Systematic Coupling of Multiple Magnetic Field Systems and Circuits Using Finite Element and Modified Nodal Analyses

Existing circuit-field coupling schemes can deal with a single magnetic field model connected to an external circuit. However, modern electrical systems are a complex interconnection of multiple magnetic devices, which opens up the question of how to consider multiple interacting field models. In this paper, we propose a scheme based on the finite element and modified nodal analyses, to solve the problem of coupling multiple magnetic field systems with circuit networks. The proposed methodology is systematic since each element within the electrically connected problem has a building block, which is easily inserted into the global system of equations. This applies to any magnetic field system, where massive and filamentary conductors are equally accommodated. Hence, each electrical network component can be modeled with any desired level of detail: as a magnetic system (distributed parameter model) or as a circuit (lumped parameter model). To show the flexibility and power of the proposed methodology, the finite-element models of a three-phase induction motor and a transformer are electrically interconnected through circuits that represent an infinite bus bar and a short transmission line.