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提出了一种新的基于机械弹性的储能方法, 推导了永磁电机式机械弹性储能机组的非线性动力学模型, 论证了机组储能过程中某些参数及运行条件下会出现混沌运动, 分析了机组非线性动力学模型的线性稳定性. 在此基础上, 基于本实验室正在研发的0.16 kWh/0.8 kW机械弹性储能机组运行参数, 将机组3维非线性模型降阶为带时变参数的2维投影子系统, 采用坐标平面投影法研究了机组的混沌特性, 分析了降维子系统平衡点位置及特征方程随时变参数的变化关系, 并对机组混沌运动进行了数值验证, 在一定程度上解决了解析方法, 适用性较差导致对多维机电耦联系统只能仿真求解难以理论分析的问题.A new way of energy storage based on mechanical elasticity is proposed. Nonlinear dynamic model of permanent magnet motor based mechanical elastic energy storage unit is derived, and the chaotic behaviors under certain parameter values and operation conditions are demonstrated. The linear stability of the nonlinear dynamic model is analyzed. Based on the operation parameters of the 0.16 kWh/0.8 kW unit that is being developed in our laboratory, three-dimensional nonlinear model is reduced to two-dimensional projection subsystem with varying parameters. Then the chaotic property of the unit is analyzed by coordinate plane projection method, the changing relationship between the locations of equilibrium point, characteristic equation of reduction subsystem and varying parameters is discussed, and the chaotic behavior is numerically verified. The issue caused by poor applicability of analytical methods and solved only by simulation is solved to some extent at a theoretical analysis level.
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[19] Cheng S J, Yu W H, Wen J Y, Sun H S, Wang H F 2007 Power Syst. Technol. 31 97 (in Chinese) [程时杰, 余文辉, 文劲宇, 孙海顺, 王海风 2007 电网技术 31 97]
[20] Mi Z Q, Wang Z Q, Yu Y, Duan W C. N. Patent 201639308 U [2010-11-17] (in Chinese) [米增强, 王璋奇, 余洋, 段巍 中国专利 201639308 U] [2010-11-17]
[21] Duan W, Feng H C, Wang Z Q 2011 Chin. J. Constr. Mach. 9 493 (in Chinese) [段巍, 冯恒昌, 王璋奇 2011 中国工程机械学报 9 493]
[22] Li Z, Jin B P, Joo Y H, Zhang B, Chen G R 2002 IEEE Trans. Circ. Syst. 49 383
[23] Yang G L, Li H G 2009 Acta Phys. Sin. 58 7552 (in Chinese) [杨国良, 李惠光 2009 58 7552]
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[25] Zheng G, Zou J X, Xu H B, Qin G 2011 Acta Phys. Sin. 60 7552 (in Chinese) [郑刚, 邹见效, 徐红兵, 秦钢 2011 60 7552]
[26] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 [任丽娜, 刘福才, 焦晓红, 李俊义 2012 61 060506]
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[29] Mohammad P A 2012 Chin. Phys. B 21 100505
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[35] Zhou X Y 2011 Acta Phys. Sin. 60 100503 (in Chinese) [周小勇 2011 60 100503]
[36] Wang Z, Li Y X, Hui X X, Lü L Acta Phys. Sin. 60 010513 (in Chinese) [王震, 李永新, 惠小健, 吕雷 2011 60 010513]
[37] Xue Y S 1999 Motion Stability quantification Theory (Nanjing: Phoenix Science Press) (in Chinese) [薛禹胜 1999 运动稳定性量化理论(南京: 江苏科学技术出版社)]
[38] Ge X H 2007 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [葛晓慧 2007 博士学位论文 (杭州: 浙江大学)]
[39] Xue Y S, Wu Q H, Zhou H Q, Tan B, Lau K W 2003 J. Nonlin. Dyn. Sci. Technol. 21 1 (in Chinese) [薛禹胜, Wu Q H, 周海强, 檀斌, Lau K W 2003 非线性动力学学报 21 1]
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[1] Cohen A I, Wan S H 1985 IEEE Trans. Power Appar. Syst. 104 2099
[2] Schainker P B, Nakhamkin M 1985 IEEE Trans. Power Appar. Syst. 4 790
[3] Hebner R, Beno J, Walls A 2002 IEEE Spectr. Mag. 39 46
[4] Ji L T, Zhang J C 2010 Proc. CSEE 31 101 (in Chinese) [姬联涛, 张建成 2010 中国电机工程学报 31 101]
[5] Ali M H, Bin Wu, Dougal R A 2010 IEEE Trans. Sust. Ener. 1 38
[6] Ma L, Huang A Q, Li J 2011 Chin. Phys. B 20 037104
[7] Han C, Li Y, Yu J, Tang Y J, Cheng S J, Pan Y 2001 Aut. Electr. Power Syst. 25 63 (in Chinese) [韩翀, 李艳, 余江, 唐跃进, 程时杰, 潘 垣 2001 电力系统自动化 25 63]
[8] Rufer A, Hotellier D, Barrade P 2004 IEEE Trans. Power Deliver. 19 629
[9] Yu H W, Xu M J, Duan W T, Sui Z 2007 Acta Phys. Sin. 56 4158 (in Chinese) [於海武, 徐美健, 段文涛, 隋展 2007 56 4158]
[10] Yan X W, Yu H W, Cao D X, Li M Z, Jiang D B, Jiang X Y, Duan W T, Xu M J 2009 Acta Phys. Sin. 58 4230 (in Chinese) [严雄伟, 於海武, 曹丁象, 李明中, 蒋东镔, 蒋新颖, 段文涛, 徐美健 2009 58 4230]
[11] Caumont O, Le Moigne P, Rombaut C, Muneret X, Lenain P 2000 IEEE Trans. Energ. Conver. 15 354
[12] Bai Y, Wang B, Zhang W F 2011 Acta Phys. Sin. 60 068202 (in Chinese) [白莹, 王蓓, 张伟风 2011 60 068202]
[13] Li J, Yang C Z, Zhang X G, Zhang J, Xia B J 2009 Acta Phys. Sin. 58 6573 (in Chinese) [李佳, 杨传铮, 张熙贵, 张建, 夏保佳 2009 58 6573]
[14] Ellis M W, Von Spakovsky M R, Nelson D J 2001 Proc. IEEE 89 1808
[15] Ruan W, Xie A D, Yu X G, Wu D L 2011 Chin. Phys. B 20 043104
[16] Liu X Y, Wang C Y, Tang Y J, Sun W G, Wu W P 2010 Chin. Phys. B 19 036103
[17] Niu X L, Deng Y F, Li X 2009 Acta Phys. Sin. 58 7313 (in Chinese) [牛雪莲, 邓玉福, 李雪 2009 58 7313]
[18] Cheng S J, Wen J Y, Sun H S 2005 Electrotechnical Application 24 1 (in Chinese) [程时杰, 文劲宇, 孙海顺 2005 电气应用 24 1]
[19] Cheng S J, Yu W H, Wen J Y, Sun H S, Wang H F 2007 Power Syst. Technol. 31 97 (in Chinese) [程时杰, 余文辉, 文劲宇, 孙海顺, 王海风 2007 电网技术 31 97]
[20] Mi Z Q, Wang Z Q, Yu Y, Duan W C. N. Patent 201639308 U [2010-11-17] (in Chinese) [米增强, 王璋奇, 余洋, 段巍 中国专利 201639308 U] [2010-11-17]
[21] Duan W, Feng H C, Wang Z Q 2011 Chin. J. Constr. Mach. 9 493 (in Chinese) [段巍, 冯恒昌, 王璋奇 2011 中国工程机械学报 9 493]
[22] Li Z, Jin B P, Joo Y H, Zhang B, Chen G R 2002 IEEE Trans. Circ. Syst. 49 383
[23] Yang G L, Li H G 2009 Acta Phys. Sin. 58 7552 (in Chinese) [杨国良, 李惠光 2009 58 7552]
[24] Li D, Wang S L, Zhang X H, Yang D 2010 Chin. Phys. B 18 1399
[25] Zheng G, Zou J X, Xu H B, Qin G 2011 Acta Phys. Sin. 60 7552 (in Chinese) [郑刚, 邹见效, 徐红兵, 秦钢 2011 60 7552]
[26] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 [任丽娜, 刘福才, 焦晓红, 李俊义 2012 61 060506]
[27] Lü L, Yu M, Wei L L, Zhang M, Li Y S 2012 Chin. Phys. B 21 100507
[28] Zhai L J, Zheng Y J, Ding S L 2012 Chin. Phys. B 21 070503
[29] Mohammad P A 2012 Chin. Phys. B 21 100505
[30] Li W L, Li S F, Li G 2012 Chin. Phys. B 21 064217
[31] Li N, Sun H Y, Zhang Q L 2012 Chin. Phys. B 21 010503
[32] Zhao H, Ma Y J, Liu S J, Gao S G, Zhong D 2012 Chin. Phys. B 20 120501
[33] Ahn C K 2011 Chin. Phys. Lett. 28 100504
[34] Brugnago E L, Rech P C 2011 Chin. Phys. Lett. 28 110506
[35] Zhou X Y 2011 Acta Phys. Sin. 60 100503 (in Chinese) [周小勇 2011 60 100503]
[36] Wang Z, Li Y X, Hui X X, Lü L Acta Phys. Sin. 60 010513 (in Chinese) [王震, 李永新, 惠小健, 吕雷 2011 60 010513]
[37] Xue Y S 1999 Motion Stability quantification Theory (Nanjing: Phoenix Science Press) (in Chinese) [薛禹胜 1999 运动稳定性量化理论(南京: 江苏科学技术出版社)]
[38] Ge X H 2007 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [葛晓慧 2007 博士学位论文 (杭州: 浙江大学)]
[39] Xue Y S, Wu Q H, Zhou H Q, Tan B, Lau K W 2003 J. Nonlin. Dyn. Sci. Technol. 21 1 (in Chinese) [薛禹胜, Wu Q H, 周海强, 檀斌, Lau K W 2003 非线性动力学学报 21 1]
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