Strategic Planning for Electric Vehicle Charging Infrastructure Considering Multi-Stakeholder Games

Widely considered as a clean and sustainable alternative to road transportation, electric vehicles (EVs) are playing a pivotal role in combating climate change and the energy crisis. To accelerate the decarbonization of transportation sector, there is a growing need of a more well-established EV charging infrastructure industry. To do this, extensive works have been elaborated on the planning of EV charging networks so as to guide. However, the strategic interaction among multiple stakeholders imposes an added layer of complexities to the analysis and planning of EV charging network, mitigating the efficiencies of existing approaches.

In response to the inefficiency of existing methods, this dissertation endeavors the planning of charging networks within a strategic environment. Particularly, the strategic interactions are characterized by a set of equilibrium concepts according to the investment scenario, and adeptly involved in the optimization problems. Three diverse scenarios dominated by government, market, and grid, are duly considered to establish a comprehensive methodology.

The first part of this dissertation investigates the government-led planning of charging facilities within intercity highways networks. Initially, it introduces a variational model for the strategic assignment of en-route charging flows. A dynamic path generation method is established to expedite the solution process while taking into account EV range limits. Subsequently, this part proposes an equilibrium-constrained approach for deploying enroute charging facilities among electrified highway networks. It incorporates a mathematical programming with equilibrium constraint (MPEC) formulation for the decision-making and a regularized alternative direction method for problem solving. The effectiveness and superiority of the proposed algorithms are validated through case studies. The results reveal the loss of social welfare in case of a strategic environment and the trade-offs among multiple planning objectives.

The second part of this dissertation further considers the charging facility planning in a market setting. Initially, it establishes a variational model for estimating the pattern of charging demand and prices of urban Charging-as-a-service markets. The existence and sensitivities of equilibrium are also studied. Further, it investigates collusion in the charging service market through Nash bargaining theory. To promote market efficiency, a hierarchical game approach is proposed to balance the benefits of users and service providers, along with a descent search algorithm for expediting the problem solving. The results highlight that non-competitive behaviors like monopolies and collusion could damage the users’ welfare and impede the development of EV industry. The findings also emphasize the role of governmental investment and regulation for market efficiency.

The final part of this dissertation extends the discussion from uncoordinated to coordinated charging and investigates the planning of grid-oriented charging facility planning based on real-world charging data. Initially, for standard coordinated charging, a data-driven optimization approach is introduced in awareness of users’ participating equilibrium. Following that, for fast-charging stations, data-driven analytics is proposed for planning the economic benefit of coordinated charging. This analytics examines the impact of multiple real-world factors on the economic planning of rapid V2G mode. Case studies and data analysis validate the effectiveness of the proposed models and algorithms. The findings demonstrate that coordinated charging can significantly reduce operational costs for grids and operators. They also reveal the pivotal role of user behaviors in coordinated charging planning.

From the perspective of game theory, this dissertation systematically studies planning methods for charging infrastructure networks across different scenarios. The models, algorithms, and findings offer a conceptual framework for the decision-making in real-world charging infrastructure investment. By doing this, this dissertation holds theoretical and practical value for the development of the electric vehicle economy and the decarbonization of the transportation industry.

近年来，电动汽车作为一种清洁且高效的交通工具，在应对全球气候变化和能源危机方面发挥着日益关键的作用。为了加速交通行业从依赖化石燃料的传统模式向电气化转型，构建一个便捷且高效的电动汽车充电网络显得尤为重要。在当前阶段，充电设施规划的主要挑战是如何在不同应用场景下刻画多参与主体的博弈均衡以及在考虑其策略均衡的前提下优化选址方案。本文分为三个部分，分别探讨了在政府主导、市场主导和电网主导的不同场景下，电动汽车充电设施规划的策略。

第一部分聚焦于政府主导的城际高速路网充电设施规划。首先，本文构建了一个考虑电动汽车续航限制的途中充电博弈模型，并分析了均衡解的数学特性。同时，设计了一种基于动态路径生成的高效求解算法。进一步地，提出了一种适用于城际电力交通网络环境的充电设施规划方法，并设计了一种基于正则化的交替方向法进行分布式求解。该方法能在考虑到电网和用户博弈行为的同时保护规划过程中各方的数据隐私。通过算例分析，验证了所提出模型和方法的有效性，并揭示了策略行为对系统运行效率的潜在负面影响以及多方主体间的利益冲突。

第二部分转向市场主导的城市充电设施规划问题。本文基于变分不等式对用户充电策略和运营商定价策略进行了建模，提出一种充电服务市场的需求-价格均衡模型，并讨论了其数学性质。此外，运用纳什议价理论，研究了充电服务市场中的合谋行为。为了促进市场效率，提出了一种多层主从博弈方法，旨在平衡用户与运营商的福利，并设计了一种基于灵敏度分析的演化下降算法来求解。算例分析结果揭示了垄断和合谋等非竞争行为对用户福利和电动汽车行业的负面影响，以及政府投资和监管在促进行业有序健康发展中的重要作用。

最后一部分将研究范围扩展到有序充电，并基于实际数据研究了电网主导的充电设施规划。针对常规有序充电站规划问题，提出了一种基于均衡约束和历史订单数据的有序充电场站规划方法，以降低场站运行成本。对于快速充电站，提出了一种数据驱动的有序充电经济性评估方法，并探讨了多种现实因素对有序充电经济性的实际影响。算例和数据分析证明所提出模型和算法的有效性。其结果证明有序充电技术可为电网和运营商降低成本提高收益，并揭示了用户行为模型在有序充电规划中的重要影响。

综上所述，本文从多主体博弈的角度，系统地研究了不同充电场景下的电动汽车充电设施规划问题。所提出的模型、算法和结论不仅拓宽了传统充电设施规划的研究视野，还为实际的充电设施规划提供了理论框架和决策支持，对于推动电动汽车经济的发展和交通行业的低碳转型具有一定助力作用。

[1] The Development Plan for the New Energy Vehicle Industry (2021-2035) [EB/OL].
[2020-10-20]. https://www.gov.cn/zhengce/content/2020-11/02/content_5556716.htm.
[2] Guo F, Yang J, Lu J. The battery charging station location problem: Impact of users’ range anxiety and distance convenience[J]. Transportation Research Part E: Logistics and Transportation Re-view, 2018, 114: 1-18.
[3] Xu M, Yang H, Wang S. Mitigate the range anxiety: Siting battery charging stations for electric vehicle drivers[J]. Transportation Research Part C: Emerging Technologies, 2020, 114: 164-188.
[4] Li H, Guensler R, Ogle J, et al. Descriptive Analysis of Long-Distance Travel by Personal Vehicles Using 2004 Commute Atlanta Data[C]//Transportation Research Board 86th Annual Meeting. 2007: 07-1688.
[5] Bonges III H A, Lusk A C. Addressing electric vehicle (EV) sales and range anxiety through park-ing layout, policy and regulation[J]. Transportation Research Part A: Policy and Practice, 2016, 83: 63-73.
[6] Kang J, Kong H, Lin Z, et al. Mapping the dynamics of electric vehicle charging demand within Beijing’s spatial structure[J]. Sustainable Cities and Society, 2022, 76: 103507.
[7] Borlaug B, Yang F, Pritchard E, et al. Public electric vehicle charging station utilization in the United States[J]. Transportation Research Part D: Transport and Environment, 2023, 114: 103564.
[8] Times G. Pure electric vehicles feel charging pinch on highways during National Day holidays - Global Times [EB/OL].
[2023-12-03]. https:// www.globaltimes.cn/ page/ 202110/ 1235651.shtml.
[9] EV drivers queue to recharge during holiday [EB/OL].
[2023-12-03]. //global.chinadaily.com.cn/a/202110/11/WS61639f31a310cdd39bc6e0b7.html.
[10] Hodgson M J. A flow capturing location-allocation model[J]. Geographic Analysis, 1990, 22.
[11] Kuby M, Lim S. The flow-refueling location problem for alternative-fuel vehicles[J]. J Socio-Economic Planning Sciences, 2005, 39(2): 125-145.
[12] C. Upchurch M K. A Model for Location of Capacitated Alternative‐Fuel Stations[J]. Geograph-ical Analysis, 2009, 41(1):85-106.
[13] Dong G, Ma J, Wei R, et al. Electric vehicle charging point placement optimisation by exploiting spatial statistics and maximal coverage location models[J]. Transportation Research Part D: Transport and Environment, 2019, 67: 77-88.
[14] Frade I, Ribeiro A, Gonçalves G, et al. Optimal Location of Charging Stations for Electric Vehi-cles in a Neighborhood in Lisbon, Portugal[J]. Transportation Research Record: Journal of the Transportation Research Board, 2011, 2252(1): 91-98.
[15] Sun Z, Gao W, Li B, et al. Locating charging stations for electric vehicles[J]. Transport Policy, 2020, 98: 48-54.
[16] Zhang H, Moura S J, Hu Z, et al. PEV Fast-Charging Station Siting and Sizing on Coupled Trans-portation and Power Networks[J]. IEEE Transactions on Smart Grid, 2018, 9(4): 2595-2605.
[17] Zhang H, Moura S J, Hu Z, et al. A Second-Order Cone Programming Model for Planning PEV Fast-Charging Stations[J]. IEEE Transactions on Power Systems, 2018, 33(3): 2763-77.
[18] Deb S, Tammi K, Kalita K, et al. Review of recent trends in charging infrastructure planning for electric vehicles[J]. WIREs Energy and Environment, 2018, 7(6): e306.
[19] Deb S, Gao X Z, Tammi K, et al. Nature-Inspired Optimization Algorithms Applied for Solving Charging Station Placement Problem: Overview and Comparison[J]. Archives of Computational Methods in Engineering, 2019, 28(1): 91-106.
[20] Bilal M, Rizwan M. Electric vehicles in a smart grid: a comprehensive survey on optimal location of charging station[J]. IET Smart Grid, 2020, 3(3): 267-279.
[21] Kchaou-Boujelben M. Charging station location problem: A comprehensive review on models and solution approaches[J]. Transportation Research Part C: Emerging Technologies, 2021, 132: 103376.
[22] Ahmad F, Iqbal A, Ashraf I, et al. Optimal location of electric vehicle charging station and its im-pact on distribution network: A review[J]. Energy Reports, 2022, 8: 2314-2333.
[23] Metais M O, Jouini O, Perez Y, et al. Too much or not enough? Planning electric vehicle charging infrastructure: A review of modeling options[J]. Renewable and Sustainable Energy Reviews, 2022, 153.
[24] Jiang X, Zhao L, Cheng Y, et al. Optimal configuration of electric vehicles for charging stations under the fast power supplement mode[J]. Journal of Energy Storage, 2022, 45: 103677.
[25] Zhang H, Hu Z, Xu Z, et al. An Integrated Planning Framework for Different Types of PEV Charging Facilities in Urban Area[J]. IEEE Transactions on Smart Grid, 2016, 7(5): 2273-2284.
[26] Othman A M, Gabbar H A, Pino F, et al. Optimal electrical fast charging stations by enhanced de-scent gradient and Voronoi diagram[J]. Computers & Electrical Engineering, 2020, 83: 106574.
[27] Hong I, Kuby M, Murray A T. A range-restricted recharging station coverage model for drone delivery service planning[J]. Transportation Research Part C: Emerging Technologies, 2018, 90: 198-212.
[28] Lam A Y S, Yiu-Wing Leung, Xiaowen Chu. Electric Vehicle Charging Station Placement: For-mulation, Complexity, and Solutions[J]. IEEE Transactions on Smart Grid, 2014, 5(6): 2846-2856.
[29] Zhang L, Shaffer B, Brown T, et al. The optimization of DC fast charging deployment in Califor-nia[J]. Applied Energy, 2015, 157: 111-122.
[30] Huang K, Kanaroglou P, Zhang X. The design of electric vehicle charging network[J]. Transporta-tion Research Part D: Transport and Environment, 2016, 49: 1-17.
[31] Arslan O, Karaşan O E. A Benders decomposition approach for the charging station location prob-lem with plug-in hybrid electric vehicles[J]. Transportation Research Part B: Methodological, 2016, 93: 670-695.
[32] Miralinaghi M, Keskin B B, Lou Y, et al. Capacitated Refueling Station Location Problem with Traffic Deviations Over Multiple Time Periods[J]. Networks and Spatial Economics, 2017, 17(1): 129-151.
[33] Nie Yu Marco, Ghamami M. A corridor-centric approach to planning electric vehicle charging infrastructure[J]. Transportation Research Part B: Methodological, 2013, 57: 172-190.
[34] Hosseini M, MirHassani S A, Hooshmand F. Deviation-flow refueling location problem with ca-pacitated facilities: Model and algorithm[J]. Transportation Research Part D: Transport and Envi-ronment, 2017, 54: 269-281.
[35] Lee C, Han J. Benders-and-Price approach for electric vehicle charging station location problem under probabilistic travel range[J]. Transportation Research Part B: Methodological, 2017, 106: 130-152.
[36] Wang Y, Shi J, Wang R, et al. Siting and sizing of fast charging stations in highway network with budget constraint[J]. Applied Energy, 2018, 228: 1255-1271.
[37] Xie F, Liu C, Li S, et al. Long-term strategic planning of inter-city fast charging infrastructure for battery electric vehicles[J]. Transportation Research Part E: Logistics and Transportation Review, 2018, 109: 261-276.
[38] Xu M, Meng Q. Optimal deployment of charging stations considering path deviation and nonline-ar elastic demand[J]. Transportation Research Part B: Methodological, 2020, 135: 120-142.
[39] Kumar N, Kumar T, Nema S, et al. A comprehensive planning framework for electric vehicles fast charging station assisted by solar and battery based on Queueing theory and non-dominated sort-ing genetic algorithm-II in a coordinated transportation and power network[J]. Journal of Energy Storage, 2022, 49: 104180.
[40] Bai X, Chin K S, Zhou Z. A bi-objective model for location planning of electric vehicle charging stations with GPS trajectory data[J]. Computers & Industrial Engineering, 2019, 128: 591-604.
[41] Awasthi A, Venkitusamy K, Padmanaban S, et al. Optimal planning of electric vehicle charging station at the distribution system using hybrid optimization algorithm[J]. Energy, 2017, 133: 70-78.
[42] Gan X, Zhang H, Hang G, et al. Fast-Charging Station Deployment Considering Elastic De-mand[J]. IEEE Transactions on Transportation Electrification, 2020, 6(1): 158-169.
[43] Pahlavanhoseini A, Sepasian M S. Optimal planning of PEV fast charging stations using an auc-tion-based method[J]. Journal of Cleaner Production, 2020, 246: 118999.
[44] Li J, Liu Z, Wang X. Public charging station localization and route planning of electric vehicles considering the operational strategy: A bi-level optimizing approach[J]. Sustainable Cities and Society, 2022, 87: 104153.
[45] Shaker M H, Farzin H, Mashhour E. Joint planning of electric vehicle battery swapping stations and distribution grid with centralized charging[J]. Journal of Energy Storage, 2023, 58: 106455.
[46] Moupuri S K R, Selvajyothi K. Optimal planning and utilisation of existing infrastructure with electric vehicle charging stations[J]. IET Generation, Transmission & Distribution, 2021, 15(10): 1552-1564.
[47] Zhu Y, Zhang M, Dong Y, et al. Optimal planning strategy for EV charging stations considering travel demands based on non-cooperative game theory[J]. IET Generation, Transmission & Dis-tribution, 2022, 17(3): 684-695.
[48] Liu Q, Liu J, Le W, et al. Data-driven intelligent location of public charging stations for electric vehicles[J]. Journal of Cleaner Production, 2019, 232: 531-541.
[49] Liang Y C, Guo C L, Yang J J, et al. Optimal planning of charging station based on discrete distri-bution of charging demand[J]. Iet Generation Transmission & Distribution, 2020, 14: 965-974.
[50] Hussain K, Mohd Salleh M N, Cheng S, et al. Metaheuristic research: a comprehensive survey[J]. Artificial intelligence review, 2019, 52: 2191-2233.
[51] Yidiz B, Arslan O, Karasan O E. A branch and price approach for routing and refueling station location model[J].European Journal of Operational Research, 2016, 248: 815-826.
[52] Arslan O, Karaşan O E, Mahjoub A R, et al. A Branch-and-Cut Algorithm for the Alternative Fuel Refueling Station Location Problem with Routing[J]. Transportation Science, 2019, 53: 1107-1125.
[53] Song M, Cheng L, Du M, et al. Charging station location problem for maximizing the space-time-electricity accessibility: A Lagrangian relaxation-based decomposition scheme[J]. Expert Systems with Applications, 2023, 222: 119801.
[54] An K. Battery electric bus infrastructure planning under demand uncertainty[J]. Transportation Research Part C: Emerging Technologies, 2020, 111: 572-587.
[55] Ma Q, Tong X, Huang Y, et al. IMOCS Based EV Charging Station Planning Optimization Con-sidering Stakeholders’ Interests Balance[J]. IEEE Access, 2022, 10: 52102-52115.
[56] Efthymiou D, Chrysostomou K, Morfoulaki M, et al. Electric vehicles charging infrastructure lo-cation: a genetic algorithm approach[J]. European Transport Research Review,2017, 9: 1-9.
[57] Shojaabadi S, Abapour S, Abapour M, et al. Optimal planning of plug-in hybrid electric vehicle charging station in distribution network considering demand response programs and uncertain-ties[J]. IET Generation, Transmission & Distribution, 2016, 10(13): 3330-3340.
[58] Zhang Y, Zhang Q, Farnoosh A, et al. GIS-Based Multi-Objective Particle Swarm Optimization of charging stations for electric vehicles[J]. Energy, 2019, 169: 844-853.
[59] Islam M M, Shareef H, Mohamed A. Optimal location and sizing of fast charging stations for elec-tric vehicles by incorporating traffic and power networks[J]. IET Intelligent Transport Systems, 2018, 12(8): 947-957.
[60] Aljanad A, Mohamed A, Shareef H, et al. A novel method for optimal placement of vehicle-to-grid charging stations in distribution power system using a quantum binary lightning search algo-rithm[J]. Sustainable Cities and Society, 2018, 38: 174-183.
[61] Jiang N, Xie C, Duthie J C, et al. A network equilibrium analysis on destination, route and parking choices with mixed gasoline and electric vehicular flows[J]. EURO Journal on Transportation and Logistics, 2014, 3(1): 55-92.
[62] Xu M, Meng Q, Liu K. Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints[J]. Transpor-tation Research Part B: Methodological, 2017, 99: 138-166.
[63] Liu Z, Song Z. Network user equilibrium of battery electric vehicles considering flow-dependent electricity consumption[J]. Transportation Research Part C: Emerging Technologies, 2018, 95: 516-544.
[64] He F, Yin Y, Lawphongpanich S. Network equilibrium models with battery electric vehicles[J]. Transportation Research Part B: Methodological, 2014, 67: 306-319.
[65] Zhou Z, Moura S J, Zhang H, et al. Power-traffic network equilibrium incorporating behavioral theory: A potential game perspective[J]. Applied Energy, 2021, 289: 116703.
[66] Wei W, Wu L, Wang J, et al. Network Equilibrium of Coupled Transportation and Power Distri-bution Systems[J]. IEEE Transactions on Smart Grid, 2018, 9(6): 6764-6779.
[67] Colson B, Marcotte P, Savard G. Bilevel programming: A survey[J]. 4OR, 2005, 3(2): 87-107.
[68] Dempe S. Foundations of bilevel programming[M]. Springer Science & Business Media, 2002.
[69] Dempe S, Franke S. Solution of bilevel optimization problems using the KKT approach[J]. Opti-mization: 2019, 68: 1471-1489.
[70] Zhou B, Chen G, Song Q, et al. Robust chance-constrained programming approach for the plan-ning of fast-charging stations in electrified transportation networks[J]. Applied Energy, 2020, 262: 114480.
[71] Chen R, Qian X, Miao L, et al. Optimal charging facility location and capacity for electric vehicles considering route choice and charging time equilibrium[J]. Computers & Operations Research, 2020, 113: 104776.
[72] Zhou G, Dong Q, Zhao Y, et al. Bilevel optimization approach to fast charging station planning in electrified transportation networks[J]. Applied Energy, 2023, 350: 121718.
[73] He F, Yin Y, Zhou J. Deploying public charging stations for electric vehicles on urban road net-works[J]. Transportation Research Part C: Emerging Technologies, 2015, 60: 227-240.
[74] Chen Z, He F, Yin Y. Optimal deployment of charging lanes for electric vehicles in transportation networks[J]. Transportation Research Part B: Methodological, 2016, 91: 344-365.
[75] Zheng H, He X, Li Y, et al. Traffic Equilibrium and Charging Facility Locations for Electric Vehi-cles[J]. Networks and Spatial Economics, 2017, 17(2): 435-457.
[76] Wei W, Wu L, Wang J, et al. Expansion Planning of Urban Electrified Transportation Networks: A Mixed-Integer Convex Programming Approach[J]. IEEE Transactions on Transportation Elec-trification, 2017, 3(1): 210-224.
[77] Wang X, Shahidehpour M, Jiang C, et al. Coordinated Planning Strategy for Electric Vehicle Charging Stations and Coupled Traffic-Electric Networks[J]. IEEE Transactions on Power Sys-tems, 2019, 34(1): 268-279.
[78] Riemann R, Wang D Z W, Busch F. Optimal location of wireless charging facilities for electric vehicles: Flow-capturing location model with stochastic user equilibrium[J]. Transportation Re-search Part C: Emerging Technologies, 2015, 58: 1-12.
[79] Zhou B, Chen G, Song Q, et al. Robust chance-constrained programming approach for the plan-ning of fast-charging stations in electrified transportation networks[J]. Applied Energy, 2020, 262.
[80] Ghamami M, Kavianipour M, Zockaie A, et al. Refueling infrastructure planning in intercity net-works considering route choice and travel time delay for mixed fleet of electric and conventional vehicles[J]. Transportation Research Part C: Emerging Technologies, 2020, 120: 102802.
[81] Zhang X, Li P, Hu J, et al. Yen’s Algorithm-Based Charging Facility Planning Considering Con-gestion in Coupled Transportation and Power Systems[J]. IEEE Transactions on Transportation Electrification, 2019, 5(4): 1134-1144.
[82] He F, Wu D, Yin Y, et al. Optimal deployment of public charging stations for plug-in hybrid elec-tric vehicles[J]. Transportation Research Part B: Methodological, 2013, 47: 87-101.
[83] Yang W, Liu W, Chung C Y, et al. Joint Planning of EV Fast Charging Stations and Power Distri-bution Systems with Balanced Traffic Flow Assignment[J]. IEEE Transactions on Industrial In-formatics, 2020, 17(3): 1795-1809.
[84] Li C, Dong Z, Chen G, et al. Data-Driven Planning of Electric Vehicle Charging Infrastructure: A Case Study of Sydney, Australia[J]. IEEE Transactions on Smart Grid, 2021, 12(4): 3289-3304.
[85] Bernardo V, Borrell J R, Perdiguero J. Fast charging stations: Simulating entry and location in a game of strategic interaction[J]. Energy Economics, 2016, 60: 293-305.
[86] Luo C, Huang Y F, Gupta V. Placement of EV Charging Stations--Balancing Benefits Among Multiple Entities[J]. IEEE Transactions on Smart Grid, 2015, 8(2): 759-768.
[87] Guo Z, Deride J, Fan Y. Infrastructure planning for fast charging stations in a competitive mar-ket[J]. Transportation Research Part C: Emerging Technologies, 2016, 68: 215-227.
[88] Duan X, Hu Z, Song Y, et al. Planning Strategy for an Electric Vehicle Fast Charging Service Pro-vider in a Competitive Environment[J]. IEEE Transactions on Transportation Electrification, 2022, 8(3): 3056-3067.
[89] Bae S, Jang I, Gros S, et al. A Game Approach for Charging Station Placement Based on User Preferences and Crowdedness[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(4): 3654-3669.
[90] Facchinei F, Pang J S. Finite-dimensional variational inequalities and complementarity prob-lems[M]. New York: Springer, 2003.
[91] Nagurney A. Network Economics: A Variational Inequality Approach[M]. Dordrecht: Springer Netherlands, 1993.
[92] Nash J. Non-cooperative games[J]. Annals of mathematics, 1951: 286-295.
[93] Fudenberg D, Tirole J. Game theory[Z]. MIT press, 1991.
[94] Karaca, Orcun, et al. Designing coalition-proof reverse auctions over continuous goods[J]. IEEE Transactions on Automatic Control, 2019, 64(11): 4803-4810..
[95] Dasgupta P S, Maskin E S. Debreu’s social equilibrium existence theorem[J]. Proceedings of the National Academy of Sciences, 2015, 112(52): 15769-15770.
[96] Border K C. Fixed point theorems with applications to economics and game theory[M]. Cam-bridge University Press, 1985.
[97] Paccagnan D, Gentile B, Parise F, et al. Nash and Wardrop equilibria in aggregative games with coupling constraints[J]. IEEE Transactions on Automatic Control, 2019, 64(4): 1373-1388.
[98] Altman E, Wynter L. Equilibrium, Games, and Pricing in Transportation and Telecommunication Networks[J]. Networks and Spatial Economics, 2004, 4(1): 7-21.
[99] Haurie A, Marcotte P. On the relationship between Nash—Cournot and Wardrop equilibria[J]. Networks, 1985, 15(3): 295-308.
[100] Luo Z, Pang J, Ralph D. Mathematical programs with equilibrium constraints[M], 1996.
[101] Kanzow C, Mehlitz P, Steck D. Relaxation schemes for mathematical programs with switching constraints[J]. Optimization Methods and Software 2021, 36(6): 1223-1258.
[102] Scholtes S. Convergence Properties of a Regularization Scheme for Mathematical Programs with Complementarity Constraints[J]. SIAM Journal on Optimization, 2001, 11(4): 918-936.
[103] Fukushima M, Gui-Hua Lin. Smoothing methods for mathematical programs with equilibrium constraints[C]//International Conference on Informatics Research for Development of Knowledge Society Infrastructure, 2004. ICKS 2004. Kyoto, Japan: IEEE, 2004: 206-213.
[104] Pecci F, Abraham E, Stoianov I. Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks[J]. Computational Optimization and Appli-cations, 2017, 67(1): 201-223.
[105] Muratori M. Impact of uncoordinated plug-in electric vehicle charging on residential power de-mand[J]. Nature Energy, 2018, 3(3): 193-201.
[106] Wang G, Xu Z, Wen F, et al. Traffic-Constrained Multiobjective Planning of Electric-Vehicle Charging Stations[J]. IEEE Transactions on Power Delivery, 2013, 28(4): 2363-2372.
[107] Yao W, Zhao J, Wen F, et al. A Multi-Objective Collaborative Planning Strategy for Integrated Power Distribution and Electric Vehicle Charging Systems[J]. IEEE Transactions on Power Sys-tems, 2014, 29(4): 1811-1821.
[108] Gan W, Shahidehpour M, Yan M, et al. Coordinated Planning of Transportation and Electric Power Networks with the Proliferation of Electric Vehicles[J]. IEEE Transactions on Smart Grid, 2020, 11(5): 4005-4016.
[109] Mozaffari M, Askarian Abyaneh H, Jooshaki M, et al. Joint Expansion Planning Studies of EV Parking Lots Placement and Distribution Network[J]. IEEE Transactions on Industrial Informatics, 2020, 16(10): 6455-6465.
[110] Cui Q, Weng Y, Tan C W. Electric Vehicle Charging Station Placement Method for Urban Are-as[J]. IEEE Transactions on Smart Grid, 2019, 10(6): 6552-6565.
[111] Davidov S, Pantoš M. Planning of electric vehicle infrastructure based on charging reliability and quality of service[J]. Energy, 2017, 118: 1156-1167.
[112] Gan W, Shahidehpour M, Guo J, et al. A Tri-Level Planning Approach to Resilient Expansion and Hardening of Coupled Power Distribution and Transportation Systems[J]. IEEE Transactions on Power Systems, 2022, 37(2): 1495-1507.
[113] Raman G, Raman G, Peng J C H. Resilience of urban public electric vehicle charging infrastruc-ture to flooding[J]. Nature Communications, 2022, 13: 3213.
[114] Lin X, Sun J, Ai S, et al. Distribution network planning integrating charging stations of electric vehicle with V2G[J]. International Journal of Electrical Power & Energy Systems, 2014, 63: 507-512.
[115] Zheng Y, Dong Z Y, Xu Y, et al. Electric Vehicle Battery Charging/Swap Stations in Distribution Systems: Comparison Study and Optimal Planning[J]. IEEE Transactions on Power Systems, 2014, 29(1): 221-229.
[116] Bayram I S, Tajer A, Abdallah M, et al. Capacity Planning Frameworks for Electric Vehicle Charging Stations with Multiclass Customers[J]. IEEE Transactions on Smart Grid, 2015, 6(4): 1934-1943.
[117] Mirzaei M J, Kazemi A, Homaee O. A Probabilistic Approach to Determine Optimal Capacity and Location of Electric Vehicles Parking Lots in Distribution Networks[J]. IEEE Transactions on Industrial Informatics, 2016, 12(5): 1963-1972.
[118] Pan Z J, Zhang Y. A novel centralized charging station planning strategy considering urban power network structure strength[J]. Electric Power Systems Research, 2016, 136: 100-109.
[119] Shukla A, Verma K, Kumar R. Multi-objective synergistic planning of EV fast-charging stations in the distribution system coupled with the transportation network[J]. IET Generation, Transmis-sion & Distribution, 2019, 13(15): 3421-3432.
[120] Amer A, Azab A, Azzouz M A, et al. A Stochastic Program for Siting and Sizing Fast Charging Stations and Small Wind Turbines in Urban Areas[J]. IEEE Transactions on Sustainable Energy, 2021, 12(2): 1217-1228.
[121] Yao F, Wang J W, Wen F S, et al. An Integrated Planning Strategy for a Power Network and the Charging Infrastructure of Electric Vehicles for Power System Resilience Enhancement[J]. Ener-gies, 2019: 12(20): 3918.
[122] Mao D, Tan J, Wang J. Location Planning of PEV Fast Charging Station: An Integrated Approach Under Traffic and Power Grid Requirements[J]. IEEE Transactions on Intelligent Transportation Systems, 2021, 22: 483-492.
[123] Gan W, Yan M, Yao W, et al. Multi-Network Coordinated Hydrogen Supply Infrastructure Plan-ning for the Integration of Hydrogen Vehicles and Renewable Energy[J]. IEEE Transactions on Industry Applications, 2022, 58(2): 2875-2886.
[124] Li C Z, Zhang L B, Ou Z H, et al. Robust model of electric vehicle charging station location con-sidering renewable energy and storage equipment[J]. Energy, 2022, 238: 121713.
[125] Mejia M A, Macedo L H, Munoz-Delgado G, et al. Multistage Planning Model for Active Distri-bution Systems and Electric Vehicle Charging Stations Considering Voltage-Dependent Load Be-havior[J]. IEEE Transactions on Smart Grid, 2022, 13(2): 1383-1397.
[126] Shao C, Li K, Hu Z, et al. Coordinated Planning of Electric Power and Natural Gas Distribution Systems with Refueling Stations for Alternative Fuel Vehicles in Transportation System[J]. IEEE Transactions on Smart Grid, 2022, 13(5): 3558-3569.
[127] Liu Z, Wen F, Ledwich G. Optimal Planning of Electric-Vehicle Charging Stations in Distribution Systems[J]. IEEE Transactions on Power Delivery, 2013, 28(1): 102-110.
[128] Zhang H, Moura S J, Hu Z, et al. A Second-Order Cone Programming Model for Planning PEV Fast-Charging Stations[J]. IEEE Transactions on Power Systems, 2018, 33(3): 2763-2777.
[129] Hashemian S N, Latify M A, Yousefi G R. PEV Fast-Charging Station Sizing and Placement in Coupled Transportation-Distribution Networks Considering Power Line Conditioning Capabil-ity[J]. IEEE Transactions on Smart Grid, 2020, 11(6): 4773-4783.
[130] Lin Y, Zhang K, Shen Z J M, et al. Multistage large-scale charging station planning for electric buses considering transportation network and power grid[J]. Transportation Research Part C: Emerging Technologies, 2019, 107: 423-443.
[131] Conejo A J, Castillo E, Minguez R, et al. Locational Marginal Price Sensitivities[J]. IEEE Trans-actions on Power Systems, 2005, 20(4): 2026-2033.
[132] Li F. Continuous Locational Marginal Pricing (CLMP)[J]. IEEE Transactions on Power Systems, 2007, 22(4): 1638-1646.
[133] Li B, Xu Z, Zhang Y. Two-stage multi-sided matching dispatching models based on improved BPR function with probabilistic linguistic term sets[J]. International Journal of Machine Learning and Cybernetics, 2021, 12(1): 151-169.
[134] Saric A, Albinovic S, Dzebo S, et al. Volume-delay functions: A review[C]//International Sympo-sium on Innovative and Interdisciplinary Applications of Advanced Technologies. Springer: 3-12.
[135] Wei W, Mei S, Wu L, et al. Optimal Traffic-Power Flow in Urban Electrified Transportation Net-works[J]. IEEE Transactions on Smart Grid, 2017, 8: 84-95.
[136] Xie S, Wu Q, Hatziargyriou N, et al. Collaborative Pricing in a Power-Transportation Coupled Network: A Variational Inequality Approach[J]. Power Systems, IEEE Transactions on, 2022, 38(1): 783-795.
[137] Braess D, Nagurney A, Wakolbinger T. On a paradox of traffic planning[J]. Transportation sci-ence, 2005, 39(4): 446-450.
[138] Cao X, Wang J, Zeng B. A Study on the Strong Duality of Second-Order Conic Relaxation of AC Optimal Power Flow in Radial Networks[J]. IEEE Transactions on Power Systems, 2022, 37(1): 443-455.
[139] Farivar M, Low S H. Branch Flow Model: Relaxations and Convexification—Part I[J]. IEEE Transactions on Power Systems, 2013, 28(3): 2554-2564.
[140] Rey D. Computational benchmarking of exact methods for the bilevel discrete network design problem[J]. Transportation Research Procedia, 2020, 47: 11-18.
[141] Baran M E, Wu F F. Optimal capacitor placement on radial distribution systems[J]. IEEE Transac-tions on power Delivery, 1989, 4(1): 725-734.
[142] Esmaeili Aliabadi D, Kaya M, Şahin G. Determining collusion opportunities in deregulated elec-tricity markets[J]. Electric Power Systems Research, 2016, 141: 432-441.
[143] Liang Y, Guo C, Ding Z, et al. Agent-based modeling in electricity market using deep determinis-tic policy gradient algorithm[J]. IEEE transactions on power systems, 2020, 35(6): 4180-4192.
[144] Razmi P, Oloomi Buygi M, Esmalifalak M. A Machine Learning Approach for Collusion Detec-tion in Electricity Markets Based on Nash Equilibrium Theory[J]. Journal of Modern Power Sys-tems and Clean Energy, 2021, 9(1): 170-180.
[145] Ciliberto F, Williams J W. Does multimarket contact facilitate tacit collusion? Inference on con-duct parameters in the airline industry[J]. The RAND journal of economics, 2014, 45(4): 764-791.
[146] Zhang Y, Round D K. Price wars and price collusion in China’s airline markets[J]. International Journal of Industrial Organization, 2011, 29(4): 361-372.
[147] Xiong W, Xiong L. Anti-collusion data auction mechanism based on smart contract[J]. Infor-mation Sciences, 2021, 555: 386-409.
[148] Karaca O, Sessa P G, Walton N, et al. Designing Coalition-Proof Reverse Auctions Over Continu-ous Goods[J]. IEEE Transactions on Automatic Control, 2019, 64(11): 4803-4810.
[149] Signor R, Ballesteros-Pérez P, Love P E. Collusion detection in infrastructure procurement: A modified order statistic method for uncapped auctions[J]. IEEE transactions on engineering man-agement, 2021, 70(2): 464-477.
[150] Train K. Discrete choice methods with simulation[M]. Cambridge university press, 2009.
[151] Kaya Ö, Tortum A, Alemdar K D, et al. Site selection for EVCS in Istanbul by GIS and multi-criteria decision-making[J]. Transportation Research Part D: Transport and Environment, 2020, 80: 102271.
[152] Nash Jr J F. The bargaining problem[J]. Econometrica: Journal of the econometric society, 1950: 155-162.
[153] Harrington J E, Hobbs B F, Pang J S, et al. Collusive game solutions via optimization[J]. Mathe-matical Programming, 2005, 104(2-3): 407-435.
[154] Nagurney A, Shukla S. Multifirm models of cybersecurity investment competition vs. cooperation and network vulnerability[J]. European Journal of Operational Research, 2017, 260(2): 588-600.
[155] Patriksson M. Sensitivity Analysis of Traffic Equilibria[J]. Transportation Science, 2004, 38(3): 258-281.
[156] Chiou S. Bilevel programming for the continuous transport network design problem[J]. Transpor-tation Research Part B: Methodological, 2005, 39(4): 361-383.
[157] Long J, Gao Z, Zhang H, et al. A turning restriction design problem in urban road networks[J]. European Journal of Operational Research, 2010, 206(3): 569-578.
[158] Yang H, Yagar S. Traffic assignment and traffic control in general freeway-arterial corridor sys-tems[J]. Transportation Research Part B: Methodological, 1994, 28(6): 463-486.
[159] Sovacool B K, Kester J, Noel L, et al. Actors, business models, and innovation activity systems for vehicle-to-grid (V2G) technology: A comprehensive review[J]. Renewable and Sustainable Ener-gy Reviews, 2020, 131: 109963.
[160] Habib S, Aghakhani S, Nejati M G, et al. Energy management of an intelligent parking lot equipped with hydrogen storage systems and renewable energy sources using the stochastic p-robust optimization approach[J]. Energy, 2023, 278: 127844.
[161] Li S, Gu C, Li J, et al. Boosting Grid Efficiency and Resiliency by Releasing V2G Potentiality Through a Novel Rolling Prediction-Decision Framework and Deep-LSTM Algorithm[J]. IEEE Systems Journal, 2021, 15(2): 2562-2570.
[162] Yanagawa G, Aki H. rid Flexibility Provision by Optimization of Fast-Charging Demand of Bat-tery Electric Vehicles[J]. IEEE Transactions on Smart Grid, 2023, 14(3): 2202-2213.
[163] Hussain A, Musilek P. Resilience enhancement strategies for and through electric vehicles[J]. Sus-tainable Cities and Society, 2022, 80: 103788.
[164] Habib S, Ahmarinejad A, Jia Y. A stochastic model for microgrids planning considering smart prosumers, electric vehicles and energy storages[J]. Journal of Energy Storage, 2023, 70: 107962.
[165] Bibak B, Tekiner-Mogulkoc H. The parametric analysis of the electric vehicles and vehicle to grid system’s role in flattening the power demand[J]. Sustainable Energy, Grids and Networks, 2022, 30: 100605.
[166] Kavianipour M, Fakhrmoosavi F, Singh H, et al. Electric vehicle fast charging infrastructure plan-ning in urban networks considering daily travel and charging behavior[J]. Transportation Re-search Part D: Transport and Environment, 2021, 93: 102769.
[167] Cai H, Jia X, Chiu A S F, et al. Siting public electric vehicle charging stations in Beijing using big-data informed travel patterns of the taxi fleet[J]. Transportation Research Part D: Transport and Environment, 2014, 33: 39-46.
[168] Dong J, Liu C, Lin Z. Charging infrastructure planning for promoting battery electric vehicles: An activity-based approach using multiday travel data[J]. Transportation Research Part C: Emerging Technologies, 2014, 38: 44-55.
[169] Shahraki N, Cai H, Turkay M, et al. Optimal locations of electric public charging stations using real world vehicle travel patterns[J]. Transportation Research Part D: Transport and Environment, 2015, 41: 165-176.
[170] Guler D, Yomralioglu T. Suitable location selection for the electric vehicle fast charging station with AHP and fuzzy AHP methods using GIS[J]. Annals of GIS, 2020, 26(2): 169-189.
[171] Xu Y, Çolak S, Kara E C, et al. Planning for electric vehicle needs by coupling charging profiles with urban mobility[J]. Nature Energy, 2018, 3(6): 484-493.
[172] Xydas E, Marmaras C, Cipcigan L M, et al. A data-driven approach for characterising the charging demand of electric vehicles: A UK case study[J]. Applied Energy, 2016, 162: 763-771.
[173] Powell S, Cezar G V, Rajagopal R. Scalable probabilistic estimates of electric vehicle charging given observed driver behavior[J]. Applied Energy, 2022, 309: 118382.
[174] Clairand J M, González-Rodríguez M, Cedeño I, et al. A charging station planning model consid-ering electric bus aggregators[J]. Sustainable Energy, Grids and Networks, 2022, 30: 100638.
[175] Ziras C, Kazempour J, Kara E C, et al. A Mid-Term DSO Market for Capacity Limits: How to Es-timate Opportunity Costs of Aggregators?[J]. IEEE Transactions on Smart Grid, 2020, 11(1): 334-345.
[176] Asrari A, Ansari M, Khazaei J, et al. A Market Framework for Decentralized Congestion Manage-ment in Smart Distribution Grids Considering Collaboration Among Electric Vehicle Aggrega-tors[J]. IEEE Transactions on Smart Grid, 2020, 11(2): 1147-1158.
[177] Wang H, Jia Y, Shi M, et al. A Hybrid Incentive Program for Managing Electric Vehicle Charging Flexibility[J]. IEEE Transactions on Smart Grid, 2023, 14(1): 476-488.
[178] Lei T, Guo S, Qian X, et al. Understanding charging dynamics of fully-electrified taxi services using large-scale trajectory data[J]. Transportation Research Part C: Emerging Technologies, 2022, 143: 103822.
[179] Hao X, Wang H, Lin Z, et al. Seasonal effects on electric vehicle energy consumption and driving range: A case study on personal, taxi, and ridesharing vehicles[J]. Journal of Cleaner Production, 2020, 249: 119403.
[180] Reyes J R M D, Parsons R V, Hoemsen R. Winter happens: The effect of ambient temperature on the travel range of electric vehicles[J]. IEEE Transactions on Vehicular Technology, 2016, 65(6): 4016-4022.
[181] Brinkel N, Schram W, AlSkaif T, et al. A quantitative analysis of the short-term and structural impact of COVID-19 measures on electric vehicle charging patterns[C]//2021 International Con-ference on Smart Energy Systems and Technologies (SEST). IEEE, 2021: 1-6.
[182] Palomino A, Parvania M, Zane R. Impact of covid-19 on mobility and electric vehicle charging load[C]//2021 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2021: 01-05.