Inclusion of Line Charging Capacitors

So far we have assumed that the transmission lines are modeled with lumped series impedances without the shunt capacitances. However in practice, the Y_bus matrix contains the shunt admittances for load flow analysis in which the transmission lines are represented by its π -equivalent. Note that whether the line is assumed to be of medium length or long length is irrelevant as we have seen in Chapter 2 how both of them can be represented in a p -equivalent.

Consider now the power system of Fig. 3.2. Let us assume that all the lines are represented in an equivalent- π with the shunt admittance between the line i and j being denoted by Y_chij . Then the equivalent admittance at the two end of this line will be Y_chij/2. For example the shunt capacitance at the two ends of the line joining buses 1 and 3 will be Y_ch13/2. We can then modify the admittance diagram Fig. 3.4 as shown in Fig. 3.6. The Y_bus matrix of (3.10) is then modified as

                                                    (3.22)

where

(3.23)

Fig. 3.6 Admittance diagram of the power system Fig. 3.2 with line charging capacitors.