Decomposition of Currents in Three- and Four-Wire Systems

Various methods of instantaneous decomposing of three-phase currents in three- and four-wire systems for the purpose of instantaneous compensation without energy storage are reviewed, analyzed, and compared. It is found that the method of Akagi et al. and other equivalent methods are optimum in the three- and four-wire systems where the neutral current is constrained to be zero after compensation, whereas the more general method of Depenbrock et al. is optimum in the four-wire systems where the neutral current after compensation is not restricted. Furthermore, both methods can be expressed in a simpler equation if the correct "null" voltage reference is used. The equation is shown to be optimum through the mathematical properties of vector space. The orthogonal instantaneous nonactive current components are accordingly identified. The required compensating currents are compared.