Electrical Engineering ⇒ Topic : Power Determination Using Complex Notation

Power Determination Using Complex Notation

If the voltage and current in an a.c. circuit are expressed in complex form, we can easily determine the true power or active  power consumed in the circuit. Let the circuit voltage and circuit current be expressed as

                                           figure (a)

Fig. (a) shows the phasors V and I resolved into rectangular components. The component V₁ of voltage and component I₁ of current are in phase and contribute to true power given by

                                               P₁ = V₁ I₁

The component V₂ of voltage and component I₂ of current are 180° out of phase and, therefore,contribute to negative true power given by

                                                   P₂ = -V₂ I₂

The components V₂ and I₁ as well as V₁ and I₂ are 90° out of phase and contribute to no power.Therefore, total power P consumed in the circuit is the algebraic sum of P₁ and P₂ because power is a scalar quantity.

                    Total power consumed, P = P₁+ P₂ = (V₁I₁) + (-V₂I₂)

                                                          P =  V₁I₁ - V₂I₂

Hence the total power consumed in an a.c. circuit is the algebraic sum of product of in-phase components of V and I and the product of quadrature components of V and I. Note that operator j is not to be included in the multiplication.