trial method(cm) :  1.20

Example E5 - Pg 191

In [4]:
#calculate g1max(kV/cm)
import math
#Given data :
r=2.5/2.##cm
epsilon_r=4.##constant
r1=3./2.##cm
r2=9./2.##cm
V=20.##kV(rms)
#Formula : gmax=q/(2*epsilon*r)
g2maxBYg1max=r/epsilon_r/r1##unitless
#Formula : V=g1max*r*log(r1/r)+g2max*r1*log(r2/r1)
g1max=V/(r*math.log(r1/r)+g2maxBYg1max*r1*math.log(r2/r1))##in kV/cm
print '%s %.2f' %("g1max(kV/cm) = ",g1max)#
print '%s' %("Corona will be present.g1max > go")#

g1max(kV/cm) =  35.01
Corona will be present.g1max > go

Example E6 - Pg 192

In [5]:
#calculate Line to line visual critical voltage for local corona(kV-rms),Line to line visual critical voltage for general corona(kV-rms)
import math
#Given data :
Ph=3.##phase
r=10.4/2##mm
r=r/10.##in cm
d=2.5##meter
d=d*100.##in cm
t=21.##degree C
T=t+273.##K
b=73.6##cm-Hg
mo=0.85# 
mv_l=0.7#
mv_g=0.8#
go=21.21##kV/cm : assumed
dela=3.92*b/T##Air density factor
#Formula : Vdo=go*del*mo*r*log(d*100/r)##kV
Vdo=go*dela*mo*r*math.log(d/r)##kV
Vdo_line=math.sqrt(3.)*Vdo##kV
Vvo=go*dela*mv_l*r*(1+.3/math.sqrt(dela*r))*math.log(d/r)##kV
Vvo_line_local=Vvo*math.sqrt(3.)##kV(rms)
print '%s %.1f' %("Line to line visual critical voltage for local corona(kV-rms)  : ",Vvo_line_local)
Vvo_line_general=Vvo_line_local*mv_g/mv_l##kV(rms)
print '%s %.f' %("Line to line visual critical voltage for general corona(kV-rms)  : ",Vvo_line_general)
#Note : Answer in the book is not accurate.

Line to line visual critical voltage for local corona(kV-rms)  :  115.1
Line to line visual critical voltage for general corona(kV-rms)  :  132

Example E7 - Pg 193

In [6]:
#calculate Corona Loss at 113 kV in kW ,Disruptive critical voltage between lines(kV)
#Given data :
import math
Pc1=53.##in kW
V1=106.##in kV
Pc2=98.##in kW
V2=110.9##in kV
Vph1=V1/math.sqrt(3.)##in kV
Vph2=V2/math.sqrt(3.)##in kV
#Formula : Pc=3*244/del*(f+25)*sqrt(r/d)*(Vph-Vdo)**2*10**-5##kW/Km
print '%s' %("Using proportionality : Pc is proportional to (Vph-Vdo)**2")#
print '%s' %("We have, Pc1/Pc2 = (Vph1-Vdo)**2/(Vph2-Vdo)**2")#
Vdo=(Vph1-math.sqrt(Pc1/Pc2)*(Vph2))/(1-math.sqrt(Pc1/Pc2))#
V3=113.##in kV
Vph3=V3/math.sqrt(3.)##in kV
Pc3=Pc2*(Vph3-Vdo)**2./(Vph2-Vdo)**2##in kW
print '%s %.1f' %("Corona Loss at 113 kV in kW : ",Pc3)#
VLine=math.sqrt(3.)*Vdo##in kV
print '%s %.1f' %("Disruptive critical voltage between lines(kV):  ",VLine)#

Using proportionality : Pc is proportional to (Vph-Vdo)**2
We have, Pc1/Pc2 = (Vph1-Vdo)**2/(Vph2-Vdo)**2
Corona Loss at 113 kV in kW :  121.5
Disruptive critical voltage between lines(kV):   92.4

Example E8 - Pg 194

In [7]:
#calculate Total corona loss under foul weather condition using Peek formula in kW,Total corona loss under foul weather condition using Peterson formula in kW 
import math
#Given data :
f=50.##Hz
l=160.##km
r=1.036/2.##cm
d=2.44*100.##cm
g0=21.1##kV/cm(rms)
m0=0.85##irregularity factor
mv=0.72##roughness factor
b=73.15##cm
t=26.6##degree C
dela=3.92*b/(273.+t)##air density factor
Vd0=g0*dela*m0*r*math.log(d/r)##kV(rms)
print '%s %.2f' %("Critical disruptive voltage(rms) in kV : ",Vd0)#
Vv0=g0*dela*mv*r*(1+0.3/math.sqrt(dela*r))*math.log(d/r)##kV
print '%s %.1f' %("Visual Critical voltage(rms) in kV : ",Vv0)#
Vph=110./math.sqrt(3.)##in kV
Pc_dash=d/dela*(f+25)*math.sqrt(r/d)*(Vph-0.8*Vd0)**2*10**-5##kW/km/phase
T_Corona_loss=l*3*Pc_dash##kW
print '%s %.f' %("Total corona loss under foul weather condition using Peek formula in kW : ",T_Corona_loss)#
VphBYVd0=Vph/Vd0/0.8#
K=0.46##constant
Corona_loss=21*10**-5*f*Vph**2*K/(math.log10(d/r))**2##kW/km/phase
T_corona_loss=Corona_loss*3*l##kW
print '%s %.1f' %("Total corona loss under foul weather condition using Peterson formula in kW : ",T_corona_loss)#

Critical disruptive voltage(rms) in kV :  54.73
Visual Critical voltage(rms) in kV :  66.1
Total corona loss under foul weather condition using Peek formula in kW :  1645
Total corona loss under foul weather condition using Peterson formula in kW :  1308.7

Example E9 - Pg 195

In [8]:
#calculate Power loss due to corona for fair weather condition,Total corona loss using Peek formula in kW,Total corona loss under foul weather condition using Peterson formula in kW 
import math
#given data :
f=50.##Hz
l=175.##km
r=1./2.##cm
d=3.*100.##cm
g0=21.1##kV/cm(rms)
m0=0.85##irregularity factor
mv=0.72##roughness factor
mv_dash=0.82##roughness factor
b=74.##cm
t=26.##degree C
Vph=110./math.sqrt(3.)##kV
dela=3.92*b/(273.+t)##air density factor
Vd0=g0*dela*m0*r*math.log(d/r)##kV(rms)
Vvo=g0*dela*mv*r*(1.+0.3/math.sqrt(dela*r))*math.log(d/r)##kV rms
Vvo_dash=Vvo*mv_dash/mv##kV rms
Pc=244./dela*(f+25.)*math.sqrt(r/d)*(Vph-Vd0)**2.*10.**-5##kW/Km/phase
T_CoronaLoss=Pc*l*3.##kW
print '%s' %("Power loss due to corona for fair weather condition : ")#
print '%s %.f' %("Total corona loss using Peek formula in kW : ",T_CoronaLoss)#
K=0.0713##constant for Vph/Vdo=1.142
Pc=21.*10.**-5*f*Vph**2./(math.log10(d/r))**2.*K##kW/Km/phase
T_CoronaLoss=Pc*l*3##kW
print '%s %.1f' %("According Peterson formula, Total corona loss for 175 km 3-phase line(kW): ",T_CoronaLoss)#
print '%s' %("Power loss due to corona for stormy weather condition : ")#
Vd0=0.8*Vd0##kV
Pc_dash=l*3.*244./dela*(f+25.)*math.sqrt(r/d)*(Vph-Vd0)**2.*10.**-5##kW/Km/phase
print '%s %.f' %("Total corona loss using Peek formula in kW : ",Pc_dash)#
K=0.395##constant for Vph/Vdo=1.42
Pc=21.*10.**-5*f*Vph**2./(math.log10(d/r))**2.*K##kW/Km/phase
T_CoronaLoss=Pc*l*3.##kW
print '%s %.f' %("According Peterson formula, Total corona loss for 175 km 3-phase line(kW): ",T_CoronaLoss)#
#Answer is wrong in the book for corona loss fair weather condition using Peek formula.

Power loss due to corona for fair weather condition : 
Total corona loss using Peek formula in kW :  249
According Peterson formula, Total corona loss for 175 km 3-phase line(kW):  205.4
Power loss due to corona for stormy weather condition : 
Total corona loss using Peek formula in kW :  1457
According Peterson formula, Total corona loss for 175 km 3-phase line(kW):  1138