基于事故链和Markov过程时滞电力系统稳定性分析
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摘要
随着时滞的存在使电力系统稳定分析和控制变得愈加复杂,已成为系统不稳定及性能变差的根源。因此,对时滞稳定性的研究需要更进一步才能满足电力系统稳定性研究的需求。提出了一种用马尔科夫动态过程(Markov)分析系统连环故障时的时滞稳定性。第一步是分析网络潮流求得合理的事故链,给出了事故链的求导方式及最优解法,然后结合Markov过程,在考虑Markov跳变的前提条件下建立一类Lyapunov-Krasovskii泛函,然后通过牛顿-拉夫逊算法将函数进行线性化求解,并构造自由权项,同时降低保守性。最终目的是计算电力系统所能承受的最大时滞,这个值是由广义矩阵特征根求得。最后对理论推导进行了仿真验证,利用H_2/H_∞控制方法设计了IEEE 16机68节点系统的阻尼控制器,并将阻尼控制器分3个时段设置时滞,测量不同发电机之间的相对功角差的动态响应曲线,发现仿真结论与理论推导的结果一致。
With the existence of time delay,the control of power system becomes more and more complex,which has become the root for the instability and poor performance of the system.Therefore,more research should be conducted on the stability of time delay so as to meet the needs of the system. Based on fault chains generated by electric power flow,the stability of time delay when a chain of accidents occurs is analyzed by using the Markov process. First of all,the reasonable accident chain is obtained by power flow calculation and the differentiation formula as well as its optimum solution is given. Secondly,by combining the Markov process,on the premise of Markov jump,the Lyapunov-Krasovskii function is then set up. Through the Newton-Ralph Monson formula,the function is linearly solved and the free weights are constructed. Meanwhile,the conservativedegree is reduced. The purpose is to obtain the maximum time delay that the system can undertake,which can be calculated by the eigenvalue of a generalized matrix. Finally,the method proposed in this paper is validated by simulation with an IEEE68 node prototype designed by H_2/H_∞ control method.
With the existence of time delay,the control of power system becomes more and more complex,which has become the root for the instability and poor performance of the system.Therefore,more research should be conducted on the stability of time delay so as to meet the needs of the system. Based on fault chains generated by electric power flow,the stability of time delay when a chain of accidents occurs is analyzed by using the Markov process. First of all,the reasonable accident chain is obtained by power flow calculation and the differentiation formula as well as its optimum solution is given. Secondly,by combining the Markov process,on the premise of Markov jump,the Lyapunov-Krasovskii function is then set up. Through the Newton-Ralph Monson formula,the function is linearly solved and the free weights are constructed. Meanwhile,the conservativedegree is reduced. The purpose is to obtain the maximum time delay that the system can undertake,which can be calculated by the eigenvalue of a generalized matrix. Finally,the method proposed in this paper is validated by simulation with an IEEE68 node prototype designed by H_2/H_∞ control method.
引文
[1]余晓丹,贾宏杰,王成山.时滞电力系统全特征谱追踪算法及其应用[J].电力系统自动化,2012,36(24):10-14.
[2]胡志坚,赵义术.计及广域测量系统时滞的互联电力系统鲁棒稳定控制[J].中国电机工程学报,2010,30(19):37-43.
[3]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.
[4]尚蕊.电力系统时滞稳定裕度求解方法[J].电网技术,2007,31(2):5-11.
[5]NEJAT O.A novel stability study on multiple timedelay systems(MTDS)using the root clustering paradigm[C].Proceedings of the American Control Conference,2004:5422-5427.
[6]NEJAT O.An exact method for the stability analysis of time-delayed linear time-invariant(LTI)systems[J].IEEE Transactions on Automatic Control,2002,47(5):793-797.
[7]刘兆燕,江全元,徐立中,等.基于特征根聚类的电力系统时滞稳定域研究[J].浙江大学学报(工学版),2009,43(8):1473-1479.
[8]刘健辰,章兢,张红强,等.时滞系统稳定性分析与镇定:一种基于Finsler引理的统一观点[J].控制理论与应用,2011,28(11):1577-1582.
[9]PARK P.A delay-dependent stability criterion for systems with uncertain time-invariant delays[J].IEEE Transactions on Automatic Control,1999,44(4):876-877.
[10]MOON Y S,PARK P,KWON W H,et al.Delaydependent robust stabilization of uncertain state-delayed systems[J].International Journal of Control,2004,74(14):1447-1455.
[11]FRIDMAN E,SHAKED U.A descriptor system approach to H∞control of linear time-delay systems[J].IEEE Transactions on Auto-matic Control,2002,47(2):253-270.
[12]HE Yong,WANG Q,LIN C,et al.Delay-rangedependent stability for systems with time-varying delay[J].Automatica,2007,43(2):371-376.
[13]XU S,LAM J,MAO X.Delay-dependent control and filtering for uncertain Markovian jump systems with time-varying delays[J].IEEE Transactions on Circuits and Systems I:Regular Papers,2007,54(9):2070-2077.
[14]WANG J,LUO Y.Further improvement of delaydependent stability for Markov jump systems with timevarying delay[C].In:Proceedings of the 7th World Congress on Intelligent Control and Automation.Chongqing:IEEE Press,2008:6319-6324.
[15]ZHAO X D,ZENG Q S.Delay-dependent stability analysis for Markovian jump systems with interval timevarying-delays[J].International Journal of Automation and Computing,2010,7(2):224-229.
[16]吴文可,文福拴,薛禹胜,等.基于马尔可夫链的电力系统连锁故障预测[J].电力系统自动化,2013,37(5):29-37.
[17]刘文颖,杨楠,张建立,等.计及恶劣天气因素的复杂电网连锁故障事故链模型[J].中国电机工程学报,2010,30(19):37-43.
[18]陈恩泽,刘涤尘,廖清芬,等.基于事故链的电网低频振荡及脆弱性分析[J].中国电机工程学报,2011,31(28):42-48.
[19]FENG X,LOPARO K A,JI Y,et al.Stochastic stability properties of jump linear systems[J].IEEE Transactions on Automatic Control,1992,37(1):38-53.
[20]BOYD S,EL GHAOUI L,FERON E,et al.Linear matrix inequalities in system and control theory[M].Philadelphia,USA:SIAM,1994.
[21]TRUDNOWSKI D J,JOHNSON J M,HAUER J F.Making prony analysis more accurate using multiple signals[J].IEEE Transactions on Power Systems,1999,14(1):226-231.
[2]胡志坚,赵义术.计及广域测量系统时滞的互联电力系统鲁棒稳定控制[J].中国电机工程学报,2010,30(19):37-43.
[3]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.
[4]尚蕊.电力系统时滞稳定裕度求解方法[J].电网技术,2007,31(2):5-11.
[5]NEJAT O.A novel stability study on multiple timedelay systems(MTDS)using the root clustering paradigm[C].Proceedings of the American Control Conference,2004:5422-5427.
[6]NEJAT O.An exact method for the stability analysis of time-delayed linear time-invariant(LTI)systems[J].IEEE Transactions on Automatic Control,2002,47(5):793-797.
[7]刘兆燕,江全元,徐立中,等.基于特征根聚类的电力系统时滞稳定域研究[J].浙江大学学报(工学版),2009,43(8):1473-1479.
[8]刘健辰,章兢,张红强,等.时滞系统稳定性分析与镇定:一种基于Finsler引理的统一观点[J].控制理论与应用,2011,28(11):1577-1582.
[9]PARK P.A delay-dependent stability criterion for systems with uncertain time-invariant delays[J].IEEE Transactions on Automatic Control,1999,44(4):876-877.
[10]MOON Y S,PARK P,KWON W H,et al.Delaydependent robust stabilization of uncertain state-delayed systems[J].International Journal of Control,2004,74(14):1447-1455.
[11]FRIDMAN E,SHAKED U.A descriptor system approach to H∞control of linear time-delay systems[J].IEEE Transactions on Auto-matic Control,2002,47(2):253-270.
[12]HE Yong,WANG Q,LIN C,et al.Delay-rangedependent stability for systems with time-varying delay[J].Automatica,2007,43(2):371-376.
[13]XU S,LAM J,MAO X.Delay-dependent control and filtering for uncertain Markovian jump systems with time-varying delays[J].IEEE Transactions on Circuits and Systems I:Regular Papers,2007,54(9):2070-2077.
[14]WANG J,LUO Y.Further improvement of delaydependent stability for Markov jump systems with timevarying delay[C].In:Proceedings of the 7th World Congress on Intelligent Control and Automation.Chongqing:IEEE Press,2008:6319-6324.
[15]ZHAO X D,ZENG Q S.Delay-dependent stability analysis for Markovian jump systems with interval timevarying-delays[J].International Journal of Automation and Computing,2010,7(2):224-229.
[16]吴文可,文福拴,薛禹胜,等.基于马尔可夫链的电力系统连锁故障预测[J].电力系统自动化,2013,37(5):29-37.
[17]刘文颖,杨楠,张建立,等.计及恶劣天气因素的复杂电网连锁故障事故链模型[J].中国电机工程学报,2010,30(19):37-43.
[18]陈恩泽,刘涤尘,廖清芬,等.基于事故链的电网低频振荡及脆弱性分析[J].中国电机工程学报,2011,31(28):42-48.
[19]FENG X,LOPARO K A,JI Y,et al.Stochastic stability properties of jump linear systems[J].IEEE Transactions on Automatic Control,1992,37(1):38-53.
[20]BOYD S,EL GHAOUI L,FERON E,et al.Linear matrix inequalities in system and control theory[M].Philadelphia,USA:SIAM,1994.
[21]TRUDNOWSKI D J,JOHNSON J M,HAUER J F.Making prony analysis more accurate using multiple signals[J].IEEE Transactions on Power Systems,1999,14(1):226-231.