Benders Decomposition on Large-Scale Unit Commitment Problems for Medium-Term Power Systems Simulation

Abstract

The Unit Commitment Problem (UCP) aims at finding the optimal commitment for a set of thermal power plants in a Power System (PS) according to some criterion. Our work stems from a collaboration with RSE S.p.A., a major industrial research centre for PSs in Italy. In this context the UCP is formulated as a large-scale MILP spanning countries over a year with hourly resolution to simulate the ideal behaviour of the system in different scenarios. Our goal is to refine existing heuristic solutions to increase simulation reliability. In our previous studies we devised a Column Generation algorithm (CG) which, however, shows numerical instability due to degeneracy in the master problem. Here we evaluate the application of Benders Decomposition (BD), which yields better conditioned subproblems. We also employ Magnanti-Wong cuts and a “two-phases scheme”, which first quickly computes valid cuts by applying BD to the continuous relaxation of the problem and then restores integrality. Experimental results on weekly instances for the Italian system show the objective function to be flat. Even if such a feature worsens convergence, the algorithm is able to reach almost optimal solutions in few iterations.