Short Transmission Line - Equivalent circuit and Phasor diagram

Short Transmission LineThe 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 termVs ≈ 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 thatVs = Vr + Ir ( R + jX) = Vr + IrZIs = IrIn a four terminal passive network the voltage and current on the receiving end and sending end are related by following pair of equationsVs = AVr + BIrIs = CVr + DIrComparing 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.

Classification of transmission lines Transmission lines are classified as short, medium and long. When the length of the line is less than about 80Km the effect of shunt capacitance and conductance is neglected and the line is designated as a short transmission line. For these lines the operating voltage is less than 20KV.For medium transmission lines the length of the line is in between 80km - 240km and the operating line voltage wil be in between 21KV-100KV.In this case the shunt capacitance can be assumed to be lumped at the middle of the line or half of the shunt capacitance may be considered to be lumped each end of the line.The two representations of medium length lines are termed as nominal-T and nominal- π respectively.Lines more than 240Km long and line voltage above 100KV require calculations in terms of distributed parameters.Such lines are known as long transmission lines.This classification on the basis of length is more or less arbitrary and the real criterion is the degree of accuracy required.Performance of Transmission Lines - Efficiency and Regulation Performance of Transmission LinesThe performance of a power system is mainly dependent on the performance of the transmission lines in the system.It is necessary to calculate the voltage,current and power at any point on a transmission line provided the values at one point are known.The transmission line performance is governed by its four parameters - series resistance and inductance,shunt capacitance and conductance.All these parameters are distributed over the length of the line.The insulation of a line is seldom perfect and leakage currents flow over the surface of insulators especially during bad weather.This leakage is simulated by shunt conductance.The shunt conductance is in parallel with the system capacitance.Generally the leakage currents are small and the shunt conductance is ignored in calculations.

Performance of transmission lines is meant the determination of efficiency and regulation of lines.The efficiency of transmission lines is defined as

The end of the line where load is connected is called the receiving end and where source of supply is connected is called the sending end.The Regulation of a line is defined as the change in the receiving end voltage, expressed in percent of full load voltage, from no load to full load, keeping the sending end voltage and

frequency constant.