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The purpose of this study is to determine the steady state of an electromagnetic structure using the finite element method (FEM) without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important.

In the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated with the Newton method to accelerate the convergence.

The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient state is very low, it is preferable to use the classical approach, namely, the time-stepping FEM.

The main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources.

In the context of the use of the time-stepping FEM, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and directly gives the steady state.

The proposed approach will permit to model and study the electromagnetic systems in the steady state, and particularly the transformers. Because of the gain in computing time, the use of optimisation techniques will be facilitated.

The novelty of this study is the proposal of the waveform relaxation–Newton method to directly obtain the steady state when applied to the three-phase transformer.

The purpose of this paper is to make a quantitative comparison between induction machine (IM) and interior permanent magnet machine (IPM) for electric vehicle applications, in terms of electromagnetic performance and material cost.

The analysis of IM is based on an analytical method, which has been validated by test. The analysis of IPM is based on finite element analysis. The popular Toyota Prius 2010 IPM is adopted directly, and the IM is designed with the same stator outer diameter and stack length as Prius 2010 IPM for a fair comparison.

The torque capability of IM is lower than IPM for low electric loading and competitive to IPM for high electric loading. The maximum torque/power-speed characteristic of IM is competitive to IPM; while the rated torque/power-speed characteristic of IM is poorer than IPM. The power factor of IM is competitive and even better than IPM for high electric loading in low-speed region. The torque ripple of IM is comparable to IPM for high electric loading and much lower than IPM for low electric loading. The overall efficiency of IM is lower than IPM, and the maximum efficiency of copper squirrel cage IM is approximately 2-3 percent lower than IPM. The material cost of IM is about half of IPM when IM and IPM are designed with the same stator outer diameter and stack length.

The electromagnetic performances and material costs of IM and IPM are quantitatively compared and discussed.

The purpose of this paper is to minimize the optimization parameter number of synchronous reluctance machine (SynRM) and permanent magnet (PM) assisted SynRM, and compare their relative merits with interior permanent magnet (IPM) machine for electric vehicle applications, in terms of electromagnetic performance and material cost.

The analysis of electromagnetic performance is based on finite element analysis, by using software MAXWELL. The genetic algorithm is utilized for optimization.

The rotor design of SynRM can be significantly simplified by imposing some reasonable conditions. The number of rotor design parameters can be reduced to three. The electromagnetic performance of SynRM is much poorer than that of IPM, although the material cost is much cheaper, approximately one-third of IPM. The ferrite-SynRM is competitive and even better than IPM especially for high electric loading, in terms of torque capability, torque-speed characteristic, power factor, threshold speed and efficiency. In addition, ferrite-assisted SynRM has great advantage over IPM in material cost, 55 percent cheaper. The performance of NdFeB-assisted SynRM is close to IPM in terms of torque capability, torque-speed characteristic, power factor, torque ripple and efficiency. The material cost of NdFeB-assisted SynRM is ∼25 percent lower than IPM.

Some conditions, which can simplify the optimization of SynRM rotor, are discussed. The electromagnetic performances and material costs of SynRM, ferrite-assisted, NdFeB-assisted SynRMs and IPM are quantitatively compared and discussed.

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.

Rotor shape optimization is crucial in designing synchronous reluctance machines (SynRMs) because the machine performance is directly proportional to the rotor’s magnetic saliency ratio. The rotor geometry in synchronous reluctance machines is complex, and many geometrical parameters must be optimized. When fluid flux-barrier geometry is desirable, using analytic equations to prepare the rotor geometry for finite element analysis could be tedious. This paper aims to provide a robust numerical procedure to draw the fluid flux-barrier geometry in transversally laminated radial flux inner and outer rotor SynRMs by directly solving the magnetic vector potential equation using the finite difference method..

In this paper, the goal is to have a robust procedure for drawing the rotor geometry for an arbitrary number of slots (Ns), poles (p) and flux-barrier layers (Nfb). Therefore, this paper targeted several combinations to investigate the performance of the proposed algorithm. The MATLAB software is used to implement the proposed algorithm. The ANSYS Maxwell software is used for counterpart finite element simulation to check the correctness of the results derived by the proposed method.

Several inner and outer rotor SynRMs considering a different number of poles and a different number of flux-barrier layers per pole are studied to investigate the performance of the proposed algorithm. Results corresponding to each case are presented, and it is shown that the method is robust, flexible and fast enough, which could be used for the generation of the rotor geometry for the finite element analysis effectively.

The value of the proposed algorithm is its simplicity and straightforwardness in its implementation for the preparation of the rotor geometry with the desired fluid flux-barrier layer curvature resolution suitable for the finite element analysis. The procedure presented in this paper is based on the ideal magnetic loading concept, and in future works, a similar idea could be used for linear and axial flux SynRMs.

The purpose of this paper is performance enhancement of ferrite-assisted synchronous reluctance (FASR) motor using multi-objective differential evolution (MODE) algorithm, considering the significant geometric design parameters.

This work illustrates the optimization of FASR motor using MODE algorithm to enhance the performance of the motor considering barrier angular positions, magnet height, magnet axial length, flux barrier angles of the rotor and air gap length. In the optimization routine to determine the performance parameters, generalized regression neural network-based interpolation is used. The results of MODE are validated with multi-objective particle swarm optimization algorithm and multi-objective genetic algorithm.

The design optimization procedure developed in this work for FASR motor aims at achieving multiple objectives, namely, average torque, torque ripple and efficiency. With multiple objectives, it is essential to give the designer the tradeoff between different objectives so as to arrive at the best design suitable for the application. The results obtained in this work justify the application of the MODE approach for FASR motor to determine the various feasible solutions within the bounds of the design.

Analysis, design and optimization of synchronous reluctance motor has been explored in detail to establish its potential for variable speed applications. In recent years, the focus is toward the electromagnetic design of hybrid configurations such as FASR motor. It is in this preview this work aims to achieve optimal design of FASR motor using multi-objective optimization approach.

The results of this work will supplement and encourage the application of FASR motor as a viable alternate for variable speed drive applications. In addition, the application of MODE to arrive at better design solutions is demonstrated.

The approach presented in this work focuses on obtaining enhanced design of FASR motor considering average torque, torque ripple and efficiency as performance measures. The posteriori analysis of optimization provides an insight into the choice of parameters involved and their effects on the design of FASR motor. The efficacy of the optimization routine is justified in comparison with other multi-objective algorithms.

Classically the magnetic material models are considered with a deterministic approach. Nevertheless, when submitted to the fabrication process, the magnetic core properties are negatively impacted and may be subject to variability during the process. This variability can be of such importance that the performances of the final device (electrical machine) will also present a noticeable variability. The aim of this research is to develop a stochastic model of the magnetic behaviour law of slinky stators used in claw pole generators. The proposed methodology is general and can be applied to other physical properties of electrical devices.

The approach is based on a methodology that uses experimental data and a statistical description of the magnetic properties. To that end, a set of samples issued from the same chain of assembly is considered. The hysteresis model is then developed by accounting for the parameter correlation structure.

It is found that the magnetic hysteresis properties of the studied samples can be modelled by means of statistical tools applied to the parameters of the hysteresis model. The dependency of the parameters can also be accounted for a more accurate modelling.

The paper proposes a statistical approach and a methodology that are applied to the hysteresis modelling accounting for the variability of the magnetic properties. The developed model can be further used in a numerical tool to represent the impact on the performances of electrical devices that are subject to the fabrication process variability.

To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions.

The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions.

Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic.

Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist.

Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time.

Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.

This paper aims to propose a novel direct method for indefinite algebraic linear systems. It is well adapted for sparse linear systems, such as those of two-dimensional (2-D) finite elements problems, especially for coupled systems.

The proposed method is developed on an example of an indefinite symmetric matrix. The algorithm of the method is given next, and a comparison between the numbers of operations required by the method and the Cholesky method is also given. Finally, an application on a magnetostatic problem for classical methods (Gauss and Cholesky) shows the relative efficiency of the proposed method.

The proposed method can be used advantageously for 2-D finite elements in stepping methods without using a block decomposition of matrices.

This method is advantageous for direct linear solving for 2-D problems, but it is not recommended at this time for three-dimensional problems.

The proposed method is the first direct solver for algebraic linear systems proposed since more than a half century. It is not limited for symmetric positive systems such as many of direct and iterative methods.

During the design process of synchronous reluctance motors (SynRMs), one crucial step, after its main dimensioning, is optimizing the rotor geometry for maximum average torque and minimum torque ripple. However, because of the complexity of rotor flux-barrier layers geometry, the number of rotor geometrical parameters is high and this step could be quite complex and time-consuming. To obtain a good performance, one needs a robust algorithm to optimize the rotor geometry. The purpose of this paper is to present a sequential iterative method for rotor shape optimization in SynRMs based on the per-unit rotor model to maximize the average torque and minimize the torque ripple.

In the presented method, at first, rotor geometrical parameters are classified into several groups based on their geometrical similarities, and then optimization is done on these individual groups iteratively. The method starts with an arbitrary feasible rotor geometry and proceeds to optimize it. Because the method’s performance depends on initial rotor geometry, different cases are studied to investigate the convergence and robustness of the method. The MATLAB software is used to implement the optimization algorithm, and the ANSYS Maxwell software is used for the finite element analysis.

The performance of the proposed method is studied on a three-phase 0.75 kW-1,500 rpm permanent magnet assisted SynRM. The results show that the method improves the average torque while reducing the torque ripple. Even if the method starts with an inappropriate initial rotor geometry, it is robust enough and converges within an acceptable number of iterations.

The value of this paper is in introducing a per-unit rotor model. When the authors optimize the rotor geometry for a specific motor rating, it can be scaled up or down for other ratings with little effort. In this work, the number of rotor poles is four and the number of rotor flux-barrier layers per pole is three. Other combinations could be analyzed in future studies.