Energy-constraint operation strategy for high-speed railway

With given trip time on each section, conventional train energy-efficient operation problem optimizes the reference speed profile such that the energy consumption for tracking the profile is minimized. Alternatively, this study aims to solve its anti-problem that minimizes the trip time under certain energy constraint, namely the train energy-constraint operation problem. In particular, this study focused on high-speed railway, for which the resistance mainly comes from the air friction. Firstly, we apply the Pontrya-gin maximum principle to prove that the optimal speed profile consists of four phases including acceleration, cruising, coasting and braking. Furthermore, we prove that the switching strategy among different phases is uniquely determined by the cruising speed, and then we solve the optimal cruising speed with an analytical approach. Finally, we prove some theorems on the energy-constraint operation strategy, which provide useful guidance for improving the train operation efficiency.