Quadratically Constrained Linear Programming-based energy-efficient driving for High-speed Trains with neutral zone and time window

Among the numerous challenges that are faced during the daily operation of high-speed rail, the management of the neutral zones in the catenary during unexpected disturbances remains underinvestigated. This study proposes a computerised method for managing the operations of a high-speed train with regenerative braking for passing neutral zones under disturbance to minimise energy consumption. For the first time, different mechanism-based Automatic Passing Neutral Zone systems, including the Magnetic Induction System and Automatic Train Protection, are analysed and modelled as location-based and time-based constraints, respectively. Motion constraints caused by disturbances are described by time windows. Forced coasting and air brake-allowed passing neutral zone rules are considered in these models. The original nonlinear model with location-based constraints is transcribed as a quadratically constrained linear model and then solved. The optimality consistency and its establishment condition between the original and transcribed models are analysed based on the Karush-Kuhn-Tucker conditions. A high-quality solution is obtained when the establishment condition holds. The model with time-based constraints is novelly transformed into an optimal switching point problem. A series of sub-problems are iteratively and efficiently solved. Comprehensive experiments are conducted based on practical data from a high-speed rail system in China. The proposed method is significantly beneficial when compared to Mixed-integer Linear Programming and Artificial Driving Algorithms. Moreover, the impacts of different mechanism-based automatic passing neutral zone systems, operation rules, and a combination of time window settings are extensively analysed.