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This paper aims to propose the use of isogeometric analysis (IGA) for the simulation of electrical machines to represent their geometries exactly and obtain numerical solutions of high accuracy and regularity.

IGA makes use of non-uniform rational b-splines to parametrise the domain and approximate the solution spaces. Dealing with the different stator and rotor topologies, the computational domain is split into two non-overlapping parts on which Maxwell’s equations are solved independently and are interconnected by a classical Schwarz domain decomposition scheme. The results are compared with the conventional polynomial finite element method (FEM).

The new methodology is reliable and efficient. The obtained solutions of the fields are in good agreement with the ones obtained by the FEM approach. IGA offers a better accuracy than FEM.

The application of IGA combined with domain decomposition to the model of an electric machine is a new and original contribution.

The purpose of this paper is to show that constructing magnetic equivalent circuits (MECs) for simulating accelerator magnets is possible by defining a three-port magnetic element for modelling the T-shape field distribution, where the flux leaves the yoke and enters the aperture.

A linear three-port magnetic element is extracted from an analytical field solution and can be represented by a number of two-port elements. Its nonlinear counterpart is obtained as a combination of the corresponding nonlinear two-port elements. An improved nonlinear three-port element is developed on the basis of an embedded nonlinear one-dimensional finite element model.

The T-shaped field distribution comes together with a complicated interplay between the saturation of the ferromagnetic yoke parts and flux leaking to the aperture. This is more accurately modelled by the improved nonlinear three-port magnetic element.

MECs have a limited validity range, especially for configurations where a high saturation level and fringing flux effects coexist.

The results of the paper appeal to be careful with applying nonlinear MECs for simulating bending magnets.

A new nonlinear three-port magnetic element for ferromagnetic yoke parts with T-shaped flux distribution has been developed.

The purpose of this paper is to present the applicability of data-driven solvers to computationally demanding three-dimensional problems and their practical usability when using real-world measurement data.

Instead of using a hard-coded phenomenological material model within the solver, the data-driven computing approach reformulates the boundary value problem such that the field solution is directly computed on raw measurement data. The data-driven formulation results in a double minimization problem based on Lagrange multipliers, where the sought solution must conform to Maxwell’s equations while at the same time being as close as possible to the available measurement data. The data-driven solver is applied to a three-dimensional model of a direct current electromagnet.

Numerical results for data sets of increasing cardinality verify that the data-driven solver recovers the conventional solution. Additionally, the practical usability of the solver is shown by using real-world measurement data. This work concludes that the data-driven magnetostatic finite element solver is applicable to computationally demanding three-dimensional problems, as well as in cases where a prescribed material model is not available.

Although the mathematical derivation of the data-driven problem is well presented in the referenced papers, the application to computationally demanding real-world problems, including real measurement data and its rigorous discussion, is missing. The presented work closes this gap and shows the applicability of data-driven solvers to challenging, real-world test cases.

The purpose of this paper is to offer a fast and reliable discretisation scheme for computing the electromagnetic fields inside a ferromagnetic cylinder, accounting for motional eddy currents under high velocities and accounting for the severe ferromagnetic saturation of the rotor surface.

A nonlinear spectral‐element (SE) formulation is developed and compared to existing analytical and finite‐element approaches.

The proposed SE method results in a higher accuracy, allows for smaller models, avoids upwinding and needs less computation time. Disadvantages are the dense system matrix and the bad condition number.

The SE approach is only developed and tested for 2D models with a single cylindrical domain.

The results of the paper may improve the design and optimisation of solid‐rotor induction machines and magnetic bearings.

The paper offers an appropriate solution for a computational problem, which already has been encountered by a large community of researchers and engineers dealing with high‐speed rotating devices.

To provide a reliable numerical technique for the time integration of the electromagnetic models with sinusoidal excitation.

The numerical integration of an electrotechnical problem is commonly carried out using adaptive time stepping. For one particular selected time step, Runge‐Kutta (RK) adaptive integration methods deliver two approximations to the solution with different order of approximation. The difference between both is used to estimate the local error.

Standard error‐controlled RK time integration fails for electromagnetic problems with sinusoidal excitation when the adaptive time step selection relies upon the comparison of a main solution and an embedded solution where the difference of orders is one. This problem is overcome when the embedded solution differs by two orders of approximations. Such embedded solution is efficiently constructed by putting appropriate order conditions on the coefficients of the Butcher table.

Using the technique proposed in the paper, electromagnetic problems with sinusoidal dynamics can also be effectively tackled.

The purpose of this paper is to offer a simulation method for predicting the impedance of machine windings at higher frequencies.

A transmission‐line model (TLM) is developed based on parameters calculated on the basis of electroquasistatic and magnetoquasistatic finite‐element (FE) model of the winding cross‐section.

The FE formulations for the low‐ and high‐frequency limits give acceptable results for the respective frequency ranges. An eddy‐current formulation is only accurate on a broader region when the FE mesh is sufficiently fine to resolve the skin depth.

The paper is restricted to frequency‐domain simulations.

The results of the paper improve the understanding of higher‐frequency parasitic effects in electrical drives with long windings.

The paper shows the limitations of the FE methods used for determining the parameters of the TLMs and remedies to avoid these.

To propose an air‐gap element for electrical machine simulation which accounts for static and dynamic rotor eccentricity.

The air‐gap element technique is extended to account for a non‐centered rotor. The consistency, stability and convergence of the discretisation error are studied. A specialized efficient solution technique combining the conjugate gradient algorithm with fast Fourier transforms is developed.

The eccentric air‐gap technique offers better discretisation properties than the classical techniques based on remeshing. Thanks to the specialized solver, the computation times remain comparable.

The introduction of eccentricity in the air‐gap element used for finite element electrical machine simulation is a new development.

To propose trigonometric interpolation in combination with both sliding‐surface and moving‐band techniques for modelling rotation in finite‐element electrical machine models. To show that trigonometric interpolation is at least as accurate and efficient as standard stator‐rotor coupling schemes.

Trigonometric interpolation is explained concisely and put in a historical perspective. Characteristic drawbacks of trigonometric interpolation are alleviated one by one. A comparison with the more common locked‐step linear‐interpolation and mortar‐element approaches is carried out.

Trigonometric interpolation offers a higher accuracy and therefore can outperform standard stator‐rotor coupling techniques when equipped with an appropriate iterative solver incorporating Fast Fourier Transforms to reduce the higher computational cost.

The synthetic interpretation of trigonometric interpolation as a spectral‐element approach in the machine's air gap, the efficient iterative solver combining conjugate gradients with Fast Fourier Transforms. The unified application to both sliding‐surface and moving‐band techniques.