# 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

Standard
kVA rating of Three Phase Transformer |

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