Three-Phase Power Equations

Electrical 3-phase equations

Most AC power today is produced and distributed as three-phase power where three sinusoidal voltages are generated out of phase with each other. With single-phase AC power there is only one single sinusoidal voltage.

Some common three-phase power equations can be expressed as

Real Power

Wapplied = 31/2 U I cos Φ

             = 31/2 U I PF        (1)


Wapplied = real power (W, watts)

U = voltage (V, volts)

I = current (A, amps)

PF = cos Φ = power factor (0.7 - 0.95) 

For purely resistive load: PF = cos Φ = 1 

  • resistive loads converts current into other forms of energy, such as heat
  • inductive loads use magnetic fields like motors, solenoids, and relays

Example - Pure Resistive Load

For purely resistive load and power factor = 1, the real power in a 415 voltage 20 amps circuit can be calculated as

  Wapplied = 31/2 415 (V) 20 (A) 1

         = 14400 W

         = 14.4 kW

Total Power

W = 31/2 U I         (2)

Brake Horsepower

WBHP = 31/2 U I PF μ / 746         (3)


WBHP = brake horse power (hp)

μ = device efficiency

Related Topics

  • Electrical - Amps and electrical wiring, AWG - wire gauge, electrical formulas, motors and units

Related Documents

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  • en: 3 three-phase electrical power voltage current

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