# Short transmission lines: Phasor Diagram, Voltage Regulation, Efficiency

The transmission line having a length lesser than 80KM  and an operating voltage lower than 20 KV falls under a short transmission line. The capacitance effects are neglected in short transmission lines due to smaller distances and lower line voltage. In a short transmission line, the shunt conductance and shunt capacitance are neglected and only the series resistance and inductive reactance are considered. Therefore the performance of a short transmission line depends upon the resistance and inductance of the line. The resistance and the inductance in the case of the short transmission line are assumed to be lumped in one place.

The equivalent circuit of a short transmission line is a simple ac series circuit. The equivalent circuit of short transmission line is shown below:

The above equivalent circuit represents a 3-phase short transmission line if R and X represent the resistance and inductive reactance to neutral. (I) is current in one conductor. (VR) is the receiving end voltage to neutral, (VS) is the sending end voltage to neutral. The load is in one of the phases and the voltage drop is the drop between a phase and a neutral.

From the equivalent circuit ,

Receiving end voltage,

where the quantity IZ is the voltage drop along the line.

## Phasor Diagram of short transmission lines

• Phasor I =as the reference phasor for an inductive load (lagging power factor load).
• phasor OA, OI, AB, BC, AC, and OC represents the load current.
• VR=Receiving end voltage
• IR=resistive drop in line
• IX=reactive drop in line
• IZ=line impedance drop
• VS=sending end voltage

From the phasor diagram,

Sending end voltage,

sending-end phase angle,

Sending-end power factor,

## Voltage regulation of short transmission lines

For determination of approximate value of sending end voltage,

## Percentage voltage regulation

The voltage regulation depends upon the resistance and reactance of the line for supplying a given load at a given voltage. Larger the value of the line resistance and line reactance higher will be the voltage regulation.

## Regulation per unit

where Vr and Vx are the per unit values of resistance and reactance of the line.