#### Electrical Systems

##### Complex Power

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

$\text{S = V . I*}$ $\text{P = |S| Cos (φ)}$ $\text{Q = |S| Sin (φ)}$

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.