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

In short transmission lines, capacitance effects are not significant and we can neglect the effect. So their performance depends upon the resistance and the inductance of the line.

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

Here, we neglect the shunt capacitance of the line. So, we only take account of the series resistance and inductive reactance. The figure below shows the equivalent circuit diagram of a short transmission line with the per phase resistance R and per phase inductive reactance X.

Short Transmission Lines Equivalent Circuit

Figure: Equivalent Circuit of Short Transmission Line

Where I is the conductor current. VR is the sending end phase voltage, VS is the receiving end phase voltage.

From this equivalent circuit shown above it is clear that

The quantity IZ represents the voltage drop along the line.

Phasor Diagram of Short Transmission Line

The figure below shows a 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.

Figure: Phasor diagram for lagging p.f.

This phasor diagram is for unity power factor operation.

Figure: Phasor diagram for unity p.f.

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

Figure: Phasor diagram for leading p.f.

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

Voltage Regulation of Short Transmission Line

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

Mathematically,

Here, VS and VR are the magnitudes of the voltages.

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

Phasor Diagram of Short Transmission Lines

Figure: Phasor diagram of short transmission line

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

VS is sending end voltage and VR is receiving end voltage.

IR is the resistive drop in the line.

IX is the reactive drop in the line.

IZ is an impedance drop.

From the phasor diagram, sending end voltage VS is:

Sending end phase angle,

Sending end power factor,

Percentage voltage regulation is:

Voltage Regulation of Short Transmission Lines

For a simpler approximation, we can approximate the sending end voltage as

So, percentage voltage regulation is

Voltage Regulation of Short Transmission Lines

For the leading power factor, the voltage regulation relation is:

Voltage Regulation for Short Transmission Lines

Efficiency

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

For the efficiency of short transmission lines.

Efficiency of Short Transmission Lines


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