GATE 2024 EE – Question 19
The figure shows the single line diagram of a 4-bus power network. Branches $b_1$, $b_2$, $b_3$, and $b_4$ have impedances $4z$, $z$, $2z$, and $4z$ per-unit (pu), respectively, where $z=r+jx$, with $r>0$ and $x>0$. The current drawn from each load bus (marked as arrows) is equal to $I$ pu, where $I\ne0$ pu. If the network is to operate with minimum loss, the branch that should be opened is
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Correct answer: (C) $b_3$
Explanation
The source bus feeds $b_1$ (to the left load bus) and $b_2$ (to the right load bus); $b_3$ and $b_4$ connect these to the bottom load bus. Total load current is $3I$. Losses (in units of $I^2\,\text{Re}(z)$) for each option: open $b_1$: $b_2$ carries $3I$, $b_4$ carries $2I$, $b_3$ carries $I$: $9(1)+4(4)+1(2)=27$. Open $b_2$: $b_1$ carries $3I$, $b_3$ carries $2I$, $b_4$ carries $I$: $9(4)+4(2)+1(4)=48$. Open $b_3$: $b_1$ carries $I$, $b_2$ carries $2I$, $b_4$ carries $I$: $1(4)+4(1)+1(4)=12$. Open $b_4$: $b_2$ carries $I$, $b_1$ carries $2I$, $b_3$ carries $I$: $1(1)+4(4)+1(2)=19$. The minimum loss is with $b_3$ opened.