Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods

2 In this paper we propose a stochastic unit commitment model for a power generation company that takes part in an electricity spot market. The relevant feature of this model is its detailed representation of the spot market during a whole week, including seven day-ahead market sessions and the corresponding adjustment market sessions. This representation takes into account the influence that the company's decisions exert on the market clearing price by means of a residual demand curve for each market session. Uncertainty is introduced in the form of several possible spot market outcomes for each day, which leads to a weekly scenario tree. The model also represents in detail the operation of the company's generation units, as usual in unit commitment models. The proposed unit commitment model leads to large-scale mixed linear-integer problems that are hard to solve with current commercial optimizers. This suggests the use of alternative solution methods. In this paper four solution approaches are tested with a realistic numerical example in the context of the Spanish electricity spot market. The first one is direct solution with a commercial optimizer, which illustrates the mentioned limitations. The second method is a standard Lagrangean relaxation algorithm. The third and fourth methods are two original variants of Benders decomposition for multistage stochastic integer programs. We analyze the advantages and disadvantages of these four methods and establish a comparison between them. The results obtained suggest interesting conclusions and lines for future research.