# SPQ and Power Factor in AC Systems

### SPQ

Apparent power, \( S \), as a product of measured RMS voltage and current, can be split into the real and complex power conterparts.

Where \( \phi \) is the phase angle, \( S \) is the apparent power, \( Q \) is the reactive power, \( P \) is the active power.

Since \( Q \) is purely complex, the direction of the vector is important and is defined as leading or lagging. Sign conventions are such that a leading reactive power is capacitive and generates power; lagging reactive power is inductive and absorbs power.

Calculations involving reactive power substitute resistance with reactance.

$$ Q = \frac{V^2}{X} $$

$$ Q = I^2 X $$

Where inductors are positive and capacitors and negative.

### Power Factor

Defined as

$$ p.f. = \cos \phi $$