Discussion on Instantaneous $p$ – $q$ Strategiesfor Control of Active Filters

Active filters (AFs) compensate harmonic currents demanded by non linear or time variants loads, with the aim to draw sinusoidal currents from the source. Different control strategies for AF have been proposed: among them, p-q theory is the most popular. However, the p-q strategy presents some drawbacks. As already reported in the literature, unexpected harmonic frequencies are generated in the source current as a consequence of such a control strategy. The aim of this paper is to provide, by means of the space vector approach to the p-q theory, analytical expressions that allow to determine the order and the amplitude of the harmonic components in the source current as function of load current or voltage harmonic distortion. By means of these expressions the limits and drawbacks of p-q strategies are quantified and a tool able to quantitatively predict the results of such a control is provided. Simulation results presented in the literature are interpreted according to the proposed expressions; moreover, further simulations are carried out in order to analyze some relevant cases not considered in previous works.