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.Comment: 8 pages, 4 figures, keywords: Charging games - electrical vehicle - distribution networks - potential games - Nash equilibrium - price of anarch

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.Comment: 6 pages, 3 figures, keywords: electric vehicle charging, electricity distribution network, optimal control, distributed policies, game theor

Sensitivity analysis of a simulation model for evaluating renewable distributed generation on a power network

International audienceWe present a sensitivity analysis of a simulation model for the evaluation of the performance of a renewable distributed generation (DG) network. Uncertainties in renewable energy sources, components failure and repair events, loads and grid power supply are taken into account. The sensitivity analysis is performed individually with respect to the characteristic uncertain variables associated to each type of DG technology available. The impact of these uncertain variables is evaluated in terms of two performance functions, global cost (C g) and energy not supplied (ENS). The results show the trends of performance of the DG-integrated network under different conditions. This allows evaluating the impact of the different DG technologies

La traçabilité de l'électricité : une méthode équitable pour l'allocation des coûts de transmission

International audienceDans le contexte international de l'ouverture des marchés de l'électricité, le volume croissant d'échanges ne permet leur tarification équitable que par le biais d'une estimation des responsabilités physiques des acteurs. Or, du fait de l'impossibilité d'affecter « physiquement » les transits aux acteurs, différentes méthodes peuvent être utilisées. Soucieux de définir une traçabilité équitable, ce papier présente une nouvelle méthode pour déterminer les échanges bilatéraux équivalents entre générateurs et consommateurs. Elle est basée sur le calcul de distances électriques équivalentes et la prise en compte des pertes dans la répartition. Ses résultats sont présentés et comparés à ceux d'autres méthodes de traçabilité dans le cas d'un réseau standard

Impact des véhicules électrifiés sur le dimensionnement du réseau HTA

Le développement annoncé des Véhicules Electriques et des Véhicules Hybrides Rechargeables va augmenter la consommation électrique, notamment dans le secteur résidentiel, ainsi que les pertes dans les lignes. Cette augmentation doit être prise en compte dans le dimensionnement de la section des conducteurs. En effet, un gestionnaire de réseau de distribution dimensionne celle-ci en cherchant l'optimum économique entre le coût du matériau conducteur et le coût des pertes par effet Joule capitalisées sur la durée de vie de la ligne. Dans cette contribution, nous estimons ce nouvel optimum et le surcoût engendré par la pénétration de véhicules électrifiés pour une ligne HTA. Nous montrons que ce surcoût peut être réduit en choisissant des profils de recharge adaptés. Ensuite une étude de la sensibilité du résultat aux paramètres montre que parmi ceux-ci, le choix du taux d'actualisation des pertes futures est prépondérant. Enfin est évalué l'impact de la production photovoltaïque distribuée sur le dimensionnement. Les résultats montrent que l'impact des véhicules électrifiés est environ 4 fois plus important que l'impact de la production photovoltaïque

A Market Based Approach to Evaluate the Efficiency of Transmission Loss Allocation

International audienceIn the deregulated electrical power system, the allocation of transmission losses is becoming a key issue. The electric transmission power system is more and more constrained due to the increasing volume of power flows, while the active power losses' costs are increasing. In this context, the traditional “postage stamp” allocation is no longer sufficient to give right incentives. One solution could be to charge each actor depending on his responsibilities on the active power losses. This is why a number of transmission loss allocation (TLA) methods have recently been proposed. Their economic impact, however, has rarely been taken into account. This paper resumes the most common TLA methods and designs a frame to compare their efficiency. A simplified market design is proposed in order to evaluate the impact of the integration of transmission loss costs. These methods are applied to the IEEE 14 bus system. An over cost of 1.16% of the global production costs is then estimated for the “postage stamp” allocation while flow based methods reach 0.38%. The influence of the simulation parameters is analyzed

Charging Games in Networks of Electrical Vehicles

International audienceIn 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

Valorisation des services système sur un réseau de transport d'électricité en environnement concurrentiel

Liberalization of electricity markets has led to an economical (at least) separation between production and transmission utilities. So new interface rules have to be defined. This contribution tends to go further into a method to valorize reactive power production capacities on power grids in a competitive environment, which has been proposed by Xu, Kundur and da Silva. The method is based on the comparison between generators and static devices. Indeed, the generators are controlled by the producers whereas static devices are controlled by the Transmission System Operator. That's why this method tends to provide the technical value of the reactive power production for the TSO. In this work, the position of static devices is optimized tending to minimize their capacity with respect to the voltage bounds at each node while the reactive power output of a generator is decreased. The reactive power production can also be replaced by increasing reactive power production of generators where capacities are available. In this case generators located in parts of the grids which lack reactive power production capacities will have greater value tan those located in parts where capacities are numerous. This method has been successfully tested on the IEEE 118 bus benchmark grid and on a part of the French grid.Dans le cadre de l'ouverture des marchés de l'électricité à la concurrence, de nouvelles règles doivent régir les relations entre producteur et transporteur d'électricité pour ce qui concerne les services au système tels que la fourniture de puissance réactive. Xu, Kundur et da Silva ont développé une méthode permettant d'évaluer le service rendu, et donc la valeur, d'un MVAr fourni par un générateur en calculant le nombre de MVAr qui doivent être fournis aux nœuds de charge pour maintenir leur tension lorsque le générateur réduit sa production. Nous avons amélioré cette méthode en optimisant l'emplacement et en minimisant la capacité de moyens de compensation permettant de remplacer la production réactive d'un générateur tout en maintenant la tension de chaque nœud dans sa plage acceptable. De plus les capacités de production réactives disponibles auprès d'autres générateurs sont mises à contribution, ce qui permet de prendre en compte la pénurie ou l'abondance de capacités de production. Cette méthode a été appliquée sur un réseau à deux nœuds, puis sur un réseau de test IEEE à 118 nœuds et enfin sur une partie du réseau électrique français. Les résultats obtenus permettent de valoriser chaque MVAr généré en fonction de la localisation du générateur sur le réseau, de l'état de charge du réseau, de la disponibilité des autres producteurs et du niveau de production du générateur. Ainsi les premiers MVAr fournis par un générateur sont difficilement remplaçables par des moyens de compensation et ont donc une valeur plus grande que les derniers qui eux sont facilement remplaçables