随机激励下基于微分包含理论的电力系统低频振荡分析
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摘要
可再生能源大规模、高密度的接入显著改变了电力系统静/动态特性,对系统建模、仿真、分析和控制带来了挑战。该文针对含不确定性的电力系统稳定性分析问题,引入微分包含理论,建立一种随机激励下电力系统低频振荡分析模型。针对含不确定性的电力系统稳定性问题,采用线性多胞体(polytopic linear differential inclusion,PLDI)微分方法,将包含不确定性的随机激励表征为有限个元素的凸包。基于凸包李雅谱诺夫(Lyapunov)函数法推导多胞体系统稳定判据,并给出强阻尼系统约束条件;进而,基于Hankel范数逼近法,给出一种适用于大规模柔性互联系统的低频振荡分析方法。以简单两机系统、10机39节点系统验证所提出方法及稳定判据。仿真结果表明,该文所提方法能准确地刻画随机激励下的电力系统本质。
The large-scale, high-density integration of renewable generations significantly influence on the static\dynamic characteristics of power system, and bring challenges to system modeling, simulation, analysis and control.Aiming at solving stability analysis issue containing uncertainty, differential inclusion theory was introduced to establish a small-signal stability model in this paper. Based on the polytopic linear differential inclusion theory(PLDI), a power system under stochastic disturbances was described as variety elements of convex hull. Convex hull Lyapunov function(CHLF) was used to derive the stability criterion and construct strongly damping constraints for PLDI system.Subsequently, Hankel normal approximation was introduced to obtain the model reduction, and an optimization technique was built for stability analysis. The validity of the proposed method and criterion was tested under both simple two-machine system and New England system. The simulation results show that the proposed method can accurately reflect the intrinsic character of power system with stochastic disturbance.
The large-scale, high-density integration of renewable generations significantly influence on the static\dynamic characteristics of power system, and bring challenges to system modeling, simulation, analysis and control.Aiming at solving stability analysis issue containing uncertainty, differential inclusion theory was introduced to establish a small-signal stability model in this paper. Based on the polytopic linear differential inclusion theory(PLDI), a power system under stochastic disturbances was described as variety elements of convex hull. Convex hull Lyapunov function(CHLF) was used to derive the stability criterion and construct strongly damping constraints for PLDI system.Subsequently, Hankel normal approximation was introduced to obtain the model reduction, and an optimization technique was built for stability analysis. The validity of the proposed method and criterion was tested under both simple two-machine system and New England system. The simulation results show that the proposed method can accurately reflect the intrinsic character of power system with stochastic disturbance.
引文
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[13]Pan Yanfei,Liu Feng,Chen Laijun,et al.Towards the robust small-signal stability region of power systems under perturbations such as uncertain and volatile wind generation[J].IEEE Transactions on Power Systems,2018,33(2):1790-1799.
[14]Zhou Jinghao,Shi Peng,Gan Deqiang,et al.Large-scale power system robust stability analysis based on value set approach[J].IEEE Transactions on Power Systems,2017,32(5):4012-4023.
[15]Aubin J P,Cellina A.Differential inclusions:set-valued maps and viability theory[M].Berlin:Springer-Verlag,1984:57-83.
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[18]Yao Yao,Fassinou F,Hu Tingshu.Stability and robust regulation of battery-driven boost converter with simple feedback[J].IEEE Transactions on Power Electronics,2011,26(9):2614-2626.
[19]黄柳强,郭剑波,徐式蕴,等.适用于多工况的多FACTS广域协调控制研究[J].电力系统保护与控制,2013,41(18):1-8.Huang Liuqiang,Guo Jianbo,Xu Shiyun,et al.Wide-area multi-FACTS coordinated control strategy for multiple load cases[J].Power System Protection and Control,2013,41(18):1-8(in Chinese).
[20]韩正之,蔡秀珊,黄俊.微分包含控制系统理论[M].上海:上海交通大学出版社,2013:151-168.Han Zhengzhi,Cai Xiushan,Huang Jun.Differential inclusion control system theory[M].Shanghai:Shanghai Jiaotong University Press,2013:151-168(in Chinese).
[21]Gautam D,Vittal V,Harbour T.Impact of increased penetration of DFIG-based wind turbine generators on transient and small signal stability of power systems[J].IEEE Transactions on Power Systems,2009,24(3):1426-1434.
[22]Zhou J Z,Ding Hui,Fan Shengtao,et al.Impact of short-circuit ratio and phase-locked-loop parameters on the small-signal behavior of a VSC-HVDC converter[J].IEEE Transactions on Power Delivery,2014,29(5):2287-2296.
[23]Bu S Q,Du W,Wang H F,et al.Probabilistic analysis of small-signal stability of large-scale power systems as affected by penetration of wind generation[J].IEEETransactions on Power Systems,2012,27(2):762-770.
[24]Hassibi A,How J,Boyd S.A path-following method for solving BMI problems in control[C]//Proceedings of the1999 American Control Conference.San Diego,CA,USA:IEEE,1999:1385-1389.
[25]周克敏,Doyle J C,Glover K.鲁棒与最优控制[M].毛剑琴,等,译.北京:国防工业出版社,2002.Zhou Kemin,Doyle J C,Glover K.Robust and optimal control[M].Mao liqin,et al,translate.Beijing:National Defense Industry Press,2002(in Chinese).
[26]魏毅立,韩素贤,时盛志.风力发电系统中组合风速的建模及仿真[J].可再生能源,2010,28(2):18-20.Wei Yili,Han Suxian,Shi Shengzhi.The modeling and simulation of the combined wind speed in the wind power system[J].Renewable Energy Resources,2010,28(2):18-20(in Chinese).
[2]Ten-year network development plan 2014[R].European Network of Transmission System Operators for Electricity:Final Report,2014.
[3]周孝信,鲁宗相,刘应梅,等.中国未来电网的发展模式和关键技术[J].中国电机工程学报,2014,34(29):4999-5008.Zhou Xiaoxin,Lu Zongxiang,Liu Yingmei,et al.Development models and key technologies of future grid in China[J].Proceedings of the CSEE,2014,34(29):4999-5008(in Chinese).
[4]Kundur P,Paserba J,Ajjarapu V,et al.Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[J].IEEETransactions on Power Systems,2004,19(3):1387-1401.
[5]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社,2002:181-215.Ni Yixin,Chen Suntao,Zhang Baolin.Theory and analysis of dynamic power system[M].Beijing:Tsinghua University Press,2002:181-215(in Chinese).
[6]中国电力企业联合会.GB/T 26399-2011电力系统安全稳定控制技术导则[S].北京:中国标准出版社,2011.China Electricity Council.GB/T 26399-2011 Technical guide for electric power system security and stability control[S].Beijing:China Standard Press,2011(in Chinese).
[7]Gautam D,Vittal V,Harbour T.Impact of increased penetration of DFIG-based wind turbine generators on transient and small signal stability of power systems[J].IEEE Transactions on Power Systems,2009,24(3):1426-1434.
[8]Preece R,Milanovi?J V.Risk-based small-disturbance security assessment of power systems[J].IEEETransactions on Power Delivery,2015,30(2):590-598.
[9]Bu S Q,Du W,Wang H F,et al.Probabilistic analysis of small-signal stability of large-scale power systems as affected by penetration of wind generation[J].IEEETransactions on Power Systems,2012,27(2):762-770.
[10]陈磊,闵勇,侯凯元.考虑风电随机性的静态电压稳定概率评估[J].中国电机工程学报,2016,36(3):674-680.Chen Lei,Min Yong,Hou Kaiyuan.Probabilistic steady-state voltage stability assessment considering stochastic wind power[J].Proceedings of the CSEE,2016,36(3):674-680(in Chinese).
[11]周明,元博,张小平,等.基于SDE的含风电电力系统随机小干扰稳定分析[J].中国电机工程学报,2014,34(10):1575-1582.Zhou Ming,Yuan Bo,Zhang Xiaoping,et al.Stochastic small signal stability analysis of wind power integrated power systems based on stochastic differential equations[J].Proceedings of the CSEE,2014,34(10):1575-1582(in Chinese).
[12]李洪宇,鞠平,余一平,等.随机激励下电力系统有界波动域及域内概率解析分析方法[J].中国电机工程学报,2015,35(14):3561-3568.Li Hongyu,Ju Ping,Yu Yiping,et al.Bounded fluctuations region and analytic method of intra-region probability in power system under stochastic excitations[J].Proceedings of the CSEE,2015,35(14):3561-3568(in Chinese).
[13]Pan Yanfei,Liu Feng,Chen Laijun,et al.Towards the robust small-signal stability region of power systems under perturbations such as uncertain and volatile wind generation[J].IEEE Transactions on Power Systems,2018,33(2):1790-1799.
[14]Zhou Jinghao,Shi Peng,Gan Deqiang,et al.Large-scale power system robust stability analysis based on value set approach[J].IEEE Transactions on Power Systems,2017,32(5):4012-4023.
[15]Aubin J P,Cellina A.Differential inclusions:set-valued maps and viability theory[M].Berlin:Springer-Verlag,1984:57-83.
[16]Smirnov G V.Introduction to the theory of differential inclusions[M].Rhode Island:AMS,2002:114-139.
[17]Hu Tingshu,Lin Zongli.Properties of the composite quadratic Lyapunov functions[J].IEEE Transactions on Automatic Control,2004,49(7):1162-1167.
[18]Yao Yao,Fassinou F,Hu Tingshu.Stability and robust regulation of battery-driven boost converter with simple feedback[J].IEEE Transactions on Power Electronics,2011,26(9):2614-2626.
[19]黄柳强,郭剑波,徐式蕴,等.适用于多工况的多FACTS广域协调控制研究[J].电力系统保护与控制,2013,41(18):1-8.Huang Liuqiang,Guo Jianbo,Xu Shiyun,et al.Wide-area multi-FACTS coordinated control strategy for multiple load cases[J].Power System Protection and Control,2013,41(18):1-8(in Chinese).
[20]韩正之,蔡秀珊,黄俊.微分包含控制系统理论[M].上海:上海交通大学出版社,2013:151-168.Han Zhengzhi,Cai Xiushan,Huang Jun.Differential inclusion control system theory[M].Shanghai:Shanghai Jiaotong University Press,2013:151-168(in Chinese).
[21]Gautam D,Vittal V,Harbour T.Impact of increased penetration of DFIG-based wind turbine generators on transient and small signal stability of power systems[J].IEEE Transactions on Power Systems,2009,24(3):1426-1434.
[22]Zhou J Z,Ding Hui,Fan Shengtao,et al.Impact of short-circuit ratio and phase-locked-loop parameters on the small-signal behavior of a VSC-HVDC converter[J].IEEE Transactions on Power Delivery,2014,29(5):2287-2296.
[23]Bu S Q,Du W,Wang H F,et al.Probabilistic analysis of small-signal stability of large-scale power systems as affected by penetration of wind generation[J].IEEETransactions on Power Systems,2012,27(2):762-770.
[24]Hassibi A,How J,Boyd S.A path-following method for solving BMI problems in control[C]//Proceedings of the1999 American Control Conference.San Diego,CA,USA:IEEE,1999:1385-1389.
[25]周克敏,Doyle J C,Glover K.鲁棒与最优控制[M].毛剑琴,等,译.北京:国防工业出版社,2002.Zhou Kemin,Doyle J C,Glover K.Robust and optimal control[M].Mao liqin,et al,translate.Beijing:National Defense Industry Press,2002(in Chinese).
[26]魏毅立,韩素贤,时盛志.风力发电系统中组合风速的建模及仿真[J].可再生能源,2010,28(2):18-20.Wei Yili,Han Suxian,Shi Shengzhi.The modeling and simulation of the combined wind speed in the wind power system[J].Renewable Energy Resources,2010,28(2):18-20(in Chinese).
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