Regenerative braking technology has been widely used by subway trains, where regenerative braking energy (RBE) will be generated during train braking processes. An RBE usage method is proposed for subway trains, where train braking processes are predicted based on the field data of the train control system, and the braking information will be obtained in advance. The RBE will be calculated, and then, part or all of it will be distributed to neighboring trains in the same or adjacent power supply sections. Several feasible schemes for the RBE distribution are given, where the speed profiles of the neighboring trains will be adjusted to absorb the distributed RBE. An optimal RBE distribution scheme with the most effective usage of RBE will be obtained based on calculation results of the given schemes. For each adjusted speed profile of the neighboring train, a power process will be normally introduced. Existence of the optimal solution for speed profile adjustment is analyzed under the precondition that the train runs in a long speed-holding journey, and then, the necessary condition of the optimal solution is found by perturbance analysis. A simulation case of Yizhuang Line in Beijing subway is studied, and the simulation results show that the proposed method can use the RBE efficiently.

The Regenerative Braking Energy (RBE) of metro trains plays an important role in metro energy saving. If the regenerative energy can be directly absorbed by the adjacent trains, the investment in other RBE usage equipments like super capacitors will be reduced. To increase the RBE usage, the overlaps of traction and braking processes of adjacent trains can be increased by timetable optimization or real-time train regulation. But if the overlaps cannot be realized, the RBE cannot be efficiently absorbed by the other trains. To solve this problem, this paper proposes an optimal train control method to absorb the RBE of the braking train by adjusting the speed profile of an adjacent train that runs at non-braking stage. A speed profile adjustment algorithm for the adjacent train is given considering the speed limits and gradients, in which a traction process is incorporated in the adjusted speed profile. Connected and unconnected DC power supply networks are both considered. In the connected DC power supply network, the RBE of the braking train can be absorbed by the adjacent adjusted train, which runs in the different power supply section. To test the robustness of the proposed algorithm, random train delays are considered in the simulations. The interstation running time will be regulated to reduce the train delay by a linear programming model, based on which, the speed profile of the cooperative train will be adjusted. Simulations are conducted based on a whole day data of Beijing Metro Line 4. The simulation results show that the proposed method improves the energy efficiency over 13% by improving RBE usage, and the proposed method also shows strong robustness in the train delay simulations, which makes it a promising method to be applied in real metro system.

This paper proposes an optimization method of train scheduling for metro lines with a train dwell time model according to passenger demand. An optimization problem of train scheduling is established with constraints of a headway equation, passenger equation, and train dwell time equation, where the train dwell time is modeled as a function of boarding and alighting passenger volumes. The aim of the optimization problem is to minimize the waiting time of passengers and train operation cost. Lagrangian duality theory is adopted to solve this optimization problem with high dimensionality. Finally, simulation results illustrate that this method is efficient to generate the train schedule, which meets the passengers' exchanging requirements between trains and platforms. The contribution of this paper is that a dwell time model is introduced in train schedule optimization, which provides the possibility of reducing the operation cost in the precondition that the exchanging time of passengers between platforms and trains is assured.

Once a freight train is delayed on a busy railway under a quasi-moving-block signaling system, the speed of its following trains may fluctuate, without proper adjustment. Updating the reference speed profile of the delayed freight train is an urgent task to improve the train operation performance and rail utilization ratio. To this end, this article proposes a speed profile optimization method for following delayed trains that is based on the idea of model predictive control (MPC). The state change time of the block section ahead is predicted for each following train according to the speed profile of its preceding train, based on which the distance between the following train and each speed protection curve (DTC) is predicted. The DTC is taken as a key optimization index for the speed profile optimization, and the other optimization indices are train delay and energy consumption. A two-step hierarchical optimization algorithm is proposed in this article. In the upper level, each prediction step is defined as the traveling time of the preceding train in each block section ahead, and the train target cruising speed sequence is calculated, with the dimension decided by the prediction horizon, using particle swarm optimization. In the lower level, the optimal speed profile is calculated based on the rolling optimization algorithm of the train speed curve in the prediction horizon. The proposed algorithm repeats the optimization process with updated train information after each control horizon. Three simulations are presented, which consider a downhill scenario, steep uphill scenario, and temporary speed limit, respectively. Then, the MPC parameters are analyzed and the optimized speed profiles are compared with the other algorithm.

Given the considerable length and weight of freight trains, their operation can be quite challenging. Improper operation may lead to train decoupling and derailment. Driver Advisory Systems (DASs) are used in some countries to assist train drivers by providing the speed curves, which are desired to be easy to track. Multi-mass train model is a good choice to depict the in-train forces in train speed curve generating, but its application is often hindered by the computation time. A single mass train model is considered as another choice to simplify the computation. To exploit the advantages of the multi-mass and single-mass models, this paper proposes a Two-step Optimization Method to generate the optimal speed curves for the freight trains. In the first step, the Rolling Optimization Algorithm (ROA) is proposed to optimize the speed curve on the basis of the single-mass model, taking the train energy consumption and punctuality as the optimization objectives. In order to assist the driver in operating the train smoothly, the speed curve generated by the ROA was tested on DAS, but it could not be followed accurately in the actual operation. To solve this problem, a Model Predictive Control (MPC) algorithm based on a multi-mass model is adopted as the second optimization step, which takes the output speed curve of the ROA as the reference speed curve. The MPC algorithm will generate a new speed curve, taking in-train forces, energy consumption and punctuality as the optimization indices. Simulations are carried out using the data from the Dalailong railway in China to evaluate the proposed method. The simulation results show that the speed curves generated by the Two-step Optimization Method are smoother than that of the ROA, and the throttle sequences are more conducive for the driver to follow in practical operation. The simulation results show that the energy consumption is reduced by 17.1% compared to that of the ROA simulation. The speed curve also can be integrated into the onboard DAS or the Automatic Train Operation (ATO) system, aiming to obtain a smooth and energy-efficient train operation.