采样系统的稳定性分析及其在电力市场的应用  

Stability Analysis of Sampling System and Its Application in Electric Power Market

作　　者：刘晓桂 曾树华[1,2] 刘小勇 肖会芹[4] LIU Xiao-gui;ZENG Shu-hua;LIU Xiao-yong;XIAO Hui-qin(School College of Railway Power Supply and Electricity,Hunan Vocational College of Railway Technology,Zhuzhou 412006,China;Hunan High-speed Railway Engineering and Technology Research Center for Operation Safety,Zhuzhou 412006,China;School of Railway Communication and Telecommunication Technology,Hunan Vocational College of Railway Technology,Zhuzhou 412001,China;School of Electrical and Information Engineering,Hunan University of Technology,Zhuzhou 412007,China)

机构地区：[1]湖南铁路科技职业技术学院铁道供电与电气学院,湖南株洲412006 [2]湖南省高铁运行安全保障工程技术研究中心,湖南株洲412006 [3]湖南铁道职业技术学院轨道交通电务技术学院,湖南株洲412001 [4]湖南工业大学电气与信息工程学院,湖南株洲412007

出　　处：《数学的实践与认识》2021年第8期146-157,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金资助项目(61703153);湖南省自然科学基金(2020JJ7054);湖南省教育厅科学研究项目(19C1214);湖南省职业院校教育教学改革研究项目(ZJGB2016017)。

摘　　要：基于Lyapunov稳定理论研究非周期采样控制系统的稳定性问题.首先,通过充分利用系统的状态信息,构建出新的增广型Lyapunov-Krasovskii泛函,并引入零等式来放宽泛函的正定条件;其次,在对泛函导数进行界定时,应用自由矩阵积分不等式方法估计泛函导数中的积分项,得到了更小保守性的稳定性判据.最后,借助一个经典的数值实例来验证所提方法的有效性.同时,还将所提方法应用于电力市场的稳定性分析,分析了时滞与市场结算周期对电力市场稳定性的影响,进一步表明了方法的有效性与实用性.This paper studies stability of aperiodic sampling control system based on Lyapunov stability theory.First,it constructs a new augmented Lyapunov-Krasovskii functional by making full use of the state information of the system,and it introduces zero equation to relax the terms of the positive definition.Secondly,in defining the functional derivative,it applies free-matrix-based integral inequality method to estimate the functional derivative integral item so as to get less conservative stability criterion.Finally,by virtue of a classic numerical example,it verifies the validity of the proposed method.Meanwhile,it will also applies method mentioned above to the stability analysis of electric power market,analyzing influence of the time delays and market settlement period on stability of the electric power market and further showing effectiveness and practicality of the method.

关 键 词：LYAPUNOV-KRASOVSKII泛函 线性矩阵不等式 鲁棒稳定判据 时变时滞 电力市场 

分 类 号：F426.61[经济管理—产业经济] F224