2 research outputs found
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.Comment: 8 pages, 6 figures, keywords: EV charging - Electricity Distribution
Networks - Composite game - Composite Equilibriu
Balancing Traffic in Networks: Redundancy, Learning and the Effect of Stochastic Fluctuations
We study the distribution of traffic in networks whose users try to minimise
their delays by adhering to a simple learning scheme inspired by the replicator
dynamics of evolutionary game theory. The stable steady states of these
dynamics coincide with the network's Wardrop equilibria and form a convex
polytope whose dimension is determined by the network's redundancy (an
important concept which measures the "linear dependence" of the users' paths).
Despite this abundance of stationary points, the long-term behaviour of the
replicator dynamics turns out to be remarkably simple: every solution orbit
converges to a Wardrop equilibrium.
On the other hand, a major challenge occurs when the users' delays fluctuate
unpredictably due to random external factors. In that case, interior equilibria
are no longer stationary, but strict equilibria remain stochastically stable
irrespective of the fluctuations' magnitude. In fact, if the network has no
redundancy and the users are patient enough, we show that the long-term
averages of the users' traffic flows converge to the vicinity of an
equilibrium, and we also estimate the corresponding invariant measure.Comment: 39 pages, 4 figures. Incorporated material on nonatomic potential
games and Braess's paradox; some minor typos have now been correcte