###### Abstract  
This paper deals with the quasi-instantaneous determination of an apparent-, active-, and reactive (i.e., blind and distortion) power mean values, including total power factor, total harmonic distortion, and phase shift of fundamentals of power electronic system (PES) using the \(p\)-\(q\) method. The power components' mean values are investigated both during transients and steady states. Using an integral calculus over one period and the moving average method (or digital filtering), the power components' mean values can be determined within the next calculation step directly from phase current and voltage quantities. Consequently, with known values of a phase shift of fundamentals (using Fourier analysis), the power factor can be evaluated. The results of this study show how a distortion power component during transients is generated even under harmonic supplying and linear resistive-inductive load. The paper contains a theoretical base, modeling, and simulation for the 5-, 3-, and 2-phases of PES transients. A system compensated by switched capacitors as well as an active power filter shows a possibility to compensate for distortion and reactive power components in the next calculation step. Worked-out results can be used for the right determination and sizing of any PES. The presented approach brings the detailed time-waveform and improved quality of electrical quantities (time-waveforms), and through quasi-instantaneous (single step) response time of compensation, minimizes nascent overvoltage of the system. AC system; apparent power; active power; blind power; distortion power; Clarke transform; instantaneous reactive power theory (\(p\)-\(q\)); power component mean value; 5-, 3- and 2-phase connection; power electronic system (PES); total harmonic distortion; modeling and simulation; PAF active filter; blind and distortion power components compensation +
Footnote †: journal: Applied  
In an AC power network, the electric power features basically by apparent, active, blind, and distortion components [4; 5; 6; 7; 8], whereas only the active power component is of physical importance. The active-, blind-, and distortion power give together an apparent power That is maximally transferred from the source to the load and whose size must be taken into account in the design. While active power is possible relatively easy to determine and measure, the measurement of blind and/or distortion power is associated with some difficulties, and the'sinusoidal' wattmeter (power meter) of conventional design cannot be used for this [5]. In general, by substituting rotating phasors of instantaneous time waveforms of voltages and currents in complex plain, the active power is presented by the scalar product of voltage and current phasors and the blind power by the vector product of them. By using this calculus, the knowledge of phase displacement between phasors is needed. Related to this, similarly, is the determination of the value of the performance power factor. A new origin idea of instantaneous determination reactive power is presented by [PERSON] et al. in [7; 8] for a three-phase system. They use a Clarke transform with an \(\alpha\),\(\beta\),0-orthogonal coordination system with the invariant power conversion constant. There are also investigated 3-phase systems with the non-linear load as in [8; 9]. Adverse effects of such systems as blind and distorted power components are possible to compensate using active power filters, whether three-phase or single-phase [9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. The above-mentioned literature [1; 1; 1; 12; 13; 14; 15; 16; 17; 18] mostly presented methods for an instantaneous calculation of power components as a function of time in steady- and transient states. On the other hand, one often needs to determine an average value of apparent, active, blind, and distorted power components.