# Short transmission line

The shunt capacitance and shunt conductance are neglected therefore only resistance and reactance is shown in the short transmission line. All the parameters are given considering three phase transmission line.

Here

VS = Sending end voltage to neutral

VR = Receiving end voltage to neutral

I = Current in one conductor

R = Resistance of transmission line, resistance to the neutral in the three-phase line

X = Reactance of transmission line, reactance to the neutral in the three-phase line

A, B, C and D = Constant

Generalized Constant of the transmission line is given by sending end voltage and sending end current equation

VS = AVR + BIR……. ( 1 )

IS = CVR + DIR……....( 2 )

## Short Transmission Line: ABCD Parameters

The sending end current is equal to receiving end current in the short transmission line.

IS = IR…… ( 3 )

Similarly

Vs = VR + IZ….. ( 4 )

Compare equation ( 2 ) and ( 3 )

IS = CVR + DIR

IS = IR

Therefore C = 0 and D = 1

Compare equation ( 1 ) and ( 4 )

VS = AVR + BIR

Vs = VR + IZ

Therefore A = 1 and B = Z

From the above value of A, B, C and D