Three-phase power is the transmission and use of three alternating voltages of the same frequency and magnitude, displaced by 120° from one another. A balanced three-phase system delivers constant total power and uses conductors efficiently.
Learning objectives
- Calculate balanced three-phase active, reactive and apparent power
- Relate line and phase voltages and currents in star and delta
- Explain why three-phase transmission is efficient
- Measure three-phase power correctly
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
Homes usually receive a single phase from a three-phase distribution network. Industry uses all three phases for motors, which are smaller and smoother-running than equivalent single-phase motors.
Intermediate How it behaves in a circuit
In a star connection VL = √3 × Vph and IL = Iph. In a delta connection VL = Vph and IL = √3 × Iph. The total power is the same for the same load, but the voltages and currents in the windings differ.
Advanced Limits, assumptions, engineering detail
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Active power | P | watt (W) |
| Apparent power | S | volt-ampere (VA) |
| Reactive power | Q | volt-ampere reactive (var) |
| Line voltage | VL | volt (V) |
Worked examples
Balanced motor load
Problem. A three-phase motor draws 50 A per line at 400 V with a power factor of 0.85. Find the active, apparent and reactive power.
Solution. P = √3 × 400 × 50 × 0.85 = 1.732 × 400 × 50 × 0.85 = 29 444 W. S = √3 × 400 × 50 = 34 641 VA. Q = √(S² − P²) = √(34 641² − 29 444²) = 18 248 var.
Three single-phase heaters in star
Problem. Three 2 kW heaters are connected in star to a 400 V three-phase supply. What is the total power and the line current?
Solution. Total P = 3 × 2000 = 6000 W. Per phase Vph = 400/√3 = 231 V. Iph = 2000/231 = 8.66 A, and in star IL = Iph.
Star versus delta
Problem. Three 10 Ω resistors are connected first in star and then in delta to the same 400 V supply. Compare the total power.
Solution. Star: Vph = 231 V, Iph = 23.1 A, P = 3 × 231 × 23.1 = 16.0 kW. Delta: Vph = 400 V, Iph = 40 A, P = 3 × 400 × 40 = 48.0 kW.
Practical applications
- Industrial motor drives
- Power distribution networks
- Distribution and power transformers
- Variable-frequency drives
- Three-phase EV chargers
- Generators and alternators
Automotive applications
Alternators generate three-phase AC that is rectified to charge the 12 V system, and electric-vehicle traction inverters produce three-phase AC for the motor. High-power AC charging can use all three phases to reduce current per conductor.
Industrial applications
Three-phase motors, distribution boards, protection relays and power-factor correction are the backbone of industrial electrical systems. Balanced loading across phases keeps neutral currents and losses low, and phase rotation must be checked before connecting motors.
Measurement procedure
- Use a three-phase power analyser or the two-wattmeter method for a three-wire system.
- Measure each line current with a clamp meter to check balance.
- Confirm phase rotation before connecting a motor; the wrong sequence reverses the direction.
- Measure phase-to-phase and phase-to-neutral voltages to verify the supply configuration.
Common mistakes
- Using phase current instead of line current in the star line-current formula.
- Forgetting the √3 factor and obtaining only one third of the correct power.
- Using phase voltage in a formula that requires line voltage, or the reverse.
- Assuming the neutral current is zero when harmonic loads are present.
Safety considerations
- Three-phase systems commonly operate at 400 V or more; use equipment rated for the full line voltage.
- Check phase rotation and isolation before connecting or reversing a motor.
- Arc-flash energy is high in three-phase distribution; follow switching and PPE procedures.