ABCD Parameters of 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 )

Important Points to be noted

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_SZ

      = 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 )

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

 

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

A = ( 1 + YZ )

B = Z

C = Y

D = 1

Therefore

AD – BC = 1

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