Three-Phase Systems and Transformers
Scope
Three-Phase Systems and Transformers tests star and delta relationships, three-phase power, transformer action, turns ratio, losses, efficiency and basic current/voltage calculations.
Core rules
- Star: line voltage = √3 × phase voltage; line current = phase current.
- Delta: line current = √3 × phase current; line voltage = phase voltage.
- Balanced three-phase power: P = √3 × VL × IL × cos φ.
- Ideal transformer: V1/V2 = N1/N2 = I2/I1. The ratio is fixed by turns, not by load.
- Copper loss varies as I²R; iron loss is approximately constant at fixed voltage and frequency.
- Efficiency = output power/input power × 100%.
Worked example
A balanced 415 V three-phase load draws 10 A at 0.8 power factor. P = √3 × 415 × 10 × 0.8 = 5751 W, about 5.75 kW. The apparent power is √3 × 415 × 10 = 7188 VA, and Q = 7188 × 0.6 = 4313 var. If the load is delta-connected, phase current = 10/√3 = 5.77 A while phase voltage remains 415 V. In star, phase voltage would be 415/√3 = 240 V.
Traps
- Using √3 in the wrong direction for delta voltage or current.
- Adding line and phase values directly.
- Calculating kW from VA without multiplying by power factor.
- Assuming transformer efficiency is 100% when copper and iron losses are given.