# An efficient method for coupling finite-element-based models of electromechanical devices with circuit simulators

#### Abstract

The application of the Finite Element Method (FEM) to the numerical solution of electromagnetic field and force distributions inside electric machinery and transformers requires a priori knowledge of the distribution of current density. This information is typically unavailable when these devices are voltage-fed through external drive circuitry, thus making the coupling of field and circuit equations nontrivial. Methods thus far described in the literature for the solution of coupled field-circuit problems are based on either an indirect coupling approach via a set of lumped circuit parameters, or on a direct coupling methodology wherein the field and circuit equations are solved simultaneously. Direct coupling of field and circuit equations can be accomplished either via winding currents or flux linkages. The flux-linkage-based approach leads to the so-called inverse finite element problem, wherein the field equations are reformulated to accept flux linkages as inputs with currents as outputs. Thus far, all methods proposed in the literature for solving the inverse problem do so by repeatedly solving the forward problem with different values of supply current(s), each such solution being iterative if material nonlinearities exist, thus resulting in a doubly-iterative loop. While both current-based and flux-linkage-based approaches possess superior convergence properties to indirect coupling methods, the current-based approach is more widely used due to the lack of efficient methods for solving the inverse finite element problem. ^ In this thesis, a new approach to the solution of the inverse finite element problem is set forth, which permits the direct evaluation of winding currents from flux linkages, iterating only at a single layer in the presence of nonlinear materials, thus offering a definite computational advantage over previous methods. This approach permits a natural coupling of field equations to circuit equations in state-space form with flux linkages as state variables. In addition to the elimination of an iterative loop, this method produces a state model with superior eigenstructure and improved convergence properties for nonlinear systems compared with existing current-based models. This methodology has been applied to the transient simulation of a switched-reluctance machine, and to a toroidal-core inductor operated under heavy saturation. Results obtained with this method have been validated numerically against commercial FE packages and are in excellent agreement with experimentally measured data.^

#### Degree

Ph.D.

#### Advisors

Oleg Wasynczuk, Purdue University.

#### Subject Area

Engineering, Electronics and Electrical

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