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22-Elec-B7 Power Systems Engineering: December 2018

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

  1. Question 1 Ferranti Effect and Long-Line ABCD Performance
  2. Question 2 Salient-Pole Machine on an Infinite Bus
  3. Question 3 Transformer Losses and the Cantilever Equivalent Circuit
  4. Question 4 Exact Two-Bus Power Flow and Reactive Compensation
  5. Question 5 Network Reduction and Three-Phase Fault Analysis
  6. Question 6 Sequence Networks and a Double Line-to-Ground Fault
  7. Question 7 Equal-Area Stability under a Sustained Fault

Start with Question 1 →

Paper format. National Exams, December 2018 — 16-Elec-B7 Power Systems Engineering, 3 hours, open book, any non-communicating calculator permitted. The paper prints seven questions, headed “Problem 1” to “Problem 7”; the rubric states that any five questions constitute a complete paper and that all questions are of equal value. Every one of the seven is solved in full here, because the set is a study resource rather than a three-hour sitting. Sub-part point values are quoted as printed; note that the printed splits total 25 points on Problems 1, 2, 4, 5 and 6, 20 points on Problem 3, and Problem 7 carries no printed split at all — under the “equal value” rubric each question is worth one fifth of the paper regardless.

Reference texts. M. E. El-Hawary, Electrical Power Systems: Design and Analysis, rev. ed., IEEE Press / Wiley — the reference text named in the Engineers Canada syllabus for this examination code, and the source of the “cantilever” transformer model used in Problem 3. Supporting texts: J. D. Glover, M. S. Sarma and T. J. Overbye, Power System Analysis and Design, 6th ed.; J. J. Grainger and W. D. Stevenson, Power System Analysis; S. J. Chapman, Electric Machinery Fundamentals, 5th ed. Canadian practice context (protection philosophy, grounding) follows CSA and IEEE C37 relaying practice as applied by Canadian transmission utilities.

Check — two places where the printed data are not internally consistent, and what was done about each.

(1) Problem 1. The pair A = 0.95∠2°, B = 195∠87.5° forces a shunt parameter with a large real part (Re C = 3.00 × 10−4 S). No real transmission line has a shunt conductance of that size — on a physical line C lands within about a degree of +90°. The consequence is a transmission efficiency of only 80.9 %, of which about 156 MW of the 236 MW loss is charged to that fictitious conductance. The arithmetic below is exactly what the printed constants give and is what the marker will be looking for; the physical caveat is stated so the low efficiency is not read as a slip.

(2) Problem 6. Table (2) lists the line negative-sequence reactance as 0.320 pu against a positive-sequence 0.30 pu. A transmission line is a static, symmetric element, so physically X− must equal X+. The printed 0.320 is used throughout (the paper governs). Taking 0.30 instead moves the answer to Problem 6(b) from 1.4169∠145.58° pu to 1.4212∠146.04° pu — a change of 0.3 %, so neither reading changes any conclusion.