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22-Elec-B7 Power Systems Engineering: May 2016

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 ABCD to equivalent pi, parallel lines, and the machine behind them
  2. Question 2 Reactive power in the system, and the two-reaction salient-pole machine
  3. Question 3 Single-phase transformer: parameters from a load test, and input power from a known impedance
  4. Question 4 Completing the bus table of a four-bus network
  5. Question 5 Fault consequences, transformer protection, and a mid-line three-phase short
  6. Question 6 Single line-to-ground fault on an industrial bus
  7. Question 7 Transient stability under a sequence of faults and switchings

Start with Question 1 →

Paper format. National Exams, May 2016 — 07-Elec-B7 Power Systems Engineering. Open-book, 3 hours duration. Seven problems are printed; any five constitute a complete paper, only the first five appearing in the answer book are marked, and all questions are of equal value (20 points each). All seven are solved in full below, because this set is a study resource rather than a timed sitting.

Reference texts. The syllabus for this code follows M. E. El-Hawary, Electrical Power Systems: Design and Analysis (IEEE Press) — the notation used throughout (the ABCD two-port and its equivalent pi, the two-reaction salient-pole construction, the sequence-network fault reduction) is his, and the phrase “all power formulae in the text” in Problem 1 refers to that book. Corroborating references: J. D. Glover, M. S. Sarma and T. J. Overbye, Power System Analysis and Design, 6th ed. (ch. 3 transformers, ch. 5 transmission lines, ch. 6 power flow, ch. 7–9 faults and symmetrical components, ch. 11 transient stability); J. J. Grainger and W. D. Stevenson, Power System Analysis; and S. J. Chapman, Electric Machinery Fundamentals, 5th ed., for the machine and transformer chapters. Canadian practice references where grounding and protection are discussed: CSA C22.1 Canadian Electrical Code, Part I, CSA C22.3 No. 1 for overhead systems, and IEEE C37 series for protective relaying.

Check: four data points read off the printed figures. (i) In Figure (2) of Problem 4 the three branch reactances are j0.25, j0.20 and j0.10 pu, with bus 4 hanging off bus 2 through the j0.10 branch — the topology is taken from the drawing. (ii) Figure (3) of Problem 5 shows three sources, not two: generators at bus 1 and bus 4 and a third machine below bus 5. The sentence “the voltage at both sources is 1 p.u.” is taken to mean all sources are at 1.0 pu, which is the only reading that lets the network be solved. (iii) In Figure (4-a) of Problem 6, transformer T2 carries its delta on the generator side and T1 carries its delta on the motor side; motor 1 is an ungrounded wye and motor 2 is grounded through a reactor. Those four winding connections, not the reactance values, decide the answer. (iv) Problem 7 gives the switching angles in radians (1.2, 1.25 and 1.9 rad).

Check: Problem 3(a) as printed is over-determined and internally inconsistent. Rated kVA, the load power factor, the efficiency and the primary voltage are four data for two unknowns, and at 0.85 power factor lagging no positive series reactance satisfies them all. The inconsistency is quantified and resolved inside the answer rather than hidden.