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ElectricalPower System
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The ABCD constants of three phase transposed transmission line with linear and passive elements

A

Are always equal

B

Never equal

C

A and D are equal

D

B and C are equal

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleElectricalPower System
Option C

A and D are equal

Quick Summary:

For a three-phase transmission line consisting of linear, passive, and bilateral elements, the ABCD matrix represents a reciprocal network. According to the Reciprocity Theorem, for such a network, the condition ADтИТBC=1AD - BC = 1ADтИТBC=1 must be satisfied, and for a symmetrical line, the constants A and D are always equal.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

For a three-phase transmission line consisting of linear, passive, and bilateral elements, the ABCD matrix represents a reciprocal network. According to the Reciprocity Theorem, for such a network, the condition ADтИТBC=1AD - BC = 1ADтИТBC=1 must be satisfied, and for a symmetrical line, the constants A and D are always equal.

ЁЯФв Key Formulas

ADтИТBC=1AD - BC = 1ADтИТBC=1 тАФ Condition for Reciprocity

A=DA = DA=D тАФ Condition for Symmetry in two-port networks

тЪЩя╕П Working Principle

The transmission line is a two-port network. If the network is linear and passive, it is reciprocal, implying the determinant of its transmission matrix is unity (ADтИТBC=1AD - BC = 1ADтИТBC=1). If the line is additionally symmetrical (which is true for a transposed transmission line), the input and output conditions are identical, forcing A=DA = DA=D.

ЁЯУМ Key Points
  • тЦ╕

    Transposed lines ensure symmetry between phases.

  • тЦ╕

    Passive networks follow the Reciprocity Theorem.

  • тЦ╕

    For any two-port network, the constant A represents the ratio of input voltage to output voltage on open circuit.

  • тЦ╕

    For symmetric lines, the voltage ratio is the same regardless of which end is considered the input.

тЬЕ Advantages
  • тЦ╕

    Simplified power flow calculations.

  • тЦ╕

    Allows easier analysis of long transmission lines using the PI or T model.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Applies only to linear and passive elements.

  • тЦ╕

    Does not hold if the system includes active components like power electronics or non-linear loads.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Power system steady-state stability analysis.

  • тЦ╕

    Calculating voltage regulation and efficiency of transmission systems.

ЁЯУД Additional Information
  • тЦ╕

    In a two-port network defined by [VsIs]=[ABCD][VrIr]\begin{bmatrix} V_s \\ I_s \end{bmatrix} = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \begin{bmatrix} V_r \\ I_r \end{bmatrix}[VsтАЛIsтАЛтАЛ]=[ACтАЛBDтАЛ][VrтАЛIrтАЛтАЛ], the symmetry requires A=DA=DA=D.

  • тЦ╕

    Option D (B and C are equal) is incorrect as B represents impedance and C represents admittance; they have different dimensions and are generally not equal.

ЁЯУК Diagram / Illustration
Reciprocity and Symmetry ConditionsAD - BC = 1 (Reciprocity)A = D (Symmetry)For Transposed Lines: A = D
тЬЕ

C is correct тАФ In a symmetrical, passive two-port network representing a transposed transmission line, the transmission constants A and D are always equal.

Core Concepts Used
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Two-Port Network Theory Reciprocity Theorem Transmission Line Symmetry
ЁЯТб EXAM TIP

Always remember that for reciprocal networks ADтИТBC=1AD - BC = 1ADтИТBC=1 and for symmetric networks A=DA = DA=D; these are fundamental to solving any ABCD constant problem in electrical power systems.

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