Power Factor & Complex Power

Power Factor & Complex Power =)

Power Factor 

v(t) = Vm cos(ωt + θv)

and

i(t) = Im cos(ωt + θi)

The average power is a product of two terms. The product Vrms Irms is known as the apparent power S. The factor cos(θv − θi) is called the power factor (pf).

S = Vrms Irms

The apparent power (in VA) is the product ofthe rms values ofvoltage and current.

The power factor is dimensionless, since it is the ratio of the average power to the apparent power,

pf =P/S= cos(θv − θi)

The angle θv − θi is called the power factor angle, since it is the angle whose cosine is the power factor.

The power factor is the cosine ofthe phase difference between voltage and current. It is also the cosine ofthe angle ofthe load impedance.

Complex Power

        Complex power (in VA) is the product ofthe rms voltage phasor and the complex conjugate ofthe rms current phasor. As a complex quantity, its real part is real power P and its imaginary part is reactive power Q.

It is a standard practice to represent S, P, and Q in the form of

a triangle, known as the power triangle, shown below,

Overview and Insights

- Real Power (P) in measured in W, Reactive Power (Q) in VAR, and Apparent Power (S) in VA.

- For Power Factor (PF), when theta increases PF decreases, and when theta decreases PF increases.

Reactive Power:

Q = 0 for resistive loads (unity pf).

Q < 0 for capacitive loads (leading pf).

Q > 0 for inductive loads (lagging pf).