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This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models.

Determine the discrete integral operator of periodic functions and develop an iterative algorithm determining steady-state solutions by a multiplication of matrices only.

An alternative method to creating finite-difference relations directly determining steady-state solutions in the time domain.

Reduction of software and hardware requirements for determining steady-states of electromagnetic.

A unified approach for directly finding steady-state solutions for ordinary nonlinear differential equations presented in the normal form.

Eliminate the necessity of solving high-order finite-difference equations for steady-state analysis of electromagnetic devices described by circuit models.

To review and discuss recently proposed homogenization methods for laminated magnetic cores and multi‐turn windings in FE models of electromagnetic devices.

The frequency‐domain homogenization is based on the adoption of complex and frequency‐dependent material characteristics (e.g. reluctivity) in the homogenized domain. The value of the complex quantity is obtained analytically or by means of a simple 2D FE model. The time‐domain counterpart requires the introduction of additional unknowns and equation.

The homogenization methods allow to take into account the global eddy current effect in the individual laminations and wires, with a reasonable precision and computational cost.

The homogenization methods have been validated numerically, i.e. by comparison with brute‐force FE computations where the eddy current effects are directly and accurately taken into account. Experimental validation should follow.

The analogy between the homogenization of laminated cores and windings has been evidenced.

The purpose of this paper is to present a constructive algorithm to design multilayer perceptron neural networks used as approximation models of electromagnetic devices.

The proposed procedure allows automatic determination of both the number of neurons and the synaptic weights of networks with a single hidden layer. The approximation model is used in design optimization problems. The inputs of the neural network correspond to the design parameters whereas the output corresponds to the objective function of the optimization problem. The neural model is then inverted in order to determine which input is associated to a prefixed output.

The performance of the algorithm has been tested on analytical function and on the TEAM workshop problem 25.

As the reliability of the optimum solution is strongly affected by the accuracy of the neural approximation model, the approximation error is kept as low as possible, especially in the maximum/minimum points.

This paper deals with the two‐dimensional finite element analysis in the frequency domain of saturated electromagnetic devices coupled to electrical circuits comprising nonlinear resistive and inductive components. The resulting system of nonlinear algebraic equations is solved straightforwardly by means of the Newton‐Raphson method. As an application example we consider a three‐phase transformer feeding a nonlinear RL load through a six‐pulse diode rectifier. The harmonic balance results are compared to those obtained with time‐stepping and the computational cost is briefly discussed.

The purpose of this paper is to propose to simulate an arbitrary movement in electromagnetic problems by means of a 3D nonconforming finite volume method (NC-FVM). The moving part can be displaced according to the x, y and/or z direction.

The 3D nonconforming mesh technique coupled to the FVM is used to handle arbitrary displacement of moving parts. Accordingly, the whole problem domain is divided into two parts: moving part and fixed part. Both parts are meshed independently. By using a suitable connection between both fixed and moved meshes, the movement can be performed according to the three axes.

The TEAM Workshop Problem No. 23 is used to test the proposed method. The calculated values of the magnetic force applied to the permanent magnet for different positions of the magnet show the efficiency of the proposed method.

This paper introduces the NC-FVM to solve electromagnetic problems which contain moving parts. Here, the movement can be performed according to the three axes.

This paper aims to introduce the decomposed harmonic balance finite element method (HBFEM) to decrease the memory requirement in large‐scale computation of the DC‐biasing magnetic field. Harmonic analysis of the flux density and flux distribution was carried out to investigate the DC biased problem in a laminated core model (LCM).

Based on the DC bias test on a LCM, the decomposed HBFEM is applied to accurately calculate the DC‐biasing magnetic field. External electric circuits are coupled with the magnetic field in the harmonic domain. The reluctivity matrix is decomposed and the block Gauss‐Seidel algorithm solves each harmonic solution of magnetic field and exciting current sequentially.

The calculated exciting currents and flux density are compared with that obtained from measurement and time domain finite element analysis, respectively, which demonstrates consistency. The DC bias leads to the significant saturation of the magnetic core and serious distortion of the exciting current. The flux density varies nonlinearly with DC bias excitation.

The harmonic balance method is only applicable in solving the steady state magnetic field. Future improvements in the method are necessary in order to manage the hysteresis effects in magnetic material.

The proposed method to solve the DC biased problem significantly reduces the memory requirement compared to the conventional HBFEM. The decomposed harmonic balance equations are solved efficiently by the block Gauss‐Seidel algorithm combined with the relaxation iterative scheme. An investigation on DC bias phenomena is carried out through the harmonic solution of the magnetic field. The decomposed HBFEM can also be applied to solve 3‐D DC‐biasing magnetic field and eddy current nonlinear problems in a practical power transformer.

Designers of electrical machines need a clear understanding of the mechanism of noise generation, in order to be able to reduce the noises which are produced under the influence of forces due to the magnetic field. The purpose of this paper is to develop a new approach to give a best estimation of these forces.

A model is developed to calculate the distribution of local forces using the virtual work principle in finite element context including ferromagnetic hysteresis. The forces are calculated using a formulation based on the energy derivation. The nonlinear behaviour of ferromagnetic material is considered by combining a Jiles‐Atherton model and finite element method through the fixed‐point iterative technique.

The effects of accurate behaviour of magnetic material are not always taken into account when calculating the local forces in electromagnetic devices. The introduction of hysteresis phenomenon in the analysed device gives a good prediction of magnetic induction. The expression used to compute the force includes an integral which is estimated numerically and not a constant term.

The developed approach is more accurate than the classical methods using constant magnetic permeability or a first magnetization curve.

The paper aims to estimate the thermal impact of temperature dependency of material characteristics on induction machines, for which a coupled electromagnetic thermal analysis is carried out.

Both electromagnetic and thermal fields are calculated using a weak coupled finite element analysis algorithm. The electromagnetic behavior of the induction motor is obtained by coupling the field equations to the voltage equations of the windings. The nonlinearity due to the saturation of the iron core and the temperature dependency of the electrical conductivity are taken into account. When the heat sources are evaluated the temperature distribution in the induction motor is obtained. In order to improve the accuracy of the formulation, thermal contact resistances, external and internal convection are considered.

The results presented in this paper prove that the temperature dependency of electric material characteristics must be considered, to accurately simulate the behavior of the induction motors during the design stage.

The presented field‐circuit coupling completes the two‐dimensional finite element analysis by introducing the possibility to take into account the three‐dimensional part of the motor (R_tête, L_tête). Another advantage is the ability to include voltage sources. Consequently, a realistic approach for the electromagnetic and thermal behavior of the electrical machine is achieved.

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.

This paper aims to report the modelling and simulation work that predicts the behaviours of both a Josephson junction (JJ) and a dc superconducting quantum interference device (SQUID). It is pertinent to predict the SQUID magnetometers’ behaviours via simulations, before subjecting them to real experiments because they are quite expensive to acquire, and can be easily damaged during test analysis.

To achieve this, power simulation (PSIM) was used to model and simulate a JJ, using the basic equation that describes the effective current through it. A dc SQUID magnetometer, which is composed of two JJs, was then modelled and simulated using the modelled JJ. Thermal noise simulation is also included, to observe its effects on the magnetometer’s output. A directly coupled flux-locked loop circuit was later included in the simulation to amplify and linearise the SQUID’s output, which is usually sinusoidal.

When steady bias currents were applied to the JJ, the resulting voltage across it was seen to oscillate. The JJ’s and SQUID’s voltage–current characteristics, and voltage–flux characteristics were also observed in the simulations, and the results respectively agree with the behaviours of a typical JJ and dc SQUID magnetometer.

A way of simulating SQUIDs, without a superconducting simulation tool, is presented. The work provides a much simpler way of studying the behaviour of dc SQUID magnetometers, due to the easy accessibility and fast simulation capability of the software used, with an added advantage of being able to simulate the thermal noise effects, without having to import this facility from secondary software.