A theoretical investigation of original and modified instantaneous power theory applied to four-wire systems

This paper investigates whether the instantaneous reactive currents calculated by the instantaneous power theories contain all currents which do not contribute to the instantaneous power. In 1962, Depenbrock published a power theory generally valid for N-wire systems. In 1983, independently, Akagi, Kanazawa, and Nabae introduced the original "theory of instantaneous power," valid with few restrictions for N=3. Because of more problems at N=4, Nabae et al. introduced a modified version of the instantaneous power theory in 1995. By a discussion of this modified power theory, Akagi et al. in 1999 showed that, under certain conditions, the modified theory leads to compensation results slightly inferior to those resulting from the original theory. This paper gives the compensation rules based on the older generally valid FBD power theory and analyzes the differences with regard to the other theories.