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GATE power systems: 5 practice questions with solutions
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Power Systems is a section of the GATE EE paper in which most questions are short calculations on a standard model: per-unit quantities, a transmission line, a fault or a dispatch problem. The skill that pays is a clean routine, with a consistent base, a single-phase equivalent and units written on every line. The five original questions below practise five of those routines.
What GATE tests in power systems
The GATE 2027 EE paper lists Power Systems as a section, and it was revised for 2027, so confirm your list on the official syllabus page. The standard content is the per-unit system, transmission line parameters and performance, load flow, symmetrical components and fault analysis, economic dispatch, protection, and stability.
Typical questions ask for a per-unit value after a base change, the line voltage regulation or surge impedance loading, a fault current or MVA, sequence components, an optimal generator schedule, or a relay or breaker rating. The real paper has MCQ, MSQ and NAT questions. All five below are MCQ.
Practice questions
Question 1
A generator is rated 25 MVA, 11 kV, and its reactance is 0.15 per unit on its own ratings. On a common base of 100 MVA and 10 kV, its reactance in per unit is:
- A. 0.496
- B. 0.600
- C. 0.660
- D. 0.726
Question 2
A lossless 400 kV transmission line has an inductance of 1.2 mH/km and a capacitance of 0.012 μF/km. Its surge impedance loading is approximately:
- A. 160 MW
- B. 253 MW
- C. 506 MW
- D. 1012 MW
Question 3
At a bus, the Thevenin equivalent impedance seen in a balanced system is j0.25 per unit, and the pre-fault voltage is 1.0 per unit. For a base of 100 MVA, the three-phase fault level at that bus is:
- A. 400 MVA
- B. 250 MVA
- C. 100 MVA
- D. 25 MVA
Question 4
In a three-phase system, a fault leaves phase currents Ia = 30 A, Ib = 0 and Ic = 0. The zero-sequence component of the phase a current is:
- A. 3.33 A
- B. 10 A
- C. 17.3 A
- D. 30 A
Question 5
Two generators have fuel costs C1 = 0.1 P1² + 20 P1 and C2 = 0.2 P2² + 15 P2 (cost per hour, P in MW). The total demand is 100 MW, with no losses and no limits. For the minimum total cost, P1 is:
- A. 75 MW
- B. 66.7 MW
- C. 58.3 MW
- D. 50 MW
Answers and explanations
- D. A per-unit reactance changes with the base as X_new = X_old × (MVA_new / MVA_old) × (kV_old / kV_new)². That gives 0.15 × (100 / 25) × (11 / 10)² = 0.15 × 4 × 1.21 = 0.726 per unit. Option B changes only the MVA base, and option C applies the voltage ratio without squaring it.
- C. The surge impedance is Z0 = √(L / C) = √(1.2 × 10⁻³ / 12 × 10⁻⁹) = √(10⁵) ≈ 316 Ω. The surge impedance loading is V² / Z0 = (400 × 10³)² / 316.2 ≈ 5.06 × 10⁸ W ≈ 506 MW. Here V is the line-to-line voltage, which gives the three-phase power.
- A. The per-unit fault current is 1.0 / 0.25 = 4 per unit. The fault MVA is the per-unit current times the base MVA: 4 × 100 = 400 MVA. The fault level is the product of the pre-fault voltage and the fault current in per unit, times the base.
- B. The zero-sequence current is Ia0 = (Ia + Ib + Ic) / 3 = 30 / 3 = 10 A. A single phase carrying current while the other two carry none gives equal zero, positive and negative-sequence components of 10 A each.
- C. At the optimum the incremental costs are equal. dC1/dP1 = 0.2 P1 + 20 and dC2/dP2 = 0.4 P2 + 15. With P2 = 100 − P1, 0.2 P1 + 20 = 0.4 (100 − P1) + 15, so 0.6 P1 = 35 and P1 = 58.3 MW. Then P2 = 41.7 MW, and both incremental costs equal 31.67 per MWh.
How to prepare power systems
- Work every problem in per unit. Choose one MVA base for the system, convert each kV base through the transformer ratios, and convert every impedance once. Mistakes in base conversion are the commonest source of error.
- Learn the transmission-line models (short, medium nominal-pi, long), their ABCD parameters, voltage regulation and efficiency, and the Ferranti effect.
- Practise all fault types with sequence networks: three-phase, single line to ground, line to line, and double line to ground, including how the sequence networks connect for each.
- Understand load flow qualitatively and compute one iteration of Gauss-Seidel by hand for a two-bus system. Know what the Y-bus is and how to build it.
- Revise economic dispatch with and without limits, and the equal-area criterion for transient stability.
- Read the protection section as a list: types of relays, circuit breakers, CT and PT characteristics, and the principle behind distance and differential protection.
Power systems builds on electrical machines and links to control systems through stability. The GATE electrical preparation guide gives subject order and resources.
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