Nonlinear time-harmonic finite-element analysis of coupled circuits and fields in low frequency electromagnetic devices

Many electromagnetic devices operate under sinusoidal excitation, in which case a time-harmonic (TH) analysis may be applied; in particular, a TH field solution is much more economic than a time-transient field solution. Although the material nonlinearity cannot be strictly taken into account in the TH case, it determines the true operating condition of the device, together with the external circuit connections. In this paper, an efficient finite-element (FE) formulation to solve the 2D TH circuit-field (CF) problem posed by low-frequency (LF) electromagnetic devices is presented, approximately taking into account the effect of the material nonlinearity. Consideration is given to theoretical aspects that had not been previously studied: the resulting nonlinear complex equation does not possess an exact Jacobian, because one of its terms involves a nonanalytic function. This is circumvented by using pseudo-Jacobians derived from the Cauchy–Riemann expressions. Solid and filamentary conductors may be connected to external circuits of arbitrary topology using a novel Modified Nodal Analysis (MNA) approach. Methods for correcting magnetization curves and calculating the electromagnetic force are proposed. An induction motor test case is used to illustrate the capabilities of the formulation, and the numerical results are compared with those of a validated commercial package.