Collaborative Vehicle-to-grid Operations in Frequency Regulation Markets

40 Pages Posted: 5 Oct 2021

See all articles by Ho-Yin Mak

Ho-Yin Mak

University of Oxford - Said Business School

Runyu Tang

Xi'an Jiaotong University (XJTU) - School of Management

Date Written: October 4, 2021


We study the operations of electric vehicles (EVs) providing frequency regulation services to the electric grid in vehicle-to-grid (V2G) systems. In particular, these individually-owned EVs collaboratively bid in the regulation market, coordinated by a platform that operates the network of charging equipment enabling V2G. We study how the platform determines optimal pricing incentives for drivers to plug in their EVs, taking into account their heterogeneous driving schedules. As EV adoption progresses past the nascent stage, V2G business models become more viable. V2G participation in frequency regulation provides a valuable resource to stabilize the electric grid against fluctuations between demand and supply, and complements the continued growth of clean but intermittent renewable (e.g., solar and wind) power. On the other hand, successful implementation of V2G provides another economic incentive for switching to EVs and potentially helps sustain adoption growth, especially as government subsidies phase out. Such operations are difficult to plan for, as it is important to model both the transportation (i.e., travel schedule) and energy (operations of regulation market) features of EV fleets. We model the platform's pricing optimization problem as a bilevel program: At the upper level, the platform determines hourly rebates for EVs to plug in their EVs, and capacity bids in the regulation market; At the lower level, individual travelers optimize their travel and charging schedules in response to pricing incentives. To account for uncertainties and heterogeneity in regulation market prices and travel patterns, we adopt distributionally-robust optimization techniques to formulate the problem as a mixed-integer second-order cone program, which can be efficiently solved with commercial solvers. We further derive a class of valid inequalities for the problem based on the theory of complements and substitutes of convex cost network flow problems. We conduct a computational study based on the California Household Travel Survey dataset and actual frequency regulation prices. Our results show that the ability to offer time-varying rebates and install workplace chargers can significantly improve the V2G platform's expected profits. We also find stark differences between the optimal rebate schedules under a profit-maximizing platform and the alternative model where the platform is collectively owned by the drivers. Our findings shed lights on business model design of V2G systems.

Suggested Citation

Mak, Ho-Yin and Tang, Runyu, Collaborative Vehicle-to-grid Operations in Frequency Regulation Markets (October 4, 2021). Available at SSRN: or

Ho-Yin Mak (Contact Author)

University of Oxford - Said Business School ( email )

Park End Street
Oxford, OX1 1HP
Great Britain

Runyu Tang

Xi'an Jiaotong University (XJTU) - School of Management ( email )

28,Xianning West Road
Xi'an, Shaanxi 710049

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