Short Transmission Line:

For Short Transmission Line of length 100 km or less, the total 50 Hz shunt admittance (jωCl) is small enough to be negligible resulting in the simple equivalent circuit of a short line is shown in Fig. 5.1.

Short Transmission Line

This being a simple series circuit, the relationship between sending-end receiving-end voltages and currents can be immediately written as:

Short Transmission Line

The phasor diagram for the short line is shown in Fig. 5.2 for the lagging current case. From this figure we can write

 The last term is usually of negligible order

Expanding binomially and retaining first order terms, we get

Short Transmission Line

The above equation is quite accurate for the normal load range. The Fig. 5.2 shows the Phasor diagram of a short line for lagging current

Short Transmission Line