# 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

V_{S} =
Sending end voltage to neutral

V_{R} =
Receiving end voltage to neutral

I_{S} = Sending
end current

I_{R} =
Receiving end current

I_{C} =
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

Y = jX_{C}
= Admittance

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 )

**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.

I_{S} = I_{R }+ I_{C}

I_{S} = I_{R
}+ YV_{R}

I_{S} = YV_{R}
+ I_{R }…… ( 3 )

Similarly

Vs = V_{R}
+ I_{S}Z

= V_{R} + ( I_{R }+ YV_{R}
)Z

= V_{R} + ZI_{R }+ ZYV_{R}

= ( 1 + YZ )V_{R} + ZI_{R }….. ( 4 )_{}

Compare equation (
2 ) and ( 3 )

I |
I |
C = Y and D = 1 |

Compare equation (
1 ) and ( 4 )

V |
Vs = ( 1 + YZ )V |
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

AD – BC = 1

Standard
kVA rating of Three Phase Transformer |

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