Electric Power Generation, Transmission, and Distribution

To calculate the capacitance, the negative charge of the earth can be replaced by an equivalent charge
of an image conductor with the same radius as the overhead conductor, lying just below the overhead
conductor (Fig. 13.18).
The same principle can be extended to calculate the capacitance per phase of a three-phase system.
Figure 13.19 shows an equilateral arrangement of identical single conductors for phases A, B, and C
carrying the chargesqA,qB, andqCand their respective image conductors A^0 ,B^0 , and C^0.
DA,DB, andDCare perpendicular distances from phases A, B, and C to earth’s surface.DAA^0 ,DBB^0 , and
DCC^0 are the perpendicular distances from phases A, B, and C to the image conductors A^0 ,B^0 , and C^0.
Voltage VABcan be obtained as

VAB¼

1

2 p« 0

qAln

DAB

rA



þqBln

rB

DAB



þqCln

DBC

DAC





qAln

DAB^0

DAA^0



qBln

DBB^0

DAB^0



qCln

DBC^0

DAC^0



2

(^66)
6
4
3
(^77)
7
5
ðÞV (13:92)
− − −

• Earth's Surface
  H


• 
  


• 
  


• 
  
  
  
  • 
    
    
    
    • 
      
    
    
    
    
  
  
  
  


• 
  


• q
  − − −−−
  FIGURE 13.17 Distribution of electric field lines from an overhead conductor to earth’s surface.


• 
  

  q+

  
  

• −


• 
  

−−

−

−

−

−

−

+

++

+

+

+

+

+

−q

q

2 H

Earth’s Surface

Equivalent Earth Charge

FIGURE 13.18 Equivalent image conductor representing the charge of the earth.