The correlation functions of power as a new proposition to describe power states in circuits with periodical voltage and current waveforms

The analysis of energy transfer in the circuits is based on the instantaneous power p(t), which is the product of the two waveforms u(t),i(t) . An interesting thing is the search for mutual relations between these two waveforms. In the paper the authors made an attempt to describe power states in electrical circuits with periodic waveforms with the help of the correlation of the two functions. In mathematics correlation is the measure of similarity or mutual dependence between the two functions. Electrical energy is a simultaneous and mutual cooperation of voltage and current waveforms - therefore, the authors defined and examined the correlation function Psi(t) of these waveforms. On the basis of the defined correlation function between the voltage and the current, the authors introduced two new powers: the sine power function Psi_s t and the cosine power function Psi_c t.