Electrical theory and fundamentals
The relationships you cannot avoid
Ohm's law (V = IR), the power relationships (P = VI = I²R = V²/R) and the impedance triangle (Z = √(R² + X²)) underpin almost every calculation question. For AC, inductive reactance X_L = 2πfL, capacitive reactance X_C = 1/(2πfC), and current is V/Z. Energy is power × time, and one kilowatt-hour is one unit on the meter.
AC and three-phase quantities
Australian supply is 50 Hz, so the period is 20 ms, and the nominal low-voltage system is 230/400 V. Meters and nameplates quote RMS values: RMS = peak/√2, so 230 V RMS is about 325 V peak. In star, V_L = √3 V_ph and I_L = I_ph; in delta, V_L = V_ph and I_L = √3 I_ph. Balanced three-phase power is P = √3 V_L I_L cos φ, with S = √3 V_L I_L and Q = √(S² − P²). Motor synchronous speed is N_s = 120f/p, and a transformer's voltage ratio equals its turns ratio with the current ratio inverted.
Traps
Using peak values where RMS is required; mixing line and phase quantities in a three-phase calculation; dropping cos φ so that kVA is reported as kW; quoting 240/415 V where the current standard uses 230/400 V; assuming a three-phase neutral carries full line current, when it carries only the imbalance; forgetting that a 10% rise in voltage raises the power of a resistive load by about 21%.
Worked example
A 400 V three-phase motor draws 20 A per line at 0.8 power factor. S = √3 × 400 × 20 = 13.9 kVA; P = 13.9 × 0.8 = 11.1 kW; Q ≈ 8.3 kvar. Rule of thumb: at 0.8 pf, kW = kVA × 0.8, so every 10 kVA of load is 8 kW of real power.