不論在解決交通壅塞、提升運輸容量、減輕空氣污染、節省能源消耗等，軌道運輸系统是非常有效的工具，在大眾運輸系统中佔有重要的地位。本論文進行捷運列車站間節能的最佳化，首先將站間距離與速度命令離散化，利用所提出的列車牽引系統電氣模型，在最佳化前事先進行電能消耗及行駛時間的計算，其中納入加速、減速、等速與滑行四種列車運行模式，最後以粒子群演算法求得最佳列車速度曲線。
過去探討列車運行省能的相關研究僅考量機械能耗，或以常數效率直接將機械能轉換為電能。然而列車使用最低的機械能並不能確保此時列車的輸入電能最低。因此直接最小化電能消耗才能達到列車省能的目的。本論文所提出的牽引系統電氣模型省略精確模型中的諧波成分。並在模擬結果發現傳統機械模型無法呈現真實的電能消耗。比較精確模型與本文所提出模型的模擬結果，兩者的能耗計算结果差距不大，但使用本文所提出的模型可以節省大量模擬時間，依據實際模擬結果顯示，可以節省約二分之一的計算時間，因此更適合使用於列車運行模擬。最後，多加入滑行模式的選擇後，可以降低能耗約58％。

Rail transport systems play a crucial role in public transport systems in that they are highly effective in mitigating traffic jams, maximizing transportation capacity, minimizing air pollution, and reducing energy consumption. This study optimized the operation of a rapid transit train between stations for energy conservation.
Past studies investigating energy conservation in train operation only considered the consumption of mechanical energy or assumed a constant efficiency value for the direct conversion of mechanical energy to electrical energy consumption. However, a train using minimal mechanical energy does not necessarily imply its input electrical energy is minimal. Therefore, only through direct minimization of electrical energy consumption can the goal of energy conservation in train operation be achieved. Simulation results from conventional mechanical model, the exact model, and the proposed model indicated that the conventional mechanical model could not reflect the actual electrical energy consumption and consequently could not yield the optimal train-speed curve. Simulation results from the exact and the proposed models revealed small differences between their energy consumption calculation results. The model this study proposed greatly reduced the simulation time. Moreover, when the coasting mode was added to the proposed model, the operational energy consumption was reduced by approximately 58%.

[1] S. Su, X. Li, T. Tang, and Z. Gao, “A subway train timetable optimization approach based on energy-efficient operation strategy,” IEEE Transactions on Intelligent Transportation Systems, vol. 14, no. 2, pp. 883–893, June 2013.
[2] A. Gonzlez-Gil, R. Palacin, P. Batty, and J. Powell, “A systems approach to reduce urban rail energy consumption,” Energy Conversion and Management, vol. 80, pp. 509 – 524, 2014.
[3] M. Dominguez, A. Fernandez-Cardador, A. P. Cucala, and R. R. Pecharroman, “Energy savings in metropolitan railway substations through regenerative energy recovery and optimal design of ato speed profiles,” IEEE Transactions on Automation Science and Engineering, vol. 9, no. 3, pp. 496–504, July 2012.
[4] C. S. Chang and S. S. Sim, “Optimising train movements through coast control using genetic algorithms,” IEE Proceedings - Electric Power Applications, vol. 144, no. 1, pp. 65–73, Jan 1997.
[5] K. Wong and T. Ho, “Dynamic coast control of train movement with genetic algorithm,” International Journal of Systems Science, vol. 35, no. 13-14, pp. 835 – 846, 2004.
[6] Y. DING, H. LIU, Y. BAI, and F. ZHOU, “A two-level optimization model and algorithm for energy-efficient urban train operation,” Journal of Transportation Systems Engineering and Information Technology, vol. 11, no. 1, pp. 96 – 101, 2011.
[7] Z. Li and X. Wei, “Energy-saving optimization of train speed curve based on pso,” in 2016 35th Chinese Control Conference (CCC), July 2016, pp. 10 210–10 215.
[8] Y. V. Bocharnikov, A. M. Tobias, C. Roberts, S. Hillmansen, and C. J. Goodman, “Optimal driving strategy for traction energy saving on dc suburban railways,” IET Electric Power Applications, vol. 1, no. 5, pp. 675–682, Sept 2007.
[9] S. Lu, S. Hillmansen, T. K. Ho, and C. Roberts, “Single-train trajectory optimization,” IEEE Transactions on Intelligent Transportation Systems, vol. 14, no. 2, pp. 743–750, June 2013.
[10] N. H. Ha, “Train mechanical - kinematic modeling and control for traction network analysis,” Master’s Thesis, Universidad De Oviedo, 2016.
[11] B. R. Ke, M. C. Chen, and C. L. Lin, “Block-layout design using max-min ant system for saving energy on mass rapid transit systems,” IEEE Transactions on Intelligent Transportation Systems, vol. 10, no. 2, pp. 226–235, June 2009.
[12] W. ShangGuan, X. H. Yan, B. G. Cai, and J. Wang, “Multiobjective optimization for train speed trajectory in ctcs highspeed railway with hybrid evolutionary algorithm,” IEEE Transactions on Intelligent Transportation Systems, vol. 16, no. 4, pp. 2215–2225, Aug 2015.
[13] 陸億恭，「全自動駕駛系統的節能技術的研究」，北京交通大學碩士論文，2011年。
[14] 邱信瑋，「考量捷運實際運轉特性之列車運行模擬與分析」，國立臺灣科技大學碩士論文，民國102 年。
[15] Hari Maghfiroh, “Modeling and Speed Control of a Single Train of Taipei Mass Rapid Transit System,” Master Thesis, National Taiwan University of Science and Technology, 2014.
[16] D. H. Lee, and M. Dong, “Dynamic Network Design for Reverse Logistics Operations Under Uncertainty,” Transportation Research Part E, Vol. 45, No. 1, pp. 61-71, 2009.
[17] H. R. Lourenco, J. P. Paixao, and R. Portugal, “Multiobjective Metaheuristics for the Bus Driver Scheduling Problem,” Transportation Science, Vol. 35, No. 3, pp. 331-343, 2001.
[18] B. R. Ke, C. L. Lin, and C. C. Yang, “Optimization of Train Energy-Efficient Operation for Mass Rapid Transit Systems,” IET Intelligent Transport Systems, Vol. 6, No. 1, pp. 58-66, 2012.
[19] 陳詩韻，「軌道列車電能消耗極小化之速率最佳化模式」，國立成功大學土木工程學系碩博士班碩士論文，2004.
[20] B. R. Ke, H. Maghfiroh, K. L. Lian, N. Chen, and D. F. Teshome, “Model of traction system and speed control for single train of taipei mass rapid transit system,” in 2016 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), July 2016, pp. 781–787.
[21] 曾乙申，「捷運與輕軌供電系統電腦化模擬(上)—列車運行模擬」，捷運技術，台北捷運局，27，第161-184頁，民國91年。
[22] P. Vas, Vector Control of AC Machines, Clarendon Press Oxford, 1990.
[23] P. W. Lehn, and K. L. Lian, “Frequency Coupling Matrix of a Voltage-Source Converter Derived From Piecewise Linear Differential Equations,” IEEE Transactions on Power Delivery, Vol. 22, No. 3, pp. 1603-1612, Jul. 2007.
[24] D. G. Holmes, and T. A. Lipo, Pulse Width Modulation for Power Converters Principles and Practice, John Willey & Sons, pp. 120-123, 2003.
[25] M. Ned, M. U. Tore, and . W. P. Robbins, Power electronics: converters, applications, and design, 3rd ed, Ed. Wiley, 2003.
[26] C.W. HO, A. E. Ruehli, and P. A. Brennan, “The Modified Nodal Approach to Network Analysis,” IEEE Transactions on Circuits and System, Vol. Cas-22, No. 6, June 1975.
[27] 黃仲欽，「電機機械理論」，上課講義，民國100年。
[28] 劉昌煥，「交流電機控制」，東華書局，民國102 年。
[29] J. Kennedy and R. Eberhart, “Particle swarm optimization,” vol. 4, Perth, Aust, 1995, pp. 1942 – 1948.
[30] R. Chevrier, “An evolutionary multi-objective approach for speed tuning optimization with energy saving in railway management,” in 13th International IEEE Conference on Intelligent Transportation Systems, Sept 2010, pp. 279–284