COMPLEX POWER

Complex power is the product of voltage peak (Vm) and the conjugate(*) of the current divided by two.

or  Vrms multiply by Irms.

symbol is bold S or “S“ and the unit is VA.

S = V . I*

V is the phasor representation of voltage and I* is the conjugate of current phasor.

So if  V is the reference phasor then V can be written as |V| ∠0.
(Usually one phasor is taken reference which makes zero degrees with real axis. It eliminates the necessity of introducing a non zero phase angle for voltage)

Let current lags voltage by an angle φ, so

  I = | I | ∠-φ

(current phasor makes -φ degrees with real axis)                     

       I*=  | I | ∠φ

So,
S = |V|  | I | ∠(0+φ) =  |V|  | I | ∠φ

(For multiplication of phasors we have considered polar form to facilitate calculation)

Writting the above formula for S in rectangular form we get

S =  |V|  | I | cos φ  +  j  |V|  | I | sin φ

 The real part of complex power S is |V| | I | cos φ which is the real power or average power and the imaginary part  |V| | I | sin φ is the reactive power.

 

So,             

 S = P + j Q        

    

 Where      

  P = |V| | I | cos φ    and    Q = |V| | I | sin φ

In this topic, I've learned that  resistors absorbs the real power and dissipates in the form of heat. Capacitors absorbs the reactive power and dissipates in the form of electric. Inductor absorbs the reactive power and dissipates in the form of magnetic field. Using this topic complex power, we can determine if it is inductive, resistive or capacitive. In complex power, we have to consider the phase network which voltage and current represented in complex form.