Electrical Systems

Complex Power

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V and I are the voltage and current phasors(rms values)

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S is the Apparent power
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S = P + Q j
Where P is the real power(or average power) and Q is the reactive power
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If V and I are the rms or effective voltage and current phasors represented in complex form.

The complex power 'S' is defined as the product of V and conjugate of I

S = V . I* S = P + Q j P = |S| Cos (φ) Q = |S| Sin (φ) |S|2  =  |P|2  +  |Q|2

I* is the conjugate of I.

S is a complex number the real part (P) is the real or average power and the imaginary part (Q) is the reactive power.

φ is the phase angle.