Mathematical programming approach to underground timetabling for maximizing the use of regenerative braking power

Abstract

Underground transportation is crucial in big modern cities as a way to achieve a clean, rapid and massive transport. While in peak hours the first objective is to move as many people as possible increasing the train frequency, in off-peak hours other considerations can be taken into account. Energy consumption should be an important issue in the design of train timetables in offpeak hours. Energy saving can be obtained by using regenerative brakes. The model presented here is a particular case of train timetabling problem. It is stated as a mixed integer optimization problem. The objective function is to maximize the overlapping time among trains that arrive and depart from the same station or from different stations connected to the same electrical substation. Under that condition the energy produced by a train in its slow-down process can be consumed by another close train in its speed-up process. The constraints include maximum bounds on changes in the current timetable in service with respect to the new synchronised schedule, keeping the total travel time of each train, and the computation of the coincidence time among trains. The detection of the overlapping condition requires binary variables and, therefore, integrality conditions, which make the problem difficult to solve. The train timetabling model has been tested with real cases corresponding to lines of Metro de Madrid and the preliminary results show that time coincidence can be increased dramatically and, therefore, energy saving by train synchronization.