Table Of ContentJOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 1
Socio-technical Smart Grid Optimization via
Decentralized Charge Control of Electric Vehicles
Evangelos Pournaras, Seoho Jung, Huiting Zhang, Xingliang Fang and Lloyd Sanders
Abstract—Electrical vehicles (EVs) play a key role in the have disastrous consequences on the reliability of power. To
sustainabilityoftheenvironmentastheycontributetothereduc- nullify such threats to power stability, many studies have
tion of carbon emissions and the harness of natural resources.
investigated different charging schemes from centralized op-
However, when the Smart Grid powers the charging of EVs,
timized charging to so-called aggregators that pool together
7 high energy costs and power peaks challenge system reliability
1 with risks of blackouts. This is especially the case when the a number of vehicles and optimize their charging regimes
0 Smart Grid has to moderate additional uncertainties such as under various constraints, e.g. operational levels of grids [2],
2 the penetration of renewable energy resources or energy market [3].Theorganizationofchargingcanhavemultipleobjectives
dynamics. In addition, social dynamics such as the participation
n asidefromthestabilityofthepowergridinfrastructure.These
in demand-response programs, discomfort experienced from
a objectivescanbeconsideredasglobalorlocalobjectives.The
alternative suggested usage of the EVs and even the fairness
J
inthedemand-responseamongtheparticipatingcitizensperplex foremostofwhichisspotpricesavings.Thisistochargeone’s
4
evenfurthertheoperationandregulationoftheSmartGrid.This vehicle when the spot price on the grid is the least. This can
2
paper introduces a fully decentralized mechanism for charging have the implicit implication of also reducing the load on the
control of EVs that regulates three Smart Grid socio-technical grid, if managed appropriately. Studies have also looked into
]
aspects: (i) robustness, (ii) discomfort and (iii) fairness. By
Y EVs as a means of storing reserve power, for example, to
exclusively using local knowledge, a software agent generates
S energy demand plans in each EV that encode different charging lower the volatility of renewable resource energy production,
. patterns. Agents interact to make collective decisions of which and provide back-up supply to the grid [4].
s
c plantoexecutesothatpowerpeaksandenergycostarereduced. Herein this paper proposes a new Vehicle to Grid (V2G)
[ The impact of improving robustness on discomfort and fairness charging paradigm for EVs as a Smart Grid enabler: socio-
1 iosfeEmVppirairctailcliypashtioown.nTuhseinfigndreinagl-swaorreldusdeadtatoupnrdoejrecattvhaerieefdfelcetvoefl technicaldecentralizedoptimizationofEVcharging.Although
v optimizationinafutureforecastingscenariowithmassadoption the means of scheduling through decentralization has been
1 of EVs charged from the Smart Grid. lookedatbefore,e.g.,[5],thisworkisbasedontheEPOS[6]
1
mechanism that finds solutions efficiently for a distributed 0-
8 Index Terms—electrical vehicle, Smart Grid, decentralized
6 system, optimization, charging control, planning, scheduling, 1 multiple-choice combinatorial optimization problem, which
0 robustness, discomfort, fairness, diffusion of innovation is NP hard. EVs are equipped with software agents that
. run EPOS, possibly via demand-response programs of utility
1
companies. Agents compute power consumption plans that
0 I. INTRODUCTION
7 minimize discomfort originated from scheduling and max-
WITH the unavoidable ramifications of climate change
1 imize fairness by design, while collective decision-making
: bearing down upon us, the collective zeitgeist is mov- contributes to lowering power peaks and energy costs. The
v
ing towards using renewable resources, and eliminating usage
i socio-technical measurements introduced here are novel with
X of ubiquitous fossil fuels. Although these notions are wide
very few related studies [7], [8].
r and varied, one progressive step is the elimination of Internal Following up the results of optimization, the future impact
a
CombustionEngines(ICEs)fortransportviaElectricVehicles
of mass EV adoption on the Smart Grid is studied. Namely,
(EVs). These vehicles, instead of running off petroleum and
the adoption diffusion of EVs and their impact given the
diesel, are plugged into the main power grid and charged.
current infrastructure is modeled over time. A measure of in-
Once charged, vehicles have a distance of a few hundred
frastructure lifetime is proposed given the hypothetical uptake
kilometers before needing a recharge. Currently, private EVs
of EPOS app in fractions of the future EV mass.
predominantly charge at home, but more charging stations are
The main contributions of this paper are as follows:
being established.
• Anewmethodologyforasocio-technicalSmartGridop-
It is predicted that by 2025, EVs could have approximately
timization via decentralized charge control. The scalable
22% of the current vehicle market [1], but without investi-
mechanism of EPOS is used for this purpose.
gating the potential impact this could have on existing power
• Understanding how optimization of system-wide objec-
infrastructure, this relatively sudden influx could potentially
tives, e.g. robustness, affect the user discomfort and the
social fairness.
ManuscriptreceivedMonthDate,Year;revisedMonthDate,20XX.
Copyright (cid:13)c 20XX IEEE. Personal use of this material is permitted. • Understanding market penetration of EVs in the future
However, permission to use this material for any other purposes must be and how this will affect the existing power infrastructure
[email protected]
by using a simplified model of innovation diffusion.
Professorship of Computational Social Science, ETH Zurich, Zurich,
Switzerland.E-mail:{epournaras,sejung,zhuiting,fangx,,lsanders}@ethz.ch This paper is outlined as follows: The following section
JOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 2
introduces the decentralized operational planning for EVs.
1 1
Section III illustrates the decentralized decision-making and C C
o0.8 o0.8
optimization process employed. It also defines the measures S S
0.6 0.6
of robustness, discomfort and fairness. Section IV illustrates
the data used for the experimental evaluation and the findings W] W]
from the results. Finally, Section V concludes this paper and k k
outlines future work. er [ 5 er [ 5
w 0 w 0
o o
P Tue 00:00 06:00 12:00 P Tue 00:00 06:00 12:00
Time Time
II. LOCALOPERATIONALPLANNING
Fig.2. PowerconsumptionoftheNissanmodelforWindow3belongingto
This section illustrates how EVs can locally and au-
theplansofFigure1cand1d
tonomouslyplantheirpowerusageinordertoachievevarious
system-wide objectives such as the improvement of system
robustness or the reduction of power costs.
B. Technical Concept
This section elaborates on the proposed the technical con-
cept. Assume a number of n EVs powered by a common
A. An overview
power system. Each EV is characterized by a model m that
This paper introduces the concept of local operational determines features such as the battery capacity and charging
planning of EVs as the means to meet system-wide objectives rate.ProductionmodelsofEVsareearlierreviewed[17].Each
of power grids. The motivation here is that if adjustments in EV is assumed equipped with an agent i that is a software
power demand can be pre-computed and scheduled, opera- application controlling the battery charging. Technology for
tional uncertainties are minimized and more effective regula- such control is available in the market [18]. The agent is
toryactionscanbeappliedunderseveraloperationalscenarios, constrained by a minimum time interval of size m during
e.g., failures of power generators, price peaks, weather events which the vehicle can continuously charge without pause.
influencingtheavailabilityofrenewableenergyresources,etc. EachagentigeneratesasequenceofvplansD =(d )v
i i,j j=1
Planning is well-established approach in literature [9], [10], that schedule for the future period T = |d | the power
i,j
[11]andinseveralrelatedreal-worldapplicationdomains[12], consumption of the vehicle when charging from the power
[13], [14], [15]. grid. These plans may be equivalent for the driver of the
The proposed technical concept concerns a multi-agent vehicle or they may cause different levels of discomfort, for
system for decentralized operational planning of EVs. Each example, each plan may disrupt the regular use of an EV to
EV runs software that can autonomously generates a number a different extent. Each agent i selects one and only one plan
of possible operational plans that schedule the power con- d =(d )T to execute according to a selection function
i,j i,j,t t=1
sumption of the vehicle when charging from the power grid. j = f (D ) ∈ {1,...,v} designed to serve a system-wide ob-
s i
Usually this happens when the EV is parked at home or at jectivesuchastheimprovementofrobustnessorthereduction
work.Eachplanmaycauseavariedlevelofdriverdiscomfort of power cost in the Smart Grid. Robustness concerns how
measured empirically by the likelihood of the plan to be homogeneousthecollectivepowerconsumptionisovertimeso
interrupted by, for example, an unintended traveling event. that power peaks that may cause cascading failures [14], [19]
Agents make coordinated selections of a plan to execute in are prevented or mitigated. Cost concerns the monetary value
ordertocollectivelyimprovetherobustnessoftheSmartGrid, ofthecollectivepowerconsumptiongovernedbythespotprice
while driver discomfort can be measured and self-regulated. signal P =(p )T (USD/kWh) of a power market [20].
t t=1
Figure 1 illustrates the concept of plan generation. Agents Reasoningaboutplangenerationislocallyperformedbased
compute flexibility windows within which their vehicle is on accumulated historic data that represent a typical temporal
usually available to charge. In practice, windows usually pattern usage of the EV and the driver profile, e.g. daily or
correspond to times in which the vehicle is parked at home. weekly usage. These data are referred to as S = (s )T ,
i i,t t=0
During these times, it charges or it is fully charged and where s ∈[0,1] stands for the state of charge (SoC) of the
i,t
does not consume battery. In each window, charging slots vehicle at time t. This signal is used as a seed for the plan
are computed in which a full charging can be performed. generation. The goal of plan generation is to compute several
The agent ranks the slots from low to high according to the ways of charging the EV during times in which the vehicle
likelihoodofvehicleusagecomputedfromhistoricdata.Each is not used, e.g., when the vehicle is parked at home. These
plan uses a varied number of slots within which the charging times are referred to in this paper as the flexibility windows,
is redistributed. W = (S )qi ⊆ S , of an agent i. Algorithm 1 illustrates
i i,w w=1 i
Each EV model has a certain level of power consumption how the windows are computed.
when it charges. The plans redistribute the power usage as The algorithm identifies the times in which the SoC stops
illustrated in Figure 2 for Window 3 that belongs to the states decreasingandstartsincreasing(line3ofAlgorithm1).These
of charge in Figure 1c and 1d. For the illustration, a Nissan timesarethebeginningsoftheflexibilitywindows.Theendof
model equipped with a 6.6 kW onboard charger is used [16]. the windows is detected by the times in which the SoC stops
JOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 3
Window 1 Window 2 Window 3
Slot 1 (Rank: 2) Slot 2 (Rank: 1) Slot 3 (Rank: 3) Slot 4 (Rank: 4)
0.1
(a) il.0.05
Ut
0
1
(b) oC 0.8
S
0.6
1
(c) oC 0.8
S
0.6
1
(d) oC 0.8
S
0.6
Mon 12:00 18:00 Tue 00:00 06:00 12:00
Time
Fig. 1. Plan generation defines flexibility windows within which the SoC increases or does not vary. In each window, severeal charging slots are defined
withinwhichafullchargingcanbeperformed.Slotsarerankedfromlowtohighandaccordingtothelikelihoodofusagecomputedfromhistoricdata.(a).
Likelihood of the vehicle usage derived from historic data. (b). Intended usage of the EV in which charging starts and completes at the very beginning of
eachwindow.(c).StatesofchargeinageneratedplanthatusesSlot2andSlot1inWindow3.Thetwoslotshavethelowestlikelihoodofusage(d).States
ofchargeinageneratedplanthatusesallslotsinWindow3.
Algorithm 1 Computation of flexibility windows.
Require: Si C C
1: w=0; So o OR
S
2: for t=1 to T do
3: if si,t <si,t−1 and si,t <si,t+1 then
4: w=w+1; t-1 t t+1 t-1 t t+1
5: while si,t >si,t−1 and si,t ≤si,t+1 and t<T do Time Time
6: Si,w =Si,w∪si,t
7: t=t+1; (a) Startofwindow (b) Endofwindow
8: end while
Fig.3. Detectionofwindowlimits.(a)SoCisloweratt−1,andhigherat
9: if |Si,w|≥Tc(m,si,x,w) then t+1.(b)SoCisequalorhigheratt−1,andloweratt+1.
10: Wi =Wi∪Si,w
11: else
12: w=w−1;
13: end if
14: end if where bm is the battery capacity of model m (kWh) and rm is
15: end for the charging rate of model m (kW).
Ensure: W , ∀i∈{1,...,n}
i
TheusualoperationofanEVsuggeststhatwithinawindow
corresponding to ‘parked at home’ or ‘parked at work’, the
user charges immediately the EV. This action has significant
increasing and starts decreasing (line 5 of Algorithm 1). This
implications. The power consumption mainly occurs at the
indicates that the EV is again in use. Figure 3 illustrates how
verybeginningofthewindowinsteadofattheend.Giventhat
the start and end of a window are detected. The algorithm
these windows among users have high temporal similarity as
excludes windows that do not have the length for a full
they correspond to user behavior and activity, the aggregate
charging1 (line 9-13 of Algorithm 1). The charging time
energy consumption at the beginning of the windows is
T (m,s ) of model m with SoC s at the beginning time
c i,t i,x,w synchronized among the EVs and results in power peaks that
x of window w is given as follows:
can potentially cause blackouts or increase the energy cost.
b Moreover,asthebatterytechnology[21]improvesbyallowing
li,w =Tc(m,si,x,w)=(1−si,x,w)rm, (1) higherchargingrates,thepowerpeaksareexpectedtobecome
m
even sharper and more dramatic. This section introduces a
1Thealgorithmassumesherethatwindowsoflengthshorterthanthefull modelthattacklesthislimitationbyestablishingki,w charging
charging time are more sensitive to user interruptions and therefore have a slots Q =(S )ki,w within each window w. The number
higheruncertaintywhenusedforschedulingthechargingofthevehicle.The i,w i,w,o o=1
of slots k > 0 is computed by Algorithm 2. Line 2-6
evaluationofthisassumptionwithseveralotheralgorithmvariationsissubject i,w
offuturework. determine the number of slots as follows:
JOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 4
Algorithm 2 Computation of slots number for each window. where T (m,s ) is the charging duration and m is the
c i,x,w
Require: Wi, Tc(m,si,x,w), v minimum time interval that a vehicle can be charged without
1: for all Si,w ∈Wi do pause. The intervals are uniformly distributed across the slots
2: ki,w =|Si,w|/Tc(m,si,x,w) used by each plan. Algorithm 4 illustrates the plan generation
3: if ki,w ≥v then process.
4: ki,w=v
5: li,w =|Si,w|/ki,w
6: end if Algorithm 4 Computation of agent plans.
7: Ki =Ki∪ki,w Require: Si, Ki, Qi,w, Ui, li,w
8: end for 1: for all Si,w ∈Wi do
Ensure: Ki, ∀i∈{1,...,n} 2: Qˆi,w=rank(Qi,w,Ui)
3: for j =1 to j =max(Ki) do
4: Sˆi=shuffle(Si,j,Qˆi,w,li,w,m)
5: di,j =di,j∪di,j,t
(cid:40)|S |/T (m,s ), if k ≤v 6: end for
ki,w = i,w c i,x,w i,w , (2) 7: end for
v, if ki,w >v Ensure: Di, ∀i∈{1,...,n}
where |S | is the size of window w, T (m,s ) is the
i,w c i,x,w
charging time of model m at window w and v determines the The plan generation algorithm iterates over the windows
maximum number of plans with which an agent can operate. (line 1 of Algorithm 4) and ranks the slots of each window
When knowing the number of slots per window, the actual according to the likelihood Ui of vehicle usage (line 2 of
slots can determined according to Algorithm 3. Algorithm 4). The window with the maximum number of
slots corresponds to the number of plans v =max(K ) (line
i
Algorithm 3 Computation of slots. 3 of Algorithm 4). Each plan j is generated by randomly
shuffling z(m,s ) charging intervals over j slots (line 4
Require: W , K , l i i,x,w
i i i,w
1: for w=1 to w=|Wi| do of Algorithm 4). The plan is computed as di,j =di,j ∪di,j,t,
2: for o=1 to o=ki,w do where:
3: for t=x+o∗li,w−li,w to x+o∗li,w−1 do
4: Si,w,o =Si,w,o∪si,t,w,o (cid:40)
5: end for d = em >0, if sˆi,t <sˆi,t+1 ,∀t∈{1,...,T −1} (5)
6: Qi,w =Qi,w∪Si,w,o i,j,t 0, if sˆi,t ≥sˆi,t+1
7: end for
8: end for Therefore, each value di,j,t ≥ 0 of a plan contain the power
Ensure: Qi,w, ∀i∈{1,...,n} and ∀w∈{1,...,qi} consumption em of model m (kW) at time t for the respective
change sˆ to sˆ in SoC.
i,t i,t+1
Plan generation is then performed by redistributing the
III. DECENTRALIZEDDECISION-MAKING
charging of EVs among the slots. A design choice here is
(i) how many slots to use and (ii) which slots to use. Agents employ the EPOS system [6] as a cooperative opti-
The number of slots determines the extent to redistribution, mizationmechanismforchargingEVsinafullydecentralized
inotherwords,howuniformchargingisdistributedovertime. fashion. EPOS has been studied earlier in demand-response
The plans are generated such that the first plan uses one slot, of residential energy consumption [14], [15]. In that scenario,
whereas the last plan uses all v slots. Each plan in between the agents control individual electrical household devices or
uses an additional slot incrementally. the aggregate consumption of the household. In contrast, this
Theslotsusedineachplanaredeterminedbythelikelihood paper contributes a new application of EPOS to Smart Grids
of the vehicle usage U = (u )T extracted from historical and provides fundamental insights on how the charging of
i i,t t=1
data. Based on these data, the slots in each window can be EVs can be modeled as a 0-1 multiple-choice combinatorial
ranked from low to high likelihood of usage. Each plan uses optimization problem.
theslotswiththelowestusagelikelihoodsothatthelikelihood InEPOS,agentsareself-organized[22]inatreetopologyas
of discomfort is minimized. Therefore, the discomfort g of a a way to structure their interactions with which they perform
i
plan can be defined as follows: thecooperativeoptimization.Atreetopologyprovidesacom-
putationally cost-effective aggregation of the power demand
1 (cid:88)T levelrequiredforcoordinatingthedecision-making.Decision-
g = (1−s )u , (3)
i T i,t i,t making is performed bottom-up and level-by-level: children
t=1 interactwiththeirparentandcollectivelydecidewhichplanto
wheresi,tistheSoCandui,tisthelikelihoodofvehicleusage executebasedon(i)theirownplansand(ii)theselectedplans
at time t. of the agents connected to each of their branches underneath.
After determining the slots for each plan, charging in Selection is computationally performed by the parent of the
each window w is performed in zi(m,si,x,w) non-overlapping children that computes the combinational plans as follows:
intervals of m size as follows:
k
z(m,s )= Tc(m,si,x,w), (4) Ci =(ci,j)vj=k1 = (cid:89)Au (6)
i i,x,w m u=1
JOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 5
where the parent agent i performs the Cartesian product We use this GPS data, pre-processed by the survey into
(cid:81)k A tocomputeallcombinationsbetweenthesequences trip profiles. Essentially, they describe each trip made by the
u=1 u
of aggregates plans A ,...,A received by its k children. The vehicle in question, as a destination (home, work, school, or
1 k
child u=1 of agent i is assumed to be the first one and the other), a start/finish trip time, and an average speed. From
child u = k the last one. An aggregate plan a ∈ A is thisdata,amongotherthings,wecananalyzehowvehiclesare
u,j u
computed by summing the plan d and all selected plans of usedonaweeklybasis,giventheirtype.Fromourdatapoolof
u,j
the agents received through the branch underneath child u. 2910GPSmonitoredvehicles,weselecttheEVdatawhichwe
Two selection functions are executed by each parent on pool together with the PHEV data to produce an aggregated
behalfofitschildrenandaredefinedasmeasuresoftheSmart pseudo-EV data pool of 130 vehicles.2 Weekly usage of all
Gridrobustness:(i)MIN-DEVandMIN-COST.Theformeraimsat GPS vehicles in the data set are as shown in Figure 9a.
minimizingthestandarddeviation,σ,ofthetotaldemandasa State of charge and driving profiles: Of interest to us
measure of load uniformity, load balancing and peak-shaving. in this data set is how EVs discharge through usage. With
The MIN-DEV selection function is defined as follows: this knowledge we can measure the various performance
objectivesofthemodelproposedinsectionII-A.Todothiswe
vk calculate the EV state of charge (SoC) (percentage of charge
j =argminσ(c ). (7)
i,j
remaining in EV batteries). As the SoC is can be used to
j=1
characterize the use of the vehicle, it is also known as the
The MIN-COST selection function aims at reducing the total
driving profile. To calculate the SoC, it is deemed sufficient
energy cost by taking into account the temporal energy prices
to a first approximation, to assume that when an EV is in
as follows:
transit, it travels at the average speed calculated in the report.
vk (cid:88)T Inthisapproximateframework,weassumethepowerrequired
j =argmin c ∗p , (8) is proportional to speed, and thus we are able to build a SoC
i,j,t t
j=1 t=1 profile for each EV in the data set.3
EV efficiency is often given in ’miles per gallon’ driven
where p is the energy price at time t.
t
either within the city or on a highway.(For the EV models
This paper studies how the technical aspect of robustness
used in this report, the details are given in Table II – see
mayinfluencehumanandsocialaspectssuchasthediscomfort
below for further explanation.) To find the energy consumed
and fairness respectively. The system discomfort G in the
d
(in kWh) during some outing via the fuel efficiency rating,
system is measured by the average discomfort as follows:
average speed of the vehicle for the duration of the said trip,
1 (cid:88)n we use the following formula:
G = g . (9)
d n i dη
i=1 Etrip = f , (11)
e
Achargingregimeisdefinedasfairifallagentshavethesame
where η = 33.705 kWh/gallon (the conversion in energy
level of discomfort. Fairness increases with the variation of
between gasoline and Joules [25]), d=s×t is the distance
discomfort. Mathematically, it is defined as follows: trip
covered in the journey (s the average speed in mph, and t
trip
the duration of the journey, in hours), and f (in miles/gallon)
G =1−σ(g ,...,g ), (10) e
f 1 n
isthefuelefficiencyofthevehiclemodelforagivenscenario,
where σ(g ,...,g ) measures the standard deviation of the either journeying through the city, or on a highway (see Table
1 n
discomfort values among the agents. II).Asourvehiculartripdatagivesanaveragespeed,weselect
f to be that of the city scenario when the average speed is
e
IV. EXPERIMENTALEVALUATION s≤60 mph, or the highway fe if s>60mph.
From Eq. (11) we can calculate the energy for every trip
This section illustrates the dataset used, the results of the
takenbyavehiclegivenitsmakeandmodel.Wecanthenbuild
decentralized optimization and the future impact of EV mass
up the SoC of the battery as a function of time, knowing its
adoption.
battery capacity, and battery charge rate (Table II).
As the proportionality of power usage is dependent upon
A. Dataset studied the make of the vehicle, we assume that the 130 EVs are split
in the same proportion as the current market share of the EVs
Our experiments are based upon data from the California
[26], [27], Table II.
Department of Transportation’s California Household Travel
Illustration of the functional form of 3 vehicle SoC profiles
Survey for 2010 – 2012 [23]. This survey carries out multiple
from the data are given in Figure 9b.
objectives in relation to transport with respect to household,
Caveat: In section II-B, the model espoused relies on his-
person, and vehicle. For our work we focus on the vehicular
toricaldriverdatatounderstandtheprobabilisticavailabilityof
data, 79011 vehicles. A proportion of the vehicles, 2910, are
thevehiclethroughouttheweek;alimitationoftheCalifornian
fitted with GPS: This monitors vehicles continuously for 7
day period (although not the same seven day period for all
2This balances the trade off of reasonable statistics, with accurate driver
vehicles)withtheresolutionofonesecond(proportionsshown
profilerepresentation.
in Figure 8). 3Althoughmoreadvancedmodelsdoexist,e.g.,[24].
JOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 6
Survey is that the data per vehicle is only a week in length. In weekly optimization, the probability of plan selection in
Therefore, we assume that the data provided by the survey MIN-DEV under 100% participation is on 0.21, 0.17, 0.23 and
is representative of that vehicle’s weekly usage. Although 0.38 for plan 1 to 4 respectively. The respective probabilities
individual vehicles were surveyed at different times, in our changedramaticallyin MIN-COST:0.57,0.30,0.07and0.06.In
calculations we assume that all data is representative and addition, under MIN-DEV the plan with the highest probability
therefore all driving profiles can be amalgamated, and said isplan1(0.31),1(0.28),4(0.33),and4(0.39)foreachofthe
to be from the same week. 25%,50%,75%and100%participationlevels.Therespective
plan with the lowest probability is 3 (0.22), 3 (0.22), 2 (0.20),
Decentralized Optimization and 2 (0.17).
EPOS is implemented in Protopeer [28] and each experi- Figure 6a illustrates the mean discomfort for MIN-DEV, MIN-
ment is repeated 50 times. Each repetition shuffles the agents COST and control data under varied participation level. A
randomly in a binary tree topology. All agents generate 4 discomfortenvelopeisdefinedbytheupperandlowerbounds
plans. Four participation scenarios are evaluated. Each sce- when all agents select plan 4 and plan 1 respectively. This
nario assumes that a subset of the EVs is equipped with the is because the slots used are ranked according to the likeli-
capability to generate plans. The rest of the non-participating hood of usage. Given the plan selections shown in Figure 5,
EVs use the default charging pattern observed in the his- this also explains why MIN-DEV and MIN-COST are positioned
toric data. The four participation levels are 25%, 50%, 75% closer to the lower bound. MIN-COST has on average 19.6%
and 100%. The planning horizon is set to T = 1440 and lower discomfort than MIN-DEV. Moreover, the striking lower
T =10080 that correspond to daily and weekly optimization discomfortofEPOScomparedtocontrolleddataisaresultof
respectively. theplangenerationdesignandtherankingoftheslotsaswell.
An overview of the load curves is given in Figure 10. By taking a careful look in Figure 1, it can be observed that
Figure 4 illustrates the performance of EPOS under MIN-DEV Figure 1b in window 3 has higher discomfort than the plan
and MIN-COST. The performance is measured by the relative of Figure 1c with zero discomfort because of the likelihood
to the control data, decrease in standard deviation and cost of utilization during charging. Moreover, the mean discomfort
respectively. The relative deviation reduction under daily op- for MIN-COST is on average 0.00187, 0.00147, 0.00161 and
timization is on average 50.3%, 53.0%, 41.0% and 23.2% for 0.00170 for 25%, 50%, 75% and 100% participation level. A
25%, 50%, 75% and 100% participation level. Respectively, similar trend is confirmed for MIN-DEV. This means that a low
the relative reduction under weekly optimization is 49.8%, number of participating agents has to make more disruptive
51.9%, 39.81% and 22.5%. The relative cost reduction under decisions to anticipate for the missing contributions of the
daily optimization is on average 48.9%, 34.7%, 23.1% and non-participating agents. The shift of the selection from plan
13.2% for 25%, 50%, 75% and 100% participation level. For 4 under 100% participation level towards plan 1 and 2 further
weekly optimization, the respective cost reduction is 47.0%, justify this finding.
33.4%, 22.0% and 12.8%. Figure 6b illustrates the fairness for MIN-DEV, MIN-COST
and control data under varied participation levels. A fairness
envelope is defined by the upper and lower bounds when all
Daily | 100% Daily | 75% Daily | 100% Daily | 75%
Relative deviation reduction3690000....00000000%%%% DWWaeeieelykk ll|yy 5 0|| 15%000%% DWWaeeieelykk ll|yy 2 5|| 72%55%% Relative cost reduction-369300000.....0000000000%%%%% DWWaeeieelykk ll|yy 5 0|| 15%000%% DWWaeeieelykk ll|yy 2 5|| 72%55%% at02iMhsg.5I0eNe%c3no-r8C,tnes%O5vfiS0esrTrme%hsliieee,sgdcd7hot5epfnpro%alartaftvanaeMeinrrrIn1ndNaeg-o1Dasef0nsE00dVdt.%.h9ipsa9clnpa6oan0mMr,t4Ifi0Noc.i-rr9pDte9.aEs6tpVMi6eo.I,cnNTt0-ilhCv.e9eOev9lSey6mTl.2.ehFAaaaannsisdrifnoma0eni.isr9lnsaa9ervs6seht0srroeaffwngoodesrr
Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat
Day of the week Day of the week
(a) MIN-DEV (b) MIN-COST B. Future forecasting
Fig.4. PerformanceofEPOSundervariedparticipationlevel. For this analysis, we model the possible future impact of
EVs on power infrastructure. As our data is from the state
Figure 5 illustrates the probability of plan selections in the of Californian, we use this state as a case study, where all
performed experiments. The probability of plan selection for auxiliary data is respective to this state.
daily optimization in MIN-DEV under 100% participation is on EV Adoption: From numerous statistics, the number of
average 0.15, 0.12, 0.15 and 0.59 for plan 1 to 4 respectively. sold EVs is growing yearly (see Figure 7 for Californian
In contrast, the respective probabilities for MIN-COST change sales) with a projected penetration in the automotive market
as follows: 0.20, 0.22, 0.14 and 0.46. The higher number of at 22% by 2025 according to various studies [1]. As these
selectionsforplan4ismoresignificantinMIN-DEV.Moreover, vehicles will be sourcing their power from the current and
in daily optimization with MIN-DEV the plan with the highest projected infrastructure, it is important to understand how the
probability is plan 4 (0.55), 4 (0.57), 4 (0.60), and 4 (0.59) adoption of EVs will affect the load on the infrastructure. We
foreachofthe25%,50%,75%and100%participationlevels. model and investigate this scenario in this section. For any
The respective plan with the lowest probability is 2 (0.14), 2 technological advancement that brings a product to market,
(0.13), 2 (0.12), and 2 (0.12). there is a well studied notion of adoption by the public –
JOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 7
1
Plan 1
(a) 0.5
y
it Plan 2
l
bi 0
ba 1 %%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%%
o 5050 5050 5050 5050 5050 5050 5050 5050 5050 Plan 3
Pr 25710 25710 25710 25710 25710 25710 25710 25710 25710
(b) 0.5 Sun 00:00 Sun 12:00 Mon 12:00 Tue 12:00 Wed 12:00 Thu 12:00 Fri 12:00 Sat 12:00 Weekly
Plan 4
-Sun 11:59 -Mon 11:59 -Tue 11:59 -Wed 11:59 -Thu 11:59 -Fri 11:59 -Sat 11:59 -Sat 11:59 Optimization
0 Time
%%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%%
5050 5050 5050 5050 5050 5050 5050 5050 5050
2570 2570 2570 2570 2570 2570 2570 2570 2570
1 1 1 1 1 1 1 1 1
Sun 00:00 Sun 12:00 Mon 12:00 Tue 12:00 Wed 12:00 Thu 12:00 Fri 12:00 Sat 12:00 Weekly
-Sun 11:59 -Mon 11:59 -Tue 11:59 -Wed 11:59 -Thu 11:59 -Fri 11:59 -Sat 11:59 -Sat 11:59 Optimization
Time
Fig.5. Planselectionsundervariedparticipationlevel.(a)MIN-DEV,(ii)MIN-COST.
0.012
rt
o
f
m 0.008 Envelope
o
(a) c
s
di 0.004
n
a Control
e
M
0
1 %%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%%
5050 5050 5050 5050 5050 5050 5050 5050 5050
2570 2570 2570 2570 2570 2570 2570 2570 2570 Min. Dev.
1 1 1 1 1 1 1 1 1
Sun 00:00 Sun 12:00 Mon 12:00 Tue 12:00 Wed 12:00 Thu 12:00 Fri 12:00 Sat 12:00 Weekly
0.995
s -Sun 11:59 -Mon 11:59 -Tue 11:59 -Wed 11:59 -Thu 11:59 -Fri 11:59 -Sat 11:59 -Sat 11:59 Optimization
s
(b) ne Time Min. Cost
r
ai 0.99
F
0.985
%%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%% %%%%
5050 5050 5050 5050 5050 5050 5050 5050 5050
2570 2570 2570 2570 2570 2570 2570 2570 2570
1 1 1 1 1 1 1 1 1
Sun 00:00 Sun 12:00 Mon 12:00 Tue 12:00 Wed 12:00 Thu 12:00 Fri 12:00 Sat 12:00 Weekly
-Sun 11:59 -Mon 11:59 -Tue 11:59 -Wed 11:59 -Thu 11:59 -Fri 11:59 -Sat 11:59 -Sat 11:59 Optimization
Time
Fig.6. DiscomfortandfairnessofMIN-DEV,MIN-COSTandcontroldataundervariedparticipationlevel.Thediscomfortenvelopedefinestheupper(plan
4)andlower(plan1)bounds.Thefairnessenvelopedefinestheupper(plan1)andlower(plan4)bounds.
known as the adoption curve [29].4 The cumulative number the peak power for a given week under different charging
of adopters follows a logistic curve, namely paradigms for different EPOS adoption rates. The results are
given in Table I.
C
S (t)= EV , (12) From these data and the projected sales encompassed by
EV 1+exp(−r [t −t ])
A EV mid Eq. (12), we can approximate the peak power of the pool of
where the cumulative adoption (sales) of EVs as a function of EVs as a function of time:
time, S (t), has a market cap, C, whose inflection point is
EV
given by tmid, and rapidity of adoption rA. If we assume that Ppeak(t)=(cid:37)SEV(t), (13)
the adoption of EVs follows the same adoption curve, given
where (cid:37) is the average contribution of each EV to the peak
thecurrentsalesdata[30],withthefutureadoptiongoalsgiven
power for a given plan. For example, (cid:37) for the control
predictionsgivenbytheCaliforniangovernment[31],[32],we
experiment is given as: (cid:37)=223kW/130EV ≈1.72kW/EV.
model the EV adoption as the dashed line in Figure 7.
GivenEq.(13)wecanthereforeforecasttheapproximateload
From this model of adoption we can assess the impact of
on the grid due to different charging paradigms and adoption
future sales on infrastructure.
rates, a selection of which is shown in Figure 7b. We note
EV Impact: From our experiments on the pool of 130
the peak power usage under the Control paradigm performs
EVsdiscussedabove,weinvestigateacomplimentarystatistic:
poorly relative to the other two paradigms. If we are able to
incentivize100%oftheEVownerstousetheEPOSsoftware,
4This assumes that the innovation of EVs spreads amongst the populace
viaanepidemic-likeprocess. we see that the minimum deviation charging paradigm shows
JOURNALOFLATEXCLASSFILES,VOL.X,NO.X,MONTH20XX 8
TABLEI
AGGREGATEPOWERUSAGESTATISTICSFROMDAILY(D)/WEEKLY(W)OPTIMIZATIONEXPERIMENTSFOR130EVS.’MC’DENOTESMIN.COST
EXPERIMENTS,WHEREAS’MD’DENOTESMINIMUMDEVIATIONEXPERIMENTS.ALLPOWERVALUESAREGIVENINKILO-WATTS.
Measurement MC100% MD100% MC75% MD75% MC50% MD50% MC25% MD25% Control
PeakPower(D) 217.43 119.43 170.83 113.06 145.74 149.75 182.56 181.64 223.00
PeakPower(W) 200.84 121.04 164.50 118.81 141.25 148.34 175.74 184.51 223.00
3 .7 8 %
1,600 3000
120 C ontrol G a so lin e
80 M in. D ev. 100% D ie se l
1,200 M in. D ev. 50%
40 M in. C ost 50% H y b rid 1 2 .5 1 %
Number of PEVs [k] 480000 20010 2012 2014 2016 Peak power [MW]12000000 M in. C ost 100% CEPO HVNthEGeVr 7 7 .6 3 % 0003....96676598%%%%
Cum ulative PEV sales
Cali. G ov. G oals
Projected sales
0
0
2010 2012 2014 2016 2018 2020 2022 2024 2026 2010 2012 2014 2016 2018 2020 2022 2024 2026
T im e [year] T im e [year] Fig. 8. Vehicles by type contained with the California Household Travel
(a) VehicleUsage (b) DriverProfile Surveyfor2010-2012[23].EVdenoteselectricvehicle,andPEH,denotes
Plug-inhybridvehicle.
Fig.7. (a)ShownarethecumulativesalesofEVs(in1000sofunits)within
the state of California from 2011 to 2015 [30], and the mandated sales by
2020, and 2025 for the state (triangular markers) [31][32]. Fitted to these EV Weekday
is a sigmodal curve, often assigned to the diffusion of new technologies in EV Weekend 1.0
Non-EV Weekday
a sector (dashed line). The fitted parameters for Eq. (12) are rA = 0.653 Non-EV Weekend
years−1,C=1.53×106 EVs,tmid=2019years.(b)Weapproximatethe 0.10 0.8
peakpoweronthegridduetoEVchargingforvariousscenarios–seetext.
Weseethatunderbothoptimisationregimes:min.cost,andmin.deviation, Usage 0.6
tpheeakEPpOowSear.lgAosritehxmpepcteerdfo,rtmhesmbeinttiemruthmandethveiaCtioonntrreoglirmegeimpeerfionrmresduthceinbgetsht.e Normalized 0.05 SoC0.4
0.2 Vehicle 1
Vehicle 2
thesubstantialsavingsonpeakpowerovertime.In2025,with Vehicle 3
0.00 0.0
1.5 million EVs, the peak power usage could approach 2573 4 8 12 16 20 24 Sun Mon Tue Wed Thu Fri Sat
Time [hour] Day of Week
MW, whereas with full EPOS adoption, this will be cut by
(a) VehicleUsage (b) DriverProfile
over 46% to 1378 MW.
Fig.9. (a)HowEVsareusedthroughouttheweek–forcomparisonnon-
EVusageisalsoshown.Dataforallvehiclesarebinnedwithinoneminute
V. CONCLUSIONANDFUTUREWORK periods, and frequency of ’occupation’ of the minute is then divided by the
totalnumberofvehicleused.Onenotesthecharacteristicpeaksduringrush
This paper concludes that a socio-technical Smart Grid hoursduringtheweek,usageduringthedayandtheintuitivedaytimeusage
optimization is feasible by decentralized charge control of during the weekend days. The qualitative shape of the curves remains the
same between the vehicle types (EV and non-EV). We pool both EVs and
electrical vehicles. This paper introduces a novel operational
PHEVs from the data into the category ’EV’ shown in this plot. (b) Three
planning mechanism running locally by a software agent in SoCprofilesfordifferentvehicles(allthesamevehiclemodel–TeslaS[33])
each EV. The plans generated minimize user discomfort and overaperiodofoneweek.
social fairness by design as shown in the experimental eval-
uation. Collective decision-making of the executed plans via
thedecentralizedEPOSmechanismcontributestosignificantly APPENDIXB:POWERCONSUMPTION
lower power peaks and energy costs. Moreover, as the partic-
Figure 10 illustrates the demand curves of the EVs under
ipation level increases, discomfort decreases concluding that
daily and weekly optimization with MIN-DEV and MIN-COST.
future demand-response programs with enabling technology
characteristics such as the ones of EPOS can contribute to
publicgoodandcreatefurtherbusinessopportunitiesforutility ACKNOWLEDGMENT
companies and other stakeholders. Moreover, the findings of
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