Non-sinusoidal Excitation Research Articles

Vibration and Noise Characteristics of Nanocrystalline Cores Under High-Frequency and Non-Sinusoidal Excitation

Vibration and Noise Characteristics of Nanocrystalline Cores Under High-Frequency and Non-Sinusoidal Excitation

Research on loss characteristic of soft magnetic composites under nonsinusoidal excitations with DC bias field

Choosing a suitable core loss model and accurately predicting energy loss are crucial in designing magnetic devices with high efficiency based on soft magnetic composites (SMCs). In this work, FeSiAl and FeSi SMCs with a uniform insulating layer were fabricated by a phosphating process. The effects of excitation waveform and DC bias field on core loss have been investigated in depth. The results show that different remagnetization rates of SMC under ideal sinusoidal and square waves result in different core losses at the same frequency and flux density. The improved general Steinmetz equation and the modified Steinmetz equation were shown to be suitable for calculating core loss under square excitation waves without DC bias field. When the DC bias field is applied, the core loss of FeSiAl and FeSi SMCs was found to increase significantly due to the magnetization state gradually approaching saturation. Interestingly, the variation tendency of core loss can be accurately predicted using the waveform coefficient Steinmetz equation under square excitation conditions with a DC bias environment. This work not only provides deep insights into core loss under different excitation waveforms and DC bias fields but also determines the application scope of different core loss models.

Periodic driving shape controls energy transmission.

In the early 2000s, Geniet and Leon [Phys. Rev. Lett. 89, 134102 (2002)0031-900710.1103/PhysRevLett.89.134102] discovered the nonlinear supratransmission (NST) in a medium with a forbidden frequency band gap. It is a process in which nonlinear structures are created by a sinusoidal harmonic boundary condition imposed at a frequency in the band gap. The present study extends this concept and shows that an optimal shape of a periodic nonsinusoidal excitation may induce (or inhibit) energy flow through the lattice below (or above) the NST threshold, demonstrating that nonlinear supratransmission is reliant not only on the driving amplitude but also on its shape. This is evidenced through numerical simulations and mathematical calculations varying the excitation signal shape in the Fermi-Pasta-Ulam case study. Setting the shape parameter to zero recovers the results of the literature in relation to the sinusoidal signal.

Hysteresis Characteristics Prediction Method of Nanocrystalline and Amorphous Strips Considering Skin Effect and Nonsinusoidal Excitation

Hysteresis Characteristics Prediction Method of Nanocrystalline and Amorphous Strips Considering Skin Effect and Nonsinusoidal Excitation

A core loss estimation method based on improved waveform coefficient Steinmetz equation for asymmetric triangular flux density waveform

Accurate estimation of high frequency magnetic core losses under non-sinusoidal excitations is critical to the design of solid-state transformers. This paper proposes a waveform transformation principle, termed the equal derivative transformation (EDT), for piecewise linear flux density waveforms. Under the same maximum flux density, an asymmetric triangular flux density wave can be transformed into a symmetric one with a different frequency in terms of the calculation of core losses, hence the introduction of the improved waveform coefficient Steinmetz equation (iWcSE). The magnetic characteristics of three different toroidal samples (nanocrystalline alloy FT-3KL, amorphous alloy 1K101, ferrite N87) under square excitation at different duty ratios and certain frequencies are measured. Core losses predicted by the model are in good agreement with the measurement.

A Novel Method for Obtaining can Loss of Canned Permanent Magnet Synchronous Motor Under Non-sinusoidal Excitation

A Novel Method for Obtaining can Loss of Canned Permanent Magnet Synchronous Motor Under Non-sinusoidal Excitation

Influence of compressive stress on the magnetic characteristics of grain-oriented material under non-sinusoidal excitation

Electric machines are subjected to mechanical stress during their operation, which significantly affects the magnetic characteristics of the core material. Furthermore, as the converter topologies evolve, the induced harmonic content increases. The analysis of magnetic properties due to both magnetomechanical effects and harmonics is rarely addressed. This work provides a deeper insight into the core loss behavior by analyzing the impact of mechanical stress on the hysteresis characteristics of magnetic materials subjected to non-sinusoidal excitation. A qualitative analysis based on the measured characteristics is presented to study the material behavior under sinusoidal and non-sinusoidal excitations. An analytical approach based on the Lavers’ formula and loss separation theory is presented.

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

The present work studies the dynamical behavior of the Van der Pol oscillator with sine nonlinearity subjected to the effects of non-sinusoidal excitations through the analysis of bifurcation structures. In this work, the classical Van der Pol oscillator is modified by replacing the linear term with the nonlinear term The idea is to see the impact of the strength of this function on the appearance of chaotic dynamics for small and large values of the nonlinear dissipation term ε. To do this, studies using numerical simulation and analogue simulation are proposed. Firstly, using nonlinear analysis tools, a similarity in the bifurcation sequences is observed despite a difference in the ranks at which the particular behaviours and bifurcation points are obtained. This study is confirmed by their respective maximum Lyapunov exponents. Secondly, a real implementation using microcontroller technology, motivated by the use of an artificial pacemaker, is carried out. For a more practical case, the excitation signal is generated by another microcontroller. The study shows a similarity with the results obtained numerically. Thirdly, in order to show that the model can be derived from mathematical modelling, an electronic simulation using OrCAD-Pspice software is also proposed. The results obtained are in qualitative agreement.

Effect of Grain Size on Magnetic Loss of Nanocrystalline Alloy Under High-Frequency Non-Sinusoidal Excitation

To investigate the effects of internal microstructure and high-frequency non-sinusoidal excitation on the magnetic loss of nanocrystalline alloy, a three-dimensional mesoscopic model based on G. Herzer’s theory of random anisotropy is developed. First, the AC test platform is used to measure the loss value of the nanocrystalline alloy under sinusoidal excitation, and then the model is subjected to the same excitation to obtain its loss value. These values are compared to verify the model’s accuracy. Using the micromagnetic model provided by OOMMF software, we investigate the microscopic effect of grain size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> on the high-frequency magnetic loss <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> of nanocrystalline alloys. Next, we apply non-sinusoidal alternating magnetic fields (square wave, trapezoidal wave, and triangular wave) to the model to explore <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> under non-sinusoidal excitation. The results show that as the grain size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> of the nanocrystalline alloy increases, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> also increases. Additionally, when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> and the frequency <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> are held constant, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> is greatest under triangular wave excitation, followed by trapezoidal wave excitation, and smallest under square wave excitation. This conclusion is due to the fact that the equivalent frequency <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eq</sub> , which contains the rate of change of magnetic flux density (d <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> /d <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> ), can replace <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> in the Original Steinmetz Formula when the excitation source is non-sinusoidal. Our calculations indicate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eq</sub> is smaller under square wave excitation than under triangular wave excitation.

Core loss analysis of soft magnetic composite under non-sinusoidal excitation based on finite element models

Due to the effect of higher harmonics on magnetic properties under actual complex operating conditions, the accurate calculation of core losses of soft magnetic composites (SMC) is complicated. First, this paper improves the existing SMC model by introducing a correction factor to correct the hysteresis loss coefficient so that the model can consider the local variation characteristics of the magnetic density waveform and then calculate the core loss under different harmonic excitation. Then, the influence of skin effect and inhomogeneous flux density within the ring sample model is analyzed. Finally, to validate the improved model, it is compared with other models in the reference based on experimental measurements, respectively. The results show that the core loss calculated by the improved model is closer to the experimental results under different harmonic excitations. In addition, the applicability of the improved SMC model under triangular and square wave excitations is also verified by the derivation of the equations.

Measurement and Simulation of Magnetic Properties of Nanocrystalline Alloys under High-Frequency Pulse Excitation

In order to broaden the application of nanocrystalline soft magnetic materials in electrical engineering under extreme conditions, nanocrystalline alloys must also have good characteristics under high-frequency and nonsinusoidal excitation. In this paper, the magnetic properties of Fe-based nanocrystalline alloys excited by high repetition frequency pulses were measured. Excitation frequency and duty cycles are two important factors in the study of magnetic properties under pulse excitation. With the amplitude of the pulse remaining constant, different local hysteresis curves were obtained by changing the frequency and duty cycle. The experimental results proved that the higher the frequency is and the smaller the duty cycle is, the narrower the local hysteresis loop is. Finally, the finite element method (FEM) was used to model the magnetic core coupling with an impulse circuit based on the measured magnetic properties. Compared with the experimental results, the simulation results showed that the field-circuit coupling analysis model can effectively reflect the influence law of the frequency and duty cycle on magnetic properties.

Magnetic property measurement and analysis of high-frequency soft magnetic materials under non-sinusoidal excitation considering temperature effect

Electrical equipment operates under various temperatures and non-sinusoidal excitation, which makes magnetic properties of soft magnetic materials quite different from those under room temperature and sinusoidal excitation. Magnetic properties and loss characteristics of the ferrite (N87) and nanocrystalline alloy (FT-3KL) are measured and analyzed in the range of 25 °C to 125 °C from 5 kHz to 20 kHz under both square and rectangular excitation with different duty ratios. The temperature dependence of these materials under different conditions is systematically compared with normalization method. The comprehensive performance of core materials is discussed in combination with the experimental phenomena and results.

Fast Detection Method on Water Tree Aging of MV Cable Based on Nonsinusoidal Response Measurement

A MV power cable will exhibit nonlinear impedance when dendritic defects appear. To solve the long time-consuming measurement of pure sinusoidal excitation and realize rapid and accurate evaluation of insulation conditions, a measurement and evaluation method based on nonsinusoidal excitation is proposed in this paper. Firstly, a nonsinusoidal excitation test system is established, which can obtain the high voltage dielectric response in the frequency range of 0.01 Hz–1 kHz. For parameterizing dielectric response characteristics of MV XLPE insulation under nonsinusoidal excitation, a Hammerstein-Wiener model is proposed to realize system parameter identification under non sinusoidal excitation with different aging degrees of water tree. The time-domain current response waveform based on the H-W model is more accurate than the traditional linear model, and the resulting fitting degree of the frequency-domain dielectric loss factor curve between the calculated H-W model and the measured curve was higher than 95%. The results show that the rotation and distortion of the u-i hysteresis ellipse under nonsinusoidal excitation can be used to diagnose the insulation defects of XLPE MV cables. The response model and its detection method proposed in this paper can improve the efficiency and accuracy of the field tests of cable insulation.

Core loss measurement and comparative analysis for soft magnetic materials under complex non-sinusoidal excitations

With the advancement of wide-bandgap power devices, the power electronics equipment is developing toward higher switching frequencies and more complex switching modes in recent years. Accurate prediction of the core loss for magnetic components has been emphasized as the excitations of magnetic materials varying depending on the operating mode of the power supplies. Therefore, this paper presents the results of an extensive core loss study performed on nanocrystalline alloy (FT-3KL), amorphous alloy (1K101) and ultra-thin oriented silicon steel (GT-50). Firstly, an automatic setup for core loss measurement of soft magnetic materials fed by a full-bridge inverter based on silicon carbide (SiC) MOSFET is proposed. Then, the effects of switching oscillations from the inverter and the characteristic parameters of complex non-sinusoidal excitations on the core loss are analyzed comparatively. The core loss shows different regular distributions with the change of each characteristic parameter of excitations respectively. However, the regular distributions will be influenced by the high-frequency switching oscillations, which makes the prediction of core loss more complicated. This paper can provide a reference for the development of high-precision core loss model and performance optimization of power electronics equipment.

Multi-physics Analysis and Loss Evaluation of High Frequency Transformer with Non-sinusoidal Excitation

Multi-physics Analysis and Loss Evaluation of High Frequency Transformer with Non-sinusoidal Excitation

IGSE-CD—An Electric-/Displacement-Field Related Steinmetz Model for Class II Multilayer Ceramic Capacitors Under Low-Frequency Large-Signal Excitation

Multilayer Ceramic Capacitors (MLCCs) are of paramount importance in electronics and ferroelectric Class II dielectrics enable outstanding energy-density values. However, the non-linear dielectric constant and associated low-frequency large-signal excitation losses of Class II MLCCs may cause critical overheating. A peak-charge based Steinmetz loss model entitled iGSE-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</sub> is known in literature and allows to accurately calculate MLCC low-frequency large-signal excitation losses under various operating conditions including biased and non-sinusoidal excitation voltage waveforms. Such a macroscopic iGSE-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</sub> model, however, is inherently limited to a specific MLCC, and in contrast to Steinmetz loss modeling for ferromagnetic inductor cores, the losses of other devices employing the same dielectric material cannot be predicted. Recent literature therefore proposed a microscopic and/or material specific MLCC Steinmetz Model entitled iGSE-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> which allows to calculate the losses of any MLCC of the same dielectric material based upon just a single set of Steinmetz parameters. However, due to the lack of information on the internal device geometry, the iGSE-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> could be verified only indirectly so far by means of a loss normalization based on the device capacitance and rated voltage. In this paper, we demonstrate the feasibility of a microscopic iGSE-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> MLCC loss model enabled by manufacturer data on the internal capacitor structure. The iGSE-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> is verified for two different MLCC series employing a conventional X7R dielectric and a novel Hiteca (with reduced non-linearity) Class II dielectric material with loss estimation error below 22%. This error results due to component tolerances and is acceptable, especially when compared to the loss calculation based on the datasheet information which can be off by up to a factor of ten. The analysis of the Hiteca dielectric reveals a frequency behavior different to the X7R material, and is discussed in the Appendix of this paper.

Investigation of Rotational Magnetization Under Non-Sinusoidal Excitation for Non-Oriented Material

Rotational loss forms a significant portion of total core losses in electrical machines. The influence of harmonics on the behavior of magnetic materials is inevitable as these machines are mostly supplied by power electronic converters. Minor loops in hysteresis curves due to harmonics lead to additional losses. While the case of alternating induction (1-D magnetization) with harmonics is thoroughly considered in the literature, the assessment of the effect of rotational magnetization (2-D magnetization) has not yet been done adequately. A qualitative evaluation of rotational hysteresis loops in the presence of minor loops is carried out. The impact of minor loops in the evolution of hysteresis loops under rotating fields is examined. A peculiar behavior of interleaving of hysteresis loops under rotational magnetization is observed, which will affect the total core loss. This analysis can be used to visualize flux patterns on account of rotational magnetization and to accurately predict the performance of a machine during its predesign stage.

A novel estimation model for hysteresis loss based on semi-minor loops

This paper proposes an estimation model of hysteresis loss based on the mapping of the hysteresis loop conducted through tiny material samples with the aid of the Superconducting Quantum Interference Device (SQUID). This approach allows precise measurement of hysteresis loops. The aim of this paper is to develop a precise estimation model for hysteresis loss, one component of core loss, so as to improve the overall estimation accuracy of the entire core loss under complex excitations. First, with the help of the SQUID system and measurements conducted on tiny samples, the proposed model manages to minimize the impact of eddy current throughout the measurement and the modeling of hysteresis loss. This contrasts with the use of the conventional Steinmetz model and its modifications. Moreover, compared with methods including the modified Steinmetz equation (MSE) and the generalized Steinmetz equation (GSE) which merely focuses on the overall iron loss under simple non-sinusoidal excitations, the model presented here enables the estimation of hysteresis loss under complex excitations where multiple peaks and DC-bias take place. This approach will be very useful in situations such as those requiring pulse-width modulation (PWM) excited converters which are quite common on occasions including wind power systems. The estimation error of this model on the actual coil is within 15% under given excitations.

Improvement on Loss Separation Method for Core Loss Calculation Under High-Frequency Sinusoidal and Nonsinusoidal Excitation

The original loss separation formula introduced by Bertotti has long been utilized mainly for low-frequency sinusoidal applications. In this article, the traditional method is improved to fit into the core loss calculation under higher frequency sinusoidal and nonsinusoidal excitations, verified by the measured data of nanocrystalline material that is often used in medium-frequency transformers (MFTs). For high-frequency sinusoidal waveform, it is proposed that the exponent of the excess loss needs to be reidentified, and it is necessary to consider the skin effect for hysteresis and eddy current loss calculation under broader frequency scope. When the core is supplied with nonsinusoidal excitation (square and rectangular waveform), a new empirical method is derived based on the concept of effective frequency and the loss separation results, with which the estimation accuracy is greatly guaranteed compared to empirical methods originated from the Steinmetz equation such as improved generalized Steinmetz equation (iGSE). Due to clear separation of loss components, the new method has the potential to precisely predict losses for higher frequency applications.

Vibration and Noise Measurement of Medium-High Frequency Transformer Cores Under Non-Sinusoidal Excitation

Vibration and acoustic noise are essential in electrical equipment. Amorphous alloy is widely used in the medium- to high-frequency transformer due to its low loss, but its significant vibration and noise cannot be ignored, which will even reduce the reliability of the equipment. Ultra-thin grain-oriented silicon steel (≤0.2 mm) is expected to design medium- to high-frequency transformers due to its high magnetic permeability, high saturation magnetic flux density, and high stability. In this article, the loss characteristic, three-dimensional vibration acceleration, and noise level of three C-type core samples made of ultra-thin grain-oriented silicon steels (GT-050, GT-100) and amorphous alloy CACC30 are measured and analyzed under sinusoidal and rectangular excitations. The mathematic analysis predicts that the vibration acceleration increases with duty cycle decrease under rectangular excitation, which is consistent with the experimental results. The ultra-thin grain-oriented silicon steel has lower vibration and noise under medium- to high-frequency excitation compared with amorphous alloy when the transformer is operated on the non-saturated state. The experimental results and analysis can promote the application of new high-efficiency magnetic materials in medium- to high-frequency electrical equipment.