Energy-efficient train operation plays an important role on reduction of energy consumption and sustainable development in Metro system. The improvement of regenerative energy (RE) utilization through multi-train collaborative optimization is an effective way. However, traditional researches on this problem mainly focus on a two-train system, which cannot be applied to train group. This paper proposes a novel optimization method for multi-train, the complex train group problem is turned into a single-train and multiple two-train problems based on the analysis of the total energy model. Then the optimal traction force of the accelerating train related to the braking power of the braking train is deduced to 100% recover the RE. Therefore, the train group can be optimized by departure orders, traction energy of the first train is minimized and speed profiles of rest trains are adjusted to maximize the utilization of RE by sequence. Specially, optimization of each train is independent, which only needs to focus on the braking power of its previous train, greatly simplifying the multi-train collaborative optimization problem. Detailed optimization methods are proposed and the effectiveness are verified by the simulation results based on Guangzhou Metro.
Energy efficient, Metro system, RE; Train group, Collaborative optimization
 Gonzlez-Gil, A., Palacin, R., Batty, P. & Powell, J., A systems approach to reduce urban rail energy consumption. Energy convers. Manag, 80, pp. 509–524, 2014.
 Peter, P. & Howlett, P., Optimal driving strategies for a train journey with speed limits. Anziam. J, 36, pp. 38–49, 1994.
 Howlett, P. & Cheng, J., Optimal driving strategies for a train on a track with continuously varying gradient. Bulletin of the Australian Mathematical Society, 38, pp. 388–410, 1997.
 Khmelnitsky, E., On an optimal control problem of train operation. IEEE Transactions on Automatic Control, 45(7), pp. 1257–1266, 2000.
 Liu, R. & Golovitcher, I.M., Energy-efficient operation of rail vehicles. Transportation Research Part A-Policy and Practice, 37(10), pp. 917–932, 2003.
 Albrecht, A., Howlett, P., Pudney, P. & Vu, X., Energy-efficient train control: From local convexity to global optimization and uniqueness. Automatica, 49(10), pp. 3072–3078, 2013.
 Shuai, S., Xiang, L., Tao, T. & Ziyou, G., A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy. IEEE Transactions on Intelligent Transportation Systems, 14(2), pp. 883–893, 2013.
 Ramos, A., Pena, M.T., Fernández, A. & Cucala, P., Mathematical programming approach to underground timetabling problem for maximizing time synchronization. Management and Organization, 35, pp. 88–95, 2008.
 Scheepmaker, G.M., Goverde, R.M.P. & Kroon, L.G., Review of energy-efficient train control and timetabling. European Journal of Operational Research, 257, pp. 355–376, 2017.
 Shuai, S., Tao, T. & Roberts, C., A Cooperative Train Control Model for Energy Saving. IEEE Transactions on Intelligent Transportation Systems, 16(2), pp. 622–631, 2015.
 Xun, J., Tao, T., Song, X., Wang, b. & Jia, z., Research on energy-saving driving model with regenerative energy considered. China Railway Soc, 36(1), pp. 104–149, 2015.
 Haichuan, T., Dick, C.T. & Xiaoyun, F., Improving Regenerative Energy Receptivity in Metro Transit Systems. Transportation Research Record: Journal of the Transportation Research Board, 2534, pp. 48–56, 2015.
 Jianqiang, L., Huailong, Guo. & Yinxue, Y., Research on the Cooperative Train Control Strategy to Reduce Energy Consumption, IEEE Transactions on Intelligent Transportation Systems, 18(5), pp. 1134–1142, 2017.
 Mo, C., Zhuang, X., Pengfei, S., Qingyuan, W., Bo, J. & Xiaoyun, F., Energy-Efficient Driving Strategies for Multi-Train by Optimization and Update Speed Profiles Considering Transmission Losses of Regenerative Energy. Energies, 12, pp. 3573, 2019.
 Horst, S., Peter, H. & Manfred, K., Contribution to Optimum Computer-Aided Control of Train Operation. Proceedings of the Second IFAC/IFIP/IFORS Conference on Control in Transportation Systems, pp. 377–385, 1974.