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Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints

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  • Xu, Min
  • Meng, Qiang
  • Liu, Kai

Abstract

There has been growing attention on battery electric vehicles (BEVs) due to their energy efficiency and environmental friendliness. This paper deals with the user equilibrium (UE) problems for the mixed BEVs and traditional gasoline vehicles (GVs) in transportation networks with battery swapping stations and road grade constraints. Under the assumption that electricity consumption rate is not affected by traveling speed or traffic flow, a nonlinear minimization model in terms of path flows is first formulated by incorporating effects of road grade on the electricity consumption rate. The battery swapping action based paths are defined for BEVs in the represented network to facilitate the model building with flow-dependent dwell time at the battery swapping stations. The Frank-Wolfe (F-W) algorithm, where descent direction is found by the multi-label method in a pseudo-polynomial time, is adopted to solve the model. Moreover, the aforementioned assumption about the flow-independent electricity consumption rate is then relaxed and a system of inequalities has been proposed to formulate the UE conditions. For the nonlinear minimization model, two numerical examples are presented to assess the propose model and algorithm, as well as to analyze the impact of usable battery capacity, BEVs’ market share and some attributes of battery swapping stations on the equilibrium link flows and/or swapping flows. The system of inequalities is exactly solved for a small network by path enumeration to demonstrate the non-uniqueness of UE link flow solutions.

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  • Xu, Min & Meng, Qiang & Liu, Kai, 2017. "Network user equilibrium problems for the mixed battery electric vehicles and gasoline vehicles subject to battery swapping stations and road grade constraints," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 138-166.
    • Handle: RePEc:eee:transb:v:99:y:2017:i:c:p:138-166
    DOI: 10.1016/j.trb.2017.01.009
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    as
    1. Wang, Shuaian & Meng, Qiang & Yang, Hai, 2013. "Global optimization methods for the discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 42-60.
    2. Egbue, Ona & Long, Suzanna, 2012. "Barriers to widespread adoption of electric vehicles: An analysis of consumer attitudes and perceptions," Energy Policy, Elsevier, vol. 48(C), pages 717-729.
    3. Ho-Yin Mak & Ying Rong & Zuo-Jun Max Shen, 2013. "Infrastructure Planning for Electric Vehicles with Battery Swapping," Management Science, INFORMS, vol. 59(7), pages 1557-1575, July.
    4. Alexander Y. Bigazzi & Kelly J. Clifton, 2015. "Modeling the effects of congestion on fuel economy for advanced power train vehicles," Transportation Planning and Technology, Taylor & Francis Journals, vol. 38(2), pages 149-161, March.
    5. He, Fang & Wu, Di & Yin, Yafeng & Guan, Yongpei, 2013. "Optimal deployment of public charging stations for plug-in hybrid electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 87-101.
    6. Meng, Qiang & Liu, Zhiyuan & Wang, Shuaian, 2012. "Optimal distance tolls under congestion pricing and continuously distributed value of time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(5), pages 937-957.
    7. He, Fang & Yin, Yafeng & Lawphongpanich, Siriphong, 2014. "Network equilibrium models with battery electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 306-319.
    8. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, August.
    9. Michael Schneider & Andreas Stenger & Dominik Goeke, 2014. "The Electric Vehicle-Routing Problem with Time Windows and Recharging Stations," Transportation Science, INFORMS, vol. 48(4), pages 500-520, November.
    10. Nie, Yu (Marco) & Ghamami, Mehrnaz, 2013. "A corridor-centric approach to planning electric vehicle charging infrastructure," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 172-190.
    11. Sathaye, Nakul & Kelley, Scott, 2013. "An approach for the optimal planning of electric vehicle infrastructure for highway corridors," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 59(C), pages 15-33.
    12. Yabe, Kuniaki & Shinoda, Yukio & Seki, Tomomichi & Tanaka, Hideo & Akisawa, Atsushi, 2012. "Market penetration speed and effects on CO2 reduction of electric vehicles and plug-in hybrid electric vehicles in Japan," Energy Policy, Elsevier, vol. 45(C), pages 529-540.
    13. Lou, Yingyan & Yin, Yafeng & Lawphongpanich, Siriphong, 2010. "Robust congestion pricing under boundedly rational user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 15-28, January.
    14. Adler, Jonathan D. & Mirchandani, Pitu B., 2014. "Online routing and battery reservations for electric vehicles with swappable batteries," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 285-302.
    15. Di, Xuan & Liu, Henry X., 2016. "Boundedly rational route choice behavior: A review of models and methodologies," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 142-179.
    16. Di, Xuan & Liu, Henry X. & Pang, Jong-Shi & Ban, Xuegang (Jeff), 2013. "Boundedly rational user equilibria (BRUE): Mathematical formulation and solution sets," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 300-313.
    17. Liao, Chung-Shou & Lu, Shang-Hung & Shen, Zuo-Jun Max, 2016. "The electric vehicle touring problem," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 163-180.
    18. ., 2016. "Electric energy utilities," Chapters, in: Public Utilities, Second Edition, chapter 4, pages 69-88, Edward Elgar Publishing.
    19. Sang Nguyen & Clermont Dupuis, 1984. "An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs," Transportation Science, INFORMS, vol. 18(2), pages 185-202, May.
    20. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    21. Schneider, M. & Stenger, A. & Goeke, D., 2014. "The Electric Vehicle Routing Problem with Time Windows and Recharging Stations," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 62382, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    Full references (including those not matched with items on IDEAS)

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