Optimizing the schedule of thermal generators is probably the most important task when the operation of power systems is managed. This issue is known as the unit commitment problem in operational research. It has been profoundly studied in the literature, where several techniques have been proposed to address a computationally tractable solution. In turn, the ongoing changes of paradigms in energy markets focus the attention on the unit commitment problem as a powerful tool to handle new trends, such as the high renewable energy sources penetration or widespread use of non-conventional energy-storage technologies. A review on the unit commitment problem is propo- sed in this paper. The easy understanding of the diverse techniques applied in the literature for new researchers is the main goal of this state-of-art as well as identifying the research gaps that could be susceptible to further developments. Moreover, an overview of the evolution of the Mixed Integer Linear Programming formulation regarding the improvements of commercial solvers is presented, according to its prevailing hegemony when the unit commitment problem is addressed. Finally, an accurate analysis of modeling detail, power system representation, and computational performance of the case studies is presented. This characterization entails a significant development against the conventional reviews, which only offer a broad vision of the modeling scope of their citations at most.

Nowadays, the changing paradigm in power systems highlights the necessity of improving detail in energy models. The deployment of non-dispatchable renewable energy resources that regulators traditionally promoted, like the European Union case and some areas of the United States, is being accelerated due to the enhanced competitiveness of clean technologies. However, the delay in the widespread use of non-conventional energy-storage techniques, like batteries, is causing an increase in the variability of the thermal-generated demand for electricity. In that context, many combined cycle gas turbine generators have redressed their proceedings, increasing their start-up and shut-down frequency for operating fewer hours than historically have done. Their fast ramping capabilities position them as the best alternative to cover demand peaks in the near term. Consequently, there is a growing interest in representing these thermal units properly. This paper exposes a great-detailed analysis of the start-up cost modeling to accomplish future market trends. Likewise, a new mathematical formulation of the unit commitment problem is also presented. Finally, the formulation is compared to one of the most renowned methodologies. Its successful performance is described in several case studies, where authentic power-demand curves and technical details of a gas-fired generation portfolio are handled in medium-term horizons.

Nowadays, electricity market paradigms are constantly changing. On the one hand, the deployment of non-dispatchable renewable energy sources is bringing out the necessity of representing hourly dynamics in medium-term fundamental models. On the other, the promotion of new interconnection capacity and the integration of markets (as is the case of the European market) makes necessary the simultaneous modeling of multiple electricity systems. Thus, the large size of power markets, together with the consideration of uncertainty in some inputs, make it computationally intractable to work rigorously on an hourly detailed time span. Temporal aggregation, integer programming relaxation or less accurate generation modeling are usually employed to obtain reasonable computation times. However, the application of these techniques often leads to infeasible or suboptimal operational outputs. This paper proposes a new soft-linking methodology to meet reliable results from medium-term models, such as hourly prices or aggregated productions, with a feasible and detailed representation of the thermal generation, considering technical constraints and risk aversion. The results of a fundamental model that represents the competitive behavior between market players in a multi-area power system are used as the starting point for the methodology. Then, a post-processing method is applied to optimize and make feasible the thermal portfolio of a market agent. The final output is a feasible hourly scheduling and an ample space for optimization, where the introduction of a strategic term represents the rational behavior of a player who tries to maximize its profit.