# Active, Apparent and Reactive Power

## Apparent, True Applied and Reactive Power - kVA

Total electrical power consumption depends on

• real power - electrical energy consumption
• reactive power - imaginary power consumption

- and can be expressed as a power triangle or in a Pythagorean relationship:

S = (Q2 + P2)1/2                     (1)

where

S = apparent power (kilovolt amps, kVA)

Q = reactive power (kilovolt amps reactive, kVAR)

P = active power (kilowatts, kW)

### Apparent Power

Apparent power is the power supplied to the circuit.

Apparent Power is measured in volt-amperes (VA) and is the voltage on an AC system multiplied by all the current that flows in it. Apparant power is the vector sum of active and reactive power.

#### Single Phase Current

S = U I                  (2a)

where

U = electric potential (V)

I = current (A)

#### Three Phase Current

S = 31/2 U I

= 1.732 U I                 (2b)

### Active Power

Active - or real or true - power is the power that is used to do work on the load.

Active power is measured in watts (W) and is the power drawn by the electrical resistance of a system doing useful work.

#### Single Phase Current

P = U I cos φ

= U I PF                   (3a)

where

φ = phase angle

PF = cos φ

=  Power Factor

#### Three Phase Current

P = 31/2 U I cos φ

= 1.732 U I PF                     (3b)

#### Direct Current

P = U I                         (3c)

### Reactive Power

Reactive power is the power not used to do work on the load.

Reactive inductive Power - Q - is measured in volt-amperes reactive (VAR) and stored in and discharged by inductive motors, transformers or solenoids.

The reactive power required by inductive loads increases the amount of apparent power - measured in kilovolt amps (kVA) - in distribution systems. Increasing the reactive and apparent power causes the power factor - PF - to decrease.

#### Single Phase Current

Q = U I sin φ

= U I PF                    (4a)

where

φ = phase angle

#### Three Phase Current

Q = 31/2 U I sin φ

=  1.732 UI PF                   (4b)

## Related Topics

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

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