Q. Evaluate complex power in power system?

The complex power ¯S in a single-phase systemis the complex sum of the real (P) and reactive (Q) power, expressed as follows:

where θ_V is the angle associated with ¯V (with respect to any chosen reference), θI is the angle associated with ¯I (with respect to the same reference chosen), θ_Z is the impedance angle, ¯V is the rms voltage phasor, ¯I is the rms current phasor, and ¯Z = R ± jX is the complex impedance with a magnitude of Z. Note that stands for complex conjugate. If the voltage phasor ¯V itself is taken to be the reference, θ_V = 0 and θI may be replaced by θ without any subscript.

The power factor PF is given by the ratio of the real power P (expressed in watts) to the apparent power S = √(P² + Q²) expressed in volt-amperes,

PF = P/S = cos θ

where θ = tan^-1Q/P. Inductive loads cause current to lag voltage and are referred to as lagging power factor loads. Conversely, capacitive loads cause current to lead voltage and are referred to as leading power factor loads.