21.1.2 Shunt Admittance
When a high-voltage transmission line is less than 50 miles in length, the shunt capacitance of the line is
typically ignored. For lightly loaded distribution lines, particularly underground lines, the shunt
capacitance should be modeled.
The basic equation for the relationship between the charge on a conductor to the voltage drop
between the conductor and ground is given by
Qn¼CngVng (21:46)whereQn¼charge on the conductor
Cng¼capacitance between the conductor and ground
Vng¼voltage between the conductor and ground
For a line consisting of ncond (number of phase plus number of neutral) conductors, Eq. (21.46) can be
written in condensed matrix form as
½¼Q ½C½V (21:47)where [Q]¼column vector of order ncond
[C]¼ncondncond matrix
[V]¼column vector of order ncond
Equation (21.47) can be solved for the voltages
½¼V ½C^1 ½¼Q ½P½Q (21:48)where ½¼P ½C^1 (21:49)21.1.2.1 Overhead Lines
The determination of the shunt admittance of overhead lines starts with the calculation of the ‘‘potential
coefficient matrix’’ (Glover and Sarma, 1994). The elements of the matrix are determined by
Pii¼ 11 : 17689 ln
Sii
RDi
(21:50)Pij¼ 11 : 17689 ln
Sij
Dij(21:51)See Fig. 21.2 for the following definitions.
Sii¼distance between a conductor and its image below ground in feet
Sij¼distance between conductor i and the image of conductor j below ground in feet
Dij¼overhead spacing between two conductors in feet
RDi¼radius of conductor i in feetThe potential coefficient matrix will be an ncondncond matrix. If one or more of the conductors
is a grounded neutral, then the matrix must be reduced using the Kron method to annphasenphase
matrix [Pabc].
The inverse of the potential coefficient matrix will give thenphasenphase capacitance matrix [Cabc].
The shunt admittance matrix is given by
½¼yabc jv½Cabc mS/mile (21:52)wherev¼ 2 pf¼376.9911