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:
| 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
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
Related Topics
-
Electrical
Electrical engineering with units, amps and electrical wiring. Wire gauges, electrical formulas, motors and more.
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.
