Simulation Of Electrical Machines Research Articles

First Approach on a Mixed Domain Decomposition Method for 2-D Magnetostatic Simulation of Electrical Machines

A mixed domain decomposition method (DDM) is presented in this article. This method falls within the needs of advanced numerical optimization of electrical machines. Thus, we aim to adapt the LATIN method to the magnetostatic equations, as it has been so far mainly used for mechanical studies. The method provides a powerful iterative scheme that relies on mixed writing of the equations on the domain interfaces, including both primal and dual fields. The method is presented in detail in this article, and its performances are evaluated on a first implementation for the simulation of Team Problem No. 24.

Torque Computation With the Isogeometric Mortar Method for the Simulation of Electric Machines

In this work isogeometric mortaring is used for the simulation of a six pole permanent magnet synchronous machine. Isogeometric mortaring is especially well suited for the efficient computation of rotating electric machines as it allows for an exact geometry representation for arbitrary rotation angles without the need of remeshing. The appropriate B-spline spaces needed for the solution of Maxwell's equations and the corresponding mortar spaces are introduced. Unlike in classical finite element methods their construction is straightforward in the isogeometric case. The torque in the machine is computed using two different methods, i.e., Arkkio's method and by using the Lagrange multipliers from the mortaring.

Nonlinear parametric simulation by proper generalized decomposition on the example of a synchronous machine

PurposeThe accurate simulation of electrical machines involves a large number of degrees of freedom. Particularly, if additional parameters such as remanence variations or different operating points have to be analyzed, the computational effort increases fast, known as the “curse of dimensionality.” The purpose of this study is to cope with this effort with the parametric proper generalized decomposition (PGD) as a model order reduction (MOR) technique. It is combined with the discrete empirical interpolation method (DEIM) and adapted to study characteristic electrical machine parameters.Design/methodology/approachThe PGD is an a priori MOR technique. The technique is adapted to incorporate several additional parameters, such as the current excitation or permanent magnet remanence, to overcome the increasing computational effort of parametric studies. Further, it is combined with the DEIM to approximate the nonlinearity of the flux guiding material.FindingsThe parametric version of the PGD in combination with the DEIM is a suitable numerical approach to reduce computational effort of parametric studies, while considering nonlinear materials. The computational reduction is related to the influence of the different parameter variations on the field and on the number of parameters.Originality/valueThe extension of the PGD by several parameters associated with parametric studies of electrical machines enables to cope with the “curse of dimensionality.” The parametric PGD and the standard PGD–DEIM have been individually used to study different problems. The combination of both techniques, the parametric PGD and the DEIM, for nonlinear parametric studies of electrical machines represents the scientific contribution of this research.

Study of magnetic force excitations in salient pole synchronous generators considering geometrical modifications by conformal mapping

The simulation of electrical machines at the first design stage requires efficient methods to characterize among other properties its vibrational behavior. Particularly when considering both designed and parasitic geometrical modifications, magnetic circuit calculations of large-dimensioned machines by finite-element methods (FEM) are cumbersome. Semi-analytical approaches by means of conformal mapping are therefore useful to estimate the impact of several effects, such as asymmetric stator laminations, rotor pole shapes and air gap imperfections. No-load operation is studied and the presented approach is validated by FEM simulations. The aim of this work is to study force excitations by the magnetic air gap field in salient multi-pole synchronous generators deviating from ideal and symmetrical geometrical conditions by using conformal maps.

Analysis of methods and approaches of the electromagnetic calculation of induction machines regarding their use to solve multiphysical problems

PurposeFor the electromagnetic simulation of electrical machines, models with different ranges of values, levels of detail and accuracies are used. In this paper, numerical and two analytical models of an induction machine (IM) are analysed with respect to these aspects. The purpose of the paper is to use these analyses to discuss the suitability of the models for the simulation of various physical quantities of an IM.Design/methodology/approachAn exemplary IM is simulated using the two-dimensional numerical finite element method, an analytical harmonic wave model (HWM) and an extended HWM. The simulation results are analyzed among themselves in terms of their level of detail and accuracy. Furthermore, the results of operating map simulations are compared with measured operating maps of the exemplary machine, and the accuracy of the simulation approaches is discussed in the context of measurement deviations and uncertainties.FindingsThe difference in the accuracy of the machine models depends on the physical quantity of interest. Therefore, the choice of the simulation method depends on the nature of the problem and the expected range of results. For modeling global machine quantities, such as mean torque or losses, analytical methods such as the HWM s are sufficient in many applications because the simulation results are within the range of measurement accuracy of current measurement systems. Analytical methods are also suitable for local flux density curves under certain conditions. However, for the simulation of the influence of local physical effects on the machine behavior and of temporally highly resolved quantities in saturated operating points, the accuracy of the analytical models decreases and the use of the finite element method becomes necessary.Originality/valueIn this paper, an extension of the HWM is used to calculate the IM, which, in contrast to the HWM, models the saturation. Furthermore, the simulation results of the different electromagnetic IM models are put into the context of the uncertainty of a measurement of several identical IMs.

Simulation of iron losses in induction machines using an iron loss model for rotating magnetization loci in no electrical steel

PurposeVarious iron loss models can be used for the simulation of electrical machines. In particular, the effect of rotating magnetic flux density at certain geometric locations in a machine is often neglected by conventional iron loss models. The purpose of this paper is to compare the adapted IEM loss model for rotational magnetization that is developed within the context of this work with other existing models in the framework of a finite element simulation of an exemplary induction machine.Design/methodology/approachIn this paper, an adapted IEM loss model for rotational magnetization, developed within the context of the paper, is implemented in a finite element method simulation and used to calculate the iron losses of an exemplary induction machine. The resulting iron losses are compared with the iron losses simulated using three other already existing iron loss models that do not consider the effects of rotational flux densities. The used iron loss models are the modified Bertotti model, the IEM-5 parameter model and a dynamic core loss model. For the analysis, different operating points and different locations within the machine are examined, leading to the analysis of different shapes and amplitudes of the flux density curves.FindingsThe modified Bertotti model, the IEM-5 parameter model and the dynamic core loss model underestimate the hysteresis and excess losses in locations of rotational magnetizations and low-flux densities, while they overestimate the losses for rotational magnetization and high-flux densities. The error is reduced by the adapted IEM loss model for rotational magnetization. Furthermore, it is shown that the dynamic core loss model results in significant higher hysteresis losses for magnetizations with a high amount of harmonics.Originality/valueThe simulation results show that the adapted IEM loss model for rotational magnetization provides very similar results to existing iron loss models in the case of unidirectional magnetization. Furthermore, it is able to reproduce the effects of rotational flux densities on iron losses within a machine simulation.

Modeling anisotropic magnetic hysteresis properties with vector stop model by using finite element method

PurposeThis paper aims to use a history-dependent vector stop hysteresis model incorporated into a two dimensional finite elements (FE) simulation environment to solve the magnetic field problems in electrical machines. The vector stop hysteresis model is valid for representing the anisotropic magnetization characteristics of electrical steel sheets. Comparisons of the simulated results with measurements show that the model is well appropriate for the simulation of electrical machines with alternating, rotating and harmonic magnetic flux densities.Design/methodology/approachThe anisotropy of the permeability of an electrical steel sheet can be represented by integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model. The parameters of the vector stop hysteresis model were identified by minimizing the errors between the simulated results and measurements. In this paper, a damped Newton method is applied to solve the nonlinear problem, which ensures a robust convergence of the finite elements simulation with vector stop hysteresis model.FindingsAnalyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows the importance to consider the anisotropic and saturation behavior of the material. Comparing the calculated and measured data corroborates the hypothesis that the presented energy-based vector stop hysteresis model is able to represent these magnetic properties appropriately. To ensure a unique way of hysteresis loops during finite elements simulation, the memory of the vector stop hysteresis model from last time step is kept unchanged during the Newton iterations.Originality/valueThe results of this work demonstrates that the presented vector hysteresis stop model allows simulation of vector hysteresis effects of electrical steel sheets in electrical machines with a limited amount of measurements. The essential properties of the electrical steel sheets, such as phase shifts, the anisotropy of magnetizations and the magnetization characteristics by alternating, rotating, harmonic magnetization types, can be accurately represented.

Parallel-in-time simulation of an electrical machine using MGRIT

We apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To resolve the fast-switching excitations, small time steps are needed, such that parallelization in time becomes highly relevant for reducing the simulation time. The MGRIT algorithm is an iterative method that allows calculating multiple time steps simultaneously by using a time-grid hierarchy. It is particularly well suited for introducing time parallelism in the simulation of electrical machines using existing application codes, as MGRIT is a non-intrusive approach that essentially uses the same time integrator as a traditional time-stepping algorithm. However, the key difficulty when using time-stepping routines of existing application codes for the MGRIT algorithm is that the cost of the time integrator on coarse time grids must be less expensive than on the fine grid to allow for speedup over sequential time stepping on the fine grid. To overcome this difficulty, we consider reducing the costs of the coarse-level problems by adding spatial coarsening. We investigate effects of spatial coarsening on MGRIT convergence when applied to two numerical models of an induction machine, one with linear material laws and a full nonlinear model. Parallel results demonstrate significant speedup in the simulation time compared to sequential time stepping, even for moderate numbers of processors.

Low‐cost hardware‐in‐the‐loop for real‐time simulation of electric machines and electric drive

This study aims to present the discrete models and the methodology to implement real-time simulations of electric machines using a low-cost digital signal processor (DSP). The DC machine and the three-phase induction machine are modelled in real-time using a Texas Instruments DSP TMS28379D, where the discrete models are implemented using C language. A minimum time-step of 1 µs can be achieved for the DC machine and 1.5 µs for the inductions machine in the experimental hardware. To validate the described models and show their precision, they are compared with commercial computational models from PSIM®. In addition, closed-loop speed control strategies are applied to the real-time DSP experimental models, showing perfect concordance with the machine theory. For the DC machine, a speed control strategy with an inner current control loop is applied and for the induction machine, a field-oriented control for the speed control. The proposed real-time simulation hardware has a great potential for low-budget research and educational purposes since it can replace a real machine setup for a very low price, with great accuracy, variable parameters and free from risks, such as accidents or equipment damage. Furthermore, it uses cheap hardware with free software and a high-level programing language.

Consideration of ferromagnetic anisotropy in electrical machines built of segmented silicon steel sheets

Electrical steel shows a distinct non-linear and anisotropic behaviour even for non-oriented steel. The flux guidance in electrical machines is realised by ferromagnetic steel sheets, and therefore it is necessary to consider the anisotropy in the simulation to have reliable and accurate results. Due to the fact that the reduction of silicon steel waste in the production process of electrical machines is crucial, and to enhance the material utilisation the segmentation is employed in the construction of electrical machines. The segmentation further allows to enhance the magnetic behaviour of the machine by considering the easy magnetisation axis in the design process. Nowadays, consideration of ferromagnetic anisotropy in the simulation of electrical machines is not accurate. To cope with these inaccuracies, in this contribution, a vectorial anisotropy model based on two-dimensional measurements is employed to the simulation of a segmented electrical machine, which is not state of the art in current machine computation. With the presented methodology, it is possible to simulate and design segmented electrical machines in an accurate fashion taking the ferromagnetic anisotropy into account.

Mathematical Model of a Three-Phase Induction Machine in a Natural abc Reference Frame Utilizing the Method of Numerical Integration of Average Voltages at the Integration Step and Its Application to the Analysis of Electromechanical Systems

Recent advances in the real-time simulation of electric machines are linked with the increase in the operation speed of the numerical models retaining the calculation accuracy. We propose utilizing the method of average voltages at the integration step (AVIS) for the design of a three-phase induction machine’s model in its natural abc reference frame. The method allows for avoiding rotational e.m.f. calculation at every step; in turn, the electromagnetic energy conversion is accounted by the change of flux-linkage. The model is integrated into the object-oriented environment in C++ for designing the computer models of electromechanical systems. The design of the model of an electromechanical system utilizing the proposed approach is explained in an example. The behavior of the numerical models of a three-phase IM has been compared for the set of conventional numerical methods as well as first- and second-order AVIS. It has been demonstrated that both first- and second-order AVIS methods are suitable tools for high-speed applications, namely, AVIS provides higher maximum possible integration step (e.g., first-order AVIS provides 4 times higher than the second-order Runge–Kutta method, and the second-order AVIS provides 2.5 times higher than the first-order method). Therefore, we consider the most preferable order of the AVIS method for the high-speed applications is the second order, while the first order may be a suitable alternative to increase the calculation speed by 30% with the acceptable decrease in the accuracy.

Real-Time HIL Emulation of Faulted Electric Machines Based on Nonlinear MEC Model

In electric machine drive systems, hardware-in-the-loop (HIL) emulation provides accurate testing of actual control system prototypes and protection devices interfaced with the electric machine model on a real-time simulator in a non-destructive environment particularly when faults are studied. A compromise between the model accuracy and computational burden makes the magnetic equivalent circuit (MEC) model ideal for real-time simulation of electric machines. However, satisfying the timing constraints of real-time simulation to accommodate internal machine faults is still challenging due to the nonlinearity and rotation of electric machines. In this paper, the transmission line modeling (TLM) method is utilized to keep the MEC coefficient matrix unchanged during nonlinear iterations. Afterward, for the first time, the entire potential of the TLM method for pre-calculation is exploited by proposing an efficient matrix re-ordering combined with the left-looking Gilbert–Peierls algorithm to minimize the computational burden of the sparse MEC matrix LU decomposition required in each time-step due to rotation. Furthermore, the massive hardware architecture of the field programmable gate array is used as the platform for implementation to fully exploit parallelism. With the proposed MEC-based real-time TLM method, the minimum time-step as low as 500 $\mu \text{s}$ can be achieved and the results validation with two-dimensional finite element model (FEM) of the commercial Jmag-Designer software shows the accuracy and efficiency of the proposed methodology.

On the correlation of crystallographic macro-texture and magnetic magnetization anisotropy in non-oriented electrical steel

Abstract In material models for the finite-element simulation of electrical machines and the preceding magnetic measurements, the magnetic anisotropy of non-grain oriented electrical steel is usually considered in an oversimplified way, if at all. The magnetization behavior between rolling and transverse direction is not linear and varies with magnetic polarization, a relation that comes in addition to the complexity of the effect. In this paper, the magnetization anisotropy of five industrial non-grain oriented electrical steels is measured with a 1-D single-sheet-tester. The results are evaluated and correlated to the crystallographic texture of the studied materials. An approach to model magnetization curves at 50 Hz in arbitrary directions of the sheet plane is presented. The model is parametrized by measured magnetization curves along three different spatial directions and by macro-texture data in form of an orientation distribution function. This approach leads to a model that replicates the crossing of magnetization curves of different orientations with adequate quantitative accuracy for the application in FE magnetic field simulations.

Modelling of a permanent magnet synchronous machine using isogeometric analysis

PurposeThis 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.Design/methodology/approachIGA 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).FindingsThe 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.Originality/valueThe application of IGA combined with domain decomposition to the model of an electric machine is a new and original contribution.

Motion in frequency domain for harmonic balance simulation of electrical machines

PurposeThe high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry.Design/methodology/approachThe high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry.FindingsThe three-phase symmetry reduces the simulated geometry to the sixth part of one pole. The motion transforms to a frequency offset in the angular Fourier series decomposition. The calculation overhead of the Fourier integrals is negligible. The air impedance approximation increases the accuracy and yields a convergence speed of three iterations per decade.Research limitations/implicationsOnly linear materials and two-dimensional geometries are shown for clearness. Researchers are encouraged to adopt recent harmonic balance findings and to evaluate the performance and accuracy of both formulations for larger applications.Practical implicationsThis method offers fast-frequency domain simulations in the optimization process of rotating machines and so an efficient way to treat time-dependent effects such as eddy-currents or voltage-driven coils.Originality/valueThis paper proposes a new, efficient and accurate method to simulate a rotating machine in the frequency domain.

Effect of grain size and magnetic texture on iron-loss components in NO electrical steel at different frequencies

The magnetic properties of non-grain-oriented (NO) electrical steels are a direct product of their inherent material properties in combination with induced changes due to material processing and external operational conditions such as magnetization and frequency. Chemical composition, grain size and texture are elementary intrinsic factors which determine the magnetic properties. Focus of this study is to improve the understanding of grain size and texture as important factors that affect different loss-components. A strong focus is placed on the frequency dependence and concurrent loss component distribution over application relevant frequency ranges of electrical machines. Due to its impact on the eddy current losses as well as the hysteresis components, the final thickness is additional subject of this study. A total of seven materials are produced on an experimental production line from one alloy. By different production and processing steps, different grain structures, textures and final thickness are achieved. The changes in the materials are attributed to the process variations and magnetically characterized. A loss separation procedure as well as loss modeling is performed and discussed. This work is part of a research field which aims to improve parametric models with low additional computational effort for the numerical simulation of electrical machines. The goal is to improve the accuracy of models with a deeper understanding of the material science.

Model‐order nonlinear subspace reduction of electric machines by means of POD and DEI methods for copper losses calculation

AbstractThe simulation of electric machines in order to calculate the copper losses is about a time‐dependent electromagnetic problem. When the finite element method associated with a time stepping scheme is used to solve the problem, the solution is strongly linked to initial conditions, among which the most important is the solution at the initial time. Because it is practically chosen as an arbitrary solution, several time‐consuming electrical excitation periods must be simulated therefore to reach finally the steady‐state conditions. The copper losses can be calculated now without any transient components that can affect the credibility of the copper losses amount. This article suggests a model‐order reduction method that benefits from the complete model finite element solution of the first transient electrical period, to calculate the reduced model solution in the subsequent periods using the proper orthogonal decomposition approach combined with the discrete empirical interpolation method. Nevertheless, in case of relatively high frequency excitation, the full reduction of the problem leads to significant imprecision in the amount of copper losses. To improve the accuracy, therefore, a nonlinear subspace model‐order reduction is adopted. It ensures concurrently higher precision and a reduced computational time.

Parametric Homogenized Model for Inclusion of Eddy Currents and Hysteresis in 2-D Finite-Element Simulation of Electrical Machines

Consideration of a fully coupled lamination model with eddy currents and magnetic hysteresis in standard finite element (FE) models is prohibitively expensive in terms of implementation effort, memory requirements and computation time. Hence this paper utilizes an algebraic approximation of the lamination model as a conventional constitutive relationship in two-dimensional FE simulations of rotating electrical machines. Extraction of model structure and parameters of the parametric model as well as iterative adaption of the homogenized FE characteristic are presented. This pragmatic approach turns out to be quite accurate and efficient simultaneously allowing for refinement of the pre-determined parametric expression by iterating between the fully coupled lamination model and the macroscopic model.

Review of Hardware Platforms for Real-Time Simulation of Electric Machines

This paper presents a review of the research status for real-time simulation of electric machines. The machine models considered are the lumped parameter models, including the phase-domain, $d$ – $q$ , and voltage-behind-reactance models, as well as the physics-based models, including the finite-element method and magnetic equivalent circuit models. These models are initially presented along with their relative advantages and disadvantages with respect to modeling fidelity and their computational intensity. A field-programmable gate array, a graphics processing unit, a chip multiprocessor, and computer clusters are the main hardware platforms for real-time simulations. An overview of such hardware platforms is presented and their comparative performances are evaluated with respect to real-time simulation of electric machines and drives on the basis of simulation acceleration, machine types, and modeling methodology.

Application of Local Fourier Transform to Mathematical Simulation of Synchronous Machines with Valve Excitation Systems

Abstract The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.