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The permanent magnet synchronous generator (PMSG) for wind turbine system operating under inevitable stochastic disturbance from wind power is a nonlinear stochastic dynamical system. With the random interaction and nonlinearity, the intense nonlinear stochastic oscillation is likely to happen in such a system, causing the system to be unstable or even collapse. However, the PMSG is usually considered as a deterministic system when analyzing its nonlinear dynamic behaviors in the past researches. Such a simplification can lead to wrong predictions for the system stability and reliability. This paper aims to discuss the effect of the stochastic disturbance on the nonlinear dynamic behavior of the PMSG. Based on the derived PMSG model considering the stochastic disturbance from the input mechanical torque, the evolution of the system global structure with the stochastic intensity is investigated using the generalized cell mapping digraph method. Meanwhile, the occurrence process and development process of the stochastic bifurcation are illustrated. Based on this global analysis, the intrinsic mechanism for the effect of the stochastic disturbance on the operating performances of the PMSG is revealed. Finally, the numerical simulations based on the Euler-Maruyama algorithm are carried out to validate the results of the theoretical analysis. The results present that as the intensity of the stochastic disturbance increases, two kinds of stochastic bifurcations can be observed in the PMSG system according to the definition of a sudden change in characteristic of the stochastic attractor. One is the stochastic interior crisis that occurs when a stochastic attractor collides with a stochastic saddle in its attraction basin interior, leading to the abrupt increase of the attractor and the disappearance of the saddle. This kind of bifurcation results in the intense stochastic oscillation and instability of the PMSG system. Another stochastic bifurcation is the stochastic boundary crisis which occurs when a stochastic attractor collides with the boundary of its attraction basin and results in the disappearance of the attractor. This sudden change of the number of stochastic attractors induces the stable solution set to vanish and thus the PMSG system to collapse. In a word, even the stochastic disturbance with small intensity may lead to the complete destruction of the stable structure of the PMSG, inducing the system to suffer a strong disordered oscillation or the operation to collapse. The results of this paper can provide significant theoretic reference for both practically operating and designing the PMSG for wind turbine systems.
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Keywords:
- permanent magnet synchronous generator /
- stochastic bifurcation /
- nonlinear /
- cell mapping
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[2] Xue W, Guo Y L, Chen Z Q 2009 Acta Phys. Sin. 58 8146 (in Chinese)[薛薇, 郭彦岭, 陈增强 2009 物理学报 58 8146]
[3] Wei D Q, Luo X S, Fang J Q, Wang B H 2006 Acta Phys. Sin. 55 54 (in Chinese)[韦笃取, 罗晓曙, 方锦清, 汪秉宏 2006 物理学报 55 54]
[4] Rasoolzadeh A, Tavazoei M S 2012 Phys. Lett. A 377 73
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[7] Wang L, Li Y H, Lu G L, Zhu X H 2011 Electric Power Automation Equipment 31 45 (in Chinese)[王磊, 李颖晖, 逯国亮, 朱喜华 2011 电力自动化设备 31 45]
[8] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 (in Chinese)[任丽娜, 刘福才, 焦晓红, 李俊义 2012 物理学报 61 060506]
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[14] Jiang J, Xu J X 1994 Phys. Lett. A 188 137
[15] Hsu C S 1995 Int. J. Bifurcat. Chaos 5 1085
[16] Xu W, He Q, Rong H W, Fang T 2003 Acta Phys. Sin. 52 1365 (in Chinese)[徐伟, 贺群, 戎海武, 方同 2003 物理学报 52 1365]
[17] Xu W, Yue X L 2010 Sci. China:Technol. Sci. 53 664
[18] Li Z G, Jiang J, Hong L 2015 Int. J. Bifurcat. Chaos 25 1550109
[19] Arnold L 1998 Random Dynamical Systems (Berlin, Heidelberg, New York:Springer) pp34-35
[20] Levitas J, Weller T, Singer J 1994 J. Sound Vib. 176 641
[21] He Q, Xu W, Li S, Xiao Y Z 2008 Acta Phys. Sin. 57 4021 (in Chinese)[贺群, 徐伟, 李爽, 肖玉柱 2008 物理学报 57 4021]
[22] Gong P L, Xu J X 1998 Appl. Math. Mech. 19 1087 (in Chinese)[龚璞林, 徐健学 1998 应用数学和力学 19 1087]
[23] Zhu W Q, Yu J S 1987 J. Sound Vib. 117 421
[24] Hong L, Xu J X 2002 Acta Phys. Sin. 51 2694 (in Chinese)[洪灵, 徐健学 2002 物理学报 51 2694]
[25] Guan Y H 2009 Statistics (Beijing:Higher Education Press) pp66-83 (in Chinese)[管于华 2009 统计学 (北京:高等教育出版社) 第66–83页]
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[1] Zhang B, Li Z, Mao Z Y, Pang M X 2001 Proc. CSEE 21 13 (in Chinese)[张波, 李忠, 毛宗源, 庞敏熙 2001 中国电机工程学报 21 13]
[2] Xue W, Guo Y L, Chen Z Q 2009 Acta Phys. Sin. 58 8146 (in Chinese)[薛薇, 郭彦岭, 陈增强 2009 物理学报 58 8146]
[3] Wei D Q, Luo X S, Fang J Q, Wang B H 2006 Acta Phys. Sin. 55 54 (in Chinese)[韦笃取, 罗晓曙, 方锦清, 汪秉宏 2006 物理学报 55 54]
[4] Rasoolzadeh A, Tavazoei M S 2012 Phys. Lett. A 377 73
[5] Yang G L, Li H G 2009 Acta Phys. Sin. 58 7552 (in Chinese)[杨国良, 李惠光 2009 物理学报 58 7552]
[6] Zheng G, Zou J X, Xu H B, Qin G 2011 Acta Phys. Sin. 60 060506 (in Chinese)[郑刚, 邹见效, 徐红兵, 秦钢 2011 物理学报 60 060506]
[7] Wang L, Li Y H, Lu G L, Zhu X H 2011 Electric Power Automation Equipment 31 45 (in Chinese)[王磊, 李颖晖, 逯国亮, 朱喜华 2011 电力自动化设备 31 45]
[8] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 (in Chinese)[任丽娜, 刘福才, 焦晓红, 李俊义 2012 物理学报 61 060506]
[9] Messadi M, Mellit A, Kemih K, Ghanes M 2015 Chin. Phys. B 24 010502
[10] Hsu C S 1980 J. Appl. Mech. 47 931
[11] Xu W 2013 Numerical Analysis Methods for Stochastic Dynamical System (Beijing:Science Press) p43 (in Chinese)[徐伟 2013 非线性随机动力学的若干数值方法及应用 (北京:科学出版社) 第43页]
[12] Hsu C S 1981 J. Appl. Mech. 48 634
[13] Tongue B H, Gu K 1988 J. Sound Vib. 125 169
[14] Jiang J, Xu J X 1994 Phys. Lett. A 188 137
[15] Hsu C S 1995 Int. J. Bifurcat. Chaos 5 1085
[16] Xu W, He Q, Rong H W, Fang T 2003 Acta Phys. Sin. 52 1365 (in Chinese)[徐伟, 贺群, 戎海武, 方同 2003 物理学报 52 1365]
[17] Xu W, Yue X L 2010 Sci. China:Technol. Sci. 53 664
[18] Li Z G, Jiang J, Hong L 2015 Int. J. Bifurcat. Chaos 25 1550109
[19] Arnold L 1998 Random Dynamical Systems (Berlin, Heidelberg, New York:Springer) pp34-35
[20] Levitas J, Weller T, Singer J 1994 J. Sound Vib. 176 641
[21] He Q, Xu W, Li S, Xiao Y Z 2008 Acta Phys. Sin. 57 4021 (in Chinese)[贺群, 徐伟, 李爽, 肖玉柱 2008 物理学报 57 4021]
[22] Gong P L, Xu J X 1998 Appl. Math. Mech. 19 1087 (in Chinese)[龚璞林, 徐健学 1998 应用数学和力学 19 1087]
[23] Zhu W Q, Yu J S 1987 J. Sound Vib. 117 421
[24] Hong L, Xu J X 2002 Acta Phys. Sin. 51 2694 (in Chinese)[洪灵, 徐健学 2002 物理学报 51 2694]
[25] Guan Y H 2009 Statistics (Beijing:Higher Education Press) pp66-83 (in Chinese)[管于华 2009 统计学 (北京:高等教育出版社) 第66–83页]
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