arXiv subjects

Olivier Beaude

Publications and source records attributed to Olivier Beaude.

At least 19 recordsLinked to original sources

arXiv2026

Integrating Aggregated Electric Vehicle Flexibilities in Unit Commitment Models using Submodular Optimization

The Unit Commitment (UC) problem consists in controlling a large fleet of heterogeneous electricity production units in order to minimize the total production cost while satisfying consumer demand. Electric Vehicles (EVs) are used as a source of flexibility and are often aggregated for problem tractability. We develop a new approach to integrate EV flexibilities in the UC problem and exploit the generalized polymatroid structure of aggregated flexibilities of a large population of users to develop an exact optimization algorithm, combining a cutting-plane approach and submodular optimization. We show in particular that the UC can be solved exactly in a time which scales linearly, up to a logarithmic factor, in the number of EV users when each production unit is subject to convex constraints. We illustrate our approach by solving a real instance of a long-term UC problem, combining open-source data of the European grid (European Resource Adequacy Assessment project) and data originating from a survey of user behavior of the French EV fleet.

math.OC↗

arXiv2026

Pricing for Information Revelation in Demand Response: A Strategic Communication Approach

Many smart grid frameworks, such as demand response programs, require accurate information about consumers' parameters (e.g., flexibility) at the aggregator side to optimize grid operations. Existing works typically rely on perfect information assumptions or complex incentive-compatible mechanisms; however, in voluntary settings, and in the presence of strategic consumers, possibly implemented by automated intelligent agents, private parameters may be misreported due to strategic incentives. We analyze this communication setting using cheap-talk game theory, delivering four key insights. First, the nontrivial scenario of multiple strategic transmitters (consumers) turns out to be tractable for the case study of interest: we prove that complex strategic interactions among multiple consumers decouple into independent subgames. Second, we demonstrate that a pre-announced retail price can be exploited as a design lever to control the information revealed by the consumers and therefore the overall system efficiency. Third, we derive a closed-form expression for the optimal uniform price that maximizes information revelation. Finally, we characterize the equilibrium structure to identify when communication is informative. Simulations show that a properly designed price for the communication scheme can recover up to 95% of the ideal system utility (i.e., under perfect information reporting), whereas a price-unaware choice leads to significant losses in social welfare.

cs.GT↗

arXiv2021

Hierarchical coupled routing-charging model of electric vehicles, stations and grid operators

Electric Vehicles' (EVs) growing number has various consequences, from reducing greenhouse gas emissions and local pollution to altering traffic congestion and electricity consumption. More specifically, decisions of operators from both the transportation and the electrical systems are coupled due to EVs' decisions. Thus, decision-making requires a model of several interdependent operators and of EVs' both driving and charging behaviors. Such a model is suggested for the electrical system in the context of commuting, which has a typical trilevel structure. At the lower level of the model, a congestion game between different types of vehicles gives which driving paths and charging stations (or hubs) commuters choose, depending on travel duration and consumption costs. At the middle level, a Charging Service Operator sets the charging prices at the hubs to maximize the difference between EV charging revenues and electricity supplying costs, which are decided by the Electrical Network Operator at the upper level of the model, whose goal is to reduce grid costs. This trilevel optimization problem is solved using an optimistic iterative bilevel algorithm and simulated annealing. The sensitivity of this trilevel model to exogenous parameters such as the EV penetration and an incentive from a transportation operator is illustrated on realistic urban networks.

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arXiv2021

Learning Pure Nash Equilibrium in Smart Charging Games

Reinforcement Learning Algorithms (RLA) are useful machine learning tools to understand how decision makers react to signals. It is known that RLA converge towards the pure Nash Equilibria (NE) of finite congestion games and more generally, finite potential games. For finite congestion games, only separable cost functions are considered. However, non-separable costs, which depend on the choices of all players instead of only those choosing the same resource, may be relevant in some circumstances, like in smart charging games. In this paper, finite congestion games with non-separable costs are shown to have an ordinal potential function, leading to the existence of an action-dependent continuous potential function. The convergence of a synchronous RLA towards the pure NE is then extended to this more general class of congestion games. Finally, a smart charging game is designed for illustrating convergence of such learning algorithms.

cs.GT↗

arXiv2021

Impact of Strategic Electric Vehicles Driving Behavior on the Grid

In the context of transport electrification, a model coupling Electric Vehicles (EV) driving and charging decisions is considered. While a Traffic Assignment Problem (TAP) is considered for the driving part, the charging operation is done with an exact load flow on a simple distribution network. This setting allows assessing precisely the coupled impact of driving and charging decisions. In particular, to schedule the charging need coming from the driving part, different charging strategies are defined and compared according to a cost metric based on the load flow computation. In view of this metric, the proposed non-load flow based strategies can perform similarly to a load flow based one, and with significantly reduced computation time and data need. Numerical simulations show how a transportation toll can influence the charging results.

eess.SY↗

arXiv2021

Online smart charging algorithm with asynchronous electric vehicles demand

The increasing penetration of Electric Vehicles (EVs) and renewable energies into the grid necessitates tools to smooth the demand curve. To this end, this paper suggests an EV charging scheduling algorithm and a smart charging price. As EVs arrive at the charging station and leave at different times, the operator of the station applies at each EV arrival an online scheduling algorithm based on the concept of "water filling. The EV charging price is guaranteed at their arrival and defined as a function of the online algorithm's output, following the idea of locational marginal pricing. A numerical comparison with the offline version of the algorithm -- in which the operator knows in advance all future arrival and departure times -- shows the efficiency of the suggested online scheduling algorithm.

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arXiv2020

A Privacy-preserving Method to Optimize Distributed Resource Allocation

We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimize a global, possibly nonconvex, cost while satisfying the agents' constraints, for instance an energy operator in charge of the management of energy consumption flexibilities of many individual consumers. We provide a privacy-preserving algorithm that does compute the optimal allocation of resources, avoiding each agent to reveal her private information (constraints and individual solution profile) neither to the central operator nor to a third party. Our method relies on an aggregation procedure: we compute iteratively a global allocation of resources, and gradually ensure existence of a disaggregation, that is individual profiles satisfying agents' private constraints, by a protocol involving the generation of polyhedral cuts and secure multiparty computations (SMC). To obtain these cuts, we use an alternate projection method, which is implemented locally by each agent, preserving her privacy needs. We adress especially the case in which the local and global constraints define a transportation polytope. Then, we provide theoretical convergence estimates together with numerical results, showing that the algorithm can be effectively used to solve the allocation problem in high dimension, while addressing privacy issues.

math.OC↗

arXiv2020

Efficient Estimation of Equilibria in Large Aggregative Games with Coupling Constraints

Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that variational Nash equilibria of a large aggregative game can be approximated by a Wardrop equilibrium of an auxiliary population game of smaller dimension. Each population of this auxiliary game corresponds to a group of atomic players of the initial large game. This approach enables an efficient computation of an approximated equilibrium, as the variational inequality characterizing the Wardrop equilibrium is of smaller dimension than the initial one. This is illustrated on an example in the smart grid context.

cs.GT↗

arXiv2020

Coupled Charging-and-Driving Incentives Design for Electric Vehicles in Urban Networks

Electric Vehicles (EV) impact urban networks both when driving (e.g., noise and pollution reduction) and charging. For the electrical grid, the flexibility of EV charging makes it a significant actor in "Demand Response" mechanisms. Therefore, there is a need to design incentive mechanisms to foster customer engagement. A congestion game approach is adopted to evaluate the performance of such electrical transportation system with multiple classes of vehicles: EV and Gasoline Vehicles. Both temporal and energy operating costs are considered. The latter is nonseparable as it depends on the global charging need of all EV, which is scheduled in time by a centralized aggregator in function of nonflexible consumption at charging location. Thus, driving and charging decisions are coupled. An adaptation of Beckmann's method proves the existence of a Wardrop Equilibrium (WE) in the considered nonseparable congestion game; this WE is unique when the charging unit price is an increasing function of the global charging need. A condition on the nonflexible load is given to guarantee the monotonicity of this function. This condition is tested on real consumption data in France and in Texas, USA. Optimal tolls are used to control this electrical transportation system and then computed in order to minimize an environmental cost on a simple network topology.

cs.GT↗

arXiv2019

A Privacy-preserving Disaggregation Algorithm for Non-intrusive Management of Flexible Energy

We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimizing a global, possibly non-convex, cost while satisfying the agents'c onstraints. We focus on the practical case of the management of energy consumption flexibilities by the operator of a microgrid. This paper provides a privacy-preserving algorithm that does compute the optimal allocation of resources, avoiding each agent to reveal her private information (constraints and individual solution profile) neither to the central operator nor to a third party. Our method relies on an aggregation procedure: we maintain a global allocation of resources, and gradually disaggregate this allocation to enforce the satisfaction of private contraints, by a protocol involving the generation of polyhedral cuts and secure multiparty computations (SMC). To obtain these cuts, we use an alternate projections method à la Von Neumann, which is implemented locally by each agent, preserving her privacy needs. Our theoretical and numerical results show that the method scales well as the number of agents gets large, and thus can be used to solve the allocation problem in high dimension, while addressing privacy issues.

cs.MA↗

arXiv2018

Efficient Estimation of Equilibria of Large Congestion Games with Heterogeneous Players

Computing an equilibrium in congestion games can be challenging when the number of players is large. Yet, it is a problem to be addressed in practice, for instance to forecast the state of the system and be able to control it. In this work, we analyze the case of generalized atomic congestion games, with coupling constraints, and with players that are heterogeneous through their action sets and their utility functions. We obtain an approximation of the variational Nash equilibria---a notion generalizing Nash equilibria in the presence of coupling constraints---of a large atomic congestion game by an equilibrium of an auxiliary population game, where each population corresponds to a group of atomic players of the initial game. Because the variational inequalities characterizing the equilibrium of the auxiliary game have smaller dimension than the original problem, this approach enables the fast computation of an estimation of equilibria in a large congestion game with thousands of heterogeneous players.

cs.GT↗

arXiv2017

Analysis and Implementation of a Hourly Billing Mechanism for Demand Response Management

An important part of the Smart Grid literature on residential Demand Response deals with game-theoretic consumption models. Among those papers, the hourly billing model is of special interest as an intuitive and fair mechanism. We focus on this model and answer to several theoretical and practical questions. First, we prove the uniqueness of the consumption profile corresponding to the Nash equilibrium, and we analyze its efficiency by providing a bound on the Price of Anarchy. Next, we address the computational issue of the equilibrium profile by providing two algorithms: the cycling best response dynamics and a projected gradient descent method, and by giving an upper bound on their convergence rate to the equilibrium. Last, we simulate this demand response framework in a stochastic environment where the parameters depend on forecasts. We show numerically the relevance of an online demand response procedure, which reduces the impact of inaccurate forecasts.

math.OC↗

arXiv2017

Demand Response in the Smart Grid: the Impact of Consumers Temporal Preferences

In Demand Response programs, price incentives might not be sufficient to modify residential consumers load profile. Here, we consider that each consumer has a preferred profile and a discomfort cost when deviating from it. Consumers can value this discomfort at a varying level that we take as a parameter. This work analyses Demand Response as a game theoretic environment. We study the equilibria of the game between consumers with preferences within two different dynamic pricing mechanisms, respectively the daily proportional mechanism introduced by Mohsenian-Rad et al, and an hourly proportional mechanism. We give new results about equilibria as functions of the preference level in the case of quadratic system costs and prove that, whatever the preference level, system costs are smaller with the hourly mechanism. We simulate the Demand Response environment using real consumption data from PecanStreet database. While the Price of Anarchy remains always close to one up to 0.1% with the hourly mechanism, it can be more than 10% bigger with the daily mechanism.

math.OC↗

arXiv2017

Demand Side Management in the Smart Grid: an Efficiency and Fairness Tradeoff

We compare two Demand Side Management (DSM) mechanisms, introduced respectively by Mohsenian-Rad et al (2010) and Baharlouei et al (2012), in terms of efficiency and fairness. Each mechanism defines a game where the consumers optimize their flexible consumption to reduce their electricity bills. Mohsenian-Rad et al propose a daily mechanism for which they prove the social optimality. Baharlouei et al propose a hourly billing mechanism for which we give theoretical results: we prove the uniqueness of an equilibrium in the associated game and give an upper bound on its price of anarchy. We evaluate numerically the two mechanisms, using real consumption data from Pecan Street Inc. The simulations show that the equilibrium reached with the hourly mechanism is socially optimal up to 0.1%, and that it achieves an important fairness property according to a quantitative indicator we define. We observe that the two DSM mechanisms avoid the synchronization effect induced by non- game theoretic mechanisms, e.g. Peak/OffPeak hours contracts.

math.OC↗

arXiv2015

Introducing Decentralized EV Charging Coordination for the Voltage Regulation

This paper investigates a decentralized optimization methodology to coordinate Electric Vehicles (EV) charging in order to contribute to the voltage control on a residential electrical distribution feeder. This aims to maintain the voltage level in function of the EV's power injection using the sensitivity matrix approach. The decentralized optimization is tested with two different methods, respectively global and local, when EV take into account their impact on all the nodes of the network or only on a local neighborhood of their connection point. EV can also update their decisions asynchronously or synchronously. While only the global approach with asynchronous update is theoretically proven to converge, using results from game theory, simulations show the potential of other algorithms for which fewer iterations or fewer informations are necessary. Finally, using Monte Carlo simulations over a wide range of EV localization configurations, the first analysis have also shown a promising performance in comparison with uncoordinated charging or with a "voltage droop charging control" recently proposed in the literature.

eess.SY↗

arXiv2015

Minimizing the impact of EV charging on the electricity distribution network

The main objective of this paper is to design electric vehicle (EV) charging policies which minimize the impact of charging on the electricity distribution network (DN). More precisely, the considered cost function results from a linear combination of two parts: a cost with memory and a memoryless cost. In this paper, the first component is identified to be the transformer ageing while the second one corresponds to distribution Joule losses. First, we formulate the problem as a non-trivial discrete-time optimal control problem with finite time horizon. It is non-trivial because of the presence of saturation constraints and a non-quadratic cost. It turns out that the system state, which is the transformer hot-spot (HS) temperature here, can be expressed as a function of the sequence of control variables; the cost function is then seen to be convex in the control for typical values for the model parameters. The problem of interest thus becomes a standard optimization problem. While the corresponding problem can be solved by using available numerical routines, three distributed charging policies are provided. The motivation is threefold: to decrease the computational complexity; to model the important scenario where the charging profile is chosen by the EV itself; to circumvent the allocation problem which arises with the proposed formulation. Remarkably, the performance loss induced by decentralization is verified to be small through simulations. Numerical results show the importance of the choice of the charging policies. For instance, the gain in terms of transformer lifetime can be very significant when implementing advanced charging policies instead of plug-and-charge policies. The impact of the accuracy of the non-EV demand forecasting is equally assessed.

math.OC↗

arXiv2015

Composite charging games in networks of electric vehicles

An important scenario for smart grids which encompass distributed electrical networks is given by the simultaneous presence of aggregators and individual consumers. In this work, an aggregator is seen as an entity (a coalition) which is able to manage jointly the energy demand of a large group of consumers or users. More precisely, the demand consists in charging an electrical vehicle (EV) battery. The way the EVs user charge their batteries matters since it strongly impacts the network, especially the distribution network costs (e.g., in terms of Joule losses or transformer ageing). Since the charging policy is chosen by the users or the aggregators, the charging problem is naturally distributed. It turns out that one of the tools suited to tackle this heterogenous scenario has been introduced only recently namely, through the notion of composite games. This paper exploits for the first time in the literature of smart grids the notion of composite game and equilibrium. By assuming a rectangular charging profile for an EV, a composite equilibrium analysis is conducted, followed by a detailed analysis of a case study which assumes three possible charging periods or time-slots. Both the provided analytical and numerical results allow one to better understand the relationship between the size (which is a measure) of the coalition and the network sum-cost. In particular, a social dilemma, a situation where everybody prefers unilaterally defecting to cooperating, while the consequence is the worst for all, is exhibited.

cs.GT↗

arXiv2015

Charging Games in Networks of Electrical Vehicles

In this paper, a static non-cooperative game formulation of the problem of distributed charging in electrical vehicle (EV) networks is proposed. This formulation allows one to model the interaction between several EV which are connected to a common residential distribution transformer. Each EV aims at choosing the time at which it starts charging its battery in order to minimize an individual cost which is mainly related to the total power delivered by the transformer, the location of the time interval over which the charging operation is performed, and the charging duration needed for the considered EV to have its battery fully recharged. As individual cost functions are assumed to be memoryless, it is possible to show that the game of interest is always an ordinal potential game. More precisely, both an atomic and nonatomic versions of the charging game are considered. In both cases, equilibrium analysis is conducted. In particular, important issues such as equilibrium uniqueness and efficiency are tackled. Interestingly, both analytical and numerical results show that the efficiency loss due to decentralization (e.g., when cost functions such as distribution network Joule losses or life of residential distribution transformers when no thermal inertia is assumed) induced by charging is small and the corresponding "efficiency", a notion close to the Price of Anarchy, tends to one when the number of EV increases.

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