## Complex Power

In electrical engineering, power is the rate at which energy is transferred or converted in an electrical system. Complex power is a concept used to describe the total power in a system that has both reactive (stored) and active (real) power components.

Mathematically, complex power is defined as the product of the voltage and the complex conjugate of the current:

where S is the complex power, V is the voltage, and I* is the complex conjugate of the current.

The real part of the complex power is the active power, which is the power that is actually consumed or delivered to a load. The reactive power is the imaginary part of the complex power, which is the power that is stored and returned to the source without being consumed. Reactive power is necessary for the operation of inductive and capacitive loads, such as motors and transformers.

Complex power is often expressed in units of volt-amperes (VA) or kilovolt-amperes (kVA), which are units of apparent power. The real power component of complex power is expressed in units of watts (W) or kilowatts (kW).