Infrastructure Topology Optimization under Competition through Cross-Entropy

International audienceIn this article, we study a two-level non-cooperative game between providers acting on the same geographic area. Each provider has the opportunity to set up a network of stations so as to capture as many consumers as possible. Its deployment being costly, the provider has to optimize both the number of settled stations as well as their locations. In the first level each provider optimizes independently his infrastructure topology while in the second level they price dynamically the access to their network of stations. The consumers' choices depend on the perception (in term of price, congestion and distances to the nearest stations) that they have of the service proposed by each provider. Each provider market share is then obtained as the solution of a fixed point equation since the congestion level is supposed to depend on the market share of the provider which increases with the number of consumers choosing the same provider. We prove that the two-stage game admits a unique equilibrium in price at any time instant. An algorithm based on the cross-entropy method is proposed to optimize the providers' infrastructure topology and it is tested on numerical examples providing economic interpretations

Is Energy Storage an Economic Opportunity for the Eco-Neighborhood?

International audienceIn this article, we consider houses belonging to an eco-neighborhood in which inhabitants have the capacity to optimize dynamically the energy demand and the energy storage level so as to maximize their utility. The inhabitants' preferences are characterized by their sensitivity toward comfort versus price, the optimal expected temperature in the house, thermal loss and heating efficiency of their house. At his level, the eco-neighborhood manager shares the resource produced by the eco-neighborhood according to two schemes: an equal allocation between the houses and a priority based one. The problem is modeled as a stochastic game and solved using stochastic dynamic programming. We simulate the energy consumption of the eco-neighborhood under various pricing mechanisms: flat rate, peak and off-peak hour, blue/white/red day, peak day clearing and a dynamic update of the price based on the consumption of the eco-neighborhood. We observe that economic incentives for houses to store energy depend deeply on the implemented pricing mechanism and on the homogeneity in the houses' characteristics. Furthermore, when prices are based on the consumption of the eco-neighborhood, storage appears as a compensation for the errors made by the service provider in the prediction of the consumption of the eco-neighborhood

Energy Demand Prediction in a Charge Station: A Comparison of Statistical Learning Approaches

International audienceIn this article, we compare the performances of 5 learning techniques: artificial neural networks, support vector machines, ARIMA processes and regret based methods. They have been tested over real database which can be associated with the energy demand generated by electric vehicles wishing to reload, in a specific charge station. Using this generic database, our simulations highlight the fact that regret based methods clearly outperform the other learning approaches. This class of methods is all the more interesting as it enables the introduction of game theory to model the interdependences between the agents composing the ecosystem and provides economic guidelines

Quantifying the Impact of Unpredictable Generation on Market Coupling

Modeling Market Coupling using an agent-based approach, we compare two organizations: centralized versus decentralized. To perform this comparison we analytically study the impact of wind farm concentration and the uncertainty resulting from the increasing penetration of renewables on the total cost of procurement, market welfare and the ratio of renewable generation to conventional supplies. We prove that the existence and uniqueness of equilibrium depend on the number of interacting demand markets. In a decentralized organization, forecast errors heavily impact the behavior of the electrical system. Simulations show that suppliers have incentives to certify the forecast uncertainty of other markets. We analytically derive the uncertainty price that might be charged by a risk certificator depending on the required confidence level

Computing an Aggregator's Long Term Profit under Uncertain Behavior of the Agents

In the retail electricity market, consumers can subscribe a contract with a conventional retailer or cooperate through an aggregator who takes forward positions in the wholesale electricity market, modeled as a two-tiered system. We characterize analytically the core of the game and give conditions for its non emptiness. Then we propose a Machine Learning algorithm to forecast the consumers' demand and use these forecasts as inputs to optimize the aggregator's pricing strategy. The viability of the aggregator's pricing strategy is finally evaluated on a case study containing the power consumptions of 370 Portuguese consumers over four years

Distributed Learning in Hierarchical Networks

International audienceIn this article, we propose distributed learning based approaches to study the evolution of a decentralized hierarchical system, an illustration of which is the smart grid. Smart grid management requires the control of non-renewable energy production and the inegration of renewable energies which might be highly unpredictable. Indeed, their production levels rely on uncontrolable factors such as sunshine, wind strength, etc. First, we derive optimal control strategies on the non-renewable energy productions and compare competitive learning algorithms to forecast the energy needs of the end users. Second, we introduce an online learning algorithm based on regret minimization enabling the agents to forecast the production of renewable energies. Additionally, we define organizations of the market promoting collaborative learning which generate higher performance for the whole smart grid than full competition

Energy Demand Prediction: A Partial Information Game Approach

International audienceThis article proposes an original approach to predict the electric vehicles (EVs)' energy demand in a charge station using a regret minimization learning approach. The problem is modelled as a two players game involving: on the one hand the EV drivers, whose demand is unknown and, on the other hand, the service provider who owns the charge station and wants to make the best predictions in order to minimize his regret. The information in the game is partial. Indeed, the service provider never observes the EV drivers' energy demand. The only information he has access to is contained in a feedback function which depends on his predictions accuracy and on the EV drivers' consumption level. The local/expanded accuracy and the ability for uncertainty handling of the regret minimization learning approach is evaluated by comparison with three well-known learning approaches: (i) Neural Network, (ii) Support Vector Machine, (iii) AutoRegressive Integrated Moving Average process, using as benchmarks two data bases: an artificial one generated using a bayesian network and real domestic household electricity consumption data in southern California. We observe that over real data, regret minimization algorithms clearly outperform the other learning approaches. The efficiency of these methods open the door to a wide class of game theory applications dealing with collaborative learning, information sharing and manipulation

Wind Farm Portfolio Optimization under Network Capacity Constraints

International audienceIn this article, we provide a new methodology for optimizing a portfolio of wind farms within a market environment, for two Market Designs (exogenous prices and endogenous prices). Our model is built on an agent based representation of suppliers and generators interacting in a certain number of geographic demand markets, organized as two tiered systems. Assuming rational expectation of the agents with respect to the outcome of the real-time market, suppliers take forward positions, which act as signals in the day-ahead market, to compensate for the uncertainty associated with supply and demand. Then, generators optimize their bilateral trades with the generators in the other markets. The Nash Equilibria resulting from this Signaling Game are characterized using Game Theory. The Markowitz Frontier, containing the set of efficient wind farm portfolios, is derived theoretically as a function of the number of wind farms and of their concentration. Finally, using a case study of France, Germany and Belgium, we simulate the Markowitz Frontier contour in the expected cost-risk plane