arXiv:2603.15934v4 Announce Type: replace-cross Abstract: The US energy system is under increasing pressure to serve expanding data centers loads and to accommodate a larger number of generating units with varying technologies and ownership structures. Therefore, developing new unit commitment (UC) methods remains a priority for reliable and affordable grid operations. We expand our novel computational method for UC to include ramping constraints and long-horizon planning, and provide a theoretical bound on its accuracy. We solve problems with thousands of generators at 5-minute market intervals. We show that our method can solve UC problems with over 20,000 generators in approximately 10 seconds on commodity hardware and that an increased planning horizon leads to sizable op- erational cost savings. This is twice as fast as the leading commercial solver, Gurobi. The gap increases when adding more constraints. Our method can be implemented using existing continuous optimization solvers and adapted for different applications. We prove a bound on the error of these solvers and show that it vanishes (in relative terms) as the problem becomes larger. Our novel algorithm could allow an operator to make horizon-aware economic decisions for large systems.