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# Three-Phase Power - 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:

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

Wapplied = 31/2 (400 V) (20 A) 1

= 13856 W

= 13.9 kW

### Total Power

W = 31/2 U I                       (2)

### Brake Horsepower

• Brake horsepower is the actual power delivered to or by a shaft.

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.

## Related Documents

### AC - Active, Reactive and Apparent Power

Real, imaginary and apparent power in AC circuits.

### AC Circuits - Power vs. Voltage and Current

The alternating current In an AC circuit is generated by a sinusoidal voltage source.

### Aluminum Conductor Characteristics

Characteristics of all-aluminum conductors (AAC).

### Electric Motors - Efficiency

Calculate electric motor efficiency.

### Electric Motors - Torque vs. Power and Speed

Electric motor output power and torque vs. rotation speed.

### Electrical Equipment - Power Consumption

Typical power consumption and running time for common electrical equipment.

### Electrical Formulas

Commonly used electrical formulas like Ohms Law and more.

### Electrical Induction Motors - Slip

Slip is the difference between an electrical induction motor's synchronous and asynchronous speed.

### Electrical Motors - Service Factors

Service factor - SF - is a measure of periodically overload capacity at which a motor can operate without beeing damaged.

### Electrical Motors - Shaft Power vs. Voltage and Current

Calculate electric motors shaft power.

### Electrical Vehicle Charging - Power vs. Voltage and Amps

EV Charging - AC vs. DC, single phase vs. three phase and power vs. voltage and amps.

### Law of Cosines

One side of a triangle when the opposite angle and two sides are known.

### Power

Power is the rate at which work is done or energy converted.

### Single Phase Power Equations

Power equations for single phased electrical systems.

### Three-Phase Electrtical Motors - Power Factor vs. Inductive Load

Inductive loads and power factors with electrical three-phase motors.

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