ABCD Parameters of Short Transmission Line

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

V_S = Sending end voltage to neutral

V_R = 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

V_S = AV_R + BI_R……. ( 1 )

I_S = CV_R + DI_R……....( 2 )

Short Transmission Line: ABCD Parameters

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

I_S = I_R…… ( 3 )

Similarly

Vs = V_R + IZ….. ( 4 )

Compare equation ( 2 ) and ( 3 )

I_S = CV_R + DI_R

I_S = I_R

Therefore C = 0 and D = 1

Compare equation ( 1 ) and ( 4 )

V_S = AV_R + BI_R

Vs = V_R + IZ

Therefore A = 1 and B = Z

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

AD – BC = 1

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