Three‑phase power is the backbone of modern industrial and commercial electrical systems. While its principles mirror those of single‑phase power, the equations you use are slightly more involved. Fortunately, once you understand the core variables—voltage, current, and power factor—solving any three‑phase problem is straightforward.
Use the formula P = √3 × pf × I × V to find power (P) in watts. Rearranging gives I = P / (√3 × pf × V) for current, or P = √3 × pf × I × V for power when current is known.
Both systems deliver alternating current (AC), but single‑phase supplies one sine wave, whereas three‑phase splits the supply into three waves 120° apart. This arrangement ensures a more constant power delivery and allows for lighter conductors and smaller motors.
The fundamental relationship ties power to voltage, current, and power factor:
P = √3 × pf × I × V
Here, P is real power in watts, pf is the power factor (typically 0.85–1.0), I is line current in amperes, and V is line‑to‑line voltage in volts. The constant √3 ≈ 1.732 accounts for the three‑phase geometry.
When you know the total power in kilowatts, the voltage, and the power factor, solve for current:
I = P / (√3 × pf × V)
Example: 1.5 kW at 230 V with a 0.85 power factor.
Convert kW to watts: 1.5 kW = 1,500 W.
Compute: I = 1,500 W ÷ (√3 × 0.85 × 230 V) = 4.43 A.
Alternatively, use kilovolts: 230 V = 0.23 kV. Then I = 1.5 kW ÷ (√3 × 0.85 × 0.23 kV) = 4.43 A.
To find power when current is known:
P = √3 × pf × I × V
Example: I = 50 A, V = 250 V, pf = 0.9.
Compute: P = √3 × 0.9 × 50 A × 250 V = 19,486 W → 19.486 kW.
These straightforward steps let you translate between the key parameters of any three‑phase circuit with confidence.
