The three phase instantaneous reactive power defined anew

We have performed a careful analysis of the three-phase instantaneous complex power defined with space-phasors and detected a fundamental inconsistency in the interpretation of the reactive power. We propose a rigorous, bottom-up analysis starting with a new definition of the single-phase instantaneous reactive power in the AC steady state. We discuss our definition grounds, explain its main properties and illustrate it with two examples: first we analyze the power balance of a simple RLC circuit; second, we express Poynting´s theorem (harmonic fields) within the new formalism. As an immediate corollary, we apply it to three-phase circuits in the steady state. Next, we propose a very satisfactory generalization to the transient state (both of single and three-phase circuits) within the framework of Yamamura´s spiral vectors. Lastly we give a worked example of a three-phase induction machine in order to compare the different power definitions and to extract some conclusions