Rotating vectors for the formulation of energetic balances under periodic conditions

Abstract

After the representation of sinusoidal voltage and current, at the generic electrical port, in terms of counter-rotating vectors, the corresponding energy balance is formalized. The consequence is an instantaneous complex power which unifies the single-phase and the three-phase cases. The classic expressions of the active, reactive and apparent powers are obtained as mean values, on the temporal period, of the complex power expression. The extension of this approach to the periodic case, i.e. under non-sinusoidal or deformed conditions, leads to the classic Budeanu's treatment, but with an immediate algorithm clarity. The disagreement between the instantaneous complex power expression and the energy conservation condition, expressed by the Tellegen's relation, deprives this quantity of every topological and physical content. Incisive for the analytical relationships elaboration, this quantity has a purely formal character.