时变时滞电力系统鲁棒稳定性新判据
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摘要
基于不确定时滞电力系统稳定保守性问题,构造新型Lyapunov-Krasovskii泛函。首先,引进一种新自由矩阵不等式方法处理泛函导数中的积分项,得到时变时滞电力系统的鲁棒稳定判据;其次,利用线性矩阵不等式工具箱进行求解。最后,以单机无穷大系统为例进行仿真,Matlab仿真结果表明了所提方法的有效性与优越性。
Based on the conservativeness of the stability of uncertain time-delay power systems, a novel Lyapunov-Krasovskii functionalis is constructed. Firstly, a new stability criterion is established by introducing and applying a new free-matrix-based integral inequalityapproach to deal with the integral terms yielded in functional derivatives, then the results are obtained that are formulated in the form of linear matrix inequalities(LMI). Finally, the single machine system is taken for a typical example to show the effectiveness and superiority of the proposed method in Matlab.
Based on the conservativeness of the stability of uncertain time-delay power systems, a novel Lyapunov-Krasovskii functionalis is constructed. Firstly, a new stability criterion is established by introducing and applying a new free-matrix-based integral inequalityapproach to deal with the integral terms yielded in functional derivatives, then the results are obtained that are formulated in the form of linear matrix inequalities(LMI). Finally, the single machine system is taken for a typical example to show the effectiveness and superiority of the proposed method in Matlab.
引文
[1]Zeng Hongbing,He Yong,Wu Min,et al.New results on stability analysis for systems with discrete distributed delay[J].Automatic,2015,60(10):189-192.
[2]Zeng Hongbing,He Yong,Wu Min,et al.Free matrix based integral inequality for stability analysis of systems with time-varying delay[J].IEEE Transactions on Automatic Control,2015,60(10):2768-2772.
[3]陈刚,王信.分析时变时滞系统稳定性的新判据[J].湖南工业大学学报,2017,31(1):60-63.Chen Gang,Wang Xin.A new criterion for the stability analysis of time varying delay systems[J].Journal of Hunan University of Technology.2017,31(1):60-63.
[4]贾宏杰,谢星星,余晓丹.考虑时滞影响的电力系统小扰动稳定域[J].电力系统自动化,2006,30(21):1-5.Jia Hongjie,Xie Xingxing,Yu Xiaodan.Power system small signal stability region with time delay considered[J].Automation of Electric Power Systems,2006,30(21):1-5.
[5]贾宏杰,陈建华,余晓丹.时滞环节对电力系统小扰动稳定性的影响[J].电力系统自动化,2006,30(5):5-8.Jia Hongjie,Chen Jianhua,Yu Xiaodan.Impact of time delay on power system small signal stability[J].Automation of Electric Power Systems,2006,30(5):5-8.
[6]贾宏杰,尚蕊,张宝贵.电力系统时滞稳定裕度求解法[J].电力系统自动化,2007,31(2):5-11.Jia Hongjie,Shang Rui,Zhang Baogui.Computation of delay stability margin of electric power systems[J].Automation of Electric Power Systems,2007,31(2):5-11.
[7]贾宏杰,安海云,余晓丹.电力系统改进时滞依赖型稳定判据[J].电力系统自动化,2008,32(19):15-19.Jia Hongjie,An Haiyun,Yu Xiaodan.An improved delay-dependent stability criteria for power system with multiple time delays[J].Automation of Electric Power Systems,2008,32(19):15-19.
[8]孙国强,屠越,孙永辉,等.时变时滞电力系统鲁棒稳定性的改进型判据[J].电力系统自动化,2015,39(3):59-62.Sun Guoqiang,Tu Yue,Sun Yonghui,et al.An improved robust stability criterion for power systems with time varying delay[J].Automation of Electric Power Systems,2015,39(3):59-62.
[9]厉文秀.随机时滞电力系统稳定性分析[J].电力与能源,2015,31(3):10-15.Li Wenxiu.Analysis of stability of stochastic time delay power systems[J].Power System and Clean Energy,2015,31(3):10-15.
[10]贾宏杰,安海云,余晓丹.电力系统时滞依赖型稳定判据及其应用[J].电力系统自动化,2010,34(3):6-11.Jia Hongjie,An Haiyun,Yu Xiaodan.A delay-dependent robust stability criterion for power system and its application[J].Automation of Electric Power Systems,2010,34(3):6-11.
[11]Xie L.Output feedback H∞control of systems with uncertainty[J].International Journal of Control,1996,63(4):741-750.
[2]Zeng Hongbing,He Yong,Wu Min,et al.Free matrix based integral inequality for stability analysis of systems with time-varying delay[J].IEEE Transactions on Automatic Control,2015,60(10):2768-2772.
[3]陈刚,王信.分析时变时滞系统稳定性的新判据[J].湖南工业大学学报,2017,31(1):60-63.Chen Gang,Wang Xin.A new criterion for the stability analysis of time varying delay systems[J].Journal of Hunan University of Technology.2017,31(1):60-63.
[4]贾宏杰,谢星星,余晓丹.考虑时滞影响的电力系统小扰动稳定域[J].电力系统自动化,2006,30(21):1-5.Jia Hongjie,Xie Xingxing,Yu Xiaodan.Power system small signal stability region with time delay considered[J].Automation of Electric Power Systems,2006,30(21):1-5.
[5]贾宏杰,陈建华,余晓丹.时滞环节对电力系统小扰动稳定性的影响[J].电力系统自动化,2006,30(5):5-8.Jia Hongjie,Chen Jianhua,Yu Xiaodan.Impact of time delay on power system small signal stability[J].Automation of Electric Power Systems,2006,30(5):5-8.
[6]贾宏杰,尚蕊,张宝贵.电力系统时滞稳定裕度求解法[J].电力系统自动化,2007,31(2):5-11.Jia Hongjie,Shang Rui,Zhang Baogui.Computation of delay stability margin of electric power systems[J].Automation of Electric Power Systems,2007,31(2):5-11.
[7]贾宏杰,安海云,余晓丹.电力系统改进时滞依赖型稳定判据[J].电力系统自动化,2008,32(19):15-19.Jia Hongjie,An Haiyun,Yu Xiaodan.An improved delay-dependent stability criteria for power system with multiple time delays[J].Automation of Electric Power Systems,2008,32(19):15-19.
[8]孙国强,屠越,孙永辉,等.时变时滞电力系统鲁棒稳定性的改进型判据[J].电力系统自动化,2015,39(3):59-62.Sun Guoqiang,Tu Yue,Sun Yonghui,et al.An improved robust stability criterion for power systems with time varying delay[J].Automation of Electric Power Systems,2015,39(3):59-62.
[9]厉文秀.随机时滞电力系统稳定性分析[J].电力与能源,2015,31(3):10-15.Li Wenxiu.Analysis of stability of stochastic time delay power systems[J].Power System and Clean Energy,2015,31(3):10-15.
[10]贾宏杰,安海云,余晓丹.电力系统时滞依赖型稳定判据及其应用[J].电力系统自动化,2010,34(3):6-11.Jia Hongjie,An Haiyun,Yu Xiaodan.A delay-dependent robust stability criterion for power system and its application[J].Automation of Electric Power Systems,2010,34(3):6-11.
[11]Xie L.Output feedback H∞control of systems with uncertainty[J].International Journal of Control,1996,63(4):741-750.