Power Energy
Three-Phase Power
For a balanced three-phase load, active power is the square root of three multiplied by line voltage, line current and power factor. The √3 factor comes from the relationship between line and phase quantities. The same expression with cos φ omitted gives apparent power in volt-amperes. Using line-to-line voltage and line current is the most common practical form because those are the quantities a technician measures.
Three-Phase Power
P = √3 × V_line × I_line × cos φ
Variables and units
| Symbol | Quantity | Unit |
|---|---|---|
| P | Active power | W |
| V_line | Line-to-line RMS voltage | V |
| I_line | Line RMS current | A |
| cos φ | Power factor | dimensionless |
Conditions of application
Balanced three-phase load with sinusoidal quantities and line-to-line voltage. Unbalanced or distorted systems need separate phase or harmonic analysis.
Worked example
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Real, reactive and apparent power for a balanced three-phase load.