PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 87 NR 1/2011 67 Alexandru BITOLEANU, Mihaela POPESCU Faculty for Electromechanical, Environmental and Industrial Informatics Engineering, University of Craiova, Romania How can the IRP p-q theory be applied for active filtering under nonsinusoidal voltage operation? Abstract. This paper presents an analysis of Akagi’s p-q theory for active filtering under nonsinusoidal voltage conditions. It is ascertained that compensating the alternative parts of the instantaneous active and reactive powers leads to a sinusoidal power supply current only under sinusoidal voltage conditions. A modified definition of the active component of the current is proposed for operation under nonsinusoidal voltage conditions and shunt active filter applications. A generic example and the full controlled rectifier-based DC motor drive system are used as case studies. Streszczenie. Artykuł przedstawia analizę teorii p-q Akagi’ego, stosowanej do filtracji aktywnej w warunkach napięć niesinusoidalnych. Stwierdzono, że kompensacja składników oscylacyjnych mocy chwilowych, czynnej i biernej, prowadzi do sinusoidalnego prądu zasilania tylko w warunkach zasilania napięciem sinusoidalnym. Zaproponowano zmodyfikowaną definicję składowej czynnej prądu na potrzeby sterowania równoległego filtru aktywnego pracującego przy niesinusoidalnym napięciu zasilania. Prostownikowy napęd silnika prądu stałego został użyty w artykule jako przykład dla przedstawionej w artykule analizy. (Jak teoria IRP p-q może być użyta do filtracji aktywnej w warunkach niesinusoidalnego napięcia?) Keywords: p-q theory; active current; nonsinusoidal voltage; active filtering. Słowa kluczowe: teoria p-q, prąd aktywny, napięcie niesinusoidalne, filtracja aktywna. Introduction Making evident the components of the current, especially the active one, is an old concern of researchers in straight connection with the need for finding efficient methods for improving power factor. Recent efforts have been concentrated on the development and control of active power filters. Thus, when total compensation is expected, the active filter has to provide the current vector (1) a L F i i i   , where i L and i a are the load current vector and its active component. The development of active filtering techniques has rendered topical the theory of instantaneous complex power. This theory was first introduced, as a unitary concept, by V. Nedelcu [1, 2] and it was developed by other authors who used it for grounding certain active filtering techniques [3]. Thus, the p-q theory of the instantaneous reactive power developed by Akagi and his coauthors [4] provides the mathematical foundations for the active filters control and it is about to become a means of identification and analysis of powers under nonsinusoidal current and/or voltage operation [5, 6, 7]. Many extensions of the original p-q theory have been developed, including the four-wire systems case. On the other hand, the p-q theory developed by Akagi has a lot of deficiencies, especially from physical phenomena point of view. Some conceptual limitations of this theory were pointed out by Willems in [8, 9]. Moreover, Professor L.S. Czarnecki from Louisiana State University has investigated how power phenomena and properties of three-phase systems are described and interpreted by the p-q theory [10, 11]. The argumentation through which Czarnecki disagrees with the p-q theory is principally based on the relativity of the active and reactive character of the currents defined by Akagi and his followers [12]. The Currents’ Physical Components introduced by Czarnecki took as a starting point the Fryze’s, Shepherd’s and Zakikhani’s powers theories in single-phase circuits under nonsinusoidal conditions [13]. The attention was directed on both power phenomena and general methods for improving the power factor. At present, this theory is applied to single and three-phase circuits with unbalanced and harmonic generating loads. It gives the interpretation of physical phenomena that affect the powers under nonsinusoidal and unbalanced conditions and can provide fundamentals for power compensators design. Correct interpretation of p-q theory In order to obviate any ambiguity in current components interpretation, a possible decomposition of the current space-vector takes into account the DC components (P and Q) and the AC components (p ~ and q ~ ) of the instantaneous powers p and q which are revealed in the complex apparent power (s) expression, i.e. (2)   ~ ~ q Q j p P jq p         * i u s 2 3 . Thus, the expression of the current vector becomes (3)       ~ ~ q Q j p P      u u i 2 1 3 2 . Starting from this expression, the active current vector (i a ), the reactive current vector (i r ) and the supplementary useless current vector (i s ) can be defined as follows: (4)   q d a ju u P    2 3 2 u i ; (5)   d q r ju u Q    2 3 2 u i ; (6)       ~ d ~ q ~ q ~ d s q u p u j q u p u      2 1 3 2 u i . As regards the sum of i a , i r and i s moduli, we found that (7)   . Qq Pp q p Q P ~ ~ ~ ~ s r a 2 2 2 2 2 2 2 2 2 2 9 8 1 9 4 u i u i i i           By integrating (7), we get