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22-Elec-B7 Power Systems Engineering: December 2016

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

  1. Question 1 Bundle Conductors, Line Capacitance and the ABCD Constants
  2. Question 2 Excitation, Reactive Power and the Salient-Pole Loading Table
  3. Question 3 Transformer Losses versus Frequency, and the Cantilever Model
  4. Question 4 Two-Bus Power Flow in Closed Form
  5. Question 5 Balanced Three-Phase Fault and the Line 1–2 Current
  6. Question 6 System Grounding and Single Line-to-Ground Fault Currents
  7. Question 7 Excitation Voltage and Transient Stability under a Sustained Fault

Start with Question 1 →

Paper format. National Exams, December 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. This exam code follows M. E. El-Hawary, Electrical Power Systems: Design and Analysis (IEEE Press) — the notation is his throughout: the “cantilever” transformer equivalent of Problem 3, the two-reaction salient-pole construction of Problem 2, the ABCD two-port of Problem 1 and the sequence-network fault reduction of Problem 6. Corroborating references: J. D. Glover, M. S. Sarma and T. J. Overbye, Power System Analysis and Design, 6th ed. (ch. 3 transformers, ch. 4–5 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 C22.2 and the IEEE C62 / IEEE 142 (Green Book) series on system grounding.

Check: four judgement calls carried through the solutions, all recorded here rather than hedged in the answers.

(i) Problem 1 does not state a frequency. Parts (c) and (d) need one, and the paper is a Canadian national exam, so 60 Hz is used throughout — consistent with the 60 Hz stated in Problems 3 and 7. At 50 Hz the capacitance and surge impedance are unchanged (they do not involve frequency) and only the propagation constant of part (d) rescales by 5/6.

(ii) Problem 2 prints “neglecting armature reaction”. Armature reaction is precisely what the direct- and quadrature-axis reactances represent, so the phrase is read as its standard counterpart, neglecting armature resistance — the only reading under which the two given reactances can be used at all.

(iii) Problem 6 prints a part label “c-” with no question text. The five parts that do carry text (a, b, d, e, f) are marked 4 points each and total the 20 points the paper allots to every problem, so nothing is missing from the assessment; the sequence networks that the empty label most plausibly asked for are drawn anyway.

(iv) Problem 5 gives no reactance between buses 2 and 3. Figure (3) confirms the topology: bus 3 hangs radially off bus 1 through the j0.12 pu line, and the only other tie is line 1–2.