Isomorphic Relationships between Voltage-Source and Current-Source Converters

Graph isomorphism phenomenon has been identified since the 1930s, which was first addressed in the graph-theoretical field and was thoroughly studied as a critical topic of computer science. In many research disciplines, isomorphism theory and dual principles are identified as powerful tools in the study of related subjects. However, during the development of power converters, only dual principles have been adopted, such as in the study of the relationships between voltage-source converter (VSC) and current-source converter (CSC), while the isomorphic relationship between them was never discovered. This, indeed, limits the understanding of the relationships among converter topologies. In this letter, such isomorphic relationships are first revealed in the power converter field. Several topologies are discovered as isomorphic pairs, and the modulation isomorphism between single-phase N-level VSC and N-phase CSC (N = 3) is also demonstrated. The experimental results verify that the physical meaning of direct pulsewidth modulation for CSC is the modulation process of the dc-side voltage of three-phase CSC, as its isomorphic pair shows. With the aid of isomorphic transformation, the existing knowledge of VSCs can be directly transformed into corresponding CSCs to deal with problems where dual principle has difficulties, which provides another opportunity for the innovation of power converters.