Mathematical Programming bounds for Large-Scale Unit Commitment Problems in Medium-Term Energy System Simulations

Abstract

We consider a large-scale unit commitment problem arising in medium-term simulation of energy networks, stemming from a joint project between the University of Milan and a major energy research centre in Italy. Optimal plans must be computed for a set of thermal and hydroelectric power plants, located in one or more countries, over a time horizon spanning from a few months to one year, with a hour-by-hour resolution. We propose a mixed-integer linear programming model for the problem. Since the complexity of this unit commitment problem and the size of real-world instances make it impractical to directly optimise this model using general purpose solvers, we devise ad-hoc heuristics and relaxations to obtain approximated solutions and quality estimations. We exploit an incremental approach: at first, a linear relaxation of an aggregated model is solved. Then, the model is disaggregated and the full linear relaxation is computed. Finally, a tighter linear relaxation of an extended formulation is obtained using column generation. At each stage, metaheuristics are run to obtain good integer solutions. Experimental tests on real-world data reveal that accurate results can be obtained by our framework in affordable time, making it suitable for efficient scenario simulations.