Short transmission lines

Short transmission line

Transmission line having the length lesser than 80KM  and operating voltage lower than 20 KV falls under short transmission line.The capacitance effects are neglected in short transmission line due to smaller distance 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 case of the short transmission line are assumed to be lumped at 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:

                        fig:equivalent circuit diagram of short transmission line

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 the 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 phase 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.

   fig: phasor diagram of short transmission line

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 impeadnce drop

VS=sending end voltage

From the phasor diagram,

sending end voltage,

sending-end phase angle,

 

and sending-end power factor,

 

voltage regulation of short transmission line

 

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.

Efficiency of short transmission line

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