The GATE Grind

GATE 2023 EE – Question 41

Power Systems · Per-unit quantities, Bus admittance matrix, Gauss-Seidel and Newton-Raphson load flow methods · 2 marks · Multiple choice

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude $|V_3|=1.0$ p.u. and angle of −15°. A variable current source $|I|\angle\phi$ is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, $\phi=\theta_1\pm\frac\pi2$, where $\theta_1$ is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as

Diagram for GATE 2023 EE question 41
  1. Bus 1: Slack bus; Bus 2: P−|V| bus; Bus 3: P−Q bus
  2. Bus 1: P−|V| bus; Bus 2: P−|V| bus; Bus 3: Slack bus
  3. Bus 1: P−Q bus; Bus 2: P−Q bus; Bus 3: Slack bus
  4. Bus 1: P−|V| bus; Bus 2: P−Q bus; Bus 3: Slack bus

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) Bus 1: P−|V| bus; Bus 2: P−Q bus; Bus 3: Slack bus

Explanation

Bus 3 is the infinite bus with fixed magnitude and angle: the slack bus. At bus 1 the current is 90° out of phase with the voltage, so the source injects only reactive power ($P=0$), while its magnitude is controlled to hold $|V_1|=1.05$ pu: a $P$–$|V|$ bus. Bus 2 has specified $P=200$ MW and $Q=40$ MVAr: a $P$–$Q$ bus.