On Three Phase Reactive Power

It is well known that in single-phase alternating current (AC) electric power systems, both average power and reactive power, which are the real and imaginary parts of single-phase complex power, can be made to appear explicitly in the time-domain formulation of sinusoidal instantaneous power. However, unlike the single-phase case, in three-phase electric power systems, only (constant) three-phase average power appears in the three-phase instantaneous power counterpart. The mathematical reasons for this are explained and an algebraic reformulation of three-phase instantaneous power is contrived to unify complex power and instantaneous power across both cases.