Power analysis of one-ports under periodic multi-sinusoidal linear operation

In this paper, a complete theory of the power behavior of one-ports under periodic multi-sinusoidal linear operation is presented. It is based on a time-domain vector space approach in two steps. First, the one-port instantaneous current is decomposed into four orthogonal currents. Second, their power counterparts (absolute powers) are defined as products of norms. Hence, vector and scalar expressions for the absolute powers in the frequency domain are derived both in terms of voltage and current rootmean square (rms)-phasor vectors and in terms of the voltage rms-phasor vector and of the multi-frequency admittance matrix. Finally, the hyper-power, a quantity consisting of a scalar/matrix pair, is devised. Like the well-known complex power, the hyper-power condenses all power information and obeys the usual conservation laws.