A Graph and Number Theory Based Description Method and Equivalence Judgment of Power Electronics Topology

In the study of power electronics topology, the existing graph structure description methods cannot comprehensively manifest properties of topologies, leading to difficulties in their equivalence judgment. To address this issue, this paper proposes a novel power electronics topology description method based on the fusion of graph and number theory. First, prime number weights are assigned to represent physical properties, such as components and connections. Then, the fundamental theorem of arithmetic and bijection functions are used to map the topology into a unique, concise and reversible graph form with physical properties. Therefore, power electronics topology equivalence judgment can be conducted straightforwardly based on graph isomorphism. The proposed method effectively simplifies physical topology descriptions and related equivalence judgment. Case studies demonstrate the proposed method's effectiveness.