scholarly journals A Novel Mean Field Game-Based Strategy for Charging Electric Vehicles in Solar Powered Parking Lots

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8517
Author(s):  
Samuel M. Muhindo ◽  
Roland P. Malhamé ◽  
Geza Joos
Keyword(s):  
Nash Equilibrium ◽  
Solar Energy ◽  
Electric Vehicles ◽  
Large Population ◽  
Mean Field ◽  
Mean Field Games ◽  
Parking Lot ◽  
Equal Sharing ◽  
Solar Powered ◽  
Energy Forecast

We develop a strategy, with concepts from Mean Field Games (MFG), to coordinate the charging of a large population of battery electric vehicles (BEVs) in a parking lot powered by solar energy and managed by an aggregator. A yearly parking fee is charged for each BEV irrespective of the amount of energy extracted. The goal is to share the energy available so as to minimize the standard deviation (STD) of the state of charge (SOC) of batteries when the BEVs are leaving the parking lot, while maintaining some fairness and decentralization criteria. The MFG charging laws correspond to the Nash equilibrium induced by quadratic cost functions based on an inverse Nash equilibrium concept and designed to favor the batteries with the lower SOCs upon arrival. While the MFG charging laws are strictly decentralized, they guarantee that a mean of instantaneous charging powers to the BEVs follows a trajectory based on the solar energy forecast for the day. That day ahead forecast is broadcasted to the BEVs which then gauge the necessary SOC upon leaving their home. We illustrate the advantages of the MFG strategy for the case of a typical sunny day and a typical cloudy day when compared to more straightforward strategies: first come first full/serve and equal sharing. The behavior of the charging strategies is contrasted under conditions of random arrivals and random departures of the BEVs in the parking lot.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

scholarly journals Price Formation and Optimal Trading in Intraday Electricity Markets with a Major Player

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 133
Author(s):  
Olivier Féron ◽  
Peter Tankov ◽  
Laura Tinsi
Keyword(s):  
Nash Equilibrium ◽  
Electricity Markets ◽  
Mean Field ◽  
Optimal Strategies ◽  
Price Formation ◽  
Mean Field Games ◽  
Optimal Trading ◽  
Major Player ◽  
Major Producer ◽  
Small Producers

We study price formation in intraday electricity markets in the presence of intermittent renewable generation. We consider the setting where a major producer may interact strategically with a large number of small producers. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in a closed form in the asymptotic framework of mean field games with a major player.

scholarly journals Mean field games models of segregation

2017 ◽  
Vol 27 (01) ◽  
pp. 75-113 ◽  
Author(s):  
Yves Achdou ◽  
Martino Bardi ◽  
Marco Cirant
Keyword(s):  
Numerical Methods ◽  
Existence Of Solutions ◽  
Large Population ◽  
Mean Field ◽  
Mean Field Games ◽  
Residential Choice ◽  
Urban Settlements ◽  
Thomas Schelling ◽  
Two Populations ◽  
Large Population Limit

This paper introduces and analyzes some models in the framework of mean field games (MFGs) describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games, a large population limit is proved. For differential games with noise, the existence of solutions is established for the systems of partial differential equations of MFG theory, in the stationary and in the evolutive case. Numerical methods are proposed with several simulations. In the examples and in the numerical results, particular emphasis is put on the phenomenon of segregation between the populations.

scholarly journals Mean Field Games Flock! The Reinforcement Learning Way

2021 ◽  
Author(s):  
Sarah Perrin ◽  
Mathieu Laurière ◽  
Julien Pérolat ◽  
Matthieu Geist ◽  
Romuald Élie ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Nash Equilibrium ◽  
Population Distribution ◽  
Mean Field ◽  
High Dimensional ◽  
Mean Field Games ◽  
Fictitious Play ◽  
Mean Field Game ◽  
Best Response

We present a method enabling a large number of agents to learn how to flock. This problem has drawn a lot of interest but requires many structural assumptions and is tractable only in small dimensions. We phrase this problem as a Mean Field Game (MFG), where each individual chooses its own acceleration depending on the population behavior. Combining Deep Reinforcement Learning (RL) and Normalizing Flows (NF), we obtain a tractable solution requiring only very weak assumptions. Our algorithm finds a Nash Equilibrium and the agents adapt their velocity to match the neighboring flock’s average one. We use Fictitious Play and alternate: (1) computing an approximate best response with Deep RL, and (2) estimating the next population distribution with NF. We show numerically that our algorithm can learn multi-group or high-dimensional flocking with obstacles.

scholarly journals Solar Powered Self-Charging Circuit for Mobile Applications

2021 ◽  
pp. 43-47
Author(s):  
Padmashree V Kulkarni ◽  
A Jahnavi ◽  
Madhurya L
Keyword(s):  
Solar Energy ◽  
Electric Vehicles ◽  
Mobile Applications ◽  
Solar Panels ◽  
Environment Friendly ◽  
Solar Powered

Electric vehicles were invented as an alternative to save fuel and to make more environment-friendly vehicles. With the increase in pricing for fuels, all are looking at effective alternatives for fuelled vehicles. Although electric vehicles [EV] are alternatives for our daily means of travel, they have not been very effective with the distance we can travel by fully charging them. The problem with EV is that once fully charged they may run for about 60 km. But considering our society, most of us travel more than 60 km every day. An alternate EV will make a better future. In this project we have aimed at making EVs more efficient and effective for normal usage. We have implemented a prototype of a new circuit with two batteries where each battery works alternatively. Apart from this, we have used solar panels to charge these batteries with solar energy.

scholarly journals On the Convergence of Model Free Learning in Mean Field Games

2020 ◽  
Vol 34 (05) ◽  
pp. 7143-7150
Author(s):  
Romuald Elie ◽  
Julien Pérolat ◽  
Mathieu Laurière ◽  
Matthieu Geist ◽  
Olivier Pietquin
Keyword(s):  
Learning Algorithms ◽  
Large Population ◽  
Single Agent ◽  
Mean Field ◽  
Space Environment ◽  
Iteration Step ◽  
Mean Field Games ◽  
Scalable Algorithms ◽  
Model Free ◽  
Approximate Nash Equilibrium

Learning by experience in Multi-Agent Systems (MAS) is a difficult and exciting task, due to the lack of stationarity of the environment, whose dynamics evolves as the population learns. In order to design scalable algorithms for systems with a large population of interacting agents (e.g., swarms), this paper focuses on Mean Field MAS, where the number of agents is asymptotically infinite. Recently, a very active burgeoning field studies the effects of diverse reinforcement learning algorithms for agents with no prior information on a stationary Mean Field Game (MFG) and learn their policy through repeated experience. We adopt a high perspective on this problem and analyze in full generality the convergence of a fictitious iterative scheme using any single agent learning algorithm at each step. We quantify the quality of the computed approximate Nash equilibrium, in terms of the accumulated errors arising at each learning iteration step. Notably, we show for the first time convergence of model free learning algorithms towards non-stationary MFG equilibria, relying only on classical assumptions on the MFG dynamics. We illustrate our theoretical results with a numerical experiment in a continuous action-space environment, where the approximate best response of the iterative fictitious play scheme is computed with a deep RL algorithm.

scholarly journals Sustainable E-Bike Charging Station That Enables AC, DC and Wireless Charging from Solar Energy

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3549 ◽  
Author(s):  
Gautham Ram Chandra Mouli ◽  
Peter Van Duijsen ◽  
Francesca Grazian ◽  
Ajay Jamodkar ◽  
Pavol Bauer ◽  
...  
Keyword(s):  
Solar Energy ◽  
Wind Energy ◽  
Electric Vehicles ◽  
Wireless Charging ◽  
Inductive Power Transfer ◽  
Photovoltaic Panels ◽  
Charging Station ◽  
Dc Power ◽  
Solar Powered ◽  
Grid Operation

If electric vehicles have to be truly sustainable, it is essential to charge them from sustainable sources of electricity, such as solar or wind energy. In this paper, the design of solar powered e-bike charging station that provides AC, DC and wireless charging of e-bikes is investigated. The charging station has integrated battery storage that enables for both grid-connected and off-grid operation. The DC charging uses the DC power from the photovoltaic panels directly for charging the e-bike battery without the use of an AC charging adapter. For the wireless charging, the e-bike can be charged through inductive power transfer via the bike kickstand (receiver) and a specially designed tile (transmitter) at the charging station, which provides maximum convenience to the user.

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