So far as the end conditions are concerned, the Equivalent Circuit of a Long Line can be established in the form of a T- or π-network.
The parameters of the equivalent network are easily obtained by comparing the performance equations of a π-network and a transmission line in terms of end quantities.
For a π-network shown in Fig. 5.15 [refer to Eq. (5.13)].
According to exact solution of a long line [refer to Eq. (5.23)
For exact equivalence, we must have
From Eq. (5.50)
is the factor by which the series impedance of the nominal-π must be multiplied to obtain the Z’ parameter of the equivalent-π, Substituting Z’ from Eq. (5.50) in Eq. (5.51), we get
is the factor by which the shunt admittance arm of the nominal- π must be multiplied to obtain the shunt parameter ( Y’/2) of the equivalent- π.
is a consistent equation in terms of the above values of Y’ and Z’
For a line of medium length
so that the equivalent- π network reduces to that of nominal- π.
Equivalent-T network parameters of a transmission line are obtained on similar lines. The equivalent-T network is shown in Fig. 5.16.
As we shall see in Chapter 6 equivalent- π (or nominal- π) network is easily adopted to load flow studies and is, therefore, universally employed.