所有的運輸模式皆朝著脫碳化的方向。在此趨勢下，電動車越來越普及，充電的需求也不斷地增加。未來需要各種充電策略、充電模式和充電基礎設施，以滿足使用者需求。使用者偏好的充電時間會根據不同的季節、當天的時間、工作日或假日而有所不同。使用者充電的需求可以透過電價、駕駛的模式、state of charge 值、充電的類型、充電站的位置以及使用者整體的體驗來預估。
本研究的目標是建立一機制可以在即時電價的架構下管理充電排程，以穩定電力系統的負載。雖然通常使用者是自私的，只想降低自己的充電成本，本研究想要改進這種情況，站在增進社會整體福利與電網管理者的宏觀角度，希望降低所有使用者的充電成本，透過即時電價可以鼓勵使用者改變他們的充電規劃。我們假設電動車的數量、充電站的數量和電池儲存容量與充電需求電量是已知的，並假設當時的電價是未知的，以一天為單位，在不確定基礎電力負載的情境下，我們的目標是希望能降低整體使用者充電成本與電網尖峰負載。提出兩階段穩健最佳化方法排程電動車之充電，利用電動車本身之電池做為緩衝，第一階段要決定每個使用者的充電開始時間，第二階段決定每個時間段每個使用者的充電電量，充電時間為可以分割不連續的時間段。我們希望可以處理所有可能的基礎電力負載情境，所提出的模型希望有效的協調電動車、電池和電網的整合，我們採用兩階段最佳化的原因為雖然當天的基礎電力負載不難預估，但我們希望透過歷史過去的基礎電力負載資料，能夠在未來未知的基礎電力負載情境下生成一個保守的充電排程與充電電力規劃。目標是最小化所有使用者的充電成本和電網尖峰用電之負載。

We explores the management of electric vehicle charging schedules under a scenario where EVs are widely adopted in households. With the global push toward decarbonization, EV usage is rapidly increasing,leading to heightened charging demands. However, this rise introduces challenges such as extended charging times,elevated costs, and potential grid instability due to uncoordinated charging. These issues are further complicated by uncertainties in electricity prices and EV charging demands, influenced by factors like driving patterns, battery state of charge, and user preferences.
To address these challenges, we proposes a robust optimization approach to schedule EV charging, aiming to minimize total charging costs for users and reduce peak grid loads. The study assumes that the number of EVs, charging stations, and storage capacities are known, while electricity prices and charging demands remain uncertain. Electricity prices fluctuate with base load variations, higher loads correlating with higher prices, prompting the model to treat base loads as part of an uncertainty set. This enables conservative charging decisions that account for worst-case load scenarios within a daily timeframe.

Al-Alwash, H. and Borcoci, E. (2022). Optimal charging scheme for electric vehicles(evs) in sdn-based vehicular network, scheduling, and routing. In 2022 14th International Conference on Communications (COMM), pages 1–8.
Albadi, M. H. and El-Saadany, E. F. (2008). A summary of demand response in electricity markets. Electric Power Systems Research, 78(11):1989–1996.
Alizadeh, M., Wai, H.-T., Chowdhury, M., Goldsmith, A., Scaglione, A., and Javidi, T.(2017). Optimal pricing to manage electric vehicles in coupled power and transporta-tion networks. IEEE Transactions on Control of Network Systems,4(4):863–875.
Amin, A., Tareen, W. U. K., Usman, M., Ali, H., Bari, I., Horan, B., Mekhilef, S., Asif,M., Ahmed, S., and Mahmood, A.(2020). A review of optimal charging strategy for electric vehicles under dynamic pricing schemes in the distribution charging network.Sustainability, 12(23).
Bertsimas, D., Brown, D. B., and Caramanis, C. (2010). Theory and applications of robust optimization.
Bertsimas, D. and Sim, M. (2004). The price of robustness. Operations Research,52(1):35–53.
Beyer, H.-G. and Sendhoff, B. (2007). Robust optimization – a comprehensive survey.Computer Methods in Applied Mechanics and Engineering, 196(33):3190–3218.
Bibak, B. and Tekiner-Mo˘gulkoc¸, H. (2021). A comprehensive analysis of vehicle to grid (v2g) systems and scholarly literature on the application of such systems. Renewable Energy Focus, 36:1–20.
Chung, H.-M., Li, W.-T., Yuen, C., Wen, C.-K., and Crespi, N. (2019). Electric vehicle charge scheduling mechanism to maximize cost efficiency and user convenience.IEEE Transactions on Smart Grid, 10(3):3020–3030.
Chung, H.-M., Maharjan, S., Zhang, Y., and Eliassen, F. (2021). Intelligent charging management of electric vehicles considering dynamic user behavior and renewable energy: A stochastic game approach. IEEE Transactions on Intelligent Transportation Systems, 22(12):7760–7771.
Danandeh, A., Zhao, L., and Zeng, B. (2014). Job scheduling with uncertain local generation in smart buildings: Two-stage robust approach. IEEE Transactions on Smart Grid, 5(5):2273–2282.
Deng, H., Yang, B., Ning, C., Chen, C., and Guan, X. (2023). Distributionally robust day-ahead scheduling for power-traffic network under a potential game framework. International Journal of Electrical Power Energy Systems, 147:108851.
Diaz-Londono, C., Orfanoudakis, S., Vergara, P. P., Palensky, P., Ruiz, F., and Gruosso,G. (2024). A simulation tool for v2g enabled demand response based on model predictive control.
Dom´ınguez-Navarro, J. A., Dufo-L´opez, R., Yusta-Loyo, J. M., Artal-Sevil, J. S., and Bernal-Agust´ın, J. L. (2019). Design of an electric vehicle fast-charging station with integration of renewable energy and storage systems. International Journal of Electrical Power Energy Systems, 105:46–58.
Elma, O. (2020). A dynamic charging strategy with hybrid fast charging station for electric vehicles. Energy, 202:117680.
Gu, C., Pan, Y., Liu, R., and Chen, Y. (2024). Learning and optimization for price-based demand response of electric vehicle charging.
He, Y., Venkatesh, B., and Guan, L. (2012). Optimal scheduling for charging and discharging of electric vehicles. IEEE Transactions on Smart Grid, 3(3):1095–1105.
Holt, C. A. and Roth, A. E. (2004). The nash equilibrium: A perspective. Proceedings of the National Academy of Sciences, 101(12):3999–4002.
Hu, J., Morais, H., Sousa, T., and Lind, M. (2016). Electric vehicle fleet management in smart grids: A review of services, optimization and control aspects. Renewable and Sustainable Energy Reviews, 56:1207–1226.
Kalakanti, A. K. and Rao, S. (2024). Dynamic pricing for electric vehicle charging using multi-objective optimization. arXiv:2408.14169.
Leijon, J. and Bostr¨om, C. (2022). Charging electric vehicles today and in the future. World Electric Vehicle Journal, 13(8).
Liu, Y., Yuen, C., Huang, S., Ul Hassan, N., Wang, X., and Xie, S. (2014). Peak-to-average ratio constrained demand-side management with consumer’s preference in residential smart grid. IEEE Journal of Selected Topics in Signal Processing,8(6):1084–1097.
Liu, Z., Wu, Q., Huang, S., Wang, L., Shahidehpour, M., and Xue, Y. (2018). Optimal day-ahead charging scheduling of electric vehicles through an aggregative game model. IEEE Transactions on Smart Grid, 9(5):5173–5184.
Logenthiran, T., Srinivasan, D., and Shun, T. Z. (2012). Demand side management in smart grid using heuristic optimization. IEEE Transactions on Smart Grid,3(3):1244–1252.
Long, T., Jia, Q.-S., Wang, G., and Yang, Y. (2021). Efficient real-time ev charging scheduling via ordinal optimization. IEEE Transactions on Smart Grid, 12(5):4029–4038.
Luo, Z., Ren, H., Xin, G., Xu, M., Wang, F., and Zhang, Y. (2024). Optimal operation of microgrid with consideration of v2g’s uncertainty. IET Generation, Transmission Distribution, 18(2):289–302.
Mehrabi, A. and Kim, K. (2018). Low-complexity charging/discharging scheduling for electric vehicles at home and common lots for smart households prosumers. IEEE Transactions on Consumer Electronics, 64(3):348–355.
Paparella, F., Hofman, T., and Salazar, M. (2023). Cost-optimal fleet management strategies for solar-electric autonomous mobility-on-demand systems.arXiv:2305.18816.
Rad, A. and Leon-Garcia, A. (2010). Optimal residential load control with price prediction in real-time electricity pricing environments. IEEE Transactions on Smart Grid,1:120–133.
Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. (2017). Proximal policy optimization algorithms.
Siano, P. (2014). Demand response and smart grids—a survey. Renewable and Sustainable Energy Reviews, 30:461–478.
Song, H., Liu, C., Jalili, M., Yu, X., and McTaggart, P. (2021). Multi-objective scheduling of electric vehicle charging/discharging with time of use tariff. arXiv:2108.05062.
Song, Y., Zhao, H., Luo, R., Huang, L., Zhang, Y., and Su, R. (2022). A sumo framework for deep reinforcement learning experiments solving electric vehicle charging dispatching problem. arXiv:2209.0292.
Sortomme, E. and El-Sharkawi, M. A. (2011). Optimal charging strategies for unidirectional vehicle-to-grid. IEEE Transactions on Smart Grid, 2(1):131–138.
Spencer, S. I., Fu, Z., Apostolaki-Iosifidou, E., and Lipman, T. E. (2021). Evaluating smart charging strategies using real-world data from optimized plugin electric vehicles. Transportation Research Part D: Transport and Environment, 100:103023.
Tan, J. and Wang, L. (2017). Real-time charging navigation of electric vehicles to fast charging stations: A hierarchical game approach. IEEE Transactions on Smart Grid,8(2):846–856.
Tran, T. D., Nguyen, N.-D., Chu, H. T. M., El Ghaoui, L., Ambrosino, L., and Calafiore,G. (2025). A robust optimization model for cost-efficient and fast electric vehicle charging with l2-norm uncertainty.
Wan, Z., Li, H., He, H., and Prokhorov, D. (2019). Model-free real-time ev charging scheduling based on deep reinforcement learning. IEEE Transactions on Smart Grid,10(5):5246–5257.
Wang, Y. and Sun, W. (2024). A two-stage robust pricing strategy for electric vehicle aggregators. Sustainability,16(9):3593.
Zeng, B. and Zhao, L. (2013). Solving two-stage robust optimization problems by a column-and-constraint generation method. Operations Research Letters, 41:457–461.
Zhao, Y., Wang, Z., Shen, Z.-J. M., and Sun, F. (2021). Data-driven framework for large-scale prediction of charging energy in electric vehicles. Applied Energy, 282:116175..