电力系统改进时滞依赖型鲁棒稳定判据
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摘要
广域量测系统在采集和传输电力信息过程中由于通信链路限制和传输距离太大会使信号产生延时。针对电力系统时滞问题,给出了一种改进的含不确定时滞环节的电力系统稳定性Lyapunov鲁棒稳定判据。首先根据状态轨迹定义将状态变量在相应积分区间上定义为线性函数与对线性部分的偏离函数之和,以使Lyapunov泛函导函数中的二次型积分项取得极大值。然后结合"时滞分割"的思想,推导出改进的单时滞系统渐近鲁棒稳定判据,并将该方法推广到多时滞系统。最后借助典型二阶系统、单机无穷大系统以及WSCC3机9节点系统,对含不确定性的时滞系统保持稳定时系统所能承受的最大时滞进行分析。结果显示,该方法在保证一定计算效率的前提下改善了稳定性判据的保守性。
Due to the limitation of communication links and the wide range of transportation,time delays arise from the collection and transmission of signals in a wide-area measurement system. In this paper,an improved Lyapunov robuststability criterion for the power system with uncertain time-delays is presented. First,according to the definition of statetrajectory,state variables are defined as the sum of linear function and the error function with respect to the linear partin the corresponding integral interval,such that the maximum value of the quadratic integral term in the derivative ofLyapunov functional is obtained. Then,with the combination of the"delay-partitioning"theory,an asymptotic robuststability criterion for the power system with one single time-delay is derived,which is further extended to the power sys-tem with multiple time-delays. Finally,a typical second-order delay system,a single-generator infinite-bus system,anda WSCC 3-generator 9-node system are employed to analyze the maximum delay margin that the time-delay system withuncertainties can sustain. The results demonstrate that by using the proposed method,the conservation of stability criteria is improved with acceptable calculation efficiency.
Due to the limitation of communication links and the wide range of transportation,time delays arise from the collection and transmission of signals in a wide-area measurement system. In this paper,an improved Lyapunov robuststability criterion for the power system with uncertain time-delays is presented. First,according to the definition of statetrajectory,state variables are defined as the sum of linear function and the error function with respect to the linear partin the corresponding integral interval,such that the maximum value of the quadratic integral term in the derivative ofLyapunov functional is obtained. Then,with the combination of the"delay-partitioning"theory,an asymptotic robuststability criterion for the power system with one single time-delay is derived,which is further extended to the power sys-tem with multiple time-delays. Finally,a typical second-order delay system,a single-generator infinite-bus system,anda WSCC 3-generator 9-node system are employed to analyze the maximum delay margin that the time-delay system withuncertainties can sustain. The results demonstrate that by using the proposed method,the conservation of stability criteria is improved with acceptable calculation efficiency.
引文
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[13]董朝宇,贾宏杰,姜懿郎(Dong Chaoyu,Jia Hongjie,Ji-ang Yilang).含积分二次型的电力系统改进时滞稳定判据(Time-delay stability criteria for power system withintegral quadratic form)[J].电力系统自动化(Automa-tion of Electric Power Systems),2015,39(24):35-40.
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[2]赵维兴,林成,孙斌,等(Zhao Weixing,Lin Cheng,SunBin,et al).广域电力系统稳定器闭环控制通信实现技术(Communication technology for wide-area PSS closedloop control realization)[J].电力系统及其自动化学报(Proceedings of the CSU-EPSA),2016,28(6):97-102.
[3]杨培宏,刘文颖,魏毅立,等(Yang Peihong,Liu Weny-ing,Wei Yili,et al).电力系统广域自适应阻尼控制器设计(Design of wide-area adaptive damping controller ofpower system)[J].电力系统及其自动化学报(Proceed-ings of the CSU-EPSA),2013,25(5):105-110.
[4]Wu Hongxia,Tsakalis K S,Heydt G T.Evaluation of timedelay effects to wide area power system stabilizer design[J].IEEE Trans on Power Systems,2004,19(4):1935-1941.
[5]孙琳,李天然,吴华仁(Sun Lin,Li Tianran,Wu Huaren).基于模糊自适应PID的广域阻尼控制(Fuzzy adaptivePID control based wide area damping control)[J].电力系统及其自动化学报(Proceedings of the CSU-EPSA),2015,27(5):28-33.
[6]贾宏杰,姜涛,姜懿郎,等(Jia Hongjie,Jiang Tao,JiangYilang,et al).电力系统时滞稳定域临界点的快速搜索新方法(A method to search critical points of time-delaystability region in power systems)[J].电力系统自动化(Automation of Electric Power Systems),2013,37(6):30-36.
[7]Wu Min,He Yong,She Jinhua.New delay-dependent sta-bility criteria and stabilizing method for neutral systems[J].IEEE Trans on Automatic Control,2004,49(12):2266-2271.
[8]Wu Min,He Yong,She Jin-Hua,et al.Delay-dependentcriteria for robust stability of time-varying delay systems[J].Automatica,2004,40(8):1435-1439.
[9]He Yong,Wang Qinggao,Xie Lihua,et al.Further im-provement of free-weighting matrices technique for sys-tems with time-varying delay[J].IEEE Trans on AutomaticControl,2007,52(2):293-299.
[10]Moon Y S,Park P,Kwon W H,et al.Delay-dependent ro-bust stabilization of uncertain state-delayed systems[J].In-ternational Journal of Control,2001,74(14):1447-1455.
[11]贾宏杰,安海云,余晓丹(Jia Hongjie,An Haiyun,YuXiaodan).电力系统时滞依赖型鲁棒稳定判据及其应用(A delay-dependent robust stability criterion for powersystem and its application)[J].电力系统自动化(Automa-tion of Electric Power Systems),2010,34(3):6-11.
[12]陈旭,蔡培镇(Chen Xu,Cai Peizhen).电力系统时滞稳定分析的线性矩阵不等式方法(LMI-based method forpower system stability analysis with considering time-de-lay)[J].电力系统及其自动化学报(Proceedings of theCSU-EPSA),2009,21(6):84-91.
[13]董朝宇,贾宏杰,姜懿郎(Dong Chaoyu,Jia Hongjie,Ji-ang Yilang).含积分二次型的电力系统改进时滞稳定判据(Time-delay stability criteria for power system withintegral quadratic form)[J].电力系统自动化(Automa-tion of Electric Power Systems),2015,39(24):35-40.
[14]Jiang Yilang,Jiang Tao,Jia Hongjie,et al.A novel LMIcriterion for power system stability with multiple time-de-lays[J].Science China Technological Science,2014,57(7):1392-1400.
[15]姜懿郎(Jiang Yilang).电力系统时滞小扰动稳定性研究(Study on Small Signal Stability of Power System withTime-delay)[D].天津:天津大学电气与自动化工程学院(Tianjin:School of Electrical Engineering and Automa-tion,Tianjin University),2014.
[16]Gouaisbaut F,Peaucelle D.Robust stability of time-delaysystems with interval delays[C]//46th IEEE Conference onDecision and Control.New Orleans,USA,2007:6328-6333.
[17]Sun Jian,Liu G P.On improved delay-dependent stabilitycriteria for neutral time-delay systems[J].European Jour-nal of Control,2009,15(6):613-623.
[18]Gouaisbaut F,Peaucelle D.Delay-dependent robust stabil-ity of time delay systems[C]//5th IFAC Symposium on Ro-bust Control Design.Toulouse,France,2006:453-458.