经验Gramian平衡降阶在电力系统中的改进及应用
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摘要
经验Gramian平衡降阶方法正逐步应用于电力系统的非线性控制设计。如何获得有效经验可观可控Gramian矩阵,是该方法应用的核心,对降阶效果有着很大影响。为进一步提升该方法的降阶效果,建立了电力系统非线性动态模型,分析了所研究问题与控制量选取及降阶对象之间的关系。考虑了电力系统状态量及控制量变化特点,提出了一种方案用于确定各状态量和控制量的扰动值,形成了包含丰富系统动态行为信息的经验可观可控Gramian矩阵。通过研究某实际电网验证该方案可行有效,研究表明相比原方法,所提方案在保证降阶误差上界的前提下,能够进一步有效减少模型阶数,其降阶效果得到明显提升。
The empirical Gramian balance reduction method is gradually applied to the nonlinear control and design of power system.How to obtain effective empirical controllability and observability Gramian matrices is the core of this method.In order to further improve the reduced effect, this paper forms nonlinear dynamic model of power system and analyzes the relationship of among research problem, the choice of control variables and reduction object.Given the variation characteristic of state and control variables, this paper proposes a scheme which is used to determine the disturbed values of state and control variables to form empirical controllability and observability Gramian matrices which contains rich system dynamic behaviors information.It takes advantage of some relative power system to verify the effectiveness of the proposed scheme.The simulation results show that this scheme can further decrease the reduced order and the effect of reduced model are improved greatly on the premise of guarantee the upper bound of error for order reduction.
The empirical Gramian balance reduction method is gradually applied to the nonlinear control and design of power system.How to obtain effective empirical controllability and observability Gramian matrices is the core of this method.In order to further improve the reduced effect, this paper forms nonlinear dynamic model of power system and analyzes the relationship of among research problem, the choice of control variables and reduction object.Given the variation characteristic of state and control variables, this paper proposes a scheme which is used to determine the disturbed values of state and control variables to form empirical controllability and observability Gramian matrices which contains rich system dynamic behaviors information.It takes advantage of some relative power system to verify the effectiveness of the proposed scheme.The simulation results show that this scheme can further decrease the reduced order and the effect of reduced model are improved greatly on the premise of guarantee the upper bound of error for order reduction.
引文
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[13]张钢,杜正春,倪煜,等.基于非线性系统降阶的感应电动机群聚合[J].中国电机工程学报,2015,35(8):1893-1899.ZHANG Gang,DU Zhengchun,NI Yu,et al.Induction motors aggregation based on nonlinear model reduction[J].Proceedings of the CSEE,2015,35(8):1893-1899.
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[15]ZHAO J Q,ZHANG Y J,ZHANG P,et al.Development of a WAMS based test platform for power system real time transient stability detection and control[J].Protection and Control of Modern Power Systems,2016,1(1):9-19.
[16]王积伟,陆一心,吴振顺.现代控制理论与工程[M].北京:高等教育出版社,2002:50-82.
[17]MOORE B C.Principal component analysis in linear systems:controllability observability and model reduction[J].IEEE Transactions on Automatic Control,1981,26(1):17-32.
[18]BAUR U,BENNER P,FENG L H.Model order reduction for linear and nonlinear systems:a system-theoretic perspective[J].Archives Computational Methods in Engineering,2014,21(4):331-3358.
[2]杜治,苏宇,彭昌勇,等.基于多层次启发式动态规划算法的电力系统动态等值[J].电力系统保护与控制,2016,44(17):1-9.DU Zhi,SU Yu,PENG Changyong,et al.Dynamic equivalent of power system based on global representation heuristic dynamic programming algorithm[J].Power System Protection and Control,2016,44(17):1-9.
[3]武艳,杨数强,蒋志勋.基于节点灵敏度分析的大电网等值研究[J].电力系统保护与控制,2015,43(10):68-73.WU Yan,YANG Shuqiang,JIANG Zhixun.Research on the equivalence of large-scale power system using node sensitivity analysis approach[J].Power System Protection and Control,2015,43(10):68-73.
[4]舒进,都劲松,王靖程,等.基于奇异摄动降阶的风电接入系统阻尼分析[J].电力系统保护与控制,2014,42(19):18-25.SHU Jin,DU Jinsong,WANG Jingcheng,et al.System damping analysis after wind power integration using singular perturbation system reduction[J].Power System Protection and Control,2014,42(19):18-25.
[5]王清,薛安成,毕天殊,等.基于分解降阶模型的双馈异步电机模态估计方法[J].电力系统保护与控制,2016,44(6):1-7.WANG Qing,XUE Ancheng,BI Tianshu,et al.Adecomposed-reduced model based modes eatimation method of DFIG[J].Power System Protection and Control,2016,44(6):1-7.
[6]李啸骢,郑涛,梁志坚,等.微分代数模型可控制动电阻与励磁系统多指标非线性控制[J].电力系统保护与控制,2016,43(16):1-7.LI Xiaocong,ZHENG Tao,LIANG Zhijian,et al.Multi-index nonlinear control for TCBR and generator excitation based differential algebraic model[J].Power System Protection and Control,2016,43(16):1-7.
[7]黄伟,庞琳,曹彬,等.基于分区解耦的配电网状态估计的分布式并行计算[J].电力系统保护与控制,2014,42(15):45-51.HUANG Wei,PANG Lin,CAO Bin,et al.Parallel and distributed computing for an area-decoupled state estimation method for distribution systems[J].Power System Protection and Control,2014,42(15):45-51.
[8]孔令国,蔡国伟.大规模并网光伏电站的逆变器控制方法研究[J].电力系统保护与控制,2013,41(2):57-63.KONG Lingguo,CAI Guowei.Research on control method of inverters for large-sacle grid-connected photovoltaic power system[J].Power System Protection and Control,2013,41(2):57-63.
[9]赵洪山,宋国维,江全元.利用平衡理论进行电力系统模型降阶[J].电工技术学报,2010,25(2):127-133.ZHAO Hongshan,SONG Guowei,JIANG Quanyuan.Reduction of power system model using balanced realization method[J].Transactions of China Electrotechical Society,2010,25(2):127-133.
[10]赵洪山,薛宁,时宁,等.非线性电力系统模型经验Gramian平衡降阶[J].电力自动化设备,2014,34(9):21-26,40.ZHAO Hongshan,XUE Ning,SHI Ning,et al.Empirical Gramian balanced reduction of nonlinear power system model[J].Electric Power Automation Equipment,2014,34(9):21-26,40.
[11]ZHAO Hongshan,LAN Xiaoming,XUE Ning,et al.Excitation prediction control of multi-machine power systems using balanced reduced model[J].IET Generation Transmission&Distribution,2014,8(6):1075-1081.
[12]赵洪山,兰晓明,周雪青.基于平衡降阶模型的多机电力系统非线性励磁预测控制[J].中国电机工程学报,2013,33(22):61-67.ZHAO Hongshan,LAN Xiaoming,ZHOU Xueqing.Nonlinear excitation predictive control of multi-machine power systems based on balanced reduced model[J].Proceedings of the CSEE,2013,33(22):61-67.
[13]张钢,杜正春,倪煜,等.基于非线性系统降阶的感应电动机群聚合[J].中国电机工程学报,2015,35(8):1893-1899.ZHANG Gang,DU Zhengchun,NI Yu,et al.Induction motors aggregation based on nonlinear model reduction[J].Proceedings of the CSEE,2015,35(8):1893-1899.
[14]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,2002:50-82.
[15]ZHAO J Q,ZHANG Y J,ZHANG P,et al.Development of a WAMS based test platform for power system real time transient stability detection and control[J].Protection and Control of Modern Power Systems,2016,1(1):9-19.
[16]王积伟,陆一心,吴振顺.现代控制理论与工程[M].北京:高等教育出版社,2002:50-82.
[17]MOORE B C.Principal component analysis in linear systems:controllability observability and model reduction[J].IEEE Transactions on Automatic Control,1981,26(1):17-32.
[18]BAUR U,BENNER P,FENG L H.Model order reduction for linear and nonlinear systems:a system-theoretic perspective[J].Archives Computational Methods in Engineering,2014,21(4):331-3358.