Equivalent Circuit for Single/Three Phase Magnetic Coupling With Graph Neural Networks

Owing to the high degrees of freedom and mutual interference between components and wiring, circuit design often requires iterative prototyping and simulation. When transforming a circuit into a graph network, circuit components are typically treated as nodes and wirings as edges. However, this conventional approach overlooks the connection for magnetic couplings, which do not involve physical wiring. Therefore, this study presents a novel solution by introducing equivalent circuits for single- and three-phase magnetic circuits. We use graph classification of graph neural networks (GNNs) for evaluation. Replacing magnetic circuits with the proposed equivalent circuits, which represent less than 4% of the total dataset, enhances the average inference accuracy to 98.02%, which is a 0.13% improvement from the previous best accuracy of 97.89%. Since GNN does not have a conservation law that corresponds to Kirchhoff's current conservation law, the accuracy of the asymmetric equivalent circuit deteriorates by 2.31%. Therefore, the aforementioned improvement in inference accuracy is conditional on the equivalent circuit having a symmetrical structure. Moreover, we show that a three-phase magnetic circuit can be solved theoretically by pairing three of the six simultaneous equations that represent an equivalent circuit without magnetic coupling in an asymmetric manner.