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New definition formulas for apparent power and active current of three-phase power system DOI:10.15199/48.2019.08.20

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The power theory of electrical systems has been evolving continuously for more than a century, beginning with the works of Steinmetz [1]. A significant milestone in this direction was the introduction by Professor S. Fryze of active current concept [2,3]. This concept served as a main theoretical basis for constructing active and passive filtering devices [4]. With the development of the elemental base of power semiconductor devices and signal processors, the control strategies of active filters developed in the direction of ensuring minimal power losses, unity power factor and maximum efficiency [5-9]. These strategies were based on new provisions of the theory of power, concerning the decomposition of currents and powers with giving physical meaning to the individual components. A critical review of these theoretical positions, carried out in [5-10] and many others, suggests that the main component of the current decomposition is the active current in the Fryze form, and the sum of the squares of the power components is the square of the apparent power using the Buchholz formula as product of rms values of line currents and line-to-neutral voltages. The independence of the Fryze's active current and Buchholz's apparent power from the ratio of cable resistances is doubtful that it is correct for four-wire systems (Fig. 1) with non-zero neutral current. The determination of the apparent power of a three-phase power supply system considers the limitations at which the active power is maximized, as an allowable value of the power losses caused by the flow of consumed currents [10]. This value is proportional to the square of the rms value of the consumed line currents, which appear in the Buchholz apparent power formula, only in a three-wire power system with identical values of the active resistances of the line wires. Especially this difference is manifested in a three-phase four-wire power system, where the active resista[...]

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