摘要针对电力系统中普遍存在的参数变化引起系统混沌振荡导致系统不稳定问题，提出了一种基于浸入与不变(immersion and invariance ，I&I)原理的自适应反演滑模控制(adaptive backstepping sliding mode control ，ABSMC)算法，以提高电力系统运行稳定性。首先利用电力系统非线性模型，分析无功功率的变化对系统动力学行为的影响。其次融入浸入与不变(I&I)原理，对系统中存在的未知非线性项和外部扰动进行补偿，设计扰动估计自适应律，利用反演原理设计控制器，并通过Lyapunov稳定性理论对所提出的控制方法进行收敛性证明。最后，对系统进行数值仿真实验，结果表明，所提方法可有效辨识出系统的动态扰动，使系统所有状态变量迅速收敛，提高了系统的响应速度。
Abstract：Aiming at the problem of system instability caused by system chaotic oscillation caused by the ubiquitous parameter changes in power systems, an adaptive backstepping sliding mode control (ABSMC) algorithmbased on the principle of immersion and invariance (I&I) is proposed to improve power system operation stability. Firstly, the nonlinear model of power system is used to analyze the influence of reactive power change on system dynamic behavior. Secondly, it integrates the principle of immersion and invariance (I&I) to compensate for the unknown nonlinear term and external disturbance in the system, design the disturbance estimation adaptive law, use the backstepping principle to design the controller, and use the Lyapunov stability theory to analyze the proposed proof of convergence of the control method. Finally, a numerical simulation experiment is performed on the system. The results show that the proposed method can effectively identify the dynamic disturbance of the system, make all the state variables of the system converge quickly, and improve the response speed of the system.
王定胜，张宏立，王聪，张绍华. 基于浸入与不变原理的电力系统混沌振荡分析与控制[J]. 振动与冲击, 2022, 41(4): 142-149.
WANG Dingsheng,ZHANG Hongli,WANG Cong,ZHANG Shaohua. Analysis and control of power system chaotic oscillation based on the immersion and invariance principle. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(4): 142-149.
[1] 贾宏杰, 余贻鑫, 王成山. 电力系统混沌现象及相关研究[J]. 中国电机工程学报, 2001, 21(07): 27-31.
JIA Hongjie, YU Yixin, WANG Chengshan. Chaotic phenomena in power systems and its studies[J]. Proceedings of The Chinese Society for Electrical Engineering, 2001, 21(07): 27-31.
[2] Ajjarapu V, Christy C. The Continuation power flow:A tool for state voltage stability analysis[J]. IEEE Trans on Power Systems, 1992, 7(01):416-423.
[3] 刘美菊. 电力系统混沌动力学行为分析与控制研究[D]. 沈阳：沈阳农业大学, 2009.
LIU Meiju. Study on chaotic dynamic behavior and control in power system[D]. Shengyang: Shenyang Agricultural University, 2009.
[4] 王晓东, 陈予恕. 一类电力系统的分岔和奇异性分析[J]. 振动与冲击, 2014, 33(04): 1-6.
WANG Xiaodong CHEN Yushu. Bifurcation and singularity analysis for a class of power systems [J]. Journal of Vibration and Shock. 2014, 33(04): 1-6.
[5] Makarov Y V, Reshetov V I, Stroev A, et al. Blackout prevention in the United States, Europe and Russia.[J]. Proceedings of the IEEE, 2005, 93(11): 1942-1955.
[6] 张强，王宝华. 基于变量反馈的电力系统混沌振荡控制[J]. 电力自动化设备, 2002(10): 6-9.
ZHANG Qiang, WANG Baohua. Chaos control with variable feedback in power system[J]. Electric Power Automation Equipment, 2002(10): 6-9.
[7] 张强, 王宝华. 应用延时反馈控制电力系统混沌振荡[J]. 电网技术, 2004(07): 23-26.
ZHANG Qiang, WANG Baohua. Controlling power system chaotic oscillation by time-elayed feedback[J]. Power System Technology, 2004(07): 23-26.
[8] 马幼捷, 李小双, 周雪松, 等. 基于Washout-filter方法的电力系统动分岔控制[J]. 电力系统保护与控制, 2011, 39(23): 54-59.
MA Youjie, LI Xiaoshuang, ZHOU Xuesong, et al. Control of dynamic bifurcation in power system based on Washout-filter. Power System Protection and Control, 2011, 39(23): 54-59.
[9] 杨晓辉, 王毅, 刘小平, 等. 基于反演滑模变的电力系统混沌振荡控制[J]. 科学技术与工程, 2017, 17（18）：221-225.
YANG Xiaohui, WANG Yi, LIU Xiaoping, et al. Chaos control in power system based on inversion sliding mode[J]. Science Technology and Engineering, 2017, 17(18): 221-225.
[10] 倪骏康, 刘崇新, 庞霞. 电力系统混沌振荡的等效快速终端模糊滑模控制[J]. 物理学报, 2013, 62(19): 1905071-1905077.
NI Junkang, LIU Chongxin, PANG Xia. Equivalent fast terminal fuzzy sliding mode control of power system chaotic oscillation[J], Acta Physica Sinica, 2013, 62(19): 1905071-1905077.
[11] Ahmad S A A, Saeedd B. Chaos control of the power system via sliding mode based on fuzzy supervisor[J].International Journal of Intelligent Computing and Cybernetics, 2017, 10(01): 68-79.
[12] Wang C, Zhang H L, Fan W H, et al. Adaptive control method for chaotic power systems based on finite-time stability theory and passivity-based control approach[J]. Chaos, Solitons and Fractals, 2018, 112(05): 159-167.
[13] 徐昌彪，钟德，夏诚，等. 一个新的超大范围混沌系统及其自适应滑模控制[J]. 振动与冲击, 2019, 38(03): 125-130.
XU Changbiao, ZHONG De, XIA Cheng, et al. A new chaotic system with parameter b in a super-large range and its adaptive sliding mode control.[J]. Journal of Vibration and Shock. 2019, 38(03): 125-130.
[14] Ayar M, Obuz S, Trevizan R D, et al. A distributed control approach for enhancing smart grid transient stability and resilience[J]. IEEE Transactions on Smart Grid, 2017, 8(06): 3035-3044.
[15] 陈世明, 卢家胜, 高彦丽. 基于神经网络的电力系统暂态稳定分布式自适应控制[J]. 控制与决策, 2021, 36(06):1407-1414.
CHEN Shimingy, LU Jiasheng, GAO Yanli. Neural network-based distributed adaptive control for power system Transient Stability[J]. Control and Decision ，2021, 36(06):1407-1414.
[16] Astolfi A, Ortega R. Immersion and invariance:a new tool for stabilization and adaptive control of nonlinear systems [J]. IEEE Transactions on Automatic Control, 2003, 48(04): 590-606.
[17] Astolfi A, Karagiannis D, and Ortega R. Nonlinear and adaptive control design and applications[M], London: Springer-Verlag, Chap. 2, 2007.
[18] Zhao B, Xian B, Zhang Y, et al. Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Transaction on Industrial Electronics, 2015, 62(05): 2891-2902.
[19] 侯小燕, 薛文涛, 张晨. 基于浸入与不变的气动弹性系统反演滑模控制[J]. 航天控制, 2016, 34(04): 3-9.
HOU Xiaoyan, XUE Wentao, ZHANG Chen. Backstepping sliding mode control of aeroelastic system based on immersion and invariance[J]. Aerospace Control, 2016, 34(04): 3-9.
[20] 夏琳琳, 丛靖宇, 马文杰, 等. 基于浸入与不变原理的四旋翼姿态系统反步滑模控制[J]. 中国惯性技术学报, 2017, 25(05): 695-700.
XIA Linlin, CONG Jingyu, MA Wenjie, et al. Backstepping sliding mode control of quadrotor attitude system based on immersion and invariance[J]. Journal of Chinese Inertial Technology, 2017, 25(05): 695-700.
[21] 夏冬冬, 岳晓奎. 基于浸入与不变理论的航天器姿态跟踪自适应控制[J]. 航空学报, 2020, 41(02): 312-323.
XIA Dongdong, YUE Xiaokui. Immersion and invariance based attitude adaptive tracking control for spacecraft[J], Acta Aeronautica et Astronautica Sinica, 2020, 41(02): 312-323.
