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.