This article describes a method for the active control of the deformations on a magnetically levitated moving-magnet planar motor. The planar motor under consideration is comprised of a stator on a double coil array configuration and a mover with permanent magnets, and it is designed to perform positioning tasks with nanometer level of accuracy. Due to the spatially asymmetric, nonuniform force distribution on the magnet plate, mechanical deformations are induced to the mover, which can severely hinder the desired positioning accuracy. The proposed method overcomes this challenge by properly shaping the force distribution on the moving magnet plate, which is enabled by the presence of multiple coils interacting with the mover, corresponding to an “overactuation” scheme. As a consequence, the independent control of elementary deformation shapes (modes) is achieved. The proposed overactuation scheme is experimentally validated on a planar motor prototype, proving the efficiency of the proposed method during both standstill and motion.

A mesh-free semi-analytical Fourier-based method is presented to evaluate the frequency-dependent losses in the windings of solid-state transformers (SSTs) with foil-wound transformers. In the employed diffusion equation, which accounts for induced eddy currents, the imposed current density and conductivity in the transformer window area are represented using spatial Fourier series and method of images. As a result, induced current density distribution in foil conductors and ac loss in medium frequency transformers (MFTs) is calculated using the semi-analytical method. The proposed method is verified using the finite element method (FEM). It is observed that with the considered approach one can estimate the ac winding loss in the frequency range of 5–25 kHz, with 2.7% maximum absolute error and approximately 2.5 times less number of degrees-of-freedom compared to FEM computations.

Purpose: The purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions. Using the developed method, power losses and parasitic forces that result from eddy current distributions can be computed.Design/methodology/approach: In conducting regions, the Fourier-based solutions are developed to include a spatially dependent conductivity in the expressions of electromagnetic quantities. To validate the method, it is applied to an electromagnetic configuration and the results are compared to finite element results.Findings: The method shows good agreement with the finite element method for a large range of frequencies. The convergence of the presented model is analyzed.Research limitations/implications: Because of the Fourier series basis of the solution, the results depend on the considered number of harmonics. When conducting structures are small with respect to the spatial period, the number of harmonics has to be relatively large.Practical implications: Because of the general form of the solutions, the technique can be applied to a wide range of electromagnetic configurations to predict, e.g. eddy current losses in magnets or wireless energy transfer systems. By adaptation of the conductivity function in conducting regions, eddy current distributions in structures containing holes or slit patterns can be obtained.Originality/value: With the presented technique, eddy currents in conducting structures of finite dimensions can be modeled. The semi-analytical model is for a relatively low number of harmonics computationally faster than 3D finite element methods. The method has been validated and shown to be computationally accurate.

This paper concerns the semi-analytical modeling of parasitic eddy current distributions and forces in electromagnetic devices. The harmonic, Fourier-based, model is extended to incorporate a position-dependent conductivity, and restrictions on the induced current density are added to model eddy currents in non-connected conducting elements. To model time-dependent behavior of eddy currents, multiple time harmonics can be incorporated in the solutions. The developed method is verified using the finite-element method for a wide range of frequencies. The model is applied to a coreless linear motor with electrically conducting cooling plates, and the parasitic force is analyzed.

This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification.

The paper describes a 3D semi-analytical harmonic modeling technique that is capable of modeling eddy current distributions in segmented conducting structures, such as slitted conducting plates, and the associated magnetic fields. The spatially varying conductivity of a conducting region is incorporated into the solutions of magnetic-field quantities and the induced current density. The harmonic model is compared to results obtained with finite element analysis. An experimental setup is used to measure the field distribution above differently slitted conducting plates, in which eddy currents are induced by a coil. The measurement results are compared to simulation results, and the perturbations are analyzed.