Nonlinear dynamic model and chaotic characteristics of mechanical thastic energy storage unit in energy storage process

Yu Yang; Mi Zeng-Qiang

doi:10.7498/aps.62.038403

Abstract

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.

Keywords:

Authors and contacts

1.
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Baoding 071003, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51077053), and the Fundamental Research Funds for the Central Universities, China (Grant No. 11MG40).

References

[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]

Cited By

[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]

[1]	Huang Xiao-Dong, He Bin-Xuan, Song Zhen, Mi Yuan-Yuan, Qu Zhi-Lin, Hu Gang. A review of advances in multiscale modelings, computations, and dynamical theories of arrhythmias. Acta Physica Sinica, 2024, 73(21): 218702. doi: 10.7498/aps.73.20240977
[2]	Xu Zi-Fei, Miao Wei-Pao, Li Chun, Jin Jiang-Tao, Li Shu-Jun. Nonlinear feature extraction and chaos analysis of flow field. Acta Physica Sinica, 2020, 69(24): 249501. doi: 10.7498/aps.69.20200625
[3]	Wu Zhong-Qiang, Wu Chang-Han, Zhao Li-Ru, Jia Wen-Jing. Robust control for permanent magnet synchronous motors based on Hamiltonian function. Acta Physica Sinica, 2015, 64(9): 090503. doi: 10.7498/aps.64.090503
[4]	Yu Jie, Guo Xia-Sheng, Tu Juan, Zhang Dong. Mecanism and applications of the nonlinear dynamic response to ultrasound contrast agent microbubbles. Acta Physica Sinica, 2015, 64(9): 094306. doi: 10.7498/aps.64.094306
[5]	Dang Xiao-Yu, Li Hong-Tao, Yuan Ze-Shi, Hu Wen. Chaotic map implementation based on digital-analog hybrid method. Acta Physica Sinica, 2015, 64(16): 160501. doi: 10.7498/aps.64.160501
[6]	Liu Yan, Zhang Wen-Ming, Zhong Zuo-Yang, Peng Zhi-Ke, Meng Guang. Nonlinear dynamic analysis of nano-resonator driven by optical gradient force. Acta Physica Sinica, 2014, 63(2): 026201. doi: 10.7498/aps.63.026201
[7]	Wu Zhong-Qiang, Yang Yang, Xu Chun-Hua. Fault diagnosis for permanent magnet synchronous generator under chaos conditions：LMI approach. Acta Physica Sinica, 2013, 62(15): 150507. doi: 10.7498/aps.62.150507
[8]	Wang Guang-Yi, Yuan Fang. Cascade chaos and its dynamic characteristics. Acta Physica Sinica, 2013, 62(2): 020506. doi: 10.7498/aps.62.020506
[9]	Xiao Jian-Xin, Chen Ju-Fang, Peng Jian-Hua. Dynamic behavior and chaos synchronization of a simple nonlinear time-delayed system. Acta Physica Sinica, 2013, 62(17): 170507. doi: 10.7498/aps.62.170507
[10]	Ding Hu, Yan Qiao-Yun, Chen Li-Qun. Chaotic dynamics in the forced nonlinear vibration of an axially accelerating viscoelastic beam. Acta Physica Sinica, 2013, 62(20): 200502. doi: 10.7498/aps.62.200502
[11]	Zheng An-Jie, Wu Zheng-Mao, Deng Tao, Li Xiao-Jian, Xia Guang-Qiong. Nonlinear dynamics of 1550 nm vertical-cavity surface-emitting laser with polarization- preserved optical feedback. Acta Physica Sinica, 2012, 61(23): 234203. doi: 10.7498/aps.61.234203
[12]	Wang Cong-Qing, Wu Peng-Fei, Zhou Xin. Control and modeling of chaotic dynamics for a free-floating rigid-flexible coupling space manipulator based on minimal joint torque's optimization. Acta Physica Sinica, 2012, 61(23): 230503. doi: 10.7498/aps.61.230503
[13]	Niu Chao, Li Xi-Hai, Liu Dai-Zhi. Chaotic dynamic characteristics of Z component in geomagnetic variation field. Acta Physica Sinica, 2010, 59(5): 3077-3087. doi: 10.7498/aps.59.3077
[14]	Zhang Xiao-Fang, Chen Zhang-Yao, Bi Qin-Sheng. Evolution from regular movement patterns to chaotic attractors in a nonlinear electrical circuit. Acta Physica Sinica, 2010, 59(5): 3057-3065. doi: 10.7498/aps.59.3057
[15]	Xue Wei, Guo Yan-Ling, Chen Zeng-Qiang. Analysis of chaos and circuit implementation of a permanent magnet synchronous motor. Acta Physica Sinica, 2009, 58(12): 8146-8151. doi: 10.7498/aps.58.8146
[16]	Shi Pei-Ming, Liu Bin, Hou Dong-Xiao. Chaotic motion of some relative rotation nonlinear dynamic system. Acta Physica Sinica, 2008, 57(3): 1321-1328. doi: 10.7498/aps.57.1321
[17]	Yu Hong-Jie, Liu Yan-Zhu. Synchronization of symmetrically nonlinear-coupled chaotic systems. Acta Physica Sinica, 2005, 54(7): 3029-3033. doi: 10.7498/aps.54.3029
[18]	Jiang Ke-Yu, Cai Zhi-Ming. Optimization of scaled probabilistic cleaning methods. Acta Physica Sinica, 2005, 54(10): 4596-4601. doi: 10.7498/aps.54.4596
[19]	LI GUO-HUI, ZHOU SHI-PING, XU DE-MING, LAI JIAN-WEN. AN OCCASIONAL LINEAR FEEDBACK APPROACH TO CONTROL CHAOS. Acta Physica Sinica, 2000, 49(11): 2123-2128. doi: 10.7498/aps.49.2123
[20]	WU WEI-GEN, GU TIAN-XIANG. NONLINEAR FEEDBACK FOLLOWING CONTROL OF CHAOTIC SYSTEMS. Acta Physica Sinica, 2000, 49(10): 1922-1925. doi: 10.7498/aps.49.1922

Catalog

Vol. 62, Issue 3 - 2013-02-05

Metrics

Abstract views: 7572
PDF Downloads: 937
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板