Comparisons Between the p--q and p--q--r Theories in Three-Phase Four-Wire Systems

• Published in: IEEE transactions on power electronics Vol. 24; no. 4; pp. 924 - 933
• Main Authors: Aredes, MaurÍcio, Akagi, Hirofumi, Hirokazu Watanabe, Edson, Vergara Salgado, Eumir, Frizera EncarnaÇÃo, Lucas
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-04-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Active control; Active filters; Applied sciences; Capacitors. Resistors. Filters; Circuit properties; Circuits; Comparative analysis; Control systems; Electric currents; Electric potential; Electric, optical and optoelectronic circuits; Electrical engineering. Electrical power engineering; Electrical machines; Electronic circuits; Electronics; Energy storage; Exact sciences and technology; Filtering theory; Filters; Frequency domain analysis; Frequency filters; Load flow; Mathematical analysis; p-q theory; p-q-r theory; Power harmonic filters; Power system harmonics; Preprocessing; Reactive power; Regulation and control; Strategy; Testing. Reliability. Quality control; Theory; Various equipment and components; Voltage; Voltage control; Performance evaluation; Zero sequence component; p-q theory; Shunt; Control system; Power electronics; p-q-r theory; Voltage control; Load flow; Power filters; Power flow; Flow control; Active filter; Three phase circuit; System simulation; Active filters; System load; Control method; Comparative study; Energy storage
• ISSN: 0885-8993; 1941-0107
• DOI: 10.1109/TPEL.2008.2008187

This paper presents a comparative analysis between results from applications of the p-q and the p-q-r theories in shunt active power filters for three-phase four-wire systems, discussing aspects related to the influence of the system voltage in the control methods that calculate the compensating currents. It is shown that in some cases, a preprocessing of the system voltage is required if the goal is to achieve sinusoidal compensated currents. On the other hand, when the goal is to compensate zero-sequence current, the need of energy storage elements in the active filter is discussed. In this case, if zero-sequence components are present simultaneously in the system voltage and load current, they produce zero-sequence power flow, and the control methods based on both theories must contain additional calculations to allow the elimination of energy storage elements in the active filter. A control strategy based on the p-q theory is proposed to eliminate the neutral current without the need of energy storage elements, with the advantage of avoiding the extra transformation from alphabeta0 to pqr coordinates that is needed in the p-q-r theory. Simulation results are presented for the purpose of comparing the performance of both control methods.