# 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 = (Q ^{2} + P^{2})^{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 = 3^{1/2} 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 *

#### Three Phase Current

*P = 3 ^{1/2} 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 = 3^{1/2} U I sin φ *

* = 1.732 UI PF (4b)*

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