Abstract:To suppress chaotic oscillation in seven dimensional power system model, a simple sliding mode variable structure control scheme is proposed based on the existing extended state observer. By introducing dynamic models of energy storage devices for the power system model, a complex controlled ten-dimensional power system dynamic model is constructed. After defining sliding mode functions for the controlled power system, chaos control problem can be reduced to the stabilization problem of three first-order nonlinear systems. In order to stabilize these first-order systems, extended state observers and control inputs are designed and it is proved that the state variables can converge to the neighborhood of the origin in finite time under designed control inputs. Finally, the effectiveness of designed extended state observers and chaos controllers are verified by simulation. Based on the existing extended state observer, the designed control inputs do not contain derivatives of complex controlled system functions, and effectively improve their engineering practicability.
王江彬, 刘凌, 刘崇新. 基于扩张状态观测器七阶混沌振荡电力系统的滑模变结构控制[J]. 电工技术学报, 2020, 35(21): 4524-4531.
Wang Jiangbin, Liu Ling, Liu Chongxin. Sliding Mode Variable Structure Control for Seven-Dimensional Chaotic Power System Based on Extended State Observer. Transactions of China Electrotechnical Society, 2020, 35(21): 4524-4531.
[1] Srivastava K N, Srivastava S C.Elimination of dynamic bifurcation and chaos in power systems using FACTS devices[J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1998, 45(1): 72-78. [2] Harb A M, Abdel-Jabbar N.Controlling Hopf bifurcation and chaos in a small power system[J]. Chaos, Solitons and Fractals, 2003, 18(5): 1055-1063. [3] Ginarsa I M, Soeprijanto A, Purnomo M H.Controlling chaos and voltage collapse using an ANFIS-based composite controller-static var compensator in power systems[J]. International Journal of Electrical Power & Energy Systems, 2013, 46: 79-88. [4] 王宝华, 杨成梧, 张强. 电力系统分岔与混沌研究综述[J]. 电工技术学报, 2005, 20(7): 1-8. Wang Baohua, Yang Chengwu, Zhang Qiang.Summary of bifurcation and chaos research in electric power system[J]. Transactions of China Electrotechnical Society, 2005, 20(7): 1-8. [5] 李文磊. 不确定混沌电力系统的鲁棒自适应跟踪控制[J]. 电机与控制学报, 2007, 11(2): 170-173. Li Wenlei.Robust adaptive control of chaotic power systems with uncertainty[J]. Electric Machines and Control, 2007, 11(2): 170-173. [6] Ni Junkang, Liu Chongxin, Liu Kai, et al.Variable speed synergetic control for chaotic oscillation in power system[J]. Nonlinear Dynamics, 2014, 78(1): 681-690. [7] 闵富红, 马美玲, 翟炜, 等. 基于继电特性函数的互联电力系统混沌控制[J]. 物理学报, 2014, 63(5): 1-8. Min Fuhong, Ma Meiling, Zhai Wei, et al.Chaotic control of the interconnected power system based on the relay characteristic function[J]. Acta Physica Sinica, 2014, 63(5): 1-8. [8] Ni Junkang, Liu Ling, Liu Chongxin, et al.Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system[J]. Nonlinear Dynamics, 2016, 86(1): 401-420. [9] Wang Jiangbin, Liu Chongxin, Wang Yan, et al.Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system[J]. Chinese Physics B, 2018, 27(7): 1-8. [10] Ma Caoyuan, Liu Jianhua, Wang Chonglin.Chaos of a power system model and its control[J]. Journal of Vibration and Control, 2012, 18(14): 2176-2185. [11] Ni Junkang, Liu Ling, Liu Chongxin, et al.Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2017, 64(2): 151-155. [12] Rajesh K G, Padiyar K R .Bifurcation analysis of a three node power system with detailed models[J]. International Journal of Electrical Power & Energy Systems, 1999, 21(5): 375-393. [13] Yu Yixin, Jia Hongjie, Wang Chengshan.Chaotic phenomena and small signal stability region of electrical power systems[J]. Science in China Series E Technological Sciences, 2001, 44(2): 187-199. [14] Yu Yixin, Jia Hongjie, Li Peng, et al.Power system instability and chaos[J]. Electric Power Systems Research, 2003, 65(3): 187-195. [15] 贾宏杰, 余贻鑫, 李鹏. 电力系统环面分岔与混沌现象[J]. 中国电机工程学报, 2002, 22(8): 6-10. Jia Hongjie, Yu Yixin, Li Peng.Torus bifurcation and chaos in power systems[J]. Proceedings of the CSEE, 2002, 22(8): 6-10. [16] 贾宏杰, 余贻鑫, 李鹏, 等. 电力系统混沌现象与不同失稳模式之间的关系[J]. 中国电机工程学报, 2003, 23(2): 1-4. Jia Hongjie, Yu Yixin, Li Peng, et al.Relationships of power system chaos and instability modes[J]. Proceedings of the CSEE, 2003, 23(2): 1-4. [17] Wang Jiangbin, Liu Ling, Liu Chongxin, et al.Fixed-time synergetic control for a seven-dimensional chaotic power system model[J]. International Journal of Bifurcation and Chaos, 2019, 29(10): 1-14. [18] Li Shihua, Yang Jun, Chen Wenhua, et al.Generalized extended state observer based control for systems with mismatched uncertainties[J]. IEEE Transactions on Industrial Electronics, 2012, 59(12): 4792-4802. [19] Huang Yi, Luo Z W, Svinin M, et al.Extended state observer based technique for control of robot systems[C]//The 4th World Congress on Intelligent Control and Automation, Shanghai, 2002: 2807-2811. [20] 韩京清, 张荣. 二阶扩张状态观测器的误差分析[J]. 系统科学与数学, 1999(4): 465-471. Han Jingqing, Zhang Rong.Error analysis of the second order ESO[J]. Journal of Systems Science and Mathematical Sciences, 1999(4): 465-471. [21] 罗德荣, 贺锐智, 黄守道, 等. 单定子双转子盘式对转永磁同步电机动态滑模控制[J]. 电工技术学报, 2019, 34(9): 1806-1814. Luo Derong, He Ruizhi, Huang Shoudao, et al.Dynamic sliding mode control for single stator dual rotor disc counter-rotating permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2019, 34(9): 1806-1814. [22] 李鹏瀚, 王杰, 吴飞. 双馈风电机组次同步控制相互作用的反馈线性化滑模变结构抑制[J]. 电工技术学报, 2019, 34(17): 3661-3671. Li Penghan, Wang Jie, Wu Fei.Sub-synchronous control interaction mitigation for DFIGs by sliding mode control strategy based on feedback linearization[J]. Transactions of China Electrotechnical Society, 2019, 34(17): 3661-3671. [23] 张迪, 魏艳君, 杨宗丰, 等. 不平衡电网电压下基于滑模变结构控制的双馈风电系统转子侧变流器控制策略[J]. 电工技术学报, 2016, 31(17): 121-131. Zhang Di, Wei Yanjun, Yang Zongfeng, et al.Sliding-mode control for rotor-side converters of DFIG-based wind-power generation system under unbalanced grid voltage conditions[J]. Transactions of China Electrotechnical Society, 2016, 31(17): 121-131. [24] 王德贵. 永磁同步电机调速系统的模糊趋近律滑模控制[J]. 电气技术, 2015, 16(3): 10-14. Wang Degui.Sliding mode control based on fuzzy reaching law of PMSM drive system[J]. Electrical Engineering, 2015, 16(3): 10-14. [25] 张国荣, 侯立凯, 彭勃, 等. 柔性多状态开关反馈线性化滑模控制[J]. 电力系统自动化, 2020, 44(1): 126-133. Zhang Guorong, Hou Likai, Peng Bo, et al.Feedback linearization sliding mode control strategy for soft open point[J]. Automation of Electric Power Systems, 2020, 44(1): 126-133. [26] 龚鸿, 王渝红, 李媛, 等. D-STATCOM的输入-输出反馈线性化滑模变结构控制[J]. 电力系统自动化, 2016, 40(5): 102-108. Gong Hong, Wang Yuhong, Li Yuan, et al.An input-output feedback linearized sliding mode control for D-STATCOM[J]. Automation of Electric Power Systems, 2016, 40(5): 102-108. [27] Polycarpou M M, Ioannou P A.A robust adaptive nonlinear control design[J]. Automatica, 1996, 32(3): 423-427. [28] Fang Jiakun, Yao Wei, Chen Zhe, et al.Design of anti-windup compensator for energy storage-based damping controller to enhance power system stability[J]. IEEE Transactions on Power Systems, 2014, 29(3): 1175-1185. [29] 万乐. 风电场储能装置容量及最大充放电功率的确定[J]. 江西电力职业技术学院学报, 2012, 25(2): 17-20. Wan Le.Determination of capacity and maximum charge and discharge power of energy storage device in wind farm[J]. Journal of Jiangxi Vocational and Technical College of Electricity, 2012, 25(2): 17-20.