What is the complex power and how it figures in power analysis

Power absorbed by a given load

Considerable effort has been expended over the years to express power relations as simply as possible. Power engineers have coined the term complex power, which they use to find the total effect of parallel loads.

Complex power is important in power analysis because it contains all the information pertaining to the power absorbed by a given load.

Figure 1 – The voltage and current phasors associated with a load

Consider the AC load in Figure 1 above. Given the phasor form V = V_rms∠θ_v  and I = I_rms∠θ_i of voltage v(t) and current i(t), the complex power S absorbed by the AC load is the product of the voltage and the complex conjugate of the current, which is denoted I * or , rather than I itself. This is done such that a leading current (capacitive load, negative reactance) results in negative reactive power.

or

Real power P (units in watts, W) is derived as :

For a purely resistive load, real power can be simplified to :

R denotes resistance ( real part of the complex number ) of the load Z .

Reactive power Q (units in volts-amps-reactive, var) is derived as :

For a purely reactive load, reactive power can be simplified to :

where X denotes reactance ( imaginary part of the complex number ) of the load Z .

So the complex power S (units in volt-amps, VA) may be derived as

and the apparent power (units in volt-amps, VA) as