非线性优化问题与智能电网的关键技术：理论、方法和应用

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.

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。

本课题从理论层、解法层、算法层、应用层对智能电网中的非线性优化问题、尤其最优潮流问题的可行域问题进行基础研究。通过理论分析、方法开发、数值实验、恢复策略等若干方面进行研究，开发出创新性的计算方法，实现对非线性约束优化问题可行域进行刻画、存在性进行判断，最终在智能电网中进行应用。为智能电网中各类涉及到优化问题的研究工作提供了必要的基础理论，计算方法支撑，具有重要的学术价值和应用前景。.目前论文SCI论文 22篇，EI论文 17篇。.本课题中主要在动力学系统最优潮流可行域、多目标优化问题和Trust-Tech应用等方面展开研究，并取得了众多成果。以下各成果均为本课题首创，在国内外未见相关研究，是本课题的突出创新点：.首次提出刻画电力系统的最优潮流可行域方面：1.对最优潮流问题的可行域进行了刻画；2.提出了电力系统最优潮流问题可行性检测的方法；3.提出了连续线性割方法以快速计算可行点；4.观察最优潮流问题可行域中一种新的分岔现象：伪叉型分岔，并解释其物理意义；5.提出了电力系统风功率注入可变化域的刻画方法；6.研究了（精确）交流潮流模型下负荷域的刻画理论及其应用；7.提出了含故障电流约束的最优潮流可行域刻画。.在多目标优化问题方面：1.提出共识的多目标粒子群优化方法，以提升对帕累托前沿的求解性能；2.提出了用户偏好的协同粒子群三阶段优化方法、用户偏好的混合求解方法和用户偏好的迭代优化方法以快速求解大规模复杂非线性问题的帕累托最优解。.在Trust-Tech方面：1.提出了一种粒子群技术协同的Trust-Tech全局优化技术求解无约束优化问题；2.提出了Trust-Tech增强后的遗传算法，并应用在太阳能发电预测中；3.将Trust-Tech应用在H-KTT聚类算法中，并加以应用。.在其它方面的取得的成果：1. 建立了以最小化动作数量为目标函数，基于AC潮流约束的最小控制数量问题模型，并提出了三阶段式的求解方法；2.研究了固定阈值方法在TSCOPF中加入暂态稳定约束后的性能并提出一种基于稳定区域框架的精确方法；3.提出了提高系统消纳可再生能源能力的配电网多时段重构模型和四阶段求解策略，克服了在逼近最大消纳能力时潮流不收敛的问题。