Intermediate
Three-Phase Power Formulas
Three-phase power formulas for wye and delta configurations — line/phase voltage and current relationships, kVA, and current calculations.
Formulas
P = √3 × V_LL × I_L × PF
Three-phase real power (watts)
S = √3 × V_LL × I_L
Three-phase apparent power (VA)
I = kVA × 1000 / (V × √3)
Line current from kVA rating
V_LL = V_Ph × √3 (wye)
Line-to-line voltage from phase voltage (wye)
I_L = I_Ph × √3 (delta)
Line current from phase current (delta)
Variable Definitions
V_LL=Line-to-line voltage(volts (V))
V_Ph=Phase voltage(volts (V))
I_L=Line current(amperes (A))
I_Ph=Phase current(amperes (A))
√3=Square root of 3(1.732)
PF=Power factor(dimensionless (0 to 1))
Worked Examples
Example 1
Find line current for a 225 kVA transformer, 480V three-phase.
- I = kVA × 1000 / (V × √3)
- I = 225,000 / (480 × 1.732)
- I = 225,000 / 831.4 = 270.6A
Answer: 270.6A line current
Example 2
A 480V wye system. Find phase voltage and neutral current for balanced load.
- V_Ph = V_LL / √3 = 480 / 1.732 = 277.1V
- Phase voltage is 277V (120V for 208Y systems)
- Balanced load: neutral current = 0A
Answer: 277V phase voltage, 0A neutral
When to Use
- •Sizing transformers (kVA to amps conversion)
- •Calculating three-phase motor current draw
- •Determining panel/switchboard amperage from total kVA
- •Converting between line and phase values for wye/delta
Standards & References
- NEC Table 430.250 — Three-Phase Motor FLC
- NEC 220 — Load calculations using VA