Seminar: Gaël Guillot and Ilia Shilov, Monday, 6th December 2021.

Date: December, 6th, 14h00

Place: Inria Lille-Nord Europe

Gaël Guillot: Optimal pricing for electric vehicle charging with customer waiting time.

We propose a bilevel optimization model to determine the optimal pricing for electric vehicle
within a public charging station system by taking into account the waiting time of customers.
We assume that the locations of the charging station are fixed, and model the waiting time
without using classical queuing theory. In the upper level of the bilevel model, the decision
maker sets the price of electricity and the amount of energy available at each station. The
latter quantity depends on the amount of renewable energy available at each time period. In the
lower level, electric vehicle users select a charging station and a time for recharging the vehicle,
depending on individual preferences. We present two linear models for this problem and explore
how to solve them using mixed integer bilevel optimization methods.
[1] DeNegre S., Ralphs T., Tahernejad S., A branch-and-cut algorithm for mixed integer bilevel
linear optimization problems and its implementation, Mathematical Programming Computation, Volume 12, 2020.
[2] Moore, J. T. and J. F. Bard, The mixed integer linear bilevel programming problem. Operations Research 38.5, 1990.
[3] Wei, W., Wu, L., Wang, J., and Mei, S. Network equilibrium of coupled transportation and
power distribution systems. IEEE Transactions on Smart Grid 9.6 2017.
[4] Sohet, B., Hayel, Y., Beaude, O., and Jeandin, A. Coupled charging-and-driving incentives
design for electric vehicles in urban networks. IEEE Transactions on Intelligent Transportation Systems. 2020.

Ilia Shilov: A Generalized Nash Equilibrium analysis of peer-to-peer electricity market: privacy impact and interaction with the distribution grid.

Currently, due to the large-scale integration of Distributed Energy Resources (DERs), electricity markets
are starting to restructure – from centralized to decentralized local market designs. We consider a peer-topeer design of a local market, in which prosumers (e.g. agents that can both produce and consume) negotiate
bilaterally their energy procurement with their neighbors, while holding some private information that they
might not want to share.
In [1] we focus on the communication mechanism that captures the agents’ ability to define the information
they want to report to the other market participants, while preserving their privacy. We model this problem
as a Generalized Nash Equilibrium Problem (GNEP), where the agents determine their randomized reports
to share with the other agents, while anticipating the form of the peer-to-peer market equilibrium. In this
game, each agent decides on the deterministic and random parts of her report, such that (i) the distance
between the deterministic part of the report and the truthful private information is bounded and (ii) the
expectation of the privacy loss random variable is bounded. We analytically characterize the equilibrium of
the game, prove the uniqueness of the Variational Equilibrium and provide a closed form expression of the
privacy price. We illustrate the results numerically on the 14-bus IEEE network.
In subsequent work [2] we consider the interaction between the distribution grid (physical level) managed
by the distribution system operator (DSO), and financial market similar to that considered in [1]. In this
model, we take into account the feasibility of the power flows corresponding to the bilateral trades negotiated
on the financial market, that must accommodate the distribution grid network constraints. We model the
interaction problem between the physical and financial level again as a GNEP. We compare two designs of
the financial level prosumer market: a centralized design and a peer-to-peer fully distributed design. We
prove the Pareto efficiency of the equilibria under homogeneity of the trading cost preferences. In addition,
we prove that the pricing structure of our noncooperative game does not permit free-lunch behavior. Finally,
in the numerical section we provide additional insights on the efficiency loss with respect to the different
levels of agents’ flexibility and amount of renewables in the network. We also quantify the impact of the
prosumers’ pricing on the noncooperative game social cost.

[1] I. Shilov, H. Le Cadre and A. Bušić, “Privacy Impact on Generalized Nash Equilibrium in Peer-to-Peer
Electricity Market”, Operations Research Letters, Vol. 49, pp. 759-766, 2021
[2] I. Shilov, H. Le Cadre, A. Bušić, “A Generalized Nash Equilibrium analysis of the interaction between a
peer-to-peer financial market and the distribution grid”, Proceedings of IEEE SmartGridComm 21’, 2021

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