# Long Transmission Line: End Condenser Method

The total capacitance of the transmission line is considered at the receiving end side or load side in the medium 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

IS = Sending end current

IR = Receiving end current

IC = Capacitance current

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

Z = R + j X = Impedance

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 )

## End Condenser Method : Important Formula

The sending end current is equal to receiving end current and capacitor current in the end condenser medium transmission line.

IS = IR + IC

IS = IR + YVR

IS = YVR + IR …… ( 3 )

Similarly

Vs = VR + ISZ

= VR + ( IR + YVR )Z

= VR +  ZIR + ZYVR

= ( 1 + YZ )VR +  ZIR ….. ( 4 )

Compare equation ( 2 ) and ( 3 )

 IS = CVR + DIR IS = YVR + IR C = Y and D = 1

Compare equation ( 1 ) and ( 4 )

 VS = AVR + BIR Vs = ( 1 + YZ )VR +  ZIR A = ( 1 + YZ ) and B = Z

## End Condenser Method : A, B, C and D Parameter

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

A = ( 1 + YZ )

B = Z

C = Y

D = 1

Therefore