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This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.

As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.

The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

This paper aims to elaborate the method and algorithm for the analysis of the influence of temperature on back electromotive force (BEMF) waveforms in a line start permanent magnet synchronous motor (LSPMSM).

The paper presents a finite element analysis of temperature influence on BEMF and back electromotive coefficient in a LSPMSM. In this paper, a two-dimensional field model of coupled electromagnetic and thermal phenomena in the LSPMSM was presented. The influence of temperature on magnetic properties of the permanent magnets as well as on electric and thermal properties of the materials has been taken into account. Simulation results have been compared to measurements. The selected results have been presented and discussed.

The simulations results are compared with measurements to confirm the adequacy of this approach to the analysis of coupled electromagnetic-thermal problems.

The paper offers appropriate author’s software for the transient and steady-state analysis of coupled electromagnetic and thermal problems in LSPMS motor.

This paper presents a comparative study of different stator-segmentation topologies of a permanent magnet synchronous machine (PMSM) used in traction drives and their effect on iron losses. Using stator segmentation allows one to achieve more significant copper fill factors, resulting in increased power densities and efficiencies. The segmentation of the stators creates additional air gaps and changes the soft magnetic material’s material properties due to the cut edge effect. The aim of this paper is to present an in-depth analysis of the influence of stator segmentation on iron losses. The main goal was to compare various segmentation methods under equal excitation conditions in terms of their influence on iron loss.

A transient finite element method analysis combined with an extended iron-loss model was used to evaluate discussed effects on the stator’s iron losses. The workflow to obtain a homogenized airgap length accounting for cut edge effects was established.

The paper concludes that the segmentation in most cases slightly decreases the iron losses in the stator because of the overall reduced magnetic flux density B due to the additional air gaps in the magnetic circuit. An increase of the individual components, as well as total power loss, was observed in the Pole Chain segmentation design. In general, segmentation did not change the total iron losses significantly. However, different segmentation methods resulted in the different distortion of the magnetic field and, consequently, in different iron loss compositions. The analysed segmentation methods exhibited different iron loss behaviour with respect to the operation points of the machine. The final finding is that analysed stator segmentations had a negligible influence on the total iron loss. Therefore, applying segmentation is an adequate measure to improve PMSMs as it enables, e.g. increase of the winding fill factor or simplifying the assembly processes, etc.

The influence of stator segmentation on iron losses was analysed. An in-depth evaluation was performed to determine how the discussed changes influence the individual iron loss components. A workflow was developed to achieve a computationally cheap homogenized model.

The purpose of this paper is to execute the efficiency analysis of the selected metaheuristic algorithms (MAs) based on the investigation of analytical functions and investigation optimization processes for permanent magnet motor.

A comparative performance analysis was conducted for selected MAs. Optimization calculations were performed for as follows: genetic algorithm (GA), particle swarm optimization algorithm (PSO), bat algorithm, cuckoo search algorithm (CS) and only best individual algorithm (OBI). All of the optimization algorithms were developed as computer scripts. Next, all optimization procedures were applied to search the optimal of the line-start permanent magnet synchronous by the use of the multi-objective objective function.

The research results show, that the best statistical efficiency (mean objective function and standard deviation [SD]) is obtained for PSO and CS algorithms. While the best results for several runs are obtained for PSO and GA. The type of the optimization algorithm should be selected taking into account the duration of the single optimization process. In the case of time-consuming processes, algorithms with low SD should be used.

The new proposed simple nondeterministic algorithm can be also applied for simple optimization calculations. On the basis of the presented simulation results, it is possible to determine the quality of the compared MAs.

A precise numerical simulation environment for transformer models can be challenging due to the hysteretic core behavior. Assuming linear material laws ensures efficient and straightforward solution schemes in the time domain, which, in contrast, do not incorporate saturation effects, inrush phenomena or hysteresis losses. The purpose of this paper is a time-stepping algorithm for a topologically correct lumped-element three-phase transformer model, including nonlinearities and hysteresis in the transformer’s core.

The general methodology is to set up a quasi-linear differential algebraic equation system of the transformer model based on modified nodal analysis, which is subsequently solvable using a variable step size backward differentiation formula of second order. The core sections are represented by an energy-based dry friction-like hysteresis model. The connection between the magnetic and electric domain is enabled by Hopkinson’s analogy. The presented time-stepping algorithm can be implemented straightforwardly in a numerical environment.

The time-stepping algorithm converges to high accuracy in a few iterations and yields the transient response of the three-phase transformer model. A comparison to inrush measurements demonstrates the algorithm’s practicability and additionally validates the transformer model.

The differential algebraic equation system of the lumped-element transformer model incorporates an energy-based dry friction-like hysteresis model. The solution scheme is a second-order backward differentiation formula to solve the hysteretic system in the time domain.

The purpose of this paper is to present a methodology for calculating eddy current losses in the core of a single-phase power voltage transformer, which, unlike a standard power transformer, has an open-type core (I-type core). In those apparatus, reduction of core losses is achieved by using a multipart open-type core that is created by merging a larger number of leaner cores.

3D FEM approach for calculation of eddy current losses in open-type cores based on a weak AλA formulation is presented. Method in which redundant degrees of freedom are eliminated is shown. This enables faster convergence of the simulation. The results are benchmarked using simulations with standard AVA formulation.

Results using weak AλA formulation with elimination of redundant degrees of freedom are in agreement with both simulation using only weak AλA formulation and with simulation based on AVA formulation.

The presented methodology is valid in linear cases, whereas the nonlinear case will be part of future work.

Presented procedure can be used for the optimization when designing the open-type core of apparatus like power voltage transformers.

The presented method is specifically adapted for calculating eddy currents in the open-type core. The method is based on a weak formulation for the magnetic vector potential A and the current vector potential λ, incorporating numerical homogenization and a straightforward elimination of redundant degrees of freedom, resulting in faster convergence of the simulation.

The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty.

A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied.

Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM.

The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

Small highly saturated interior permanent magnet- synchronous machines (IPMSMs) show a very nonlinear behaviour. Such machines are mostly controlled with a closed-loop cascade control, which is based on a d-q two-axis dynamic model with constant concentrated parameters to calculate the control parameters. This paper aims to present the identification of a complete current- and rotor position-dependent d-q dynamic model, which is derived by using a finite element method (FEM) simulation. The machine’s constant parameters are determined for an operation on the maximum torque per ampere (MTPA) curve. The obtained MTPA control performance was evaluated on the complete FEM-based nonlinear d-q model.

A FEM model was used to determine the nonlinear properties of the complete d-q dynamic model of the IPMSM. Furthermore, a fitting procedure based on the nonlinear MTPA curve is proposed to determine adequate constant parameters for MTPA operation of the IPMSM.

The current-dependent d-q dynamic model of the machine models the relevant dynamic behaviour of the complete current- and rotor position-dependent FEM-based d-q dynamic model. The most adequate control response was achieved while using the constant parameters fitted to the nonlinear MTPA curve by using the proposed method.

The effect on the motor’s steady-state and dynamic behaviour of differently complex d-q dynamic models was evaluated. A workflow to obtain constant set of parameters for the decoupled operation in the MTPA region was developed and their effect on the control response was analysed.