Vector Hysteresis Model Research Articles

Iron Loss and Temperature Rise Analysis of a Transformer Core Considering Vector Magnetic Hysteresis Characteristics under Direct Current Bias.

Direct current (DC) bias induced by the DC transmission and geomagnetically induced current is a critical factor in the abnormal operation of electrical equipment and is widely used in the field of power transmission and distribution system state evaluation. As the main affected component, the vector magnetization state of a transformer core under DC bias has rarely been studied, resulting in inaccurate transformer operation state estimations. In this paper, a dynamic vector hysteresis model that considers the impact of rotating and DC-biased fields is introduced into the numerical analysis to simulate the distribution of magnetic properties, iron loss and temperature of the transformer core model and a physical 110 kV single-phase autotransformer core. The maximum values of B, H and iron loss exist at the corners and T-joint of the core under rotating and DC-biased fields. The corresponding maximum value of the temperature increase is found in the main core limb area. The temperature rise of the 110 kV transformer core under various DC-biased conditions is measured and compared with the FEM (Finite Element Method) results of the proposed model and the model solely based on the magnetization curve B||H. The calculation error of the temperature rise obtained by the improved model is approximately 3.76-15.73% and is much less than the model solely based on magnetization curve B||H (approximately 50.71-66.92%).

Revisiting the dry friction-like magnetic vector hysteresis model

Physically correct simulations of magnetic devices require precise and energy-consistent hysteresis models. Electrical steel sheets of, e.g., power transformers or rotating machines represent one crucial element in such a simulation since the hysteresis is revealed uni- and multi-axial, and the steel sheets may have anisotropy. A dedicated vector hysteresis model based on dry friction-like pinning is revisited and derived in terms of thermodynamic state equations in a theoretical manner. The model is then linked to an incremental energy minimization procedure used in elasto-plasticity theory. A numerically efficient two-dimensional solution scheme of the hysteresis model is extended to the three-dimensional case. Rotational losses are also in the scope of this paper since the model cannot describe this loss type by nature. Therefore, numerical adaptations are discussed to account for vanishing rotational losses in saturation.

Incorporation of a 3-D Energy-Based Vector Hysteresis Model Into the Finite Element Method Using a Reduced Scalar Potential Formulation

Incorporation of a 3-D Energy-Based Vector Hysteresis Model Into the Finite Element Method Using a Reduced Scalar Potential Formulation

An Improved Vector Hysteresis Model Incorporating the Effect of DC-Biased Field and its Application to FEM Analysis of Three-Limb Transformer Core

An Improved Vector Hysteresis Model Incorporating the Effect of DC-Biased Field and its Application to FEM Analysis of Three-Limb Transformer Core

Magnetic hysteresis model using chained plays

A magnetic vector hysteresis model is presented using play hysterons as building blocks. The main difference compared to earlier play based magnetic hysteresis models is that instead of forming a superposition of plays with different coercivities, this work uses a set of identical plays which are connected in a chain so that the output of one play acts as input to the next. Like models using a superposition, this yields far more complex minor loop behavior than a single play is capable of. Comparisons are made with measurements on a nonoriented electric steel for BH curves and alternating and rotational losses, showing satisfactory agreement. The approach is found to have both advantages and disadvantages compared to models using superpositions of plays. The problem of determining model parameters becomes simpler and the model can be reversed so either magnetic field or magnetization may be used as known variable. On the other hand, there is no apparent connection to underlying physical processes.

Analysis of the convergence of Newton method by finite element simulation with vector hysteresis stop model

PurposeThe goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects. Incorporating the vector hysteresis model in the magnetic vector potential formulation has encountered difficulties. One of the reasons is that the Newton method is very sensitive regarding the starting point and states distinct requirements for the nonlinear function in terms of monotony and smoothness. The other reason is that the differential reluctivity tensor of the material model is discontinuous due to the properties of the stop operators. In this work, line search methods to overcome these difficulties are discussed.Design/methodology/approachTo stabilize the Newton iteration, line search methods are studied. The first method computes an error-oriented search direction. The second method is based on the Wolfe-Powell rule using the Armijo condition and curvature condition.FindingsIn this paper, the differentiation of the vector stop model, used to evaluate the Jacobian matrix, is studied. Different methods are applied for this nonlinear problem to ensure reliable and stable finite element simulations with consideration of vector hysteresis effects.Originality/valueIn this paper, two different line search Newton methods are applied to solve the magnetic field problems with consideration of vector hysteresis effects and ensure a stable convergence successfully. A comparison of these two methods in terms of robustness and efficiency is presented.

A Novel Modeling Technique via Coupled Magnetic Equivalent Circuit With Vector Hysteresis Characteristics of Laminated Steels

This paper proposes a method to include the anisotropic hysteresis characteristics of soft-magnetic laminated steels in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the nonlinearity of the anisotropic magnetic hysteresis, including the dynamic classical eddy-current and excess fields. The developed MEC model is coupled with both the single-valued <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H$</tex-math></inline-formula> curve (SVC) in magnetostatic and the dynamic vector hysteresis model (VHM) in transient analysis. Results with a single elementary MEC element show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between the magnetic flux densities calculated by the VHM and SVC at 50 and 200 Hz excitation frequencies. Moreover, the proposed modeling technique is verified experimentally using the laminated transformer core of TEAM problem 32. The induced voltage calculated by the MEC model with the VHM demonstrates a good agreement with the measurements, while the MEC model with the SVC calculates inaccurate voltage waveforms. Lastly, the total iron loss dissipated in the transformer's iron core is investigated to verify the proposed technique under different excitation levels and frequencies up to 500 Hz. It is observed that the proposed MEC model with the vector hysteresis characteristics of laminated steels is able to calculate the iron loss accurately, while the conventional single-valued curve method fails to estimate the iron loss.

The 3-D vector hysteresis model of SMC materials based on the SAE and play operator

The hysteresis modeling of ferromagnetic materials in electrical equipment is one of the basic theoretical studies in the field of electrical engineering. In this paper, a 3-D vector hysteresis model is proposed based on Stacked Auto-Encoder (SAE) model and hysteresis operator space theory. Multiple 3-D vector Play hysteresis operators are used to construct an hysteresis operator space to create the high-dimensional operator data. By the operator space, the nonlinear hysteresis relationship in the hysteresis data is transformed into a nonlinear mapping between the operator data and the output of the model. And the SAE model is used to characterize this nonlinear mapping. In the training of the SAE model, training set is composed of operator data and magnetic field strength data. The structure of the vector hysteresis model is determined by taking the output of the operator space as the input of the SAE model. The simulation results show that the model can effectively describe the nonlinear characteristics and anisotropic of the Soft Magnetic Composite under 3-D vector excitation. In addition, this model has certain generalization ability.

Research on the inverse vector hysteresis model with the deep learning parameter identification algorithm

The construction of the vector hysteresis model is significant for the electromagnetic characteristics analysis of electrical equipment. With a deep learning parameter identification algorithm, this paper presents a modeling method of the inverse vector hysteresis model. The vector Everett function is obtained by the alternating hysteresis data. In order to reduce the error of the vector Everett function, the anisotropy compensation coefficient is introduced into the model structure. Based on the white-box model theory, the Stacked Auto-Encoder (SAE) model is used to identify the relevant parameters of the inverse vector hysteresis model. And the parameters of the phase angle compensation function are calculated by the magnetic loss data to further improve the magnetic loss calculation accuracy of the vector model. Compared with the experimental data of rotating magnetization, the fitting result proves the accuracy of the model in a wide range. In addition, the validity of the model is verified by calculating the dynamic magnetic loss.

Computation of rotational hysteresis losses by vector Preisach models based on rotational operators

PurposeA major purpose of vector hysteresis models lies in the prediction of power losses under rotating magnetic fields. The well-known vector Preisach model by Mayergoyz has been shown to well predict such power losses at low amplitudes of the applied field. However, in its original form, it fails to predict the reduction of rotational power losses at high fields. In recent years, two variants of a novel vector Preisach model based on rotational operators have been published and investigated with respect to general accuracy and performance. This paper aims to examine the capabilities of the named vector Preisach models in terms of rotational hysteresis loss calculations.Design/methodology/approachIn a first step, both variants of the novel rotational operator-based vector Preisach model are tested with respect to their overall capability to prescribe rotational hysteresis losses. Hereby, the direct influence of the model-specific parameters onto the computable losses is investigated. Afterward, it is researched whether there exists an optimized set of parameters for these models that allows the matching of measured rotational hysteresis losses.FindingsThe theoretical investigations on the influence of the model-specific parameters onto the computable rotational hysteresis losses showed that such losses can be predicted in general and that a variation of these parameters allows to adapt the simulated loss curves in both shape and amplitude. Furthermore, an optimized parameter set for the prediction of the named losses could be retrieved by direct matching of simulated and measured loss curves.Originality/valueEven though the practical applicability and the efficiency of the novel vector Preisach model based on rotational operators has been proven in previous publications, its capabilities to predict rotational hysteresis losses has not been researched so far. This publication does not only show the general possibility to compute such losses with help of the named vector Preisach models but also in addition provides a routine to derive an optimized parameter set, which allows an accurate modeling of actually measured loss curves.

An anisotropic vector hysteresis model of ferromagnetic behavior under alternating and rotational magnetic field

Vector quantities and tensorial properties rule the magnetization mechanisms in ferromagnetic materials. Every ferromagnetic material is anisotropic to some degree in its magnetic response, so this anisotropy has to be considered for a general model. In this study, a multiscale approach based on a statistical description of the magnetic domain distribution and the knowledge of the crystallographic texture is used to predict the anhysteretic behavior along an arbitrary space direction. Combined with the vector Bergqvist dry-friction hysteresis model, qualitatively reliable simulation results are obtained under alternating and rotational magnetization. FeSi 3% grain-oriented (FeSi GO) electrical steel is chosen as study material: FeSi GO are widespread so that extensive data are available and strongly anisotropic, forcing the model toward the “worst-case” scenario from the viewpoint of anisotropy.Moreover, under high excitation of rotational magnetization, losses drop due to the disappearance of the magnetic domains. This behavior is represented correctly by the proposed simulation method. In such conditions, the magnetization behavior is led mainly by the anhysteretic behavior, strengthening the predictive ability of the proposed model. In this manuscript, comparisons between simulations and measurements under many amplitudes of alternating and rotational magnetization for different levels of imposed excitation or magnetization are provided and used to validate the simulation method.

A Modified Inverse Vector Hysteresis Model for Nonoriented Electrical Steels Considering Anisotropy for FEA

This paper presents a modified Mayergoyz-based vector hysteresis model to describe the anisotropic material behavior of nonoriented (NO) steels over a wide range of rotational excitations. The proposed model adopts a new representation of a vector Everett function, which is actually an elliptical interpolation motivated by the real anisotropic behavior of NO steel, to deal with the uniaxial anisotropy characteristic, which is especially pronounced at low induction levels. The biaxial anisotropy occurring at high densities is described by a nonlinear coefficient, which is actually a function of the magnitude of magnetic flux density. A systematic identification algorithm is given in detail. The validity of this model is verified through comparison with experimental data under both alternating and rotational excitations. The 2-D finite element analysis (FEA) of incorporating this model into TEAM problem 32 simulation is also illustrated.

Anisotropic Congruency-Based Vector Hysteresis Model Applied to Non-Oriented Laminated Steels

A new approach is proposed to model the hysteretic behavior of magnetic materials in 2-D electromagnetic analyses. A scalar congruency-based hysteresis model is developed using the first-order reversal curves (FORCs) and verified by comparing the model results with quasi-static measurements. An anisotropic scalar model is obtained from two scalar hysteresis models using FORCs measured parallel and perpendicular to the material rolling direction. The established anisotropic scalar model is employed as the main building block to determine the vector hysteresis model based on the Mayergoyz vector hysteresis generalization. The obtained vector hysteresis model is coupled with a finite-element solver to analyze the three-limbed transformer core investigated in the TEAM problem number 32. The comparison between the simulation results and experimental data confirms the accuracy of the proposed model with an rms flux density error of less than 0.07 T.

Finite element method for optimal transformer connection based on induction motor characteristics analysis

The Voltage Sags (VSs) may cause irrecoverable impacts on the sensitive loads, such as moving into plugging mode and high pulsations of the torque. So, the various effects of VSs on these loads should be studied, considering all conditions. The non–linear performance of the transformer causes the calculation of VS problem to be complicated. Therefore, a robustness approach should be chosen to solve the problem. In this paper, a novel classification of VS is carried out by using the non–linear solver of the transient Finite Element Method (FEM). In the proposed method, the non–linear behavior of the iron core of the transformer applied using the Jiles–Atherton (JA) vector hysteresis model to increase the precision of the results. To obtain a comprehensive classification, different connections of transformer windings as well as various types of short circuits are considered, and the influence of these classes on the Induction Motor (IM) performance is rendered. To show the accuracy of the proposed method, the VS results of other methods and FEM are compared with IEC standard data by introducing an evaluation metric. The comparison outcomes verified the effectiveness of the proposed method, as the average of errors obtained 4.9%, which is lower than other approaches. Furthermore, an IM is considered to characterize its speed and torque variations. Based on the IM speed deterioration, the best–to–worst connections of the transformer windings are appointed. Finally, the simulation results demonstrate that under single phase SC, when the primary connection of the transformer is Star or grounded Star, the deterioration of speed is lower than others, which are related to the first to third classes. In essence, the key obtained result is that the results of VS calculations with FEM could be a proper database, because of its ability in solving the non-linear problems with minimum errors.

Three-Dimensional Magnetic Hysteresis Modeling Based on Vector Hysteresis Operator

Based on the minimum energy principle of magnetization stable state, this paper presents a definition of three-dimensional (3-D) hysteresis operator by analyzing the magnetization state of the magnetic particles. The direction determination rule of magnetization is given in detail. The critical surface equation of the hysteresis operator is described in the space sphere coordinate system according to the modeling principle of the hybrid vector hysteresis model. The magnetization process of the hysteresis operator is studied under the alternating and rotational magnetic field, respectively. Moreover, a 3-D isotropic hysteresis model is initiatively established, and the hysteresis properties of soft magnetic composite (SMC) material are simulated and compared with the experimental results. This study lays a foundation to build the 3-D hybrid vector hysteresis model and simulate the 3-D magnetic properties.

Finite-element/boundary-element transient modelling of hysteresis motors

This paper presents a transient study of hysteresis motor based on the proposed hybrid method of finite element method- boundary element method (FEM-BEM) in which the Jiles-Atherton (J-A) vector hysteresis model of the hard-magnetic material of the rotor is incorporated. The air–gap region is modeled by BEM in order to avoid the discontinuity in the FEM equations due to J-A hysteresis model and the rotor movement and, therefore, the eddy current effect is taken into account in the rotor part, for the first time. To the best of the author’s knowledge, the prior time-dependent numerical models have ignored the torque component caused by eddy currents in the rotor of hysteresis motor, due to difficulty in rotating the mesh in the rotor region and the related convergence problems. The proposed model is employed to study the phenomenon of short period over-excitation in hysteresis motors. A comparison is done between the proposed time-domain model and the frequency-domain finite element model of the hysteresis motor.

An Improved Anisotropic Vector Preisach Model for Nonoriented Electrical Steel Sheet Based on Iron Loss Separation Theory

An improved anisotropic vector Preisach model is proposed in this paper to describe the hysteresis properties of nonoriented (NO) electrical steel sheet (ESS) under 50 Hz rotating magnetic fields. The proposed model consists of three components, static hysteresis component, eddy current component, and excess component, which is based on the iron loss separation theory. The static hysteresis component is constructed by the static vector Preisach model. The proposed model is identified by the measured hysteresis properties under 1 Hz and 50 Hz magnetic fields. Finally, the experimental results prove the effectiveness of the proposed anisotropic vector hysteresis model.

Analysis of vector hysteresis models in comparison to anhysteretic magnetization model

The design of electrical machines and magnetic actuators requires accurate models to represent hysteresis effects in ferromagnetic materials. The magnetic nonlinearity of the iron core is usually considered by an anhysteretic magnetization curve. With this assumption, hysteresis’ effects in the field computation are completely neglected. This paper presents a comparative study of different hysteresis models, particularly Pragmatic Algebraic Model (PAM) and vector stop model, with regard to a vector anhysteretic anisotropic model. The PAM turns out to be an efficient model implemented with one mathematical equation. The multi cells stop model relies on a consistent thermodynamic formulation, whose dissipation corresponds to a dry friction-like element. Both models implement a constitutive relationship, in which the magnetic flux density vector as independent input and magnetic field strength as output. With a rotational single sheet tester (RSST), various tests for a sample of material FeSi24-50A (FeSi) with a silicon proportion of 2.4 wt% can be proceeded under the application of relevant field distribution. The obtained measured data are applied to parameterize and validate the models. Following numerical experiments the results are compared with those obtained by means of an anhysteretic anisotropic model.

Anisotropic Vector Hysteresis Simulation of Soft Magnetic Composite Materials Based on a Hybrid Algorithm of PSO-Powell.

To simulate the anisotropic hysteresis characteristics of soft magnetic composite (SMC) materials accurately, an improved vector hysteresis model was proposed and utilized to adjust the shape of hysteresis curves by introducing two parameters. These two parameters are correlated with the amplitude of the vector Everett function and the projection of magnetic flux density along different directions. An experimental platform was built to measure the two-dimensional (2-D) magnetic properties of the SMC material under rotational magnetizations. The scalar and vector Everett functions were constructed by the measured limiting hysteresis loops. A hybrid optimization strategy based on the particle swarm optimization (PSO) and Powell technique was proposed to identify the parameters of the improved model efficiently and precisely, which significantly improved the local optimization ability of the PSO algorithm. The simulated results strongly agree with the measured ones, and thus the effectiveness of the improved vector model and the parameter identification method proposed in this paper was verified.

Implementation of Vector Hysteresis Model Utilizing Enhanced Neural Network Based on Collaborative Algorithm

A hysteresis model, based on the enhanced neural network with parallel strategy, is put forward for the prediction of the accurate magnetic behavior of electrical steel sheets (ESSs). Aimed at overcoming the drawbacks such as low convergence rate and convenient to trap into local optimum in the conventional back-propagation neural network (BPNN), a novel collaborative BPNN learning algorithm is introduced according to the error back propagation mechanism and particle swarm optimization (PSO). The reasonable selection of the test point set by the uniform design of experiment methodology, has the potential of lowering the measurement cost, together with guaranteeing the accuracy of the hysteresis modeling. A parallel strategy, which is based on the fast Fourier transformation (FFT), is applied for enhancing the train efficiency of BPNNs. The proposed algorithm is applied for the purpose of modeling the vector hysteresis behavior of ESS. Together, the comparison of the measured and predicted results of H-locus and core loss is discussed as well.