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

协作研究：基于逐次线性优化和凸松弛的二次非凸AC-OPF全局算法

• 批准号: 1851602
• 负责人: Masoud Barati
• 金额: $ 19.99万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-28 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1851602&HistoricalAwards=false
• 关键词: Collaborative; Research; Global; Algorithm; Quadratic

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.

非凸规划涉及目标函数或约束集是非凸函数的优化问题。这类问题出现在工程系统的广泛应用中。尽管有大量关于凸和非凸二次规划（一般类的优化问题）的文献，但大多数可用的优化技术要么不可扩展，要么仅对凸二次规划有效，并且不能为非凸二次规划提供足够的结果。该项目侧重于综合方法的基础研究，研究团队预计该方法将为非凸规划问题提供强大的解决方法。新的方法将适用于非凸问题出现在许多领域，如电力和能源系统，交通和通信。该项目将涉及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难度对电力和能源系统管理有直接影响。这是电力系统管理中必须处理的最基本问题之一。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，以解决与问题的非凸性相关的困难。有一个关键和迫切需要开发智能和强大的OPF求解器。目前可用于DC-OPF的常规选项非常有限。这项研究将从根本上解决交流最优潮流（AC-OPF）与有功和无功二次约束二次规划优化问题的形式，出现在电力系统的操作和规划应用。除了非凸性外，这些问题被认为是NP-困难的。所提出的解决方法是基于凸优化理论中的几个基本的和强大的优化技术，如线性化近似技术，线性和全局搜索程序，双线性和凸松弛，和交替方向的方法。此外，必须引入新的方案和理论来建立算法的收敛性并保证解结果的全局最优性。该研究小组设计了一种新的基于逐次线性优化的分支定界（SLOBB）方法，该方法基于经典线性近似、改进的凸松弛和分支定界技术的部署原理来寻找AC-OPF问题的全局最优解。由于线性规划和凸解算器是鲁棒和快速的，并且电力系统社区已经熟悉用于OPF的线性和凸规划，因此将开发的算法对于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，以检查所提出的算法的性能，并分析其效率对现有的测试床系统和合成数据集。所开发的模型和方法将在实际电网中执行。

项目成果

Decomposition and Equilibrium Achieving Distribution Locational Marginal Prices Using Trust-Region Method

• DOI: 10.1109/tsg.2018.2822766
• 发表时间: 2019-05
• 期刊: IEEE Transactions on Smart Grid
• 影响因子: 9.6
• 作者: Sarmad Hanif;Kai Zhang;C. Hackl;M. Barati;H. Gooi;T. Hamacher

A global algorithm for AC optimal power flow based on successive linear conic optimization

基于逐次线性二次曲线优化的交流最优潮流全局算法

• DOI: 10.1109/pesgm.2017.8273957
• 发表时间: 2017
• 期刊: 2017 IEEE Power & Energy Society General Meeting
• 作者: Barati, Masoud;Kargarian, Amin
• 通讯作者: Kargarian, Amin

A Pool Strategy of Microgrid in Power Distribution Electricity Market

• DOI: 10.1109/tpwrs.2019.2916144
• 发表时间: 2020-01
• 期刊: IEEE Transactions on Power Systems
• 影响因子: 6.6
• 作者: Yiwei Wu;M. Barati;G. Lim

Multiphase Distribution Locational Marginal Prices: Approximation and Decomposition

多相分布位置边际价格：近似和分解

• 发表时间: 2018
• 期刊: IEEE PES General Meeting 2018
• 作者: Sarmad Hanif, Masoud Barati