Generalized vector transform with applications in power electronics

With power electronics entering the saturation side of the technology's S-curve, we cannot expect too many new topologies or circuits. The future development should come mostly from application of new power semiconductor devices or from identification of new application fields. The only way to disrupt the contemporary incremental development consists in analyzing and branching out of the original theories that founded power electronics discipline. This paper develops the mathematical theory of a generalized vector transform able to smooth the progress of new research directions in power electronics by considering any three-phase set of nonsinusoidal waveforms instead of the conventional sinusoidal waveforms. Immediate applications are demonstrated.