The impact of wind on energy-efficient train control

An energy-efficient train trajectory corresponds to the speed profile of a train between two stations that minimizes energy consumption while respecting the scheduled arrival time and operational constraints such as speed limits. Determining this trajectory is a well-known problem in the operations research and transport literature, but has so far been studied without accounting for stochastic variables like weather conditions or train load that in reality vary in each journey. These variables have an impact on the train resistance, which in turn affects the energy consumption. In this paper, we focus on wind variability and propose a train resistance equation that accounts for the impact of wind speed and direction explicitly on the train motion. Based on this equation, we compute the energy-efficient speed profile that exploits the knowledge of wind available before train departure, i.e., wind measurements and forecasts. Specifically, we: (i) construct a distance-speed network that relies on a new non-linear discretization of speed values and embeds the physical train motion relations updated with the wind data, and (ii) compute the energy-efficient trajectory by combining a line-search framework with a dynamic programming shortest path algorithm. Extensive numerical experiments reveal that our “wind-aware” train trajectories present different shape and reduce energy consumption compared to traditional speed profiles computed regardless of any wind information.