An electric vehicle charging station access equilibrium model with M/D/C queueing

Abstract

Despite the dependency of electric vehicle (EV) fleets on charging station availability, charging infrastructure remains limited in many cities. Three contributions are made. First, we propose an EV-to-charging station user equilibrium (UE) assignment model with a M/D/C queue approximation as a nondifferentiable nonlinear program. Second, to address the non-differentiability of the queue delay function, we propose an original solution algorithm based on the derivative-free Method of Successive Averages. Computational tests with a toy network show that the model converges to a UE. A working code in Python is provided free on Github with detailed test cases. Third, the model is applied to the large-scale case study of New York City Department of Citywide Administrative Services (NYC DCAS) fleet and EV charging station configuration as of July 8, 2020, which includes unique, real data for 563 Level 2 chargers and 4 Direct Current Fast Chargers (DCFCs) and 1484 EVs distributed over 512 Traffic Analysis Zones. The arrival rates of the assignment model are calibrated in the base scenario to fit an observed average utilization ratio of 7.6% in NYC. The model is then applied to compare charging station investment policies of DCFCs to Level 2 charging stations based on two alternative criteria. Results suggest a policy based on selecting locations with high utilization ratio instead of with high queue delay.

Keywords:

• Charging stations
• electric vehicle
• M/D/C queue
• Method of Successive Averages
• New York City
• user equilibrium

Acknowledgments

This research was supported by the C2SMART University Transportation Center. Stephanie Tam is an undergraduate member of the Vertically Integrated Projects (VIP) “Clean Fleets” team at NYU (https://wp.nyu.edu/vip/nyc-clean-fleet/) that is working with NYC DCAS to develop the web-based equilibrium model. The data shared by DCAS is gratefully acknowledged. Any errors and views expressed in this study solely belong to the authors.

Authors’ contribution statement

The authors confirm contribution to the paper as follows: study conception and design: J.Y.J. Chow, T.P. Pantelidis, B. Liu; data preparation: S. Tam, T.P. Pantelidis, B. Liu; analysis and interpretation of results: B. Liu, J.Y.J. Chow, T.P. Pantelidis; draft manuscript preparation: B. Liu, T.P. Pantelidis, J.Y.J. Chow, S. Tam. All authors reviewed the results and approved the final version of the manuscript.