Collaborative Research: A Global Algorithm for Quadratic Nonconvex AC-OPF Based on Successive Linear Optimization and Convex Relaxation

非凸规划涉及目标函数或约束集为非凸函数的优化问题。这类问题在工程系统中有着广泛的应用。尽管有大量关于凸和非凸二次规划(一般类型的优化问题)的文献，但大多数现有的优化技术要么是不可扩展的，要么只对凸二次规划有效地工作，并且不能为非凸二次规划提供足够的结果。该项目专注于对一种综合方法的基础研究，研究小组希望这种方法将导致一类非凸规划问题的强大求解方法。这种新方法将适用于电力和能源系统、交通和通信等许多领域中出现的非凸问题。该项目将吸引来自代表性不足群体的学生，并将对工程教育产生积极影响。电力和能源优化问题的一般困难直接影响到电力和能源系统管理。这是电力系统管理中必须解决的最基本的问题之一。该项目的主要目标是通过开发适用于广泛的非线性能源问题，特别是最优潮流(OPF)问题的高性能优化技术来解决与问题非凸性相关的困难。迫切需要开发智能和强大的OPF解算器。目前可用于DC-OPF的传统选择相当有限。这项研究将从根本上解决交流最优潮流(AC-OPF)问题，即电力系统运行和规划应用中出现的有功和无功二次约束二次规划优化问题。这些问题除了是非凸的外，还被认为是NP-难的。所提出的求解方法基于凸优化理论中几种基本而强大的优化技术，如线性化逼近技术、线性和全局搜索过程、双线性和凸松弛方法以及交替方向方法。此外，必须引入新的方案和理论来建立算法的收敛并保证解结果的全局最优性。该研究小组基于经典线性逼近、改进的凸松弛和分支定界技术，设计了一种新的基于逐次线性优化的分支定界(SLOBB)方法来寻找AC-OPF问题的全局最优解。由于线性规划和凸规划算法具有较强的鲁棒性和快速性，而且电力系统对最优潮流的线性规划和凸规划已经很熟悉，因此将开发的算法对AC-OPF问题将是有益的和用户友好的。我们还将进行理论研究，以检验所提出的算法的性能，并分析其在现有试验台系统和合成数据集上的效率。开发的模型和方法将在现实世界的实际电网中执行。

Non-convex programming involves optimization problems where either the objective function or constraint set is a non-convex function. These kinds of problems arise in a broad range of applications in engineering systems. Despite the substantial literature on convex and non-convex quadratic programming (general classes of optimization problems), most available optimization techniques are either not scalable or work efficiently only for convex quadratic programming and do not provide adequate results for non-convex quadratic programming. This project focuses on fundamental research on an integrated approach which the research team expects will lead to powerful solution methods for classes of non-convex programming problems. The new approach will be applicable for non-convex problems arising in many areas, such as power and energy systems, transportation, and communications. The project will involve students from underrepresented groups and will positively impact engineering education.The general difficulty of power and energy optimization problems has a direct impact on power and energy systems management. This is one of the most fundamental concerns that must be dealt with in electrical power system management. The primary objective of this project is to address the difficulty associated with problem non-convexity by developing high-performance optimization techniques that apply to a broad set of nonlinear energy problems, particularly the Optimal Power Flow (OPF) problem. There is a critical and urgent need for developing smart and robust OPF solvers. The conventional options currently available for DC-OPF are quite limited. The research will fundamentally address AC Optimal Power Flow (AC-OPF) with active and reactive quadratically constrained quadratic programming optimization problems of a form that arises in operation and planning applications of the power system. Besides being non-convex, these problems are identified to be NP-hard. The proposed solution method is based on several basic and powerful optimization techniques in convex optimization theory such as linearized approximation techniques, linear and global search procedures, bi-linear and convex relaxation, and alternate direction methods. Also, new schemes and theories must be introduced to establish the convergence of the algorithm and guarantee the global optimality of the solution results. The research team devised a new successive linear optimization based branch and bound (SLOBB) method based on deploying principles of the classical linear approximation, improved convex relaxation, and the branch-and-bound technique to find the global optimal solution of the AC-OPF problem. Since the linear programming and convex solvers are robust and fast, and also the power systems community is already familiar with linear and convex programs for OPF, the algorithm that will be developed will be beneficial and user-friendly for the AC-OPF problem. We will also pursue theoretical investigations to examine the performance of the proposed algorithm and analyze its efficiency on existing test bed systems and synthetic data sets. The developed models and methodologies will be executed in real-world practical power grids.