ThreePhase Power  Equations
Electrical 3phase equations.
Most AC power today is produced and distributed as threephase power where three sinusoidal voltages are generated out of phase with each other. With singlephase AC power there is only one single sinusoidal voltage.
Real Power
Line to line voltage:
W_{applied } = 3 ^{ 1/2 } U_{ll } I cos Φ
= 3 ^{ 1/2 } U_{ll } I PF (1)
where
W_{applied } = real power (W, watts)
U_{ll } = line to line voltage (V, volts)
I = current (A, amps)
PF = cos Φ = power factor (0.7  0.95)
Line to neutral voltage:
W_{applied } = 3 U_{ln } I cos Φ (2)
where
U_{ln } = line to neutral voltage (V, volts)
For pure 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
Power Factor
Typical power factors:
Device  Power Factor 

Lamp, fluorecent uncompensated  0.5 
Lamp, fluorecent compensated  0.93 
Lamp, incandescent  1 
Motor, induction 100% load  0.85 
Motor, induction 50% load  0.73 
Motor, induction 0% load  0.17 
Motor, synchronous  0.9 
Oven, resistive heating element  1 
Oven, induction compensated  0.85 
Pure resistive load  1 
Example  Pure Resistive Load
For pure resistive load and power factor = 1 the real power in a 400/230 voltage (line to line / line to neutral) 20 amps circuit can be calculated as
W _{ applied } = 3 ^{ 1/2 } (400 V) (20 A) 1
= 13856 W
= 13.9 kW
Total Power
W = 3 ^{ 1/2 } U I (2)
Brake Horsepower
 Brake horsepower is the actual power delivered to or by a shaft.
W_{BHP } = 3 ^{ 1/2 } U I PF μ / 746 (3)
where
W_{BHP } = brake horse power (hp)
μ = device efficiency
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