In a DC system, power is the product of voltage and current. In AC, three different powers are defined, since the difference between the voltage and current functions is responsible for a partially negative power curve.
Real power is the useful (also known as active) power that is converted into the desired mechanical, light or thermal (or any other form of) energy during use by the consumer. Its symbol is P and its unit is Watt [W].
$ P[W] = V_{RMS} ⋅ I_{RMS} ⋅ cos(\varphi_V - \varphi_I) $
$ P = \dfrac{1}{2} ⋅ V_{p} ⋅ I_{p} ⋅ cos(\varphi_V - \varphi_I) $
Reactive power is the power lost to charging and discharging of coils and capacitors in the circuit. Its symbol is Q, and its unit is Volt-ampere reactive [VAR]. If negative, the circuit is dominated by capacitors (capacitive), if positive, the circuit is dominated by inductors (inductive). Ideally reactive power should be low.
$ Q[V \! AR] = V_{RMS} ⋅ I_{RMS} ⋅ sin(\varphi_V - \varphi_I) $
$ Q = \dfrac{1}{2} ⋅ V_{p} ⋅ I_{p} ⋅ sin(\varphi_V - \varphi_I) $
The product of the effective voltage and current is the apparent, or total power. It can also be calculated using the Real (P) and Reactive (Q) powers with the Pythagoras theorem. Its symbol is S, its unit is Volt-ampere [VA].
$ S[V \! A] = V_{RMS} ⋅ I_{RMS} $
$ S = \dfrac{1}{2} ⋅ V_{p} ⋅ I_{p} $
$ S = \sqrt{P^2 + Q^2} $
The Power Factor is the ratio of real to apparent power, which is used to measure the proportion of power used that is useful. Its value is ideally 1 (=100%), which is possible when there is no phase difference between the voltage and current. Reactive power, so the L and C components make this factor lower.
$ PF = \dfrac{P[W]}{S[V \! A]} = cos(\varphi_V - \varphi_I) $
Although reactive power is wasted power, it is still necessary to get all the electricity from the power plant to the consumer. The power is not used, but cables and other components of the electricity network still become hotter, reducing the efficiency of the system.
Power plants and the grid need to be able to handle reactive power, which requires more equipment and more maintenance, increasing operating costs. Energy suppliers can impose penalties for the excessive use of Q.