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Power systems and transmission: board exam questions with solutions

On the REE exam under Electrical Engineering Professional Subjects. Try each question before you open its solution, then practise with fresh numbers below: 4 computed question types on this topic.

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Questions

1. A transformer has a reactance of 0.10 pu on its own 50 MVA base. What is its reactance on a 100 MVA system base at the same voltage base?

  1. 0.20 pu
  2. 0.05 pu
  3. 0.10 pu
  4. 0.40 pu
Show the answer and solution

Answer: A. 0.20 pu

Z_new = Z_old × (S_new/S_old) × (V_old/V_new)² = 0.10 × (100/50) × 1 = 0.20 pu.

2. What is the base impedance for a 13.8 kV, 100 MVA three-phase base?

  1. 0.138 Ω
  2. 1.904 Ω
  3. 0.525 Ω
  4. 5.713 Ω
Show the answer and solution

Answer: B. 1.904 Ω

Z_base = (kV_LL)²/MVA = 13.8²/100 = 1.904 Ω.

3. A 50 MVA, 13.8 kV generator with subtransient reactance 0.15 pu is unloaded at rated voltage when a bolted three-phase fault occurs at its terminals. What is the initial symmetrical fault current?

  1. 24.2 kA
  2. 2.09 kA
  3. 13.9 kA
  4. 8.05 kA
Show the answer and solution

Answer: C. 13.9 kA

I_base = 50 × 10⁶/(√3 × 13 800) = 2092 A. I_f = 1.0/0.15 = 6.67 pu, so I_f = 6.667 × 2092 = 13946 A ≈ 13.9 kA.

4. The Thevenin impedance at a bus is 0.08 pu on a 100 MVA base. What is the three-phase short-circuit MVA at the bus (prefault voltage 1.0 pu)?

  1. 8 MVA
  2. 800 MVA
  3. 125 MVA
  4. 1250 MVA
Show the answer and solution

Answer: D. 1250 MVA

Short-circuit MVA = MVA_base/Z_pu = 100/0.08 = 1250 MVA.

5. The receiving-end voltage of a distribution line is 13.8 kV at no load and 13.2 kV at full load, with sending-end voltage held constant. What is the voltage regulation?

  1. 4.55%
  2. 4.35%
  3. 0.60%
  4. 6.00%
Show the answer and solution

Answer: A. 4.55%

VR = (V_NL − V_FL)/V_FL × 100 = (13.8 − 13.2)/13.2 × 100 = 4.55%.

6. If the spacing between the conductors of a single-phase overhead line is increased, what happens to the line's inductance and capacitance per unit length?

  1. Both increase
  2. Inductance increases and capacitance decreases
  3. Both decrease
  4. Inductance decreases and capacitance increases
Show the answer and solution

Answer: B. Inductance increases and capacitance decreases

L ∝ ln(D/r′) rises with spacing D, while C ∝ 1/ln(D/r) falls with spacing.

7. In a power-flow (load-flow) study, which two quantities are specified at a generator (PV) bus?

  1. Voltage magnitude and angle
  2. Real and reactive power
  3. Real power and voltage magnitude
  4. Reactive power and voltage angle
Show the answer and solution

Answer: C. Real power and voltage magnitude

A PV bus fixes P and |V|; Q and δ are computed. The slack bus fixes |V| and δ, and a load (PQ) bus fixes P and Q.

8. A lossless line with series reactance 0.4 pu connects a sending bus at 1.05 pu to a receiving bus at 1.00 pu. What power angle δ is needed to transmit 1.2 pu of real power?

  1. 28.7°
  2. 62.8°
  3. 30.0°
  4. 27.2°
Show the answer and solution

Answer: D. 27.2°

P = Vs Vr sin δ / X, so sin δ = 1.2 × 0.4/(1.05 × 1.00) = 0.4571 and δ = 27.2°.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. A 200 kW load runs at 0.75 pf lagging. How much capacitive kVAR raises it to 0.9?

  1. 45.1 kVAR
  2. 79.5 kVAR
  3. 176 kVAR
  4. 30 kVAR
Show the answer and solution

Answer: B. 79.5 kVAR

Qc = P(tan θ₁ − tan θ₂) = 200(0.882 − 0.484) = 79.5 kVAR.

10. What is the base impedance on a 100 MVA, 138 kV base?

  1. 190.4 Ω
  2. 1380 Ω
  3. 1.38 Ω
  4. 110 Ω
Show the answer and solution

Answer: A. 190.4 Ω

Zbase = kV²/MVA = 138²/100 = 190.4 Ω.

11. A 500 kVA, 230 V three-phase transformer has 6% impedance. Estimate the three-phase fault current at its secondary terminals with an infinite source.

  1. 75.3 A
  2. 36.2 kA
  3. 20.9 kA
  4. 1.26 kA
Show the answer and solution

Answer: C. 20.9 kA

Rated I = S/(√3·V) = 1255 A; bolted three-phase fault ≈ I/Z(pu) = 1255/0.06 = 20.9 kA (infinite source).

12. A single-phase load 30 m away draws 20 A through 8 mm² copper (ρ = 0.0172 Ω·mm²/m). What is the voltage drop in the two wires (resistance only)?

  1. 1.29 V
  2. 20.6 V
  3. 2.23 V
  4. 2.58 V
Show the answer and solution

Answer: D. 2.58 V

Out and back: R = ρ(2L)/A = 0.0172 × 60/8 = 0.129 Ω; Vd = IR = 2.58 V.

Other topics in the same subjects

DC circuits · AC circuits · Three-phase systems · Transients (RC, RL, RLC) · Semiconductors and diodes · Power electronics · Instrumentation and measurement · Control systems · Transformers · DC machines · Induction motors · Synchronous machines · Protection: fuses, breakers, relays · Illumination · Power plant engineering · PEC: branch circuits, ampacity and protection

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