Short Transmission Lines

Short transmission lines have lengths lesser than 80 km and operates on a voltage level lower than 20 kV. The overhead transmission lines are classified as short, medium and long length transmission lines depending upon the way in which the capacitance of the line is taken into account.

In short transmission lines capacitance effects are not significant and can be neglected. So their performance depends upon the resistance and the inductance of the line.

For determining the performance parameter of short transmission line lumped model can be used. Although the resistance and inductance are distributed over the whole length but in case of lumped model, these parameters are assumed to be lumped at one place. In this way analysis becomes easier and for short transmission lines this analysis holds good result.

Here, the shunt capacitance of the lines are neglected. Only the series resistance and inductive reactance are taken into account. The equivalent circuit diagram of short transmission line with the per phase resistance R and per phase inductive reactance X is shown in the figure below.

Where, I is the conductor current. V_{R} is the sending end phase voltage, V_{S} is the receiving end phase voltage.

From this equivalent circuit shown above it is clear that

The quantity IZ represent the voltage drop along the line.

## Phasor Diagram of Short Transmission Lines

The figure below shows phasor diagram of short transmission lines for different power factor.

Here the load is of lagging power factor and sending end voltage is greater than receiving end voltage.

This phasor diagram is for unity power factor operation.

This phasor diagram is for leading power factor load. For leading power factors the sending end voltage is less than receiving end voltage.

For short lines as the effect of capacitance is neglected and during no-load condition the current I= 0. Hence, for no-load condition the sending end voltage equals to receiving end voltage i.e. V_{S}=V_{R}.

## Voltage Regulation

On loading the transmission line, current flows through the line and voltage drop occurs. Due to this receiving end voltage V_{R} is less than sending end voltage V_{S}. The difference in sending end and receiving end voltage expressed as a percentage of the receiving end voltage is called the regulation.

Mathematically,

Here, V_{S} and V_{R} are the magnitude of the voltages.

The figure below is the phasor diagram of short transmission line with current I as a reference phasor.

This is for lagging power factor load or inductive load. Phasor OI, OA, AB, BC, AC and OC represents load current I.

V_{S} is sending end voltage and V_{R} is receiving end voltage.

IR is resistive drop in the line.

IX is reactive drop in the line.

IZ is impedance drop.

From phasor diagram, sending end voltage V_{S} is:

Sending end phase angle,

Sending end power factor,

Percentage voltage regulation is given by:

For a simpler approximation, the sending end voltage can be approximated as

So, percentage voltage regulation is

For leading power factor the voltage regulation relation is given by:

## Efficiency

The ratio of power delivered at the sending end to the power sent from the sending end is known as efficiency of the transmission line.

For the efficiency of short transmission lines.

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