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Engineers use three types of power to describe energy flow in a system:
Real power (P) Apparent power (S) Reactive power (Q)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 apparent power captures how much power the generating source must produce to deliever Real power (P) with a given Power factor. As the power factor degrades, the generator must do more work to produce an equivalent amount of real power.
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
As the quantities are vectors
Thus, the Apparent power is:
where φ is the phase difference between the current and voltage.
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
,
where and are the rms values of the waveforms. Subscripts a, b and c refer to the phases of the three-phase system.