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22-Elec-B7 Power Systems Engineering: May 2017

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

  1. Question 1 Bundle-Conductor Line Parameters and the Long-Line ABCD Constants
  2. Question 2 Armature Reaction, Reactive-Power Capability and the Round-Rotor Operating Table
  3. Question 3 Three-Winding Transformer — Currents, Voltages, Powers and Efficiency
  4. Question 4 Bus Classification and a Three-Bus Power-Flow Solution
  5. Question 5 Fault Consequences, Transformer Protection and a Mid-Line Three-Phase Short
  6. Question 6 Single Line-to-Ground Fault on a Sequence-Network Representation
  7. Question 7 Transient Stability by the Equal-Area Criterion

Start with Question 1 →

Paper format. National Exams, May 2017 — 16-Elec-B7 Power Systems Engineering. Open-book, 3 hours, seven problems of equal value (25 points each); any five constitute a complete paper, and only the first five in the answer book are marked. All seven are solved here, because the set is a study resource rather than a 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 bundle-conductor mean radii and long-line ABCD constants of Problem 1, the round-rotor power-angle relations of Problem 2, the three-winding equivalent circuit of Problem 3, the sequence-network fault reduction of Problem 6 and the equal-area criterion of Problem 7. Corroborating references: J. D. Glover, M. S. Sarma and T. J. Overbye, Power System Analysis and Design, 6th ed. (ch. 4–5 transmission-line parameters, ch. 6 power flow, ch. 7–9 symmetrical components and faults, 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 synchronous-machine and transformer chapters. Canadian practice references where protection and grounding are discussed: CSA C22.1 Canadian Electrical Code, Part I, CSA C22.3 for overhead systems, and IEEE C37 (protective relaying) and IEEE 142 Green Book (grounding).

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

(i) Problem 1 states neither a frequency nor a line length. Parts (a)–(c) need neither. Part (d) needs both, so 60 Hz is used (Canadian national exam) and the ABCD constants are given as closed-form functions of length, evaluated at a representative 400 km with a sensitivity table at 200 km and 600 km. The characteristic impedance and the surge-impedance loading do not depend on either quantity.

(ii) Problem 1 gives “bundle separation S” for a bundle whose figure shows eight sub-conductors on a circle. S is read as the distance between adjacent sub-conductors, so the bundle radius is $A = S/[2\sin(\pi/N)] = 0.6533\ \text{m}$ — the standard El-Hawary reading. If a marker instead reads S as the bundle diameter, every mean radius scales by the same factor and the method is unchanged.

(iii) Problem 5 says “the voltage at both sources is 1 p.u.” above a figure that draws three generators. All three are taken at 1.0 pu, which is the only reading that closes the network; the three internal e.m.f.s then merge into one node.

(iv) Problem 6: the zero-sequence source reactance is printed as $X_{0S}=j0.04$, possibly followed by a fifth digit. The value $j0.04$ is used. Reading it as $j0.045$ moves the zero-sequence Thévenin reactance from 0.19978 to 0.20051 pu and the fault current by 0.1 % — below the resolution of any answer here.