基于替代映射方法分别建立主动磁轴承和永磁同步电机的非线性模型,并与飞轮转子动力学模块、PID控制器等组件结合,构造高速飞轮转子与电机耦合的非线性动力学系统模型。仿真结果表明,替代映射方法计算得到的永磁同步电机齿槽转矩数值与有限元模型结果之间误差较小,具有良好的精度,可正确描述其基频到多次倍频的振动特性。永磁同步电机转子偏心作用力随着转子振幅的增大而增强,会显著削弱主动磁轴承对飞轮转子的控制能力。基于前人“双弹簧”模型,结合永磁同步电机替代映射模型,建立包含主动磁轴承和永磁同步电机的“三弹簧”模型。仿真计算结果表明,永磁同步电机转子偏心作用力改变了飞轮转子的第二临界转速的频率和振幅,作用力较大和位置偏置会造成第二临界转速附近的运动失稳。
Abstract
Nonlinear models of the active magnetic bearing and permanent magnet synchronous motor are built respectively based on the alternative mapping method, and combined with flywheel rotor dynamics module, PID controller and other components to construct a coupled nonlinear dynamic system model of the high-speed flywheel rotor. The simulation results show that the calculation error of the permanent magnet synchronous motor cogging torque between the alternative mapping model and the finite element model result is tiny. This indicates that the alternative mapping method has good accuracy, and can correctly describe the cogging torque vibration characteristics from the fundamental frequency to multiple frequencies. The eccentric force of the permanent magnet synchronous motor rotor increases as the rotor vibration amplitude increases, and it may significantly weaken the control capability of the active magnetic bearing to the flywheel rotor. Based on the double-spring model in previous studies, a three-spring model is built by combining it with the permanent magnet synchronous motor alternative mapping model. The simulation results show that the eccentric force of the permanent magnet synchronous motor rotor changes the frequency and amplitude of the second critical speed of the flywheel rotor, and a larger eccentric force and position offsets may cause motion instability around the second critical speed.
关键词
储能 /
飞轮转子 /
磁轴承 /
永磁同步电机 /
非线性动力学 /
替代映射
Key words
storage /
flywheel rotor /
magnetic bearing /
permanent magnet synchronous motor /
nonlinear dynamics /
alternative mapping
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参考文献
[1] 王朔, 周格, 禹习谦, 等. 储能技术领域发表文章和专利概览综述[J]. 储能科学与技术, 2017, 6(4): 810-838.
WANG S, ZHOU G, YU X Q, et al.Overview of research papers and patents on energy storage technologies[J]. Energy storage science and technology, 2017, 6(4): 810-838.
[2] 聂永辉, 张丽丽, 张立栋, 等. 一种基于VSG的风电机组与飞轮储能协调控制方法[J]. 太阳能学报, 2021, 42(8): 387-393.
NIE Y H, ZHANG L L, ZHANG L D, et al.A VSG-based coordinated control method for wind turbine and flywheel energy storage[J]. Acta energiae solaris sinica, 2021, 42(8): 387-393.
[3] 武鑫, 李洋涛, 马志勇, 等. 基于改进小波包分解的混合储能系统容量配置方法[J]. 太阳能学报, 2023, 44(8): 23-29.
WU X, LI Y T, MA Z Y, et al.Capacity configuration method of hybrid energy storage system based on improved wavelet packet decomposition[J]. Acta energiae solaris sinica, 2023, 44(8): 23-29.
[4] 任正义, 赫鹏, 杨立平. 600Wh飞轮转子形状优化设计[J]. 机械设计与制造, 2021(4): 117-120, 125.
REN Z Y, HE P, YANG L P.600Wh flywheel rotor shape optimization[J]. Machinery design & manufacture, 2021(4): 117-120, 125.
[5] MOUSAVI G S M, FARAJI F, MAJIZI A, et al. A comprehensive review of flywheel energy storage system technology[J]. Renewable & sustainable energy reviews, 2017, 67: 477-490.
[6] 武鑫, 陈玉龙, 柳亦兵. 并网型飞轮储能系统金属转子结构优化设计[J]. 太阳能学报, 2021, 42(2): 317-321.
WU X, CHEN Y L, LIU Y B.Structure optimization of metal rotor of grid-connected flywheel energy storage system[J]. Acta energiae solaris sinica, 2021, 42(2): 317-321.
[7] 张剀, 徐旸, 董金平, 等. 储能飞轮中的主动磁轴承技术[J]. 储能科学与技术, 2018, 7(5): 783-793.
ZHANG K, XU Y, DONG J P, et al.Application of active magnetic bearings in flywheel systems[J]. Energy storage science and technology, 2018, 7(5): 783-793.
[8] FENG J, WANG Q, LIU K.High-precision speed control based on multiple phase-shift resonant controllers for gimbal system in MSCMG[J]. Energies, 2018, 11(1): 32-51.
[9] 陈小飞, 刘昆. 基于ANSYS电磁场分析的磁悬浮飞轮非线性磁力研究[J]. 机械科学与技术, 2011, 30(9): 1424-1430.
CHEN X F, LIU K.Study on nonlinear magnetic force of magnetic suspended flywheel system using ansys electromagnetic analysis[J]. Mechanical science and technology for aerospace engineering, 2011, 30(9): 1424-1430.
[10] HOU E Y, LIU K.Tilting characteristic of a 2-axis radial hybrid magnetic bearing[J]. IEEE transactions on magnetics, 2013, 49(8): 4900-4910.
[11] 邱家俊. 电机的机电耦联与磁固耦合非线性振动研究[J]. 中国电机工程学报, 2002, 22(5): 109-115.
QIU J J.Investigation on coupled mechanical and electrical vibration and coupled magnetical and solid vibration of electrical machine[J]. Proceedings of the CSEE, 2002, 22(5): 109-115.
[12] 胡宇达, 邱家俊, 卿光辉. 大型汽轮发电机定子端部绕组整体结构的电磁振动[J]. 中国电机工程学报, 2003, 23(7): 93-98, 116.
HU Y D, QIU J J, QIN G H.Electromagnetic vibration of integrity end winding of large turbo-generator stator[J]. Proceedings of the CSEE, 2003, 23(7): 93-98, 116.
[13] 陈峻峰, 刘昆, 梁文杰, 等. 磁悬浮飞轮储能系统机电耦合非线性动力学研究[J]. 动力学与控制学报, 2013, 11(3): 225-234.
CHEN J F, LIU K, LIANG W J, et al.Study on nonlinear dynamics of electromechanical coupling in flywheel energy storage system based on active magnetic bearings[J]. Journal of dynamics and control, 2013, 11(3): 225-234.
[14] 何海婷, 柳亦兵, 巴黎明, 等. 基于BP神经网络的飞轮储能系统主动磁轴承非线性动力学模型[J]. 中国电机工程学报, 2022, 42(3): 1184-1198.
HE H T, LIU Y B, BA L M, et al.Nonlinear dynamic model of active magnetic bearing in flywheel system based on BP neural network[J]. Proceedings of the CSEE, 2022, 42(3): 1184-1198.
[15] 陈亮亮, 祝长生, 王忠博. 电磁轴承高速飞轮转子模态分离-状态反馈解耦控制[J]. 中国电机工程学报, 2017, 37(18): 5461-5472, 5546.
CHEN L L, ZHU C S, WANG Z B.Decoupling control for active magnetic bearing high-speed flywheel rotor based on mode separation and state feedback[J]. Proceedings of the CSEE, 2017, 37(18): 5461-5472, 5546.
[16] GAO J, WANG G, LIU X, et al.Cogging torque reduction by elementary-cogging-unit shift for permanent magnet machines[J]. IEEE transactions on magnetics, 2017, 53(11):1-5.
[17] HE H T, LIU Y B, BA L M.A nonlinear dynamic model of flywheel energy storage systems based on alternative concept of back propagation neural networks[J]. Journal of computational and nonlinear dynamics, 2022, 17(9): 091006.
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