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.
Real Power
Line to line voltage:
Wapplied = 31/2 Ull I cos Φ
= 31/2 Ull I PF (1)
where
Wapplied = real power (W, watts)
Ull = line to line voltage (V, volts)
I = current (A, amps)
PF = cos Φ = power factor (0.7 - 0.95)
Line to neutral voltage:
Wapplied = 3 Uln I cos Φ (2)
where
Uln = 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
Wapplied = 31/2 (400 V) (20 A) 1
= 13856 W
= 13.9 kW
Total Power
W = 31/2 U I (2)
Brake Horsepower
WBHP = 31/2 U I PF μ / 746 (3)
where
WBHP = brake horse power (hp)
μ = device efficiency
