Three-Phase Real Power
Three-Phase Real Power
Three-phase power is the backbone of industrial electrical distribution. This worksheet computes the real (active) power delivered by a balanced three-phase load from the line voltage, line current and power factor.
The real power is P = √3·V_L·I_L·cosφ, where V_L and I_L are the line (phase-to-phase) voltage and current and cosφ is the power factor.
Inputs
V := 400 V=400 V
I := 30 A=30 A
pf := 0.85=0.85
Real power
P := sqrt(3)·V·I·pf=17666.92 W
Results
The active power in watts (here, kilowatts) is what does useful work and what the utility bills as energy over time. Dividing by the power factor gives the apparent power (kVA) that actually sizes cables and transformers — a low power factor inflates that current.
Assumptions & limitations
- Balanced three-phase system, sinusoidal steady state.
- Line voltage and current (the √3 already accounts for the connection).
- Single power factor; harmonics ignored.