Apparent power place in the instantaneous power of a linear quadripole with a sinusoidal current

Purpose. Justification of the fallacy of using the concept of “apparent power” for quadripole circuits in alternating sinusoidal current circuits on the basis of the instantaneous power balance. Methodology. The apparent power in electric power is a generalizing value of energy processes that researchers use provided that other power components are determined. Based on the analysis of known studies, some were found, in which the authors question such a role in apparent parent. The well-known provisions of the electrical engineering theory are used with the application of mathematical methods, in particular trigonometry, the Euler transformation and the complex numbers theory to determine the instantaneous power components of sinusoidal current and voltage. Findings. The instantaneous power components of sinusoidal current and voltage are analytically determined in trigonometric and complex form. The corresponding vectors are represented graphically on complex planes of zero and doubled frequency. Accordingly, it is indicated which components of the instantaneous power correspond to the apparent power; in addition, the phase shifts of the latter on the corresponding complex planes are determined. For an elementary electrical circuit, they are defined for all elements of the circuit provided that the balance of instantaneous power (Tellejen’s theorem), active power, reactive power (Boucherot’s theorem) is observed. Originality. It has been proven that the order of determining the active power as the difference between the maximum value of the instantaneous power and apparent power determined by the effective values of voltage and current in sinusoidal current circuits cannot be accepted as general. Using the example of a sinusoidal current an elementary electrical circuit, it was found that for an element of electric energy transmission, the amplitude of power fluctuations, which in certain cases is called “apparent power” in general, can be less than the instantaneous power average value - active power. Practical value. The obtained results can be used to improve the power component compensation algorithms for series and parallel power active filters.