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

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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.