基于状态势博弈的电力系统分布式经济调度方法

未来电网中出现的主要变革之一在于电力系统电源结构的变化,分布式能源发电设备的广泛接入给传统调度与控制框架带来了严峻挑战.电力系统尤其是主动配电网中,调度控制体系的去中心化成为一种趋势.状态势博弈理论为电力系统分布式调度与控制体系的构建提供了一个良好框架.文章基于状态势博弈理论,给出了分布式电力系统经济调度的一般设计方法.该方法能够兼顾全网功率平衡约束与网络传输功率限制,同时实现主体间通信量极小化,因而具有较强的算法鲁棒性与实际应用价值.通过IEEE 9节点标准系统的仿真分析验证了所提方法的有效性及正确性.     

现代电力系统控制评述——清华大学电力系统国家重点实验室相关科研工作缩影及展望

改善与提高电力系统稳定性的最经济和最有效的手段是采用先进的控制理论和方法.自20世纪五六十年代以线性系统和最优控制为代表的现代控制理论问世以来,理论创新与工业应用成果丰硕,特别在电力系统中获得了广泛的应用.主要以清华大学电力系统国家重点实验室近四十年来在电力系统控制领域的科研工作为主线,梳理总结其中里程碑式的研究成果并对未来电力系统控制理论和技术的发展做出若干展望.     

Hamilton系统给定能量闸轨道的多重性问题

闸轨道的多重性和稳定性是Hamilton系统中重要的研究问题,辛道路的Maslov型指标理论正是研究这类问题的有力工具.这篇综述文章简要介绍闸轨道边值辛道路的Maslov型指标理论及其迭代理论.作为应用,本文证明Seifert猜想在偶凸情形成立.最后介绍与闸轨道相关的最小周期问题和稳定性问题.     

Maslov型指标及非线性 Hamilton系统中的闸轨道

研究了线性Hamilton系统关于闸轨道边值的Maslov型指标理论及其在非线性Hamilton系统中闸轨道的多重存在性研究中的应用.     

基于改进型Bessel-Legendre不等式的电力系统时滞相关鲁棒稳定性研究

基于改进型Bessel-Legendre不等式方法,探讨了电力系统时滞相关鲁棒稳定性问题.首先构建了含有时滞环节的电力系统数学模型表达式,并推广出其含有不确定参数的模型表达式,通过应用时滞系统理论分析方法,有效地处理了泛函导数中的积分项,从而推导出了一个具有更小保守性的电力系统时滞相关鲁棒稳定新判据.通过三个数值实例对仿真结果进行了对比与验证,结果表明推导出的新判据具有有效性与优越性.     

一个非线性电力系统的混沌振荡

分析了一个非线性三参数电力系统振荡的异宿分枝,给出Melnikov函数的留数计算法,并获得电力系统发生混沌振荡的锥性参数区域和带形参数区域,为大偏差状态下保障电力系统稳定运行提供了理论依据和计算方法.     

同一命题不同呈现

命题两个能够完全重合的图形,若有部分重合,则每个图形上不重合的部分的数量(线段的长度、角的度数、图形的面积)是相等的.简证因为两个图形能够完全重合,所以令两个图形的数量均为w,令重合部分的数量为p,两个图形上不重合部分的数量分别为q1和q2,∵p +q1 =w,p+q2=w,∴p+q1 =p+q2.∴q1=q2.问题得证.     

最优线性回归的计算方法

本文指出利用常用的逐步回归方法可以计算出回归分析中常用的5种准则下的局部最优回归子集,而模拟结果显示,在大部分情形下,局部最优回归子集是相重合的.这就为逐步回归方法在应用上的重要性提供了科学依据.最后作者对现今著名的几个数字例子进行计算,其效果也是十分满意的.     

广义分散控制系统的无穷远固定模

在控制系统的理论与应用研究中,广义系统、分散系统越来越受到人们的重视.不仅在理论上已有不少有意义的结果,而且这些理论研究有明显的实际背景.例如 Leontief的动态投入产出模型,Leslie 的人口增长模型,电力系统等.然而,在一些实际系统中,系统不仅具有广义性的特点,而且从控制角度来看也具有分散性的特点.因此我们把系统     

具有稳定分布噪声的多重季节模型的贝叶斯分析

本文研究了具有稳定分布噪声的多重季节时间序列模型的建模及应用.稳定分布能够描述诸如方差无限、厚尾、有偏等非正态特征,但该类分布通常没有解析的密度函数,且参数的后验分布比较复杂.本文采用基于抽样的MCMC方法和切片抽样法估计模型参数,将多重季节模型的回归参数和稳定分布中的参数一起估计.通过模拟分析,说明了稳定分布的一些统计性质和文中建模方法的有效性.将模型应用于一个具有季节性和厚尾特征的实际数据集,演示了该类模型的应用价值.     

UNIFORM ASYMPTOTIC STABILITY OF FUNCTIONAL DIFFERENTIAL EQUATIONS

With the help of a Liapunov functional with seml-negative definite derivative,Barbashin-Krasovskii's theorem is extended to nonautonomous functional differentialequations,a reducing dimension approach is presented for the uniform asymptotic stabilityof high dimension systems,and some sufficient conditions of uniform asymptotic stabilityare obtained.     

Existence of a global liapunov functional for certain classes of nonlinear distributed systems : PMM vol. 40, n 6, 1976, pp. 1135–1142

The existence of a global Liapunov functional for nonlinear evolutionary equations in a Hilbert space is investigated as a continuation of paper [1], The results obtained represent a generalization of the results of the theory of absolute stability [2, 3], for the systems with infinite dimensional phase space, and are used for investigation of the nonlocal stability and instability of nonlinear distributed systems. The conditions of existence of the global Liapunov functional obtained are illustrated by an example of a nonlinear parabolic system defined in the interval [0, 1], The concept of a Liapunov functional was first introduced and used with success in [4].     

一类四阶非线性微分方程解的渐近性态

本文利用Liapunov函数方法，研究了一类四阶非线性微分方程解的渐近稳定性及有界性。     

The uniform asymptotic stability of certain neutral differential-difference equations

In this paper we give a necessary and sufficient condition for a general class of neutral differential-difference equations to be exponentially stable. This condition is expressed in terms of certain bilinear functionals which are the equivalent of quadratic Liapunov functions for finite-dimensional systems.     

On liapunov functional in theory of stability of systems with time-lag

It is well known, that in the theory of stability in differential equations, Liapunov's second method may be the most important. The center problem of Liapunov's second method is construction of Liapunov function for concrete problems. Beyond any doubt, construction of Liapunov functions is an art. In the case of functional differential equations, there were also many attempts to establish various kinds of Liapunov type theorems. Recently Burton [2] presented an excellent theorem using the Liapunov functional to solve the asymptotic stability of functional differential equation with bounded delay. However, the construction of such a Liapunov functional is still very hard for concrete problems. In this paper, by utilizing this theorem due to Burton, we construct concrete Liapunov functional for certain and nonlinear delay differential equations and derive new sufficient conditions for asymptotic stability. Those criteria improve the result of literature [1] and they are with simple forms, easily checked and applicable.This project is supported by the National Natural Science Foundation of China.     

On O0-boundedness and -stability properties with perturbing Liapunov functional

In this paper we will extend the perturbing Liapunov functionmethod to systems of functional differential equations and discussØ₀-equiboundedness and Ø₀-equistability propertiesvia the concept of perturbing Liapunov functional.     

Stability in first approximation of stochastic systems with after effect : PMM vol. 40, n 6, 1976, pp. 1116–1121

The theorem on existence of the Liapunov functionals and the theorem on stability in first approximation for a stochastic differential equation with aftereffect are proved.The suggestion of the replacement of Liapunov functions by functionals [1] in the investigation of the stability of ordinary differential equations with lag, has been widely utilized in dealing with determinate systems, as well as in the case of linear and nonlinear stochastic systems (see e. g. [2 – 11]). Results concerning the stability in the first approximation were obtained for stochastic systems in [12 – 18] and others. Use of Liapunov functionals for the differential equations with aftereffect was first encountered in [1, 19, 20] where the inversion theorems were proved and conditions for the stability in first approximation were obtained.Below a stochastic differential equation with aftereffect is investigated where the random perturbations represent an arbitrary process with independent increments.     

Liapunov稳定性定理的推广

本文利用多个Liapunov函数研究部分变元的方法，对自治系统和非自治系统建立了解的稳定性判别准则，推广了有关文献的若干结果．     

Asymptotic stability criteria for linear systems of difference-differential equations of neutral type and their discrete analogues

Electrical networks containing lossless transmission lines are often modeled by difference-differential equations of neutral type. This paper finds sufficient conditions for asymptotic stability for linear systems of these equations. Also given is a modification of the direct method of Liapunov for difference equations. This method is applied to finding asymptotic stability criteria for the discrete analogs of the linear system of difference-differential equations.     

Global existence without uniqueness

Summary In this paper we investigate the extendability of solutions of ordinary differential equations on [to, ∞) with the use of Liapunov functions. The results extend to non-unique systems the work done by Conti and Strauss, as well as establishing an equivalence between two properties of a Liapunov function. This work is part of the author's doctoral thesis under the direction of ProfessorA. Strauss at the University of Maryland. This research was supported in part by the National Science Foundation under Grant GP-6167. Entrata in Redazione il 20 febbraio 1970.