Learning to Accelerate Globally Optimal Solutions: Applications in the AC Optimal Power Flow Problem
Date of Graduation
12-2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Engineering (PhD)
Degree Level
Graduate
Department
Industrial Engineering
Advisor/Mentor
Shen, Haoming
Committee Member
Nachtmann, Heather L.
Second Committee Member
Zhang, Shengfan
Third Committee Member
Nagarajan, Harsha
Fourth Committee Member
Bent, Russell
Keywords
Deep Neural Network; Global Optimization; Machine Learning; Optimal Power Flow; Optimization; Power systems
Abstract
The Alternating Current Optimal Power Flow (AC-OPF) problem is a fundamental optimization challenge critical to ensuring the economical and reliable operation of power grids. While fast heuristic methods provide upper-bound solutions, assessing their quality requires lower bounds obtained from relaxations of the AC-OPF problem. This dissertation focuses on finding globally optimal solutions to the AC-OPF problem by enhancing the effectiveness and efficiency of Quadratic Convex (QC) relaxations. Leveraging machine learning techniques, we aim to achieve tighter relaxations faster and improve computational performance, enabling practical scalability for real-time applications.
In Chapter 2, we propose a machine learning-based method to accelerate the Optimality-Based Bound Tightening (OBBT) algorithm by focusing on a subset of critical variables. This approach significantly reduces the number of variables subjected to tightening, improving the efficiency of the exhaustive OBBT algorithm. We develop a novel heuristic algorithm to identify voltage magnitude and phase-angle difference variables with the largest impact on QC relaxation. To address the computational cost of the heuristic, we replace it with a deep neural network (DNN) surrogate that predicts variable rankings more efficiently. This method achieves substantial speed-ups and near-global optimum solutions for the small- and medium-scale power grids.
In Chapter 3, we address the scalability of the OBBT algorithm for large-scale networks, where the range-based ranking algorithm from Chapter 2 loses effectiveness due to smaller range reductions in variable bounds. We introduce two novel heuristics: a ranking algorithm that evaluates the impact of tightened variable bounds on the AC-OPF problem and a dynamic variable selection algorithm that identifies subsets of variables adaptively before each OBBT iteration. These advancements enhance solution quality by targeting diverse variables across iterations. Replacing the ranking algorithm with a DNN surrogate further improves efficiency. Results demonstrate significant acceleration of the OBBT algorithm and improved scalability for large-scale networks.
In Chapter 4, we propose an optimality-based exact method to identify a subset of active QC constraints that enhances the efficiency of the QC relaxation while maintaining high solution quality. Formulated as a bilevel max-min problem, this approach involves selecting a subset of QC constraints (outer level) and solving the QC relaxation model (inner level). To overcome computational challenges, we transform the bilevel problem into a single-level Mixed Integer Linear Programming (MILP) formulation through linearization, Lagrangian dual reformulation, and variable consolidation. While the MILP achieves high-quality solutions, it is computationally intensive. To improve scalability, we develop a feasibility-based heuristic algorithm and further accelerate it using an ML surrogate model. The surrogate effectively approximates ground-truth solutions, offering a scalable and efficient approach for large networks.
In this dissertation, we focused on finding global optimum solutions for the AC-OPF problem by improving the effectiveness and efficiency of Quadratic Convex (QC) relaxations. By leveraging the proposed novel algorithms and machine learning-based methods, we achieved significant computational speed-ups and scalability for large-scale network instances while maintaining high-quality solutions. These advancements enhance the practicality of solving the AC-OPF problem and provide a foundation for integrating optimization and learning in power system operations.
Citation
Cengil, M. (2024). Learning to Accelerate Globally Optimal Solutions: Applications in the AC Optimal Power Flow Problem. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/5601
