## Performance of Single Phase Short Transmission Line Voltage:

As stated earlier, the effects of line capacitance are neglected for a short transmission line. Therefore, while studying the performance of such a line, only resistance and inductance of the line are taken into account. The equivalent circuit of a Single Phase Short Transmission Line Voltage is shown in Fig. 10.1 (i). Here, the total line resistance and inductance are shown as concentrated or lumped instead of being distributed. The circuit is a simple a.c. series circuit.

Let

R = loop resistance i.e., resistance of both conductors

XLÂ = loop reactance

VR = receiving end voltage

cos Î¦R = receiving end power factor (lagging)

VS = sending end voltage

cos Î¦SÂ  = sending end power factor

An approximate expression for the sending end voltage VSÂ can be obtained as follows. Draw perpendicular from B and C on OA produced as shown in Fig. 10.2. Then OC is nearly equal to OF i.e.,

Solution in complex notation: It is often convenient and profitable to make the calculations in complex notation.

Taking VR as the reference phasor, draw the phasor diagram as shown in Fig 10.3. It is clear that VSÂ is the phasor sum of VRÂ and I Z

The second term under the root is quite small and can be neglected with reasonable accuracy. Therefore, approximate expression for VSÂ becomes :

The following points may be noted :

1. The approximate formula for VSÂ (= VRÂ + I R cos Î¦RÂ + I XLÂ sin Î¦R)Â gives fairly correct results for lagging power factors. However, appreciable error is caused for leading power factors. Therefore, approximate expression for VSÂ should be used for lagging p.f. only.
2. The solution in complex notation is in more presentable,form.