Comparison between Hilbert space based power theory and Traditional power theory

The comparison between Hilbert space based power theory and three other power theories including traditional power theory, instantaneous power theory put forward by Akagi and Fryze power theory are analyzed in this paper. The consistency and difference are indicated in several different aspects: physical meaning, mathematical concept and the derivation of expressions. Analyses shows that traditional power theory can be regarded as a special case of Hilbert space based power theory, in other words, Hilbert space based power theory can be regarded as the generalization of traditional power theory. Fryze power theory is in accordance with Hilbert space based power theory in single-phase nonsinusoidal system, instantaneous power theory is in accordance with Hilbert space based power theory in three- phase symmetrical system without zero-sequence component. The definition of active current in Hilbert space based power theory is different from it in instantaneous power theory in three-phase system.