The p-q theory for active filter control: some problems and solutions

The instantaneous active and reactive power theory or the p-q Theory is widely used to design controllers for active filters. This paper deals with some problems due to the misinterpretations of this theory. A historical background of the theory is presented and the problem caused by distorted voltages at the point of common connection (PCC) is analyzed. In addition, the appearance of source current harmonic component not present in the load current (hidden current) caused by different filtering characteristics for the calculation of the oscillating real and imaginary power components is discussed. The problem caused by the voltage distortion can be solved using a phase locked loop (PLL) circuit. For the hidden current, filters with similar characteristics can avoid them. These analysis and solutions are presented to clarify some aspects of the p-q Theory not clear in the original approach of the theory.