Solved Problems

Electric Power Systems

Twenty-eight problem sets, worked line by line, mapped onto the thirty-nine chapters of the textbook — from the two factors of √3 in a three-phase circuit to the penalty factors of economic dispatch.

Prof. Mithun Mondal GATE · ESE · University Exams Free & Open Access
7Parts
40Problem Sets
39Chapters Mapped
Welcome

A problem book, not a worked-answer list

These sets are the companion to the Electric Power Systems textbook. Every problem is solved in full — not the answer with the working implied, but each step written out with the reason for taking it. Where a problem admits two routes, both are shown and the choice between them is argued rather than asserted.

Power systems is a subject in which the arithmetic is rarely difficult and the bookkeeping almost always is. A per-unit calculation that fails does so because a base was chosen carelessly three steps earlier; a fault study that gives an implausible answer does so because a nameplate impedance was never converted. The emphasis throughout is therefore on the decisions rather than the algebra — which quantity is line and which is phase, which base applies in which zone, which impedance the current actually flows through.

Every set closes with an answer that can be checked independently, and most solutions carry a verification step that costs one line and catches the errors the equations themselves would happily absorb.

How each set is built. Twenty fully worked problems, graded from warm-up to challenge, each with a stated answer and a closing observation on what the problem was really about. Then twelve practice problems with answers but deliberately without methods, three challenge problems that need an idea rather than a formula, twelve multiple-choice questions, a table of key formulas, and a diagnostic list of the mistakes that actually get made.
Warm-up — builds the method Exam level — GATE / ESE / university Challenge — combines methods
Part 1

Fundamentals

The four sets that everything else is written in. Three-phase relations, the economics that fix the transmission voltage, and the per-unit normalisation that removes transformer ratios from every diagram that follows.

Three-Phase Systems and Supply Economics — Chapters 1–3

The Per-Unit System — Chapter 4

Part 2

Transmission Line Parameters

Where the numbers in an impedance diagram come from. Inductance and capacitance computed from conductor geometry, the bundling that manages both, and the corona loss that sets the practical limit on surface gradient.

Inductance and Capacitance — Chapters 6–8

Corona — Chapter 15

Part 3

Line Performance

The same line under three levels of approximation — series impedance alone, lumped shunt admittance, and the distributed-parameter wave solution — and the regulation and efficiency figures each of them predicts.

Short Lines — Chapter 10

Medium and Long Lines — Chapters 11–13

Part 4

Network Matrices and Load Flow

The point at which the network stops being a diagram and becomes a matrix. Y-bus by inspection, Z-bus by the building algorithm, and the two iterative schemes that solve the resulting non-linear system.

Bus Matrices — Chapters 16–17

Load Flow — Chapters 18–20

Part 5

Faults and Symmetrical Components

The transformation that turns any unbalanced three-phase problem into three balanced ones, the sequence networks it produces, and the fault calculations that follow from connecting them.

Symmetrical Components and Faults — Chapters 22–25

Part 6

Stability and System Operation

What happens after the fault is cleared, and what the system is doing the rest of the time — the swing equation and the equal-area criterion, then the load characteristics and dispatch economics that decide which machine runs at what output.

Stability — Chapters 26–29

Loads and Dispatch — Chapters 30–33

Part 7

Protection and the Modern Grid

Everything so far assumed the fault would be cleared and the converter would behave. These sets are about the equipment that does the clearing, the relays that decide when, the insulation and earthing that keep the substation survivable, and the converters and renewables that are changing what the grid is.

Switchgear and Relaying — Chapters 35–36

Substations and the Modern Grid — Chapters 37–39

Start Here
Begin with Set 1 — Three-Phase Circuits and Power

Almost every error later in this book is a three-phase error wearing a disguise: a line voltage used where a phase voltage was meant, a √3 applied twice or not at all, a power factor angle taken between the wrong two phasors. Set 1 drills those reflexes on circuits simple enough that the arithmetic never hides the reasoning, and Set 3 then removes the need for them entirely by moving to per-unit. Work both before anything else. Open Set 1 →

Reading the theory alongside. Each set names the textbook chapter it maps onto. If a step in a solution assumes a result you have not met — the ABCD parameters of a nominal-π section, say, or the building algorithm for Z-bus — open the corresponding chapter of Electric Power Systems and the derivation will be there in full.