Apparent power
Apparent power is used to describe the useful (or working) power in a system, it is measured in VA volt-amperes (not watts). It is typically of most interest in power transmission and distribution.
Engineers use three types of power to describe energy flow in a system:
Real power (P)
Apparent power (S)
Reactive power (Q)
In an alternating current circuit both the current and voltage are sinusoidal. The Apparent power expresses the useful power in the system by taking into account the Power factor.
It is used to describe the resultant power due to the phase seperation between the voltage and current. If there is a phase seperation between the two quantities, the instantaneous power will have to 'work' harder to produce the equivalent power if they were in phase.
Understanding the relationship between these three quantities lies at the heart of understanding power engineering. The mathmatical realtionship between them is a vector and is typically expressed using complex numbers
<math> S = P +jQ <math>
As the quantities are vectors
<math> S^2 = P^2 + Q^2<math>
The Apparent Power is the rms value of the voltage multiplied by the rms value of the current. This definition is valid also for nonsinusoidal voltage and current waveforms in single phase systems. The concept of the apparent power may be extended to multi-phase systems by summing up the apparent powers of the individual phases. However, there are other well-grounded definitions of apparent power in multi-phase systems. E.g., one popular apparent power definition for three-phase system is
<math> S = \sqrt{U_a^2 + U_b^2 + U_c^2}\sqrt{I_a^2 + I_b^2 + I_c^2}<math>,
where <math> U <math> and <math> I <math> are the rms values of the waveforms. Subscripts a, b and c refer to the phases of the three-phase system.
