# Chapter 04 : Capacitance Of Transmission Lines¶

## Example 4.1, Page No 75¶

In [5]:
import math
#initialisation of variables
D = 20.0 #in ft
f = 60.0 #in Hz

#From Table A.1 and A.3
d = 0.642 			#in inches
X_a = 0.1074e6 		#in ohm-mi
X_d = 0.0889e6 		#in ohm-mi

r = d/(2*12) 		#divided by 12 convert in to ft

#Calculations
print('Calculations using conductor spacing and radius')
X_c = 1.779 * math.log(D/r)/f
B_c = 1 / X_c
print(" Capactive reatance = %.4fe6 ohm mi to neutral " %X_c)
print(" Capactive susceptance = %.4fe-6 mho/mi to neutral " %B_c)

#calculations using capacitive reactance at 1-ft spacing and spacing factor
print('Calculations using capacitive reactance at 1-ft spacing and spacing factor')
X_c1 = X_a + X_d
print(" Capactive reatance = %.4fe6 ohm mi per conductor " %(X_c1/10**6))
X_c11 = 2 * X_c1
B_c1 = 1 / X_c11

#Results
print(" Line-to-line capactive reatance = %.4fe6 ohm mi " %(X_c11/10**6))
print(" Line-to-line capactive susceptance = %.4fe-6 mho mi " %(B_c1*10**6))

Calculations using conductor spacing and radius
Capactive reatance = 0.1962e6 ohm mi to neutral
Capactive susceptance = 5.0970e-6 mho/mi to neutral
Calculations using capacitive reactance at 1-ft spacing and spacing factor
Capactive reatance = 0.1963e6 ohm mi per conductor
Line-to-line capactive reatance = 0.3926e6 ohm mi
Line-to-line capactive susceptance = 2.5471e-6 mho mi


## Example 4.2, Page No 80¶

In [6]:
import math
#initialisation of variables
D_12 = 20.0			#in ft
D_23 = D_12
D_31 = 38.0			#in ft
f = 60.0			#in Hz
V = 220e3			#in volts
l = 175				#in mi
k = 8.85e-12		#permittivity in F/m
#From tables A.1 and A.3
d = 1.108#in inches
X_a1 = 0.0912e6#in ohm mi
X_d1 = 0.0952e6#in ohm mi

#Calculations
r = d / ( 2 * 12)#division by 12 to convert in to ft
D_eq = (D_12*D_23*D_31)**(1.0/3)
C_n = (2*math.pi*k)/math.log(D_eq/r)
X_c = 1.0/(2*math.pi*f*C_n*1609)		#division by 1609 to convert to ohm mi

print(" Capacitance = %.4fe-12 F/m " %(C_n*1e12))
print(" Capacitive reactance = %.4fe6 ohm mi " %(X_c/1e6))

#Calculations From tables
X_c1 = X_a1 + X_d1
print('Using capacitive reactance at 1-ft spacing and spacing factor')
print(" Capacitive reactance = %.4fe6 ohm mi " %(X_c1/1e6))
X_c_l = X_c1/l			#Capacitive reactance for 175mi
I_chg = 2*math.pi*f*V*C_n*1609/math.sqrt(3.0)
I_chg_l = I_chg * l
Q =math.sqrt(3)*V*I_chg_l

#Results
print('For a lenght of 175mi')
print(" Capacitive reactance = %.4f ohm to neutral " %X_c_l)
print(" Charging current per mile = %.3f A/mi " %I_chg)
print('For a lenght of 175mi')
print(" Charging current = %.0f A " %I_chg_l)
print(" Total charging megavolt-amperes = %.1f Mvar " %(Q/1e6))

 Capacitance = 8.8472e-12 F/m
Capacitive reactance = 0.1863e6 ohm mi
Using capacitive reactance at 1-ft spacing and spacing factor
Capacitive reactance = 0.1864e6 ohm mi
For a lenght of 175mi
Capacitive reactance = 1065.1429 ohm to neutral
Charging current per mile = 0.682 A/mi
For a lenght of 175mi
Charging current = 119 A
Total charging megavolt-amperes = 45.5 Mvar


## Example 4.3, Page No 85¶

In [7]:
import math
#initialisation of variables
d = 0.45   #in m
k = 8.85e-12  #in F/m
D_ab = 8  #in m
D_bc = D_ab
D_ca = 16   #in m
f = 60  #in Hz

#From tables
D = 1.382   #in inches

#Calculations
r = D*0.3048/(2.0*12)  #divison by 12 to convert in to ft
#multiplication by 0.3048 to convert ft to m
D_b_sC = math.sqrt( r * d)
D_eq = (D_ab * D_bc * D_ca)**(1/3)
C_m = 2* math.pi*k/math.log(D_eq / D_b_sC)
X_c = 1e-3/(2*math.pi*f*C_m)  #1e-3     #to convert m to km

#Results
print(" Capacitance = %.3fe-12 F/m " %(C_m * 1e12))
print(" Capacitive reactance = %.4fe6 ohm km per phase to neutral" %(X_c/1e6))

 Capacitance = 22.972e-12 F/m
Capacitive reactance = 0.1155e6 ohm km per phase to neutral


## Example 4.4 Page No 85¶

In [8]:
import math
#initialisation of variables
f = 60.0		#in Hz
k = 8.85e-12	#in F/m
D_eq = 16.1		#in ft
D_a_a1 = 26.9
D_b_b1 = 21.0
D_c_c1 = D_a_a1 #in ft

#From Table A.1
d = 0.680#in inches

#calculations
r = d /(2*12)
D_p_sC = (math.sqrt(D_a_a1 * r) * math.sqrt(D_b_b1 * r) * math.sqrt(D_c_c1 * r))**(1.0/3)
C_n = 2 * math.pi * k / math.log(D_eq / D_p_sC)
B_c = 2 * math.pi * f * C_n * 1609.0	#1609 to convert from m to mi

#Results
print("printprint Capacitance = %.3fe-12 F/m printprint" %(C_n*1e12))
print("printprint Capacitive susceptance = %.2fe-6 mho per mi per phase to neutral" %(B_c*1e6))

printprint Capacitance = 18.812e-12 F/m printprint
printprint Capacitive susceptance = 11.41e-6 mho per mi per phase to neutral