GATE 2025 EE Q.24: solution and answer

Official answer: ASource: Official answer key, GATE 2025 EE (IIT Roorkee)

1. Newton-Raphson load flow sorts buses by which two of the four bus quantities $P$, $Q$, $|V|$, $\delta$ are specified. Slack bus: $|V|$ and $\delta$ are specified, and $P$ and $Q$ are found by the solution. PV bus: $P$ and $|V|$ are specified. PQ bus: $P$ and $Q$ are specified.

2. Every load-flow problem needs exactly one slack bus. It is the angle reference ($\delta =0^{\circ }$), and it supplies whatever real and reactive power is left over once the loads and the network losses are met. The losses are not known until the solution has been found.

3. During the power failure the grid is disconnected. The household wiring, with its lights and fans, is an isolated network, and the UPS is its only source.

4. The lights and fans are loads, so their buses are PQ buses: their $P$ and $Q$ demands are specified.

5. The UPS has to supply the total load plus the losses in the house wiring. So its output $P$ and $Q$ cannot be fixed in advance; they come out of the solution. That rules out the PQ and PV types for the UPS bus, because both need $P$ to be specified.

6. The UPS inverter holds its output voltage at a set magnitude (for example $230\text{V}$) and sets the phase that every other bus voltage is measured against. So $|V|$ and $\delta$ are specified at the UPS bus. Those are exactly the quantities specified at a slack bus.

7. As the only source in an isolated network, the UPS is the reference bus and the balancing bus. That is the slack bus. 'PQV bus' is not a standard load-flow bus type. The answer is (A).