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.

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Trains equipped with automatic train operation (ATO) systems are operated between stations according to the speed commands they receive from balises. These commands define a particular speed profile and running time, with associated energy usage (consumption). The design of speed profiles usually takes into account running times and comfort criteria, but not energy consumption criteria. In this article, a computer-aided procedure for the selection of optimal speed profiles, including energy consumption, which does not have an effect on running times, is presented. To this end, the equations and algorithms that define the train motion and ATO control have been modelled and implemented in a very detailed simulator. This simulator includes four independent modules (ATO, motor, train dynamics, and energy consumption), an automatic generator of every possible profile and a graphical assistant for the selection of speed commands in accordance with decision theory techniques. The results have been compared with measured data in order to adjust and validate the simulator. The implementation of this new procedure in the Madrid underground has led to a 13 per cent of energy saving. As a result, the decision has been taken to redesign all the ATO speed profiles on this underground.