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Lottery-based resource allocation for plug-in electric vehicle charging

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The near-future penetration of plug-in electric vehicles (PEV) is expected to be large enough to have a significant impact on the power grid. If PEVs were allowed to charge simultaneously at the maximum power rate, the distribution grid would face serious problems of stability. Therefore, mechanisms are needed to coordinate the charging processes of PEVs. In this paper, we propose an allocation policy inspired by lottery scheduling that aims at balancing fairness and selfishness, providing preferential treatment to the PEVs that have a high valuation of the electricity, while guaranteeing a non-zero share of the available power to all the PEVs to ensure fairness.
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Lottery-based Resource Allocation for Plug-in Electric
Vehicle Charging
(Extended Abstract)
Matteo Vasirani
Centre for Intelligent Information Technology
University Rey Juan Carlos
Madrid, Spain
matteo.vasirani@urjc.es
Sascha Ossowski
Centre for Intelligent Information Technology
University Rey Juan Carlos
Madrid, Spain
sascha.ossowski@urjc.es
ABSTRACT
The near-future penetration of plug-in electric vehicles (PEV)
is expected to be large enough to have a significant impact
on the power grid. If PEVs were allowed to charge simul-
taneously at the maximum power rate, the distribution grid
would face serious problems of stability. Therefore, mech-
anisms are needed to coordinate the charging processes of
PEVs. In this paper, we propose an allocation policy in-
spired by lottery scheduling that aims at balancing fair-
ness and selfishness, providing preferential treatment to the
PEVs that have a high valuation of the electricity, while
guaranteeing a non-zero share of the available power to all
the PEVs to ensure fairness.
Categories and Subject Descriptors
I.2.11 [Artificial Intelligence]: Distributed Artificial In-
telligence—Intelligent agents, multiagent systems
General Terms
Algorithms, Experimentation
Keywords
Lottery scheduling, resource allocation, smart grids, plug-in
electric vehicles
1. INTRODUCTION
Plug-in electric vehicles (PEVs) are expected to heavily pen-
etrate the automotive market around the world. Thus the
power grid could be greatly affected by the use of PEVs.
Depending on when (and also where) the PEVs are plugged
in, they could cause serious reliability problems to the local
grid [1], since historically it has not been designed for that
kind of intensive loads.
Research supported by the project “AT” (CONSOLIDER
CSD2007-0022, INGENIO 2010) and “OVAMAH”
(TIN2009-13839-C03-02)
Appears in: Proceedings of the 11th International Con-
ference on Autonomous Agents and Multiagent Systems
(AAMAS 2012), Conitzer, Winikoff, Padgham, and van der Hoek (eds.),
4-8 June 2012, Valencia, Spain.
Copyright c
2012, International Foundation for Autonomous Agents and
Multiagent Systems (www.ifaamas.org). All rights reserved.
In this paper we present an allocation policy inspired by
lottery scheduling that allows multiple PEVs to charge si-
multaneously at different charging rate.
2. ALLOCATION POLICY
We use a model of a local distribution grid composed of a
substation and several charging spots. The substation con-
verts the voltage from medium to low and feeds the charging
spots where PEVs can be plugged in.
Due to the physical limitation of the distribution grid, a
substation is able to provide a certain amount Pof power
(in kW) to the set of charging spots V. The task of the
substation agent is therefore allocating the available power
Pamong the plugged PEVs by setting an appropriate power
supply ωifor each charging spot so as Pi∈V ωiP.
The substation allocates the available power Pusing a
policy inspired by lottery scheduling, a randomised resource
allocation mechanism that has been developed for operat-
ing systems [2]. Since in our problem the resource to be
granted (i.e., the available power P) is infinitely divisible,
the outcome of the allocation is not a single winner, but
the determination of a share of the disputed resource, pro-
portional to the number of tickets, to be granted to each
participant.
Let gbe the amount of base commodity owned by each
PEV, xthe amount of tickets issued by a PEV, and rthe
exchange rate that determines the worth of one ticket in
terms of the base commodity (x=r·g). To be eligible
for receiving a share ωiof the available power P, a PEV
reports the amount of tickets issued by the PEV itself. As
in lottery scheduling [2], the power supply that is provided
to a charging spot with a plugged PEV is proportional to
the worth of the amount of tickets issued by the PEV. This
worth is given by x/r. The computation of the power supply
is carried out according to Eq. 1.
ωi=
xi
ri
·ζi
X
j∈V
xj
rj
·ζj
·P(1)
Although the amount of issued tickets xis set by the PEV,
the exchange rate ris set by the agent that controls the
substation, which is built by the distribution grid operator.
By delaying the update of the exchange rate rtowards the
“true” exchange rate x/g, the PEV is given the possibility of
reporting an inflated amount of tickets. In this way, a PEV
(a) Daily gain (b) Inequality measure
Figure 1: Experimental results
may try to increase its share ωiby inflating the worth of its
tickets so as x/r > g. However, assuming that the PEVs be-
have rationally, all of them would report an inflated amount
of tickets. In this case the outcome of the allocation policy
would be that none of them would actually be able to in-
crease its power supply. This undesired outcome is avoided
if we put a limit to the overall inflation. When more than a
fixed percentage of PEVs report an inflated amount of tick-
ets, the power supply of the inflationary agents is reduced
by the penalisation term ζ.
3. EXPERIMENTAL EVALUATION
The main objective of the evaluation is assessing the differ-
ence, in terms of average utility of PEVs, between our alloca-
tion policy (Lottery) and a uniform policy that equally dis-
tributes the available power Pamong the PEVs (Uniform).
We refer to this difference with the term daily gain, ex-
pressed in e. A PEV is assumed to have an internal combus-
tion engine that can supply driving force when the battery
is depleted. The PEV’s utility function is defined according
to Eq. 2, where pcis the price of fuel (in e/litre), γcis the
internal combustion engine efficiency (in km/litre), and γe
is the electric efficiency (in km/kWh).
u(b) = pc
γcdpc
γc(de) = pc
γcγeb(2)
To assess how fair is our allocation policy, we further con-
sider the outcome of another (theoretical) allocation policy
that assigns all the available power Pto the PEV with the
highest valuation of one unit of electricity (MaxVal). The
outcome of this policy is the same as that of an incentive-
compatible auction that assigns the disputed resource to the
PEV that submitted the highest bid (i.e., the agent with the
highest valuation).
Fig. 1(a) shows the daily gain in a small neighbourhood,
with 10 to 30 plugged PEVs. A PEV owner may gain from
10 to 40 cents of eper day, depending on the number of
PEVs that compete for the available power P. In a year,
this gain can account for more than 140 e. Due to the fact
that different PEVs have different valuations of one unit of
electricity, a uniform allocation does not reward those agents
that value electricity the most. Our allocation policy instead
enables the agents with higher valuations to increase their
share of the available power P.
Even though the allocation policy meets the selfishness of
the PEV owners, it also enforces fairness. To assess the in-
equality of the evaluated policies we compute the standard
deviation of the utility that the PEVs obtain at the end of
charging. Fig. 1(b) shows the inequality measure of the three
allocation mechanisms. As expected, Uniform is the fairest
policy that ensures the allocations with the smallest stan-
dard deviation. MaxVal is the most unfair policy, since the
available power Pis always allocated to the PEV with the
highest valuation, at the expense of the PEVs that, albeit
with a lower valuation, still have energy needs. Lottery falls
in between and tends to approach Uniform when the number
of PEVs in the system grows.
4. CONCLUSIONS
In this paper we put forward an allocation policy inspired by
lottery scheduling to automatically coordinate the simulta-
neous charging of several PEVs. We demonstrated how our
allocation policy is capable of balancing fairness and selfish-
ness: it provides preferential treatment to those PEVs that
value the electricity the most (they can report an inflated
amount of lottery tickets so as to increase their share of the
available power P), while guaranteeing a non-zero share of P
to all the PEVs. The experimental evaluation showed that
our allocation policy always ensures a utility gain compared
to a straightforward uniform allocation, with gains that can
reach up to 140 eper year in some scenarios. Furthermore,
it reduces inequality with respect to a hypothetical alloca-
tion policy that fully assigns the disputed resource to the
PEV with the highest valuation.
5. REFERENCES
[1] K. Clement-Nyns, E. Haesen, J. Driesen. The Impact
of Charging Plug-In Hybrid Electric Vehicles on a
Residential Distribution Grid . In IEEE Transactions
on Power Systems, 25(1), pp. 371-380, 2010.
[2] C. Waldspurger and W. H. Weihl. Lottery scheduling:
flexible proportional-share resource management. In
Proceedings of the 1st USENIX conference on
Operating Systems Design and Implementation, pages
1–11. USENIX Association, 1994.
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Lottery scheduling: flexible proportional-share resource management
  • C Waldspurger
  • W H Weihl
C. Waldspurger and W. H. Weihl. Lottery scheduling: flexible proportional-share resource management. In Proceedings of the 1st USENIX conference on Operating Systems Design and Implementation, pages 1-11. USENIX Association, 1994.