GATE EE 2021 Set 1 — Question 45
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Power Systems → Per-Unit System & Load Flow → Y-Bus Formation
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Question
A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the matrix correspond to Bus 1, 2 and 3, respectively, then of the network is
Correct answer
(C) bmatrix -3j & j & j \ j & -3j & j \ j & j & -3j bmatrix
Solution
In the given 3-bus network, the line impedances are . The corresponding line admittances are .
Each bus is connected to a generator. Since generators are ideal voltage sources, for calculation, they are represented by their internal series impedances to ground. From the diagram, each generator has an internal impedance of , so the shunt admittances at each bus are .
The diagonal elements of the matrix are:
The off-diagonal elements are:
Thus, the matrix is:Therefore, the correct option is (C).
Each bus is connected to a generator. Since generators are ideal voltage sources, for calculation, they are represented by their internal series impedances to ground. From the diagram, each generator has an internal impedance of , so the shunt admittances at each bus are .
The diagonal elements of the matrix are:
The off-diagonal elements are:
Thus, the matrix is:Therefore, the correct option is (C).
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