p–q power theory: Some theoretical and practical aspects

This paper presents an analysis of Akagi's p–q theory for active filtering under real nonsinusoidal voltage conditions. It is ascertained that compensating the alternative parts of the instantaneous active and reactive powers leads to a sinusoidal power source current only under sinusoidal voltage conditions. The mathematical demonstration is found and it is verified on some practical examples. It is shown that the difference between Akagi's active current and the true active current is very small for operation under real conditions of voltage total harmonic distortion factor below 10%. A modified definition of the active component of the current is proposed for operation under nonsinusoidal voltage conditions. The DC motor and full control rectifier driving system is used as a case study. Finally, a mathematical inconsequence that put under uncertainty the p–q theory correctness under nonsinusoidal voltage conditions is pointed out.