Learning and Optimization for Efficient and Optimal Operations in Sustainable Power Systems

Abstract

Sustainable energy systems have the potential to significantly reduce climate change and improve economic and social welfare. However, transitioning to renewable energy resources has brought uncertainties into all facets of the decision-making processes across the energy system. For example, the optimal power flow (OPF), a foundational resource allocation problem in power systems, has now to be solved repeatedly for numerous scenarios within tight timeframes to adjust to rapid fluctuations in electricity demands. While machine learning (ML) has emerged as a promising approach to accelerating the computation of optimization problems, standard ML algorithms face challenges in enforcing the constraints of physical systems and providing generalization guarantees. These challenges underscore the necessity for a nuanced design of ML algorithms to ensure efficient and optimal operations in energy systems, especially when faced with high penetration of renewables and significant uncertainties.In this dissertation, we propose machine learning-based algorithms for efficient and optimal operations of power systems under large uncertainty. More specifically, we develop a flow-based generative approach to model residential load behaviors and generate varied and plentiful futurescenarios for residential load demand. Then, to optimize and plan power systems across these diverse scenarios, we design neural network-based solvers to offer solutions orders of magnitude faster than conventional methods. By integrating problem-specific structural insights, we ensure learned solutions satisfy engineering and operational constraints within power systems. These insights also enhance the data efficiency and generalization capabilities of the learning algorithms. In addition, we apply the proposed algorithmic designs to the fundamental resource allocation problem in power system operations, i.e., optimal power flow, to showcase the effectiveness of these methods. The specific contributions of this dissertation include (i) a flow-based generative approach is proposed to model residential load demand and generate varied load scenarios; (ii) a convex neural network-based algorithm is developed for solving the DC Optimal Power Flow (DCOPF) problem, providing generalization guarantees; (iii) an unsupervised neural network-based algorithm is introduced for solving the two-stage DCOPF problem, ensuring feasibility guarantees; (iv) a Lagrangian-based iterative algorithm is proposed to enhance the solution quality of the AC Optimal Power Flow (ACOPF) by iteratively refining the initial point for local solvers.; (v) using insights from the Lagrangian function, a neural network-based learning algorithm is developed to provide high-quality warm starts for solving the ACOPF; (vi) an analytical method is presented to construct the convex restriction of the feasible set for AC power flows in radial networks.