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The values of A, B, C and D constants for a short transmission line are respectively
Z, 0, 1 and 1
0, 1, 1 and 1
1, Z, 0 and 1
1, 1, Z and 0
Z, 0, 1 and 1
Quick Summary: For a short transmission line, the series impedance is represented by Z and the shunt admittance is assumed to be negligible. The ABCD parameters (or transmission parameters) relate the sending end voltage and current to the receiving end values via the matrix equation [V_s, I_s]^T = [[A, B], [C, D]] [V_r, I_r]^T.
For a short transmission line, the series impedance is represented by Z and the shunt admittance is assumed to be negligible. The ABCD parameters (or transmission parameters) relate the sending end voltage and current to the receiving end values via the matrix equation [VsтАЛ, IsтАЛ]^T = [[A, B], [C, D]] [VrтАЛ, IrтАЛ]^T.
VsтАЛ=AVrтАЛ+BIrтАЛ тАФ Sending end voltage equation
IsтАЛ=CVrтАЛ+DIrтАЛ тАФ Sending end current equation
A=D=1,B=Z,C=0 тАФ ABCD constants for short line
In a short transmission line, the line length is typically less than 80 km. Due to the short length, the shunt capacitance is so small that it is neglected, leading to an admittance Y = 0. Applying Kirchhoff's Voltage and Current Laws at the receiving end yields VsтАЛ = VrтАЛ + IrтАЛ Z and IsтАЛ = IrтАЛ, which corresponds to the ABCD matrix [[1, Z], [0, 1]].
Short transmission lines are defined by lengths < 80 km or operating voltages below 20 kV.
Shunt admittance (Y) is neglected, setting C = 0.
The parameter A is equal to D due to the reciprocal nature of the transmission line.
The parameter B represents the series impedance Z of the line.
Simplifies power flow calculations for distribution networks.
Provides a highly accurate model for short-distance local power delivery.
Inaccurate for long transmission lines where shunt capacitance cannot be ignored.
Does not account for Ferranti effect or line charging currents.
Distribution networks.
Local sub-transmission lines.
For short lines, the condition ADтИТBC=1 is satisfied as (1)(1)тИТ(Z)(0)=1.
Option A is incorrect because Z should be in the B position, not A.
Option D is incorrect as it represents an inverse or invalid parameter configuration.
C is correct тАФ For a short transmission line, the ABCD constants are A=1, B=Z, C=0, and D=1.
Remember that for all passive, linear, two-port networks, the condition ADтИТBC=1 always holds; verify this in exams to eliminate wrong options.