The equivalent circuit and vector diagram of a short transmission line are shown in the figure given below.In the equivalent circuit short transmission line is represented by the lumped parameters R and L. R is the resistance (per phase) L is the inductance (per phase) of the entire transmission line.As said earlier the effect of shunt capacitance and conductance is not considered in the equivalent circuit.The line is shown to have two ends : sending end (designated by the subscript S) at the generator, and the receiving end (designated R) at the load.

The phasor diagram is drawn taking Ir, the receiving end current as the reference.

The terms with in the simple brackets is small as compared to unity, using binomial expansion and limiting only to second term

Vs ≈ Vr + IrR cosΦr + IrX sinΦr

Here Vs is the sending end voltage corresponding to a particular load current and power factor condition. It can be seen from the equivalent circuit that the receiving end voltage under no load is same as the sending end voltage under full load condition i.e Vr(no load) = Vs . Therefore

where Vr and Vx are the per unit values of resistance and reactance of the line.From the equivalent circuit diagram we can observe that

Vs = Vr + Ir ( R + jX) = Vr + IrZ

Is = Ir

In a four terminal passive network the voltage and current on the receiving end and sending end are related by following pair of equations

Vs = AVr + BIr

Is = CVr + DIr

Comparing the above two sets of equations, for a short transmission line

Normally the quantities P,Ir and cosΦr at the receiving end are given and ofcourse the ABCD constants.Then determine sending end voltage using the relation Vs = AVr + BIr. Vr(no load) at the receivind end is given by Vs/A when Ir = 0.

The phasor diagram is drawn taking Ir, the receiving end current as the reference.

The terms with in the simple brackets is small as compared to unity, using binomial expansion and limiting only to second term

Vs ≈ Vr + IrR cosΦr + IrX sinΦr

Here Vs is the sending end voltage corresponding to a particular load current and power factor condition. It can be seen from the equivalent circuit that the receiving end voltage under no load is same as the sending end voltage under full load condition i.e Vr(no load) = Vs . Therefore

where Vr and Vx are the per unit values of resistance and reactance of the line.From the equivalent circuit diagram we can observe that

Vs = Vr + Ir ( R + jX) = Vr + IrZ

Is = Ir

In a four terminal passive network the voltage and current on the receiving end and sending end are related by following pair of equations

Vs = AVr + BIr

Is = CVr + DIr

Comparing the above two sets of equations, for a short transmission line

**A = 1, B = Z, C = 0, D = 1**. ABCD constants can be used for calculation of regulation of the line as follows:Normally the quantities P,Ir and cosΦr at the receiving end are given and ofcourse the ABCD constants.Then determine sending end voltage using the relation Vs = AVr + BIr. Vr(no load) at the receivind end is given by Vs/A when Ir = 0.

## 2 comments:

nice posting

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