# 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

Wapplied = 31/2 U I cos Φ

= 31/2 U I PF                      (1)

where

Wapplied = real power (W, watts)

U = voltage (V, volts)

I = current (A, amps)

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

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:

DevicePower 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 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)

where

WBHP = brake horse power (hp)

μ = device efficiency

## Related Topics

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

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