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SIMULATING METHOD OF MAGNETIZING INRUSH CURRENT OF POWER TRANSFORMERS USING CONCEPT OF INSTANTANEOUS POWER
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作者 贺家李 段玉倩 《Transactions of Tianjin University》 EI CAS 1999年第1期1-6,共6页
In this paper,a new simulating method is presented,using only the normal magnetizing curve (B-H) of the transformer core material,its geometric dimensions,the no-load power loss data and the concept of instantaneous p... In this paper,a new simulating method is presented,using only the normal magnetizing curve (B-H) of the transformer core material,its geometric dimensions,the no-load power loss data and the concept of instantaneous power. At the end of this paper the simulating calculation using EMTP has been also performed for the same transformer. The comparison shows that the two sets of results are very close to each other,and proves the correctness of the new method. The new method presented in this paper is helpful to verify the correctness of the power transformer design,analyze the behavior of the transformer protection under switching and study the new transformer protection principles. 展开更多
关键词 power transformer magnetizing inrush current remnant flue
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Evidence of guide field magnetic reconnection in flapping current sheets
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作者 YunTian Hou SuPing Duan +1 位作者 Lei Dai Chi Wang 《Earth and Planetary Physics》 EI CAS CSCD 2024年第4期650-658,共9页
Based on current sheet flapping motion on 27 August 2018 in the dusk flank magnetotail,as recorded by instruments aboard Magnetospheric Multiscale(MMS)spacecraft,we present the first study of guide field reconnection ... Based on current sheet flapping motion on 27 August 2018 in the dusk flank magnetotail,as recorded by instruments aboard Magnetospheric Multiscale(MMS)spacecraft,we present the first study of guide field reconnection observed in the flux rope embedded in kink-like flapping current sheets near the dusk-side flank of the magnetotail.Unlike more common magnetotail reconnections,which are symmetric,these asymmetric small-scale(λ_(i)~650 km)reconnections were found in the highly twisted current sheet when the direction normal to the sheet changes from the Z direction into the Y direction.The unique feature of this unusual reconnection is that the reconnection jets are along the Z direction-different from outflow in the X direction,which is the more usual situation.This vertical reconnection jet is parallel or antiparallel to the up-and-down motion of the tail’s current sheet.The normalized reconnection rate R is estimated to be~0.1.Our results indicate that such asymmetric reconnections can significantly enlarge current sheet flapping,with large oscillation amplitudes.This letter presents direct evidence of guide field reconnection in a highly twisted current sheet,characterized by enlarged current sheet flapping as a consequence of the reconnection outflow. 展开更多
关键词 magnetic reconnection magnetOTAIL current sheet
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Study on the Effect of Magnetic Pole Clipping Angle on the Eddy Current Loss of Permanent Magnets in the Rotor of Magnetically Levitated Permanent Magnet Synchronous High-Speed Electric Spindles
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作者 Xiangjun Shen Houcai Liu +2 位作者 Huimin Kang Ruirong He Jiale Xi 《Open Journal of Applied Sciences》 2024年第11期3261-3281,共21页
Aiming at the problem of high temperature and even demagnetization failure of permanent magnet (PM) due to PM eddy current loss in PM synchronous high-speed motors, this paper proposes a technique to lessen PM eddy cu... Aiming at the problem of high temperature and even demagnetization failure of permanent magnet (PM) due to PM eddy current loss in PM synchronous high-speed motors, this paper proposes a technique to lessen PM eddy current loss by cutting the angle of PM poles to change the shape of PM structure. Firstly, an analysis is conducted on the mechanism of PM synchronous high-speed motor eddy current loss production, the theoretical analytical model of PM eddy current loss is deduced, and it is theoretically proved that the magnetic pole shaving angle can reduce PM eddy current loss. Then, a 25 KW surface-type PM synchronous high-speed motor as an object, using two-dimensional time-step finite element method (FEM) to model and analyze PM eddy current loss. The results show that the smaller the PM pole shaving angle, the less its eddy current loss will be, it is possible to minimize the pole shaving angle of eddy current loss by 9.8% compared to the unshaved angle. Finally, the temperature field of the PM is calculated using a finite element method, and the outcomes demonstrate that the maximum temperature of the PM with a magnetic pole shaving angle can be reduced by about 5% compared with the unshaved angle. 展开更多
关键词 magnetic Pole Clipping Permanent magnet (PM) Eddy current Loss Temperature Field Two-Dimensional Time-Stepped Finite Element Method (FEM)
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Grain refinement of pure aluminum by direct current pulsed magnetic field and inoculation 被引量:5
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作者 陈航 接金川 +2 位作者 付莹 马红军 李廷举 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2014年第5期1295-1300,共6页
The combined effects of direct current pulsed magnetic field (DC-PMF) and inoculation on pure aluminum were investigated, the grain refinement behavior of DC-PMF and inoculation was discussed. The experimental resul... The combined effects of direct current pulsed magnetic field (DC-PMF) and inoculation on pure aluminum were investigated, the grain refinement behavior of DC-PMF and inoculation was discussed. The experimental results indicate that the solidification micro structure of pure aluminum can be greatly refined under DC-PMF. Refinement of pure aluminum is attributed to electromagnetic undercooling and forced convection caused by DC-PMF. With single DC-PMF, the grain size in the equiaxed zone is uneven. However, under DC-PMF, by adding 0.05% (mass fraction) Al5Ti-B, the grain size of the sample is smaller, and the size distribution is more uniform than that of single DC-PMF. Furthermore, under the combination of DC-PMF and inoculation, with the increase of output current, the grain size is further reduced. When the output current increases to 100 A, the average grain size can decrease to 113 μn. 展开更多
关键词 direct current pulsed magnetic field pure aluminum inoculation grain refinement solidification micro structure
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Magnetic Current Stimulated by Strain Wave in One-dimensional Ferromagnetic Bar
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作者 邢国军 徐小荷 《应用基础与工程科学学报》 EI CSCD 1998年第4期80-87,共8页
应变波通过铁磁性杆件时,由于压磁效应,可以激发出不均匀的磁流.本文用实验证实了这种现象,而且给出了一维杆件中的磁流产生电场的计算方法和模拟结果.运用磁流理论得到的分析结果与实验结果基本一致.
关键词 磁流 磁流元 应变波 压磁效应 对偶性原则
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Outcomes in spasticity after repetitive transcranial magnetic and transcranial direct current stimulations 被引量:12
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作者 Aysegul Gunduz Hatice Kumru Alvaro Pascual-Leone 《Neural Regeneration Research》 SCIE CAS CSCD 2014年第7期712-718,共7页
Non-invasive brain stimulations mainly consist of repetitive transcranial magnetic stimulation and transcranial direct current stimulation. Repetitive transcranial magnetic stimulation exhib- its satisfactory outcomes... Non-invasive brain stimulations mainly consist of repetitive transcranial magnetic stimulation and transcranial direct current stimulation. Repetitive transcranial magnetic stimulation exhib- its satisfactory outcomes in improving multiple sclerosis, stroke, spinal cord injury and cerebral palsy-induced spasticity. By contrast, transcranial direct current stimulation has only been studied in post-stroke spasticity. To better validate the efficacy of non-invasive brain stimulations in im- proving the spasticity post-stroke, more prospective cohort studies involving large sample sizes are needed. 展开更多
关键词 REVIEWS muscle spasticity motor cortex transcranial magnetic stimulation transcranialdirect current stimulation central nervous system stroke
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Cardiac magnetic source imaging based on current multipole model 被引量:3
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作者 唐发宽 王倩 +3 位作者 华宁 陆宏 唐雪正 马平 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期258-266,共9页
It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current mult... It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current multipole model expanded to the first order terms. This magnetic imaging is realized in a reconstruction plane in the centre of human heart, where the current dipole array is employed to represent realistic cardiac current distribution. The current multipole as testing source generates magnetic fields in the measuring plane, serving as inputs of cardiac magnetic inverse problem. In the heart-torso model constructed by boundary element method, the current multipole magnetic field distribution is compared with that in the homogeneous infinite space, and also with the single current dipole magnetic field distribution. Then the minimum-norm least-squares (MNLS) method, the optimal weighted pseudoinverse method (OWPIM), and the optimal constrained linear inverse method (OCLIM) are selected as the algorithms for inverse computation based on current multipole model innovatively, and the imaging effects of these three inverse methods are compared. Besides, two reconstructing parameters, residual and mean residual, are also discussed, and their trends under MNLS, OWPIM and OCLIM each as a function of SNR are obtained and compared. 展开更多
关键词 cardiac magnetic imaging current multipole heart-torso model inverse method
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Experimental Study of Current Loss of Stainless Steel Magnetically Insulated Transmission Line with Current Density at MA/cm Level 被引量:2
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作者 吴撼宇 曾正中 +1 位作者 王亮平 郭宁 《Plasma Science and Technology》 SCIE EI CAS CSCD 2014年第6期625-628,共4页
A magnetically insulated transmission line (MITL) is used to transmit high power electric pulses in large pulse power systems. However, current loss is unavoidable, especially when the current density is up to 1 MA/... A magnetically insulated transmission line (MITL) is used to transmit high power electric pulses in large pulse power systems. However, current loss is unavoidable, especially when the current density is up to 1 MA/cm. In the paper, the current loss of an MITL made of stainless steel, which is usually used in large pulse power generators, is experimentally studied, and possible mechanisms to explain the current loss of the MITL are analyzed and discussed. From the experimental results, the relationship between loss current density and input current density follows approximately a power law. The loss is also related to the configuration of the MITL. 展开更多
关键词 magnetically insulated transmission line current loss current density ION
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Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils 被引量:2
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作者 肖春燕 张军 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第12期30-42,共13页
The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being compos... The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows: 1) the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2) the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3) the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis. 展开更多
关键词 transient pulsed eddy current analytical solution elliptical electromagnetic concentra-tive coil functional magnetic stimulation
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Reconstruction of Current Density Distribution in Weld Area During Resistance Spot Welding of Aluminum Alloy Based on Magnetic Field 被引量:1
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作者 单平 姚杞 +1 位作者 李洋 罗震 《Transactions of Tianjin University》 EI CAS 2015年第2期129-134,共6页
Magnetic flux density around the weld area was used to reconstruct the current density distribution during resistance spot welding(RSW) of aluminum alloy according to inverse problem theory. A current-magnetic field m... Magnetic flux density around the weld area was used to reconstruct the current density distribution during resistance spot welding(RSW) of aluminum alloy according to inverse problem theory. A current-magnetic field model was established and the conjugate gradient method was used to solve this model. The results showed that the current density was low at the center of nugget while high on the edge of nugget. Moreover, the welding time of 30ms—60 ms is a key period for nucleation. The current density distribution can reflect whether the weld nugget is formed or splashed, therefore it has the potential to monitor the weld quality of RSW. 展开更多
关键词 resistance SPOT welding current density distribution INVERSE problem magnetic field
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Nonmonotonic effects of perpendicular magnetic anisotropy on current-driven vortex wall motions in magnetic nanostripes 被引量:1
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作者 苏垣昌 雷海洋 胡经国 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第9期527-531,共5页
In a magnetic nanostripe, the effects of perpendicular magnetic anisotropy(PMA) on the current-driven horizontal motion of vortex wall along the stripe and the vertical motion of the vortex core are studied by micro... In a magnetic nanostripe, the effects of perpendicular magnetic anisotropy(PMA) on the current-driven horizontal motion of vortex wall along the stripe and the vertical motion of the vortex core are studied by micromagnetic simulations.The results show that the horizontal and vertical motion can generally be monotonously enhanced by PMA. However, when the current is small, a nonmonotonic phenomenon for the horizontal motion is found. Namely, the velocity of the horizontal motion firstly decreases and then increases with the increase of the PMA. We find that the reason for this is that the PMA can firstly increase and then decrease the confining force induced by the confining potential energy. In addition, the PMA always enhances the driving force induced by the current. 展开更多
关键词 domain wall motion current perpendicular magnetic anisotropy micromagnetic simulation
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Visualization and Quantitative Evaluation of Eddy Current Loss in Bar-Wound Type Permanent Magnet Synchronous Motor for Mild-Hybrid Vehicles 被引量:5
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作者 Masahiro Aoyama Jianing Deng 《CES Transactions on Electrical Machines and Systems》 CSCD 2019年第3期269-278,共10页
This paper describes the conductor eddy current loss that occurs in a permanent magnet type synchronous motor with a distributed winding stator using a rectangular copper wire designed for mild hybrid system applicati... This paper describes the conductor eddy current loss that occurs in a permanent magnet type synchronous motor with a distributed winding stator using a rectangular copper wire designed for mild hybrid system applications for small vehicles.Compared with the conventional round wire inserter method,the space factor can be improved and the coil-end length can be shortened by applying a so-called hairpin windings using a pre-formed into hairpin shape of bar conductor,and as a result,DC current resistance of the armature winding can be reduced.However,since the conductor cross-sectional area tends to increases,the conductor eddy current loss generated by the space harmonics linkage becomes too large to ignore.In order to study the reduction of the conductor eddy current loss,it is important to visualize the spatial leakage flux distribution which causes loss and finely analyze how the magnetic path is formed.Therefore,analysis of the conductor eddy current loss distribution generated in the bar-wound conductor is performed using the CAE model that faithfully reproduces the coil-end shape of the actual machine.Furthermore,it was qualitatively clarified what ratio of conductor eddy current loss at various driving points.Finally,the results of preliminary study on reduction of conductor eddy current loss are reported. 展开更多
关键词 Conductor eddy current loss hairpin windings type permanent magnet synchronous motor leakage magnetic flux.
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Mitigation of blackout problem for reentry vehicle in traveling magnetic field with induced current 被引量:1
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作者 Shaoshuai GUO Kai XIE +1 位作者 Bin SUN Shaowei LIU 《Plasma Science and Technology》 SCIE EI CAS CSCD 2020年第12期37-47,共11页
In this paper, a novel solution mitigating the radio blackout problem is proposed, which improves existing traveling magnetic field(TMF)-based methods. The most significant advance lies in replacing the external injec... In this paper, a novel solution mitigating the radio blackout problem is proposed, which improves existing traveling magnetic field(TMF)-based methods. The most significant advance lies in replacing the external injection with self-induced current, which does not require electrodes. The improved analytical model is derived to evaluate the electron density reduction taking into consideration the self-induced current for various TMF velocities. The plasma reduction performance is analyzed for several conditions including the total absence of injected current. The results show that the velocity may be used to trade off the injected current and, when sufficiently large, eliminates the need for an injected current while mitigating radio blackout. The effectiveness of this solution to the blackout problem is demonstrated in commonly used aerospace communication bands. With a field strength of less than 0.15 T, increasing the velocity from40 m s^-1 to 3100 m s^-1 is all that is required to obviate the need for an injected current. Moreover,typical reduction ratios for electronic density tolerance(2, 1.9, 1.75 and 3 times for the L-, S-, Cand X-bands, respectively, at an altitude of 40 km) remain unchanged. Increasing the velocity of the TMF is much easier than injecting current via a metal electrode into a high-temperature flow field. The TMF method appears practical in regard to possible future applications. 展开更多
关键词 BLACKOUT traveling magnetic field self-induced current traveling magnetic field velocity
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Optimal design of auxiliary-teeth to solve circulation current reduction of permanent magnet linear synchronous motor 被引量:1
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作者 JANG Ki-bong KIM Jee-hyun +1 位作者 AN Ho-jin KIM Gyu-tak 《Journal of Central South University》 SCIE EI CAS 2011年第3期690-696,共7页
A discontinuity of magnetic circuits according to the end effect is generated in the permanent magnet linear synchronous motor (PMLSM). Due to the unbalanced back electro-motive force (EMF) and impedance produced,... A discontinuity of magnetic circuits according to the end effect is generated in the permanent magnet linear synchronous motor (PMLSM). Due to the unbalanced back electro-motive force (EMF) and impedance produced, unbalanced current is generated. The cireulatin8 current, which is caused by a decrease in the thrust, is generated by the unbalanced current. The optimal design of auxiliary-teeth at the end of the mover was carried out to solve the unbalance of phase by using design of experiment (DOE), and compared with the basic model through finite element analysis (FEA). As a result, the auxiliary-teeth model compensates for the decrease of thrust caused by the unbalanced phase. Also, this model is proven to reduce the detent force by the vibration and noise of the PMLSM and copper loss caused by the circulating current. 展开更多
关键词 permanent magnet linear synchronous motor auxiliary-teeth circulation current end effect thrust reduction
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Sensorless Control of Permanent Magnet Synchronous Motor Based on New Sliding Mode Observer with Single Resistor Current Reconstruction 被引量:3
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作者 Qingguo Sun Xiaolei Zhu Feng Niu 《CES Transactions on Electrical Machines and Systems》 CSCD 2022年第4期378-383,共6页
To solve the chattering problem caused by discontinuous switching function in traditional sliding mode observer,a piecewise square root switching function with continuously varying characteristics is designed,and its ... To solve the chattering problem caused by discontinuous switching function in traditional sliding mode observer,a piecewise square root switching function with continuously varying characteristics is designed,and its stability is analyzed by using Lyapunov stability criterion.Secondly,according to the relationship among bus current,switching state and phase current,a single bus resistance sampling current reconstruction scheme without current sensors is adopted,which effectively reduces the cost of motor system.Finally,the feasibility and effectiveness of the proposed scheme are verified by simulation. 展开更多
关键词 Permanent magnet synchronous motor New sliding mode observer Phase-locked loop Single resistor current reconstruction
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Novel Rotors with Low Eddy Current Loss for High Speed Permanent Magnet Machines 被引量:5
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作者 Xin Cheng Wei Xu +2 位作者 Guanghui Du Guohui Zeng Jianguo Zhu 《CES Transactions on Electrical Machines and Systems》 CSCD 2019年第2期187-194,共8页
Due to the large rotor eddy current loss and low thermal conductivity of carbon fiber sleeve,the high temperature usually occurs in high speed permanent magnet machines(HSPMMs)at the rated operation condition,resultin... Due to the large rotor eddy current loss and low thermal conductivity of carbon fiber sleeve,the high temperature usually occurs in high speed permanent magnet machines(HSPMMs)at the rated operation condition,resulting in irreversible demagnetization of the permanent magnet(PM).To obtain low rotor temperature,two novel rotor structures with low rotor eddy current loss are proposed in this paper.With the output torque and air gap flux density unchanged,the performance of HSPMMs with the two proposed rotor structures are analyzed based on finite element algorithm(FEA),including eddy current loss and temperature.Finally,the appropriate parameters of the proposed rotor structures are selected,and the electromagnetic(EM)performance,rotor stress and temperature are compared with those of the conventional rotor structure.Index Terms-Eddy current loss,finite element algorithm(FEA),electromagnetic(EM)performance,high speed permanent magnet machines(HSPMMs). 展开更多
关键词 Eddy current loss finite element algorithm(FEA) electromagnetic(EM)performance high speed permanent magnet machines(HSPMMs).
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Research on Long Stroke Moving Secondary Permanent Magnet Linear Eddy Current Brake 被引量:2
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作者 Baoquan Kou He Zhang +2 位作者 Xiangrui Yin Yiheng Zhou Chunyan Li 《CES Transactions on Electrical Machines and Systems》 CSCD 2019年第1期19-29,共11页
In this paper,a long stroke moving secondary permanent magnet linear eddy current brake is proposed.Without exciting coils,the permanent magnet eddy current brake possesses the advantage of saving copper and better re... In this paper,a long stroke moving secondary permanent magnet linear eddy current brake is proposed.Without exciting coils,the permanent magnet eddy current brake possesses the advantage of saving copper and better reliability.The topology and operating principle are presented.The mathematical model was derived with the layer theory.The braking force characteristic was analyzed using the finite element method.The structural parameters of the long stroke moving secondary permanent magnet linear eddy current brake were studied by referring the design progress of the other types of eddy current brakes.Finally,a prototype of long stroke moving secondary permanent magnet linear eddy current brake was built and tested,and the experimental result verifies the correctness of the above analysis. 展开更多
关键词 Braking force analysis eddy current brake experimental study mathematical model permanent magnet.
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Research on Open-circuit Fault Tolerant Control of Six-phase Permanent Magnet Synchronous Machine Based on Fifth Harmonic Current Injection 被引量:3
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作者 Zhifeng Zhang Yue Wu +1 位作者 Hequn Su Quanzeng Sun 《CES Transactions on Electrical Machines and Systems》 CSCD 2022年第3期306-314,共9页
This paper proposes a novel control approach for fault-tolerant control of dual three-phase permanent magnet synchronous motor(PMSM) under one-phase open-circuit fault.A modified six-phase static coordinate transforma... This paper proposes a novel control approach for fault-tolerant control of dual three-phase permanent magnet synchronous motor(PMSM) under one-phase open-circuit fault.A modified six-phase static coordinate transformation matrix and an extended rotating coordinate transformation matrix are investigated considering the influence of the fifth harmonic space on fault-tolerant control. These mathematical models are further analyzed in the fundamental space and the fifth harmonic space after the fault and to eliminate the coupling between the d-q axis voltage equation in the fundamental wave space and the d-q axis voltage equation in the fifth harmonic space, a secondary rotation coordinate transformation matrix is proposed. To achieve the purpose of reducing torque ripple, the fault-tolerant control method proposed in this paper not only takes the minimum copper loss as the constraint condition, but also injects the fifth harmonic current. The experimental result of current and torque is used to verify the accuracy of fault-tolerant control. 展开更多
关键词 Extended rotating coordinate transformation matrix Fault-tolerant control Fifth harmonic current injection Modified six-phase static coordinate transformation matrix Dual three-phase permanent magnet synchronous motor Torque ripple
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A Novel Flyback Converter With Automatic Current Sharing for LED-lighting Systems Dependent on Integrated Magnetic Technique 被引量:3
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作者 CHEN Wei WANG Xiaobo 《中国电机工程学报》 EI CSCD 北大核心 2012年第30期I0005-I0005,共1页
关键词 LED照明系统 开关转换器 磁集成技术 自动均流 反激式 电流平衡 共享技术 耦合电感
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Persistent current in a magnetized Rashba ring
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作者 张林 汪军 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第12期357-365,共9页
We theoretically study the persistent currents flowing in a Rashba quantum ring subjected to the Rashba spinorbit interaction. By introducing uniform or nonuniform magnetization into the ring, we find that a nonzero p... We theoretically study the persistent currents flowing in a Rashba quantum ring subjected to the Rashba spinorbit interaction. By introducing uniform or nonuniform magnetization into the ring, we find that a nonzero persistent charge current circulates in the ring, which stems from the original equilibrium spin current due to the Rashba spinorbit interaction. Because of broken time reversal symmetry, the two oppositely flowing spin-up and spin-down charge currents of the equilibrium spin current are no longer equal, and so a net persistent charge current can flow in the system. It is also found that the persistent current can be modulated by the Fermi energy, the Rashba spin-orbit interaction strength and the magnetization in the ring. Moreover, the magnetization perpendicular to the ring plane can optimize the current. The persistent current flowing in the ring is a manifestation of the nonzero equilibrium spin current existing in the ring. 展开更多
关键词 persistent current equilibrium spin current Rashba ring magnetIZATION
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