This talk will present some recent work on solving the nonlinear AC-Unit Commitment problem as defined in the ARPA-E Grid Optimization Challenge 3 (https://gocompetition.energy.gov/challenges/challenge-3). Computational results will be shown on the competition datasets. We will also discuss plans on improving Gurobi's capabilities to handle these types of problems.

In this talk, we will present some recent advances in algorithms and computation techniques for solving large-scale grid optimization problems involving unit commitment and ACOPF. These problems are at the core of power grid operations and planning. We develop new methods for temporal and spatial decomposition, convex relaxations, and parallel computation. The new algorithmic framework can solving UC-AC-OPF problems on power grids with up to 23,000 buses, 12 time periods, within 10 min. The solutions obtained are highly feasible (within $10^{-8}$ tolerance) and on average have less than 1\% global optimality gap. This progress won top performance in the ARPA-E Grid Optimization Challenge 3 and has significant implications for practical applications in power grid operations.

This talk shows how the fusion of AI and Optimization can lead to orders of magnitude improvements for Security-Constrained Economic Dispatch optimizations. It presents an end-to-end self-supervised learning framework that is guaranteed to find high-quality solutions in milliseconds, significantly outperforming the state of the art solutions. The key technical contributions is the use of differential layers and primal-dual learning to restore feasibility and handle contingencies.

We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest ones publicly available, quickly and robustly yielding sharp bounds. Our primary focus concerns the (frequent) case where an ACOPF instance is considered following a small or moderate change in problem data, e.g., load changes and generator or branch shut-offs. We provide significant computational evidence that the cuts computed on the prior instance provide an effective warm-start for our algorithm.