GATE EE 2024 Set 1 — Question 19
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Power Systems → Insulators & Distribution → Radial & Ring Distribution
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Question
The figure shows the single line diagram of a 4-bus power network. Branches and have impedances and per-unit (pu), respectively, where , with and . The current drawn from each load bus (marked as arrows) is equal to pu, where . If the network is to operate with minimum loss, the branch that should be opened is
Correct answer
(C) b₃
Solution
To determine which branch should be opened for minimum power loss, we calculate the total loss for each scenario. The power loss in a branch is given by . Since , the resistance of each branch is proportional to its impedance magnitude. Let .From the diagram, let the currents in branches be respectively. Applying KCL at the buses:
.
.
.
.Comparing the results, the minimum loss occurs when branch is opened (). Therefore, the correct option is (C).
1.Left bus:
2.Right bus:
3.Bottom bus:
We evaluate the total loss for each case:- Case (A): Open ()
.
- Case (B): Open ()
.
- Case (C): Open ()
.
- Case (D): Open ()
.Comparing the results, the minimum loss occurs when branch is opened (). Therefore, the correct option is (C).
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