Dynamic Preisach Model Research Articles

A hybrid Jiles–Atherton and Preisach model of dynamic magnetic hysteresis based on backpropagation neural networks

Ferromagnetic materials are widely used for magnetic cores in electromagnetic devices such as inductors, transformers, generators, and motors. In a magnetic core, as the magnetic field varies with time, core loss is generated due to magnetic hysteresis and eddy currents. For performance analysis and design optimization of electromagnetic devices, it is essential to model the dynamic magnetization processes and associated core losses accurately. This paper proposes a hybrid model of dynamic magnetic hysteresis, which incorporates the effects of both hysteresis and eddy currents, by combining the dynamic Jiles-Atherton and Preisach models based on backpropagation neural networks. This model can accurately reproduce the dynamic hysteresis loops and core losses under different excitations. The numerical simulations are verified by experimental measurements.

Loss Prediction in DC-Biased Magnetic Sheets

Power losses in soft magnetic materials can be solidly assessed by the statistical theory of losses (STLs), which provides physical foundation to the concept of loss separation. The theory is, however, limited to the conventional case of symmetric hysteresis loops and cannot be straightforwardly applied for a magnetic core operating under a dc bias. We show, in this paper, that such constraint can be released by combining the STL with a simplified approach to the dynamic Preisach model. This approach leads to the more affordable static Preisach model with largely reduced computation time. In this way, the hysteresis and excess loss components, with and without dc bias, are identified and calculated starting from a minimum set of experimental data. We provide a wide-ranging experimental validation of the theory, which is applied to the behavior of the energy loss versus frequency, measured up to $f = 1$ kHz, in non-oriented and grain-oriented iron-silicon sheets and in iron-cobalt alloys, subject to different polarization bias levels.

Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads to a nonlinear and multivalued behavior, making their modeling and control difficult. Even though the analysis and mathematical properties of several rate-independent and rate-dependent hysteresis models are known, this is not the case for the Bertotti’s rate-dependent extension of the classical Preisach model; the so-called dynamic Preisach model for which current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics, both being crucial in practice. This paper deals with the description and mathematical analysis of the dynamic Preisach hysteresis model. Toward that end, we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field H and the magnetic induction B, in which, the values of B not only depends on the present values of H but also on the past history and its velocity. We first analyze mathematically some important properties of the model and compare them with known results for the static Preisach model. Then, we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. Under suitable assumptions, we prove the existence of a solution of a weak formulation of the problem and solve it numerically. Finally, we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic Preisach model.

Low-frequency model for single-phase transformers based on the three-component Preisach model considering deep saturation

The transformer model is very important for the transient simulations of power systems. Although a large number of researches have been carried out on the developments and applications of the transformer model, there are still some deficiencies in the study, such as hysteresis and frequency-dependence. This paper proposes an improved transformer model for the calculation of low-frequency transients in power systems. The magnetizing branches are simulated by the composite curves with hysteresis part and deep saturation part. The expression of the inverse static I-Φ Preisach model (ISPM) is derived from the classical Preisach model (CPM). The Preisach distribution function (PDF) is determined by the centered cycles method. Based on the dynamic performance of the grain-oriented electrical steel, the inverse dynamic Preisach model (IDPM) with three components is proposed. The deep saturation inductance can be obtained from the modified AC plus DC test. Then, the modified dual reversible model of the single-phase transformer is developed in ATP-EMTP. At last, the ISPM and IDPM are validated by the comparison of the measured and simulated loops. The steady-state and transient performances of the proposed transformer model are also validated by the comparison of the experiments with simulations including no-load test, DC bias test, and inrush current test.

Prediction of Energy Losses in Soft Magnetic Materials Under Arbitrary Induction Waveforms and DC Bias

The statistical theory of losses (STL) provides a simple and general method for the interpretation and prediction of the energy losses in soft magnetic materials. One basic application consists, for example, in the prediction of the loss under arbitrary induction waveform, starting from data available from conventional measurements performed under sinusoidal flux. There are, however, persisting difficulties in assessing the loss when the induction waveform is affected by a dc bias, because this would require additional experimental data, seldom available to machine designers. In this paper, we overcome this problem applying, with suitable simplifications, the dynamic Preisach model. Here, the parameters of the STL model are obtained exploiting preemptive conventional measurements only. By this new simplified method, analytical expressions for the loss components are obtained under general supply conditions, including dc-biased induction waveforms.

The prediction of iron losses under PWM excitation using the classical Preisach model

Purpose The losses incurred in ferromagnetic materials under PWM excitations must be predicted accurately to optimize the design of modern electrical machines. The purpose of this paper is to employ mathematical hysteresis models (i.e. classical Preisach model) to predict iron losses in electrical steels under PWM excitation without compromising the computational complexity of the model. Design/methodology/approach In this paper, a novel approach based on the dynamic inverse Preisach model is proposed to model the iron losses. The PWM magnetic flux density waveform is decomposed into its harmonic component using Fourier series and a weighted Everett function is computed based on these harmonic components. The Preisach model is applied for the given flux waveform and results are validated against the measurements. Findings The paper predicts the total iron loss by computing a weighted Everett function based on the harmonics present in PWM waveform. Moreover, it formulates the possibility of utilizing the classical Preisach model to predict iron losses under PWM excitation. Research limitations/implications The approach is still limited in terms of its application at high frequencies. This work may eventually lead toward the accurate prediction of iron loss under PWM excitation in electromagnetic machine design. Practical implications The paper provides a simple approach applying the Preisach model for the prediction of iron losses under PWM excitation. The proposed approach does not require additional experimental data beyond B-H loops measured under sinusoidal excitation. Originality/value A novel approach is presented to incorporate the frequency dependence into a static inverse Preisach model. The approach extends the ability of the static Preisach model to compute total iron loss under PWM excitation using a weighted Everett function.

Loss analysis of an asynchronous multiphase motor-generator for avionics applications

This paper aims at analyzing electric motor-generators specifically designed for the avionics application in More Electric Aircraft, where the machine is included inside the main gas turbine. Because of the harsh environment the problem of evaluating and reducing the losses produced in these machin es becomes crucial. For such a purpose, this paper presents an accurate estimate of the magnetic and Joule losses produced inside the machine, when operating as generator in a range of frequencies from 200 Hz up to 400 Hz. Particular attention is paid to the investigation of the effects introduced by the use of a high number (6 and 12) of phases, due to fault tolerance reasons. The analysis is developed on a small (10 kW) prototype, consisting of a four-pole twelve-phase induction machine. The numerical computations are performed through a validated 2-D finite element code, based on a step-by-step procedure and on the sliding mesh technique. A sophisticated laminated dynamic Preisach model, whose parameters are identified from a large set of measurements, provides an accurate estimate of the iron losses and their separation into the three fundamental components also under skin effect regime. The results show that six and twelve phase configurations produce significant loss decrease.

Dynamic Preisach model identification applying FEM and measured BH curve

Purpose – The purpose of this paper is to develop a viscous-type frequency dependent scalar Preisach hysteresis model and to identify the model using measured data and nonlinear numerical field analysis. The hysteresis model must be fast and well applicable in electromagnetic field simulations. Design/methodology/approach – Iron parts of electrical machines are made of non-oriented isotropic ferromagnetic materials. The finite element method (FEM) is usually applied in the numerical field analysis and design of this equipment. The scalar Preisach hysteresis model has been implemented for the simulation of static and dynamic magnetic effects inside the ferromagnetic parts of different electrical equipment. Findings – The comparison between measured and simulated data using a toroidal core shows a good agreement. A modified nonlinear version of TEAM Problem No. 30.a is also shown to test the hysteresis model in the FEM procedure. Originality/value – The dynamic model is an extension of the static one; an extra magnetic field intensity term is added to the output of the static inverse model. This is a viscosity-type dynamic model. The fixed-point method with stable scheme has been realized to take frequency dependent anomalous losses into account in FEM. This scheme can be used efficiently in the frame of any potential formulations of Maxwell's equations.

Broadband Magnetic Losses in Fe-Si and Fe-Co Laminations

We discuss comprehensive broadband (dc-10 kHz) investigations on magnetic losses in Fe-(3 wt%)Si and Fe-Co laminations. In this range of frequencies, the prediction of loss is not easy, because skin effect can be quite important. The theoretical approach generally relies on a dynamic hysteresis model in association with a diffusion equation, but it imposes heavy computational burden. We present here a computationally efficient dynamic hysteresis model based on the dynamic Preisach model (DPM), by which one can achieve fast and precise solution of the diffusion equation considering the hysteretic constitutive equation of the material. This is achieved at a greatly reduced computational cost with respect to the standard DPM. The loss results provided by this simplified model are at all frequencies in a very good agreement with the prediction by the full DPM and with the experiments.

Artificial-Neural-Network-Based Identification of a Modified Dynamic Preisach Model

We have developed an artificial-neural-network-based identification scheme for a modified version of the Preisach model for the hysteresis and relaxation observed in the variation of electrical resistance with strain in conductive polymer nanocomposites. This modeling approach models hysteresis and relaxation as two independent phenomenons. At first, the effects of the relaxation and static hysteresis have been decoupled from the total value of the resistance at different time steps. Unknown parameters in the relaxation model have been identified using a global optimization scheme. Identification of the static hysteresis has been done using an artificial neural network.

A computationally effective dynamic hysteresis model taking into account skin effect in magnetic laminations

We propose a simplified dynamic hysteresis model for the prediction of magnetization behavior of electrical steel up to high frequencies, taking into account the skin effect. This model has the advantage of predicting the hysteresis loop and loss behavior versus frequency with the same accuracy provided by the Dynamic Preisach Model with a largely reduced computational burden. It is here compared to experimental results obtained in Fe-Si laminations under sinusoidal flux up to 2kHz.

Direct recursive identification of the Preisach hysteresis density function

In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.

Identification of Soft Magnetic B-H Characteristics Using Discrete Dynamic Preisach Model and Single Measured Hysteresis Loop

In this paper, the identification of soft magnetic B - H characteristics when using the single measured hysteresis loop and fitting the discrete dynamic Preisach (DDP) model is addressed. The magnetic measurements with primary and secondary windings are performed to obtain the magnetostatic system response. The constrained least-squares estimation of the Preisach density function yields the global solution even for limited hysteresis data. The uncertainties detected during the measurement and computation of B and H values are discussed.

Magnetostochastic resonance under colored noise condition

Stochastic resonance (SR) is an amplification of the system output in correspondence of well-defined finite values of the noise strength that is injected into the system [Gammaitoni et al., Rev. Mod. Phys. 70, 223 (1998), Grigorenko et al., IEEE Trans. Magn. 31, 2491 (1995), Mantegna et al., J. Appl. Phys. 97, 10E519 (2005)]. In order to clarify the influence of a colored noise, in this paper magnetostochastic resonance (MSR) in magnetic systems described by the dynamic Preisach model is numerically investigated in the presence of colored noise. In this paper it is shown that: a) noise spectrum affects MSR; b) white noise, 1/f and 1/f2 noise induce in magnetic systems described by the dynamic Preisach model MSR; c) the maximum level of signal-to-noise (SNR) is obtained by using white noise but 1/f noise presents a range where SNR value is higher than the case of white noise; d) maximum signal amplification is obtained for white noise.

Adaptive Hysteresis Compensation with a Dynamic Hysteresis Model for Control of a Pneumatic Muscle Actuator

This paper proposes a technique for modeling the dynamic behavior of the hysteresis in pneumatic muscle actuators (PMAs) and controlling the motion of PMAs with the hysteresis model. PMAs contract according to the internal pressure level; however, the relationship between the contraction and the internal pressure is subject to hysteresis, and the hysteresis distorts depending on the acting speed of PMAs. To describe such hysteresis, the proposed technique uses the dynamic Preisach model and adaptively tunes the parameters of the model by recursive parameter estimation if the distortion occurs due to speed variations. The hysteresis model with the on-line adjusted parameters was incorporated into a PMA control system as the adaptive hysteresis compensator for the purpose of reducing undesirable effects caused by the hysteresis on the control accuracy. Additionally, as introducing a fast inversion algorithm enabled the real-time calculation of hysteresis compensator outputs, the hysteresis compensator could cope with the reference-input changes while the system was in operation. Experimental results showed that the proposed technique achieved higher tracking performance than the technique developed in our previous work, both for a single PMA and for a parallel manipulator driven by three PMAs.

Noise enhanced stability in magnetic systems

In this paper noise enhanced stability in magnetic systems is studied by both an Ising-type model and a Preisach–Arrhenius model as well as a dynamic Preisach model. It is shown that in one nonequilibrium Ising system noise enhanced stability occurs and that dynamic Preisach model has the capability to predict the occurrence of noise enhanced stability in magnetic systems. On the contrary, in a Preisach–Arrhenius model of a single quadrant magnetic material, noise enhanced stability is not detected.

Modeling the Electromagnetic Behavior of Nanocrystalline Soft Materials

A model that describes the magnetic behavior of nanocrystalline ring cores is useful for simulations of electronic circuits that contain inductors or transformers using these cores. A general but computationally demanding model combines a macroscopic model of the ribbon with a dynamic Preisach hysteresis model. In this paper, we present two models that-taking into account the principle of loss separation-make it possible to avoid the use of the CPU time consuming dynamic Preisach model. Both models compute the waveform of the magnetic flux density for an arbitrary waveform of the magnetic field, or vice versa. The first model uses a macroscopic model based on the plane wave theory and the classical rate-independent Preisach formalism. The macroscopic model operates in the frequency domain and applies the harmonic balance principle. Because of nonlinearity, the model is solved iteratively by a Newton-Raphson scheme. The second model starts from a single evaluation of the classical Preisach model. Additionally, it uses a lookup table that is a function of the flux density and its time derivative to evaluate the classical and excess field to be added. The models are validated by measurements between 2 and 100 kHz on Vitroperm nanocrystalline ring cores.

Identification of parameters of dynamic Preisach model by neural networks

In this paper, an approach that allows to identify the parameters of dynamic Preisach model is presented. The fundamental idea of this method is to identify the parameters of a material by using a neural network trained by a collection of hysteresis curves, whose Preisach model is known. After a brief description of dynamic Preisach Model, the neural network that has been used is introduced. The construction of the training data set is illustrated. Finally, the effectiveness of the method is tested on both numerical as well as experimental data.

Dynamic hysteresis modelling for nano-crystalline cores

This paper presents an artificial neural network approach based on dynamic Preisach model to compute hysteresis loops of nano-crystalline cores. The network has been trained by a Levenberg–Marquardt learning algorithm. The model is fast and does not require tremendous computational efforts. The results obtained by using the proposed model are in good agreement with experimental results.

Magnetic stochastic resonance in systems described by dynamic Preisach model

In this paper, dynamic Preisach model is applied to investigate magnetic stochastic resonance. It is shown that magnetic systems described by dynamic Preisach model presents magnetic stochastic resonance. The resonance in the power amplification disappears if the frequency of the input signal is greater than characteristic frequency of the system introduced by dynamic Preisach model and the resonance in signal to noise ratio is strongly reduced under the same condition. Finally, frequency and phase locking phenomenon is detected under resonance condition.