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# 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:

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:

Three-Phase Power Factors
DevicePower Factor
Lamp, fluorecent uncompensated 0.5
Lamp, fluorecent compensated 0.93
Lamp, incandescent 1
Motor, synchronous 0.9
Oven, resistive heating element 1
Oven, induction compensated 0.85

#### 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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## Citation

• The Engineering ToolBox (2005). Three-Phase Power - Equations. [online] Available at: https://www.engineeringtoolbox.com/three-phase-electrical-d_888.html [Accessed Day Month Year].

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7.25.9

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