Data-driven Methods for Optimal Power Flow in Smart Grids

The modern power grid is undergoing significant changes, driven by increasing complexity, the integration of renewable energy sources, and the urgent need to reduce greenhouse gas emissions. These challenges necessitate more advanced methods for power grid operations. System operators continuously solve the Optimal Power Flow (OPF) problem at regular intervals to determine the most economical dispatch of power while balancing electricity supply and demand. However, traditional OPF and convex relaxation methods often face issues related to feasibility and computational speed. Recently, machine learning methods have gained considerable attention as potential solutions to these challenges. As discussed in the literature, these methods include supervised learning, hybrid approaches that combine physical solvers or equations with machine learning, and unsupervised learning. Despite these advancements, there remain research gaps that need to be addressed. In this thesis, three mechanisms for addressing the OPF problem from different perspectives are proposed. Firstly, a supervised learning algorithm with a subsequent feasibility calibration method is introduced. Secondly, a generative adversarial network (GAN) with a representation learning module is studied and employed as an optimizer for the OPF problem. Lastly, the nearly convex nature of power flow data is investigated, motivating the development of a data-driven convex relaxation approach to solve the OPF problem. This thesis makes significant contributions to the literature by ensuring the feasibility of OPF solvers through post-process algorithms with theoretical support, relaxing the assumption of having optimal solutions for training, and demonstrating high performance of data-driven OPF methods on large systems, such as the PGLIB 2000-bus system.