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Active, Apparent and Reactive Power

Apparent, True Applied and Reactive Power - kVA

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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:

reactive apparent active power

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


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)


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)


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)


φ = phase angle

Three Phase Current

Q = 31/2 U I sin φ  

   =  1.732 UI PF                   (4b)

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  • Engineering ToolBox, (2005). Active, Apparent and Reactive Power. [online] Available at: [Accessed Day Mo. Year].

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