Power theory of electrical circuits with quasi-periodic waveforms of voltages and currents

Generally known current and power equations of electrical circuits cannot be used in situations where the voltage and current waveforms are non-periodic. The paper suggests that these equations could be applied to systems with quasi-periodic waveforms, however, as approximate models of the power-related phenomena. The concepts of the running RMS and complex RMS values, as well as the running active power are introduced for that purpose and applied for generalizing the current and power equations of the single-phase and three-phase circuits with time-variant parameters. Fast iterative algorithms for calculating the running quantities make it possible to integrate the frequency-domain and the time-domain approaches into a kind of the time and frequency-domain model of the power-related phenomena in circuits with quasi-periodic waveforms