非线性优化问题与智能电网的关键技术：理论、方法和应用

项目名称： 非线性优化问题与智能电网的关键技术：理论、方法和应用

项目编号： No.51337007

项目类型： 重点项目

立项/批准年度： 2014

项目学科： 电工技术

项目作者： 江晓东

作者单位： 天津大学

项目金额： 275万元

中文摘要： 一般非线性规划问题的可行域是否存在是一个世界级难题，传统的优化求解方法，无论是数学规划方法还是智能计算方法，都无法解决一个优化问题的可行域是否存在这一问题。本项目将关注可行域存在性的检测与恢复的方法，并在智能电网中取得应用。本项目由四个主要部分组成：理论基础、方法确定、算法开发以及实际应用。为解决这一难题，本项目将开发一种基于动态轨迹的可行域存在性判别方法，该方法将通过理论分析，建立优化问题与特定非线性动力系统之间的联系，从而实现对可行域问题的转化。之后，使用动力系统稳定域相关的理论、方法与计算技术实现对可行域存在性的判别。此外，本项目将对可行域不存在的优化问题加以关注，提出问题模型的修正策略，从而构建一个可行解。分布式电源的接入为电网的安全运行带来了极大的挑战，本项目所提出的全套方法将在智能电网中进行应用，并从可行域的角度为分布式电源制定新型控制策略，保障系统的安全运行。

中文关键词： 非线性动力系统;稳定域;动态轨迹;最优解;

英文摘要： The task of detecting the existence of feasibility region of a general nonlinear programming (NLP) problem is very challenging. The existing optimization methods such as Interior Point Method or meta-heuristic methods such as Evolution Algorithm, can not answers whether or not solving the problem is feasible, that is, whether the feasible region of a general NLP is an empty set or not. This proposal seeks to address this challenging problem to develop theory, methods on the feasibility region detection and restoration of a general NLP and develop applications in smart grids. This proposal has four parts: theoretical foundation; systematic methodologies, nonlinear computational schemes and applications in smart grid. To successfully address this challenging task, we propose a dynamical trajectory–based approach which will establish the correspondence between a NLP and a particular class of nonlinear dynamical system, and make a reformulation of the feasible region detection task. Then, feasible region detection methodologies based on the theoretical foundation of the stability region will be developed. In addition, highly efficient nonlinear computation schemes to detect the existence of feasibility region will be developed. If the feasibility region of a NLP problem is an empty set, we will develop multiple strategies to restore the feasible region and construct a feasible solution by modifying the model of a NLP. During the course of this research, the nonlinear computational schemes for feasibility detection will be sharpened and the global convergence will be proven which means that if a dynamic trajectory diverges, then the feasible region of the NLP is empty. Finally, the methodology and schemes developed in this proposal to feasibility detection and restoration will be applied to smart grids. A wide area of application in the smart grid can be expected and we will select optimal power flow problem and optimal dispatch of distributed generation firstly since most of the optimizations in a power system have a close relationship with these two classical applications. The methodologies proposed will provide a new kind of novel optimization, controlling schemes of smart grids in the perspective of feasible region of the constrained power flow equations and can be expected as a powerful tool in the planning, operation and control of the smart grids.

英文关键词： Nonlinear dynamical systems;stability regions;dynamical trajectory;optimal solutions