Antonio Conejo, The Ohio State University
Solving certain type of large-scale nonlinear scheduling problems via relaxation and convexification
We use a three-step strategy to solve the daily scheduling of electricity production units with network constraints, a large-scale nonlinear scheduling problem relevant for the power industry. First, we solve a linearized version of the original problem to obtain an initial solution and to identify potentially congested branches. Second, we solve a second-order-conic relaxation of the original problem using an active set strategy regarding branch congestion and using as initial solution that of step 1. Third, to ensure nonlinear feasibility, we fix the binary variables to their optimal values in step 2 and solve a collection of increasingly accurate continuous and convex approximations of the original problem. For very large instances, we solve the relaxed problem in step 2 via Benders’ decomposition. We discuss results from a Texas 2000-node 544-unit 3206-line power system.