# Chapter 8 : Limiting Factors for Extra High and Ultrahigh Voltage Transmission : Corona, Radio Noise, and Audible Noise¶

## Example 8.1 Page No : 417¶

In :
import math

# GIVEN DATA
m_0 = 0.90 ; # Irregularity factor
p = 74. ; # Atmospheric pressure in Hg
t = 10. ; # temperature in degree celsius
D = 550. ; # Equilateral spacing b/w conductors in cm
d = 3. ; # overall diameter in cm

# CALCULATIONS
# For case (a)
r = d/2 ;
delta = 3.9211 * p/( 273 + t ) ; # air density factor
V_0_ph = 21.1 * delta * m_0 * r * math.log(D/r) ; # disruptive critical rms line voltage in kV/phase
V_0 = math.sqrt(3) * V_0_ph ; # disruptive critical rms line voltage in kV

# For case (b)
m_v = m_0 ;
V_v_ph = 21.1*delta*m_v*r*(1 + (0.3/math.sqrt(delta*r) )) * math.log(D/r) ; # visual critical rms line voltage in kV/phase
V_v = math.sqrt(3)*V_v_ph ; # visual critical rms line voltage in kV

# DISPLAY RESULTS
print ("EXAMPLE : 8.1 : SOLUTION :-") ;
print " a) Disruptive critical rms line voltage , V_0 = %.1f kV "%(V_0) ;
print " b) Visual critical rms line voltage , V_v = %.1f kV "%(V_v) ;

EXAMPLE : 8.1 : SOLUTION :-
a) Disruptive critical rms line voltage , V_0 = 298.7 kV
b) Visual critical rms line voltage , V_v = 370.9 kV


## Example 8.2 Page No : 420¶

In :
import math

# GIVEN DATA
f = 60. ; # freq in Hz
d = 3. ; # overall diameter in cm
D = 550. ; # Equilateral spacing b/w conductors in cm
V1 = 345. ; # operating line voltage in kV
V_0 = 172.4 ; # disruptive critical voltage in kV
L = 50. ; # line length in mi
p = 74. ; # Atmospheric pressure in Hg
t = 10. ; # temperature in degree celsius
m_0 = 0.90 ; # Irregularity factor

# CALCULATIONS
r = d/2 ;
delta = 3.9211 * p/( 273 + t ) ; # air density factor
V_0 = 21.1 * delta * m_0 * r * math.log(D/r) ; # disruptive critical rms line voltage in kV/phase
V =V1/math.sqrt(3) ; # Line to neutral operating voltage in kV
P_c = (390./delta)*(f+25)*math.sqrt(r/D)*(V - V_0)**2 * 10**-5 ; # Fair weather corona loss per phase in kW/mi/phase
P_cT = P_c * L ; # For total line length corona loss in kW/phase
T_P_c = 3 * P_cT ; # Total corona loss of line in kW

# DISPLAY RESULTS
print ("EXAMPLE : 8.2 : SOLUTION :-") ;
print " a) Total fair weather corona loss of the line , P_c = %.1f kW "%(T_P_c) ;

# rounding off error.

EXAMPLE : 8.2 : SOLUTION :-
a) Total fair weather corona loss of the line , P_c = 1811.2 kW