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Three-phase power

The power in a balanced three-phase load is calculated with line voltage and line current. The power factor cos φ accounts for current and voltage not being in phase. The formula holds for both star and delta connections.

P=3 UL ILcos⁡φP = \sqrt{3}\,U_L\,I_L\cos\varphiactive power
S=3 UL ILS = \sqrt{3}\,U_L\,I_Lapparent power

Symbols

PPactive powerW
SSapparent powerVA
cos⁡φ\cos\varphipower factor

Example

Motor at 400 V, 10 A, cos⁡φ=0.85\cos\varphi = 0.85:

P=3⋅400⋅10⋅0.85≈5.9P = \sqrt3\cdot 400\cdot 10\cdot 0.85 \approx 5.9 kW.

Use line values in the formula with √3. Phase values belong to P = 3UfIf cos φ.
Practise three-phase and power for free →

← Phase and line voltage · Power factor correction →

Part of Electric Circuits: Three-phase and power.