Electrical Theory and Distribution System Fundamentals
This domain tests whether you can move confidently between line, phase and per-unit quantities, and use those numbers to size equipment, predict voltage drop and estimate fault current. Expect three-phase relationships, wye and delta connections, transformer ratios, power factor, Canadian distribution and utilization voltages, and phase rotation.
Core relationships
- Three-phase apparent power: S(kVA) = √3 × V(line-to-line, kV) × I(amperes). Single-phase is simply S = V × I. Sliding the √3 into a single-phase calculation is the most common arithmetic error on the exam.
- Wye: V(line-to-line) = √3 × V(line-to-neutral) and line current equals phase current. Delta: line voltage equals phase voltage and line current is √3 × phase current.
- Real power P = S × power factor; reactive power Q = √(S² − P²). Loads add vectorially, not arithmetically.
- Canadian secondary voltages include 120/240 single-phase, 120/208 wye, 277/480 wye and 347/600 wye; 347/600 is common in Canadian commercial installations.
- CEC Rule 8-102 limits combined consumer service, feeder and branch-circuit voltage drop to 5% of the supply voltage.
Fault current and rotation
- A quick transformer secondary estimate is bolted fault current ≈ full-load current ÷ per-unit impedance, ignoring source and conductor impedance, which reduce the real value at the far end.
- Phase rotation is ABC; swapping any two leads reverses a three-phase motor.
Worked example
A 500 kVA transformer, 12.47 kV to 347/600 V, has 5% impedance. Primary full-load current is 500 ÷ (1.732 × 12.47) = 23.1 A. Secondary full-load current is 500,000 ÷ (1.732 × 600) = 481 A, so the bolted terminal fault is roughly 481 ÷ 0.05 ≈ 9.6 kA. The reasoning matters: the √3 pairs with line-to-line voltage, and per-unit impedance is divided, not multiplied. Using 600 V on the primary side, or forgetting the division, produces answers that are wrong by an order of magnitude.
Traps that cost marks
Dropping power factor when converting kW to kVA; using 1.732 for single-phase circuits; quoting the transformer-terminal fault current as the value at the end of a long run; and misreading a nameplate that lists both winding voltages in the reverse order.