Electrical Engineering (Power): Three-Phase Systems, Machines, and Protection
Scope of the section
Power covers generation, transmission, distribution, and the machines that link them: three-phase circuits, per-unit analysis, transformers, synchronous and induction machines, DC machines, transmission-line models, fault currents, protective relaying, and power-factor correction. Expect numerical items on power, efficiency, regulation, slip, and fault levels.
Traps that cost points
- Wye–delta confusion. In a wye, V_L = √3 V_ph and I_L = I_ph; in a delta, I_L = √3 I_ph and V_L = V_ph. Total three-phase power is P = √3 V_L I_L cos θ in either connection.
- Power-factor sign. Lagging means current lags voltage (inductive); leading means capacitive. State the sense when the item asks for it.
- Transformer efficiency. It peaks when copper loss equals core loss, at load fraction √(P_core / P_cu,FL) - not at full load.
- Per-unit work. Convert everything to one base before combining; base changes use (kV_old/kV_new)² and (MVA_new/MVA_old).
- Slip. Synchronous speed is n_s = 120f/p; slip is negative for a generator and exceeds 1 during braking.
- Instrument transformers. A relay sees secondary quantities; multiply by the CT/PT ratio to recover primary values.
Worked example
A balanced 480 V (line-to-line) load draws 100 A at 0.8 lagging:
P = √3 × 480 × 100 × 0.8 = 66.5 kW Q = √3 × 480 × 100 × 0.6 = 49.9 kvar S = √3 × 480 × 100 = 83.1 kVA
To correct to 0.95 lagging: Q_c = P(tan θ₁ − tan θ₂) = 66.5(0.750 − 0.329) ≈ 28 kvar. Rule of thumb: the √3 belongs to line quantities in a balanced three-phase set; if you are given phase values, multiply by 3 instead.