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.
Line to line voltage:
W applied = 3 1/2 U ll I cos Φ
= 3 1/2 U ll I PF (1)
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)
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
Typical power factors:
|Lamp, fluorecent uncompensated||0.5|
|Lamp, fluorecent compensated||0.93|
|Motor, induction 100% load||0.85|
|Motor, induction 50% load||0.73|
|Motor, induction 0% load||0.17|
|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
W = 3 1/2 U I (2)
- Brake horsepower is the actual power delivered to or by a shaft.
W BHP = 3 1/2 U I PF μ / 746 (3)
W BHP = brake horse power (hp)
μ = device efficiency
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Power equations for single phased electrical systems.
Inductive loads and power factors with electrical three-phase motors.