On Cognate Multiport Converters through Graphbased Generalized Duality

Featured with a more complicated configuration, the modelling, analysis, and derivation of multiport converters (MPCs) requires much more effort than conventional two-port converters. The duality principles from circuit theory and graph theory can serve well as a powerful tool to deal with these challenges. However, a fundamental property of duality has been missing in the power electronics community for over 40 years, i.e., different dual MPC topologies can come from the same original MPC, even for those with planar circuits. And this indeed limits our understanding of the MPCs. To fill this gap, the missing theoretical foundations are provided in this work, forming the generalized duality principles for systematic modelling, analysis, and derivations of MPCs. The theoretical foundations are firstly presented through advanced concepts in graph theory. Then, extensive MPCs are selected as examples to validate the feasibility of this theory. It is shown that a 3-port non-isolated MPC can have 8 different duals (for MPCs with more ports, this number will go even higher) and these duals are related to each other by common electrical relationships. Therefore, their modelling, analysis, and operation design can be achieved in a systematic way.