SINGLE-PHASE PQ THEORY M. Tarafdar. Haque Electrical Engineering Department, Tabriz University, Tabriz, IRAN Phone &Fax.: (98)-(411)-3356025 e-mail:
[email protected]
Abstract-The theory of instantaneous reactive power compensation of single-phase circuits is presented. This theory is a general case of well-known pq theory and it is usable in single-phase as well as three-phase circuits. A new definition of instantaneous active and reactive powers in single-phase circuits that is based on space vector concept is presented, too. Principle of operation is explained using analytical analysis. The validity of presented method and its comparison with original pq theory is studied through simulation results. 1.
INTRODUCTION
After the presentation of original pq theory [ 1, 21 some instantaneous power based theories presented [3-61. The main objectives of these articles were extension of pq theory to three-phase three-wire and/or three-phase fourwire systems considering different utility voltage and/or load current conditions. These conditions include some cases such as imbalance and/or harmonic polluted utility voltage, imbalance and/or harmonic polluted load current and neutral current compensation [7-91. Considering this fact that the pq theory is a three-phase system based theory, it is obvious that all of the researches which are based on this theory, are usable only in threephase systems. This subject results in dependency of reference compensation current in one phase to the current and voltage waveform in other two phases. One of the results of such a dependency is disability of pq theory in generation of sinusoidal current waveforms in the utility side when utility voltages andor load currents are imbalance. This paper presents a new theory, which is named singlephase pq theory, for instantaneous reactive power compensation of single-phase loads. The theory is explained using analytical analysis. It has been shown that the presented theory is a general case of original pq theory. The control circuit is presented and the validity of its operation is studied though simulation results. Using this theory make it possible compensation for instantaneous reactive power in single-phase as well as three-phase systems. In addition, this theory has the ability of generation of sinusoidal current waveform in the utility side in imbalance utility voltage and/or load current cases which is a progress compared with original pq theory.
Single Phase Load Fig. 1. A single-phase utility and its load
Using the instantaneous space vectors concept, it is possible represent v(t) in space vector form as follows:
Where, v?) stands for instantaneous space vector v(t) and the notations of Y , p(t), Vr ( t ) and &(z) stand for the amplitude, angular position, real part and imaginary part of vij) ,respectively.
Using the same concept for i(t) results in following equation: .
Where, io) stands for instantaneous space vector presentation of i(t) and the notations I , y(f), I r ( f ) and Zi(t) stand for the amplitude, variable angular position, real
i6)
part and imaginary part of , respectively. acspace vestors which are Defining the v'
