Harmonic Magnetic Field Research Articles

An Overview of the R&D of Flywheel Energy Storage Technologies in China

The literature written in Chinese mainly and in English with a small amount is reviewed to obtain the overall status of flywheel energy storage technologies in China. The theoretical exploration of flywheel energy storage (FES) started in the 1980s in China. The experimental FES system and its components, such as the flywheel, motor/generator, bearing, and power electronic devices, were researched around thirty years ago. About twenty organizations devote themselves to the R&D of FES technology, which is developing from theoretical and laboratory research to the stage of engineering demonstration and commercial application. After the research and accumulation in the past 30 years, the initial FES products were developed by some companies around 10 years ago. Today, the overall technical level of China’s flywheel energy storage is no longer lagging behind that of Western advanced countries that started FES R&D in the 1970s. The reported maximum tip speed of the new 2D woven fabric composite flywheel arrived at 900 m/s in the spin test. A steel alloy flywheel with an energy storage capacity of 125 kWh and a composite flywheel with an energy storage capacity of 10 kWh have been successfully developed. Permanent magnet (PM) motors with power of 250–1000 kW were designed, manufactured, and tested in many FES assemblies. The lower loss is carried out through innovative stator and rotor configuration, optimizing magnetic flux and winding arrangement for harmonic magnetic field suppression. Permanent magnetic bearings with high load ability up to 50–100 kN were developed both for a 1000 kW/16.7 kWh flywheel used for the drilling practice application in hybrid power of an oil well drilling rig and for 630 kW/125 kWh flywheels used in the 22 MW flywheel array applied to the flywheel and thermal power joint frequency modulation demonstration project. It is expected that the FES demonstration application power stations with a total cumulative capacity of 300 MW will be built in the next five years.

Numerical determination of the threshold magnetic field in superconducting strips and coils triggering dynamic resistance

Abstract The threshold magnetic field is a key parameter for evaluating the current decay caused by dynamic resistance in superconducting windings and magnets. For a DC-carrying superconducting slab under an AC parallel magnetic field, the analytical theory clearly shows that there is only one electric central line (ECL) across the slab width at the onset of dynamic-resistance. However, threshold magnetic fields in superconducting strips and coils have not been fully investigated. Based onthe one-ECL criterion, this paper first presents a method for numerically determining the threshold magnetic field via the evolving internal magnetic field in superconducting strips and coils. By probing transient electromagnetic behaviours, interestingly, we found a distinctive feature of superconducting strips in which a wide region of zero electrical field is observed when dynamic resistance/loss initially occurs. With increasing magnetic fields, this region gradually shrinks and eventually become the ECL. More importantly, this numerical method can analyse the local threshold magnetic field in a targeted coil turn. The ability to quantify threshold magnetic field provides a clear guidance on the acceptable level of ripple and harmonic magnetic fields for coil windings in superconducting maglev trains and field windings of superconducting machines operating at persistent current mode.

Torque improvement investigation of a double rotor permanent magnet motor based on effective utilization of magnetic field coupling

AbstractIn this paper, a torque improvement method is presented for a double rotor (DR) permanent magnet motor, where the key is to conduct the study based on effective utilization of magnetic field coupling. To facilitate systematic analysis, the magnetomotive force (MMF) and airgap flux density considering magnetic coupling effect are deduced and analysed. It contributes to building the relationships between the output torque caused by magnetic coupling and magnetic field harmonics. By introducing the coupling sensitivity coefficient, the coupling harmonics in the inner and outer airgap magnetic fields are obtained. Then, two coupling harmonic groups are further determined in terms of phase difference and torque contribution, where one of them is required to be enhanced and the other is needed to be reduced. On the basis of this, a comprehensive coupling factor is defined purposely to realise the design and evaluation of the characteristics of coupling harmonic groups. Some motor performances are analysed in details, including the torque, torque ripple, overload capability, and so on. Finally, a prototype motor is manufactured to verify the feasibility of the presented studies of the DR motor.

AC loss analysis on an HTS field winding of the generator with T-A formulation

In this study, we proposed a coupling model utilizing finite element software to estimate AC loss on the high-temperature superconducting (HTS) field winding of a 1 MW generator. The model comprises three distinct physical modules: rotating machinery and magnetic (RMM), electrical circuit (CE) and partial differential equation (PDE). These modules collaborate to resolve the generator's magnetic field distribution, rated output parameters and degree of current magnetization on the HTS field winding, employing Maxwell equations and T-A formulation. Given the placement of the HTS field winding on the rotor core, accurately calculating its loss in an electromagnetic field that varies both temporally and spatially presents a considerable challenge. To address this issue, we adjust the coordinate system within the PDE module to vary with the material rather than space. Our analysis reveals that the instantaneous AC loss of an HTS field winding comprises two primary components: the attenuation envelope and the oscillatory variation, resulting from the charging process and external harmonic magnetic fields. Additionally, we comprehensively discuss and analyze the influence of current excitation speed on instantaneous AC loss. Accurately estimating AC loss in HTS field windings is a critical and meaningful aspect of preliminary machine design. This study provides an essential reference for addressing this issue.

Torque Ripple Suppression of a PM Vernier Machine From Perspective of Time and Space Harmonic Magnetic Field

Torque Ripple Suppression of a PM Vernier Machine From Perspective of Time and Space Harmonic Magnetic Field

Retraction Notice: Analysis of the Characteristics in Linear Generator for EDS Maglev Based on Harmonic Magnetic Field Method

Retraction Notice: Analysis of the Characteristics in Linear Generator for EDS Maglev Based on Harmonic Magnetic Field Method

Nonlinear resonance of a rotating ferromagnetic functionally graded cylindrical shell in harmonic magnetic and thermal fields

Nonlinear resonance of a rotating ferromagnetic functionally graded cylindrical shell in harmonic magnetic and thermal fields

ЗАСТОСУВАННЯ ФАЗНИХ СТРУМОВИХ КОНТУРІВ ДЛЯ МОДЕЛЮВАННЯ ГАРМОНІЙНОГО МАГНІТНОГО ПОЛЯ МАГНІТОЕЛЕКТРИЧНОГО ГЕНЕРАТОРА

The model of electromagnetic field of a magnetoelectric generator with a smooth cylindrical rotor and surface-mounted permanent magnets is investigated. Permanent magnets are interpreted using complex amplitudes of a system of current loops with harmonic currents. The aim of the study is to develop a mathematical model for calculating the harmonic magnetic field of a magnetoelectric generator with permanent magnets by replacing the permanent magnets with phase current loops with complex current amplitudes and to investigate its adequacy. Three variations of model representation of permanent magnets placed on the surface of the magnetic core are utilized. Depending on the model representation of permanent magnets, two dynamic generator models and two harmonic models have been developed. For each model, equations of the electromagnetic field are written. An example of a three-phase scheme of current loops of the rotor for modeling the electromagnetic field of the magnetoelectric generator with complex amplitudes of currents is presented. Comparison of the magnetic field induction, current, voltage, and electromagnetic torque is performed with three variations of magnet width relative to the pole pitch. References 14, figures 5, table 1.

An Experimental Study on the Dynamic Resistance of HTS Coil During Quasi-Persistent Current Operation Under External Harmonic Magnetic Field

An Experimental Study on the Dynamic Resistance of HTS Coil During Quasi-Persistent Current Operation Under External Harmonic Magnetic Field

Modelling and optimisation of the surface‐mounted permanent magnet machine with multi‐level array magnets

AbstractAn analytical and optimisation method is presented to improve the air‐gap magnetic field of the surface‐mounted permanent magnet machine with multi‐level array magnets, which can reduce air‐gap magnetic field harmonics and torque ripple. Different from the conventional analytical method (AM) around the entire single‐magnet pole, the modelling method of multi‐level equal‐thickness ferrite magnets with different remanences for improving the air‐gap flux density is investigated. Considering the influence of air‐gap relative permeability by stator slots and multi‐level magnet remanences on the air‐gap flux density, the proposed AM for improving air‐gap flux density is derived by analysing the slotless air‐gap flux density and slotted air‐gap relative permeability. The cogging torque is predicted with energy method by analysing the tangential magnetic field distribution at stator slots. Then, the back electromotive force is predicted by analysing the winding distribution and radial air‐gap flux density. Based on the proposed AM, the simulated annealing particle swarm optimisation algorithm is used by optimising the widths and thicknesses of the multi‐level array magnets to further reduce torque ripple and increase output torque. Finally, the accuracy of the proposed AM is verified by comparing with the finite element method.

Investigation of Torque and Reduction of Torque Ripples through Assisted-Poles in Low-Speed, High-Torque Density Spoke-Type PMSMs

In this article, rotor designs utilizing assisted-poles are investigated for a high-torque density spoke-type permanent magnet synchronous machine (PMSM) with fractional slot concentrated winding (FSCW) to explore the rich air-gap magnetic field harmonics and torque generation mechanism. Due to their higher average torque output, spoke-type PMSMs with FSCW are increasingly used in high-torque density applications. However, slot harmonics generate torque ripples that are difficult to eliminate in FSCW spoke-type PMSMs. Removing slot harmonics from the stator or winding results in a large drop in torque since their winding factors are identical to those of the main harmonic. Therefore, rotor designs having assisted-poles (symmetrical and asymmetrical) are investigated in this work to mitigate slot harmonics and minimize torque ripples. Firstly, the air-gap flux density is analyzed for the machines having assisted-poles, and a model of interaction between the stator and rotor-MMF harmonics is created and validated through Finite element analysis (FEA) to analyze the torque production mechanism. In addition, an analytical relationship between the assisted-poles’ dimensions and the generated torque harmonics is proposed. Furthermore, a generalized torque ripple reduction concept for the FSCW spoke-type PMSM having asymmetrically designed assisted-poles is presented. The proposed design and optimization method are validated through analytical calculations and FEA simulations, and a brief comparative analysis is presented for the analyzed machine prototypes. It has been established that the machine designed by applying the proposed asymmetrical assisted-poles can achieve a reduction in torque ripples while also significantly lowering cogging torque in comparison to the conventional spoke-type PMSMs and other spoke-type PMSMs with rotor having symmetrical assisted-poles.

Analysis of Multi-Objective Optimization Design of Interior Double Radial and Tangential Combined Magnetic Pole Permanent Magnet Drive Motor for Electric Vehicles

A new type of interior combined pole permanent magnet drive motor is proposed in this paper, which aims to improve the power and comfort of electric vehicles. In view of the complex magnetic circuit structure and rich harmonic magnetic field of the motor, the initial magnetic pole parameters of the rotor are determined by the equivalent magnetic circuit method. Then, aiming at the complex magnetic circuit and rich harmonic magnetic field, a multi-objective optimization method based on the Taguchi method and response surface method is proposed to reduce the cogging torque, high harmonic content in air gap magnetic flux density and increase the output torque. Based on the finite element analysis of the electromagnetic performance of the new type interior combined magnetic pole permanent magnet drive motor before and after optimization, it can be seen that the improved rotor structure can effectively reduce the torque ripple and increase the torque density. Finally, a prototype was developed and experiments were conducted, and experimental results verified the correctness of the proposed multi-objective optimization algorithm.

Effects of magnetic field gradient on capacitively coupled plasma driven by tailored voltage waveforms

This study utilized one-dimensional implicit particle-in-cell/Monte Carlo collision simulations to investigate the impact of different harmonic numbers and magnetic field strengths on capacitive-coupled argon plasma. Under the conditions of a pressure of 50 mTorr and a voltage of 100 V, simulations were conducted for magnetic field strengths of 0 and 100 G, magnetic field gradients of 10–40, 10–60, 10–80, 10–100, and 100–10 G, as well as discharge scenarios with harmonic numbers ranging from 1 to 5. Through in-depth analysis of the results, it was observed that the combined effect of positive magnetic field gradients and harmonic numbers can significantly enhance plasma density and self-bias properties to a greater extent. As the magnetic field gradient increases, the combined effect also increases, while an increase in harmonic numbers weakens the combined effect. Furthermore, this combined effect expands the range of control over ion bombardment energy. This provides a new research direction for improving control over ion energy and ion flux in capacitive-coupled plasmas.

Five-phase space vector carrier-based PWM for third harmonic injection

Five-phase AC drives allow a third harmonic voltage to be fed into the stator winding – in addition to the fundamental voltage – to generate a third harmonic magnetic air gap field. This allows the generation of an additional small constant torque. Furthermore, the undesirable saturation harmonics that occur with saturated iron can be compensated. The desired third harmonic voltage is commonly generated via time-consuming space vector PWM algorithms, which are not well-suited for real-time application, or via look-up tables, which require an increased storage capacity. In our case, the desired third harmonic voltage is generated in the five-phase voltages by adding a non-sinusoidal zero-sequence voltage with five times the fundamental frequency to the fundamental voltage reference signals in carrier-based pulse width modulation (PWM) with a constant switching frequency. This is equivalent to a space vector PWM method (SVPWM) and avoids a significantly high calculation effort. The PWM algorithm programmed in MATLAB in real time allows the fast generation of a third harmonic voltage per phase with freely definable amplitude and phase shift without requiring a lot of storage capacity.

Cyclic variations of the structure and energetics of solar magnetic fields

ABSTRACT The solar cycle is a complex phenomenon, a comprehensive understanding of which requires the study of various tracers. Here, we consider the solar cycle as manifested in the harmonics of the solar large-scale surface magnetic field, including zonal, sectorial, and tesseral harmonics, divided into odd and even relative to the solar equator. In addition to considering the amplitudes of the harmonics, we analyse their contribution to the magnetic energy. It turns out that the relative contribution of different types of harmonics to the magnetic energy is virtually independent of the cycle height. We identify different phases of the activity cycle using harmonics of different symmetries. A possible way to incorporate the obtained result into the solar dynamo theory is proposed.

Design of differential probe with harmonic magnetic field and its data process method

To identify the condition of steel pipelines beyond the line of sight during operation, this study presents a design methodology for a differential probe, along with a harmonic magnetic field excitation technique and its corresponding data processing methodology. The coaxial arrangement of the excitation coils in a planar configuration generates a potent induced magnetic field, ensuring a sufficient standoff distance. Under the influence of harmonic excitation, the magnetic permeability of the pipeline surface decreases, resulting in an increased detection depth. Periodic alterations in the magnetic permeability of the pipeline surface enhance the amplitude of defects. Adjusting the position of the induction coil minimizes interference from the excitation magnetic field, thereby obtaining a pure induced magnetic field. Differential processing is applied to the two induction coils to counteract interference from the background magnetic field. Finally, the effectiveness and reliability of this probe are validated through three experiments: pipeline positioning, weld seam inspection, and damage detection.

A Magnetic-Geared Machine With Improved Magnetic Circuit Symmetry for Hybrid Electric Vehicle Applications

Magnetic-geared machine (MGM) has been widely investigated as the power split device for hybrid electric vehicles with the inherently high-integration of multi-mechanical ports. It is revealed that the magnetic circuits of armature winding in MGM are essentially asymmetrical for different phases under the magnetic field modulation effect. This inevitably results in unbalanced phase back electromotive force (EMF) waveforms, severe torque ripples, acoustic noise, and difficulty for precise control. To alleviate the asymmetry problem, a generic winding design model is presented for MGMs in this paper, which allows for consideration of all potential winding configurations. Firstly, a novel back EMF harmonic factor is proposed to account for both the harmonic content and asymmetric level in MGM. The genetic algorithm (GA) is further employed to optimize the winding in terms of minimizing the back EMF harmonic factor, armature magnetomotive force harmonic contents, and phase winding resistance. The proposed winding layout exhibits superior filtering capability for three-phase asymmetric magnetic field harmonics. As compared with the conventional integral-slot distributed winding, the MGM with the proposed winding exhibits improved back EMF waveform symmetry, suppressed torque ripple, and reduced core losses. Finally, an experimental prototype is manufactured to validate the effectiveness of asymmetric magnetic field suppression for MGMs. The results show the investigated winding design method is an effective solution to the asymmetric issue of MGMs, paving the way to research opportunities for further improvements.

Design and harmonic analysis of single winding bearingless PM synchronous motor with high winding coefficient

Compared with double-winding bearingless permanent magnet synchronous motor, single-winding bearingless permanent magnet synchronous motor (SBPMSM) has the advantages of low copper loss and low failure rate. However, if the slot-pole combination of SBPMSM is not reasonably selected, the winding coefficient will be reduced, and even many advantages of the single-winding structure will be offset. In this paper, a single-winding design method based on magnetomotive force (MMF) star diagram is proposed, which can ensure high winding coefficient. The design process of the proposed single winding structure is introduced. This method can match the appropriate number of stator slots according to the number of rotor poles, and the winding phase separation design can be realized by reversing the slot number transposition. The mathematical models of the suspension force and torque of the bearingless permanent magnet synchronous motor are derived considering the magnetic field harmonics, and the 6-slot/2-pole SBPMSM and 18-slot/8-pole SBPMSM are taken as examples to analyze the magnetic field. The finite element simulation models of 6-slot/2-pole SBPMSM and 18-slot/8-pole SBPMSM are built and analyzed. Through the analysis of electromagnetic torque, suspension force and air-gap magnetic field under different magnetic fields, the general rules of main torque fluctuation and suspension force fluctuation are summarized.

Producing circular field harmonics inside elliptic magnet apertures with superconducting canted-cosine-theta coils

Superconducting magnets with noncircular aperture are desired for accelerators and many other high-field applications. This paper presents new methods for the analytic design of elliptic bore superconducting accelerator magnets. Part 1 of this work shares the derivation of current to field relations between a sheet current density on an elliptic cylinder and the magnetic field harmonics inside the aperture. This result is explored in the general context of elliptic bore magnet design with relevant scaling laws compared between elliptic and circular bore magnets. In part 2, this approach is applied to the specific geometry of canted-cosine-theta (CCT) accelerator magnets, enabling analytic winding design for single or mixed circular harmonics within elliptic aperture CCT magnets. Published by the American Physical Society 2024

Confinement of transitioning particles in bi-helical Wendelstein-type configurations

Recently, stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor was observed numerically. This validated the theoretical predictions that (i) the stochastic diffusion represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators and (ii) it is possible to prevent the escape of particles to the wall by closing the separatrix between the locally trapped and passing states. It was concluded that, in principle, the separatrix could be made closed, resulting in a reduction of fast ion losses, by compensating for the effect of the helical component of the magnetic field $(1, 1)$ with an enhanced ‘anti-helical’ harmonic $(1, -1)$ ; the enlargement of this harmonic was proposed previously for other reasons. This possibility is explored in this work. Equations of previous relevant works were generalised to include the $(1, -1)$ harmonic. Calculations were carried out for several magnitudes of the ratio of anti-helical to helical magnetic field harmonics. Positive effects were found already at the smallest anti-helical harmonic considered: when the latter ratio is 0.25, transitioning particles with the smallest and intermediate pitch parameters are confined and, moreover, their fraction decreased. When the ratio is 0.85, almost all transitioning particles are confined and their fraction is minimal; well-confined localised orbits dominate at the smallest pitch parameters.