This paper presents a mixed-integer linear programming (MILP) reformulation of the thermal unit commitment (UC) problem. The proposed formulation is simultaneously tight and compact. The tighter characteristic reduces the search space and the more compact characteristic increases the searching speed with which solvers explore that reduced space. Therefore, as a natural consequence, the proposed formulation significantly reduces the computational burden in comparison with analogous MILP-based UC formulations. We provide computational results comparing the proposed formulation with two others which have been recognized as computationally efficient in the literature. The experiments were carried out on 40 different power system mixes and sizes, running from 28 to 1870 generating units.

This paper presents a mixed-integer linear programming (MILP) formulation of start-up (SU) and shut-down (SD) power trajectories of thermal units. Multiple SU power-trajectories and costs are modeled according to how long the unit has been offline. The proposed formulation significantly reduces the computational burden in comparison with others commonly found in the literature. This is because the formulation is 1) tighter, i.e., the relaxed solution is nearer to the optimal integer solution; and 2) more compact, i.e., it needs fewer constraints, variables and nonzero elements in the constraint matrix. For illustration, the self-unit commitment problem faced by a thermal unit is employed. We provide computational results comparing the proposed formulation with others found in the literature.

Growing load factors in winter and summer peaks are a serious problem faced by the Spanish electric energy system. This has led to the extensive use of peak load plants and thus to higher costs for the whole system. Wind energy represents a strongly increasing percentage of overall electricity production, but wind normally does not follow the typical demand profile. As generation flexibility is limited due to technical restrictions, and in absence of large energy storages, the other side of the equilibrium generation-demand has to react. Demand side management measures intend to adapt the demand profile to the situation in the system. In this paper, the operation of an electric system with high wind penetration is modeled by means of a unit commitment problem. Demand shifting and peak shaving are considered in this operation problem. Demand shifting is modeled in two different ways. Firstly, the system operator controls the shift of demand; secondly, each consumer decides its reaction to prices depending on its elasticity. The model is applied to the isolated power system of Gran Canaria. The impact of an increased installed wind capacity on operation and the cost savings resulting from the introduction of responsive demand are assessed. Furthermore, results from the different implemented demand response options are compared.

This paper deals with the design of underground rail system timetables that synchronize the movement of trains to allow the energy consumption from substations to be reduced by maximizing the use of regenerative-braking energy. Nowadays, most trains are equipped with regenerative-braking systems and any of this recovered energy not used by on-board auxiliary services can be consumed by other trains in the same rail section. A mathematical programming optimization model has been designed to synchronize the braking of trains arriving at station with the acceleration of trains exiting from the same or another station. In addition, a power flow model of the electrical network has been developed to calculate the power-saving factor for each synchronization event in order to encourage better synchronizations, particularly those which have fewer energy losses. These models were applied in the design of a schedule for line 3 of the Madrid underground system. This schedule was then trialled for a week. Energy savings were measured and a significant correlation with the synchronization of train movements was observed. It was concluded that a modification in the published timetables would result in energy savings, with no effect on the quality of service for passengers and low associated investment costs.