Driving strategy optimization for trains in subway systems

Abstract

Energy-efficient operation of trains in subway systems is regarded as one of the most effective strategies to cut down the operational cost. Most of the studies about the energy-efficient operation of trains aim to minimize the consumption of mechanical energy of trains. In this paper, an energy-efficient train control model is proposed under the practical billing system by introducing the traction efficiency. In addition, a numerical solution approach is presented to solve the energy-efficient driving strategy, which consists of the control sequences and the corresponding switching points. First, the authors analyze the energy-efficient control problem by applying the maximum principle, from which the energy-efficient control regime is proved to include the maximum acceleration, coasting, cruising with partial braking, and maximum braking. Second, the control sequences for one section are fully analyzed and an algorithm is presented to calculate the switching points with the energy consumption constraint. To obtain the solution to an interval with variable speed limits and gradients, the interval is divided into several sections, where the gradient and speed limit of each section are constants. A primary energy-efficient solution, which costs a longer trip time, is given. Then, energy units are assigned into multiple sections to shorten the trip time of the primary solution. Specifically, each energy unit is added into the selected section to achieve the maximum time reduction. Finally, the energy-efficient driving strategy at all sections will be obtained when the scheduled trip time of the interval is delivered. Some examples based on the practical data are conducted to illustrate that the proposed approach has a good potential on saving energy of trains.