Real-Time Charging Strategies for an Electric Vehicle Aggregator to Provide Ancillary Services

15 Pages·2017·3.01 MB·English

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Lawrence Berkeley National Laboratory
Real-Time Charging Strategies for an
Electric Vehicle Aggregator to Provide
Ancillary Services
George Wenzel1, Matias Negrete-Pincetic1, Daniel
Olivares1, Jason MacDonald2, and Duncan S. Callaway3
1Pontificia Universidad Católica de Chile
2Lawrence Berkeley National Laboratory
3University of California, Berkeley
March 2017

Published in IEEE Transactions on Smart Grid
DOI: 10.1109/TSG.2017.2681961

Please cite as: G.!Wenzel;!M.!Negrete/Pincetic;!D.!E.!Olivares;!J.!MacDonald;!
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Aggregator!to!Provide!Ancillary!Services,"!in!IEEE#Transactions#on#Smart#
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Certification!Program (ESTCP).

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1
Real-Time Charging Strategies for an Electric
Vehicle Aggregator to Provide Ancillary Services
George Wenzel, Matias Negrete-Pincetic, Daniel Olivares, Jason MacDonald, and Duncan S. Callaway
Abstract—Real-time charging strategies, in the context of with volatility above a certain threshold can be diminished
vehicletogrid(V2G)technology,areneededtoenabletheuseof without proper flexibility capabilities [5], [6].
electric vehicle (EV) fleets batteries to provide ancillary services New ways to obtain the required flexibility are under
(AS). In this paper we develop tools to manage charging and
development. According to [7], flexibility is present in gen-
discharging in a fleet to track an Automatic Generation Control
eration (ramping capability), transmission (bottlenecks and
(AGC)signalwhenaggregated.Weproposeareal-timecontroller
that considers bidirectional charging efficiency and extend it to access), demand (demand response, storage and load control)
study the effect of looking ahead when implementing Model and system operation (institutional factors, information and
Predictive Control (MPC). Simulations show that the controller real-time decisions). The idea of exploiting the flexibility
improvestrackingerrorascomparedwithbenchmarkscheduling
associatedwiththedemandsidehasbeenwidelyinvestigated,
algorithms, as well as regulation capacity and battery cycling.
and markets aiming for flexible loads to be serviced by zero-
Index Terms—Electric Vehicles, Resource Scheduling, Ancil-
marginal cost renewable generation have been designed [8],
lary Services, Vehicle to Grid
[9].
One possible way of adding flexibility to power systems
I. INTRODUCTION is through the V2G concept, for which several implemen-
NEW generation, demand, transmission and storage sys- tation projects and impact studies have been reported such
tems are presenting opportunities to increase power as [10], [11]. In the literature, the concept [12], [13] and
system flexibility. To capitalize on these opportunities, algo- impacts [14], [15] of using EVs for grid stabilization have
rithms that coordinate distributed resources need to manage been extensively investigated. Numerous charging strategies
charging cost, efficiency and energy and power constraints. to coordinate the response of EV fleets to provide frequency
This paper focuses on the potential of a subset of flexible regulation services have been developed in the recent years
storage technologies, specifically electric vehicles. [16]–[27]. These strategies can be separated into two main
Increased variability in power generation due to renewable groups: centralized strategies, which use an EV aggregator as
energyintegrationmakesstoragecapacityparticularlyvaluable a middleman between the ISO and the EVs (e.g.: [23]–[27])
[1]. However stationary batteries are currently too expensive and decentralized strategies, which do not use an aggregator
for most grid-tied applications despite their decreasing cost to coordinate individual EV charging commands (e.g.: [16]–
[2], [3]. Electric vehicle (EV) batteries can be used during [22]). While decentralized strategies preserve individual au-
their idle time when parked to extract/inject power from/to thorityoverchargingschedules,centralizedstrategiesallowto
the grid in the same way that stationary batteries might. By reduce the uncertainty over total available power and energy,
creating revenue for EV owners – and lowering the total cost whichsimplifiestheinteractionbetweentheelectricitymarket
ofEVownership–thisvehicletogrid(V2G)frameworkcould and each individual EV as shown in [28]. Furthermore, ag-
provide a cost-effective means to add storage capacity to the gregation is still necessary to fulfill minimum power capacity
grid. requirementsimposedbytheISOtoparticipateintheancillary
Large shares of renewable generation are being integrated services (AS) market.
into the power grid mainly due to environmental concerns In general, centralized strategies provide frequency regula-
and energy supply issues. However, the key characteristics tion services by tracking regulation signals sent by the ISO;
of renewable resources in terms of volatility, intermittency however, it is also possible to follow other objectives, such as
anduncertaintypresentgreatoperationalchallengesforpower reducingtheAreaControlError(ACE)[24].Theseregulation
systems. In particular, power system flexibility, defined as signals may require both extracting and providing power
the capacity to respond to changes in load and generation, from/totheEVfleets,butonlysomepapers[23],[26]consider
becomes critical for systems with large penetration of volatile bidirectionalchargingintheirmodels.Fromtheseworks,only
resources [4]. Some authors show that the value of resources [26] considers charging and discharging efficiencies, applied
to a discrete set of possible charging rates (charging, idle,
GW,MNPandDOarewiththeOCM-LabattheDepartmentofElectrical discharging). On the other hand, most of the works dealing
Engineering at Pontificia Universidad Cato´lica de Chile, Santiago 7820436,
with decentralized charging strategies, (e.g., [17], [19], [21],
Chile(e-mail:[email protected]).DCiswiththeEnergyResourcesGroupat
the University of California, Berkeley. JM is with the Lawrence Berkeley [22])takeintoaccountbidirectionalcharging;however,onlya
NationalLab. fewconsiderbidirectionalefficiencies[17],[19].Nevertheless,
This research was partially funded by the Complex Engineering Systems
thelatterreferencesdonotoptimizetheirchargingcommands
Institute, ISCI (ICM-FIC: P05-004-F, CONICYT: FB0816), the Fondecyt
Grant11140621andUSNSFGrantCNS-1239467. in response to market signals.
2
Due to the short period of regulation signals (4 seconds TABLEI
in CAISO) EV aggregators require fast strategies that enable PARAMETERDESCRIPTIONFORTASKi
themtodistributecharging/dischargingcommandsamongEVs
Parameter Description
in real-time, while achieving the best possible performance
[29]. This has led to the consideration of heuristic algorithms rik Nominaltrajectoryfortimestepk
such as Earliest Deadline First (EDF) or Least Laxity First Eik StateofChargefortimestepk
� ,� StateofChargephysicallimits
(LLF) for this purpose. However, these heuristics can neg- i i
E ,E StateofChargegoalatdeparture
atively impact the performance of the batteries, especially i i
ai,di Arrival/departuretime
when compared to alternative algorithms based on convex pik Charging/dischargingratefortimestepk
optimization formulations, as discussed in [30]. m ,m Charging/dischargingratelimits
i i
Model Predictive Control (MPC) is an optimization-based ⌘i ,⌘i Charging/dischargingefficiency
control method that can be used to track signals for which �ik Laxityfortimestepk
forecasts are available in real-time [31]. In particular, it can
be used by an EV aggregator to track regulation signals,
The development of a modelling framework capable of
as shown in [26], where the authors propose to schedule
handling bidirectional charging resources with efficiency
charging/discharging commands based on a Linear Quadratic
considerations.
Regulator (LQR) that tracks the regulation signal, with only
Thedesignandassessmentofseveralreal-timecontrollers
three possible charging rates.
with different levels of complexity (myopic, heuristic
A practical implementation of the V2G concept is being
based and predictive) and features (e.g., reduction of
demonstrated on an operational fleet at the LAAFB. This
cycling behaviour).
project uses a hierarchical control framework, in which day-
The thorough performance assessment of the proposed
ahead and hour-ahead electricity market participation and
models in comparison with non-predictive benchmarks,
charging schedule are handled by an optimization platform:
via extensive simulations under a range of scenarios,
DER-CAM (Distributed Energy Resources Customer Adop-
for both the regulation signal and the efficiency of the
tion Model) developed at Lawrence Berkeley National Lab-
batteries.
oratory (LBNL). DER-CAM optimizes distributed energy re-
This paper is organized as follows. Section II describes the
sourcesoperationovereconomicandenvironmentalobjectives
models used for the batteries, the task concept and market
[32], [33]. DER-CAM performs a constrained economic opti-
participation. Section III presents the proposed controller and
mization to generate bids for bulk energy and AS markets
the benchmarks. Section IV describes an MPC version of
based on the forecasts of vehicle usage by calculating the
the controller. Simulation results are presented and discussed
vehicles’ state of charge (SoC). However, the time resolution
in Section V, and Section VI explains this work’s main
of DER-CAM’s optimization is not suitable for responding to
conclusions.
uncertainAutomaticGenerationControl(AGC)signalswithin
afewseconds,whichiskeyforachievinganaccurateresponse
to such signals. Scheduling methods must be designed to II. PROBLEMSETUP
allow real-time operation of the fleet, and these methods Intheproposedframework,thefunctionalunitisthebattery,
must distribute power among the vehicles while following an and it must be characterized in terms of a set of parameters.
uncertain AGC signal. Figure 1 depicts a schematic diagram The task concept is used to describe the characteristics of
ofthecontrolhierarchyfortheLAAFBV2Gproject,showing a battery when it is active, and thus can be used within its
the interaction of the real-time distribution developed for physical limits by the EV aggregator to provide frequency
that project with the rest of the project. In previous work regulation services, as opposed to an inactive task. The laxity
[30], a real-time controller based on convex optimization was concept is used as well to describe each task’s flexibility [35].
described,anditwasshownthatbetterresultscanbeachieved
with that controller as compared to some benchmarks. This
A. Tasks and Batteries
control algorithm is currently integrated into the EV fleet
management platform developed by Kisensum, Inc. [34] for AnaggregatorcoordinatingafleetofEVsinrealtimefaces,
the project. ateachtimestepk 1,...,T ,thechallengeoffulfillingthe
This paper develops a framework for designing real-time energy requirements associated with each EV i 1,...,V ,
chargingcontrollerstooperateanEVsfleetparticipatinginthe togetherwiththepowerrequirementsassociatedwiththeAGC
AS market. We extend and refine an earlier conference paper signal.Whilethenominaltrajectory,calculatedbyDER-CAM,
[30] to improve regulation capacity and accuracy in following is a parameter for vehicle i at time k, a feasible trajectory
AGC signals1 as compared with simpler approaches. A set is defined as any path for the SoC of a particular EV such
of different controllers is designed and tested, from which that both physical and scheduling requirements are fulfilled.
the more complex approaches achieve better performance This means that for any vehicle i at time k, its SoC must
(accuracy) and less cycling. In specific, the contributions lie within the interval �i ,�i to respect the limits of the
include: battery.Likewise,eachvehiclearrivesattimeai withaknown
SoC and is scheduled to leave at time d with a minimum
i
1Accuracyisparticularlyrelevantbecauseofperformancepayments. level of energy for the EV to be able to operate normally, so
3
Scheduling Arrival Trajectory Arrival Min SoC Real-time distribution
Departure Departure Max SoC
DER-CAM Trajectory Max Power Power [kW]
Pre- Generation Efficiency
Awards
processing
EV EV
ISO Bids SoC
SoC SoC
SoC [kWh]
AGC signal AGC signal Power [kW]
Fig.1. OverviewofthehierarchicalcontrolframeworkintheLAAFBproject.
E E ,E .Forsimplicity,� E isassumed.There discharged. Let x be the power necessary from a source to
idi i i i i ik
are power limits for the operation of each battery as well, charge the battery of vehicle i with p , and p be the power
ik ik
so the charging/discharging (positive/negative) rate is p necessary from a battery to provide the grid with x . This
ik ik
m ,m . This is illustrated in Figure 2. can be written in a compact way:
i i
⌘ 1 ⌘ 1
Boundaries pik i xik i xik (2)
2 2⌘ 2 2⌘
Nominal Trajectory i i
Real Trajectory
The inverse relationship is defined F p x and can
ik ik
be easily derived from Equation 2.
y
erg Definition2:AtaskTi,canberepresentedbyitsparameters
n
E (mi ,mi ,⌘i ,⌘i ,ai,di,� ,� ,Ei ,Ei ), with states Eik
and � , as described in Table I. The index set of all active
ik
tasks in time step k is defined as Tk i : k ai,di .
Each active task models an EV that is available to provide
m
regulation.
For notation simplicity, vectors are defined in bold symbols
Time
when referring to their components associated with active
tasks:xk xik,i Tk ,pk pik,i Tk ,Ek Eik,i
Fig.2. BatterymodelforEViandfeasibletrajectories. Tk , rk rik,i Tk , and �k, �ik, ,i Tk .
Definition 1: The laxity, � , is defined as the amount of
ik
time left until vehicle i must charge at its maximum charge B. Limits
rate to reach its minimum scheduled State of Charge (SoC)
Ifataskisclosetoitsboundaries,dependingontheenergy
E , at departure time d .
i i state, it is possible that the charging rate may need to be
reduced. The limits that guarantee that no upper or lower
E E
�ik di k i ik (1) boundariesareviolatedfortaskiattimestepkaredenoted�
m ik
i and � , respectively. These limits include all the information
ik
It is common for battery models to consider an efficiency neededtoensurethattheSoCstayswithinphysicallimitsand
scalar 0 ⌘ 1 to account for the difference between the isabletofulfillthetask’sminimumenergyrequirements[30].
powertheyreceivedandthepowertheywereabletotransform
into energy for storage. In the context of bidirectional charg- E E
� min m , i ik (3)
ing,thiseffectmustbeconsideredbothways,asitisshownin ik i �t
Figure3.Whenthepowervariableispositive,thebatteriesare
� E
� min max max m , i ik , 1 � m ,�
ik i �t ik i ik
(4)
Theadditionaltermsof� ,relativeto� ,areonlyrelevant
EVs Batteries pk=⌘+xk Charge Grid when �ik 2. When laxityikis in that rangiek, the lower bound
of p will be pushed in order to fulfill the minimum energy
Discharge ik
pk xk=⌘�pk xk requirement at the time the task ceases to be active, and
saturated by physical limits. Additionally, when aggregating
these expressions for the fleet, the regulation capacity of the
system can be calculated.
Fig.3. Efficiencyofthebatterieswhencharginganddischarging.
R F � , R F �
being charged and when it is negative, the batteries are being k ik k ik (5)
i Tk i Tk
4
Therefore,thefeasibleregulationregionfortimestepkwill trajectories can be understood as a nominal path for the SoC
be defined as the interval R ,R . ofeachvehicle,whichenablestheTFcontrollertoincorporate
k k
information about future arrivals and departures.
For each time step k, the following convex optimization
C. Market Participation
problemreturnstheoptimalpowervector,giventheSoCofthe
LAAFB project is being developed using CAISO’s rules
previous time step E . The proposed controller is defined
k 1
for AS, which take into account both energy and AS when
as TF k :
optimizing the system as a whole. Therefore, the EV fleet
participates, in aggregate, in two markets: the energy market
min ↵ r E ↵ e ↵ pc ↵ pd
and the frequency regulation market2. From these, the ag- pc,pd 1 k k 2 2 k 3 k 1 3 k 1
k k
gregate resource receives a frequency regulation signal every s.t. E E pc pd �t (8)
k k 1 k k
four seconds, which must be distributed among the individual
e pc ⌘ pd ⌘ g (9)
vehicles. This AGC signal g for each time step k has two k ik i ik i k
k
components: a fixed level of generation from the energy i Tk
market award (gEM), and a variable regulation quantity from �k 1 pck pdk �k 1 (10)
k
the hourly AS market award (gkFR). The generation signal pck 0, pdk 0 (11)
g gEM gFR must be followed as accurately as possible
k k k
for different magnitudes of the variable component.
Where standsforelement-wisevectormultiplication,also
The error is defined as the difference between the loads
known as the Hadamard product. In the formulation of TF
associated with the vehicles and the generation signal:
controller, due to the non-convex relationship between p and
k
x (Equation 2), we split the power variable in the EVs’ side
k
ek xik gk (6) into charging (pc) and discharging (pd) power, given that one
i Tk of them is 0. We relaxed the non-convex constraint pc pd
k k
Thus, to maximize the performance, e must be mini- 0, and added a penalty for the variables so that the solution
k
mized. The relevant metric is the Accuracy, defined next. fulfills that requirement. This penalization also achieves non-
aggressive control moves, thus reducing the cycling of the
T T batteries compared to other benchmarks.
Accuracy: 1 e gFR (7)
k k The real-time Trajectory Following (TF) controller consists
k 1 k 1 of an objective function that sums three terms with different
This metric is tied to payments for AS providers, which purposes: (1) tracking the SoC trajectories, (2) following
according to FERC’s order 755 [36], are proportional to the AGC signal and (3) penalizing the power variables for
capacity and performance, which was already adopted by feasibility, with strictly positive penalties ↵ ,↵ ,↵ . As for
1 2 3
CAISO’s AS market [37]. the constraints, Eq. 8 represents the dynamics of the batteries,
Eq. 9 represents the error in following the AGC signal and
III. MYOPICCONTROL Eqs. 10 and 11 bound the decision variables.
Ifefficiencies⌘ ,⌘ are100%,theoptimalsolutionalways
A myopic or short-sighted controller is presented, along
requires that pc pd 0 k. When they are lower, it can be
with benchmarks that use simpler approaches. The ease of k k
shownthattheconstraintalsoholdswhenasufficientcondition
implementation is a relevant subject, so it will be useful to
is fulfilled. Then, a convex relaxation based on tuning the
compare simulation results.
penalties in the objective function is described in Theorem 1.
Proof of this is presented in Appendix A.
A. Trajectory Following (TF)
Theorem 1. If the penalties ↵2,↵3i are such that:
The proposed TF controller relies on previously calculated
reference trajectories rk for the SoC of each EV in a fleet, ↵ ↵ 1 ⌘i ⌘i i,
3i 2
considering their departures and arrivals, made by an external 2⌘
i
optimizer (DER-CAM [32]). It takes as an input the reference
SoC trajectories, and reschedules at each operational time theoptimalsolutiontoTF k willsatisfypcik pdik 0 i Tk.
the actual charging trajectory for each vehicle in order to The rationale behind Theorem 1 is intuitive: there should
achieve the frequency regulation requirements, given by the be a threshold for the penalties of the control moves above
realization of an AGC signal that tells the fleet which instan- whichitisnotoptimaltochargeanddischargesimultaneously,
taneous aggregated power input/output it should have. These becauseitwouldimplyahighercostfortheobjectivefunction
prespecifiedtrajectoriesarecalculatedbasedonoptimizingthe while not making the fleet response more accurate. If there
participationofthefleetinthefrequencyregulationmarketand was no penalty for pc and pd, the controller could do double-
the charging of each EV under a retail electricity tariff. The charging (pc pd 0) if it implied better accuracy.
k k
It should be noted that TF controller will provide a fast
2Whiletheresourcesettlesitselectricitycostsattheretailprice,inorder and feasible solution due to its convexity. Evidence suggests
to effectively participate in frequency regulation, the EV fleet must create a that if pc pd 0 k constraint is included by using
baseline electricity consumption on which it will regulate around, which is k k
doneinthewholesaleenergymarket. binary variables instead of tuning the ↵3 penalty according
5
to Theorem 1, the results of the non-convex problem are the constraint with the future E as a variable is not a problem,
ik
same as in the convex problem, but computation time grows due to its concavity, but including the lower bound constraint
significantly. would imply using a nonconvex expression as a lower bound:
A relevant subject for the implementation of the algorithm
is how to tune the penalties. Due to the direct impact of e
k � E
ontheAccuracyresults,↵2 shouldbetunedasalargepenalty pik min max max mi , i �t ik , 1 �ik mi , �ik
relative to ↵ (given that E is always achieved).
1 i concave
convex
(12)
B. Benchmarks In the myopic problem, this constraint’s objective was to
fulfill the task’s minimum energy requirements at departure,
TobenchmarktheperformanceoftheTFcontrollerwecon-
which can also be achieved by transforming the laxity part
sider two methods from the Processor Time Allocation (PTA)
of the lower bound for power into an energy constraint, so
literature that have been applied to electric load scheduling
that the MPC problem is convex. For energy constraints to
[35], as well as version of the TF controller that assumes
work, efficiency effects must be fully considered by the MPC
100% round trip battery efficiency, all of which are applied
controller in the time steps along the forecast horizon, so that
in a sequential optimization simulation. In addition, a time-
the SoC can be properly estimated. Before formulating the
invariant benchmark was used.
MPC problem, some additional definitions are necessary:
1) Earliest Deadline First (EDF): EDF creates a priority
list based on the departure time of the tasks, and therefore Fk k,...,k N .
gˆ is the forecast for the AGC signal in period j, made
willallowvehicleswiththelatestdeadlinestoremainatalow jk
in time step k.
SoCuntilsufficientresourcesareavailabletochargethem.We
g , if j k
adapt this algorithm for discharging by coordinating vehicles g˜ k
j
such that those with the latest departure times are discharged gˆjk, if j k
first. Bold symbols must now include all tasks that may be
2) Least Laxity First (LLF): LLF creates a merit order list active in the forecast horizon: i j FkTj .
sorted by laxity (see Eq. 1), and therefore will allow vehicles For simulation purposes, the SoC of inactive tasks has to
with larger laxity to remain at a low SoC until sufficient be updated using a previously calculated vector for the power
resources are available to charge them. Similarly to EDF, we variable. This represents the energy used by the EVs when
adaptthealgorithmfordischargingsuchthatthevehicleswith they are not grid connected, and the values for E must be
i
the highest laxity are discharged first. consistent with that vector. Thus, the MPC problem solved
3) Trajectory Following with approximate battery state for each time step k, with feasible region , is defined as
k
Z
(TFAPPROX): We remove the nonconvexity that results from TFMPC k :
bidirectionalchargingbymakingtheapproximationp x
ik ik
in the battery dynamics equation. However, the quality of the min ↵ r E ↵ e ↵ pc ↵ pd
1 j j 2 2 j 3 j 1 3 j 1
approximation degrades with declining efficiency. pc,pd
j j j Fk
4) Time-invariant Trajectory Following (Oracle): We de-
veloped an Oracle benchmark that solves the complete run s.t. Ej Ej 1 pcj pdj �t j Fk (13)
time at once. This additional benchmark provides a best-
possible-performance case. ej pcij ⌘i pdij⌘i g˜j j Fk (14)
i Tj
m pc pd m , (15)
IV. MODELPREDICTIVECONTROL Zk i ij ij i
pc 0, pd 0, (16)
This section will explain how to extend the TF myopic ij ij
controllerbyimplementingapredictivecontroller.Weemploy �i Eij �i , (17)
model predictive control, which takes into account not only Eij Ei di j mi �t i Tj, j Fk (18)
the present current state of a system, but also its forecasted
states over a finite time horizon (of length N), when making
The terms in objective function of the real-time MPC
a decision. The underlying motivation is that MPC should
controller have the same meaning as in TF. As shown in
allowthealgorithmtoachievebetterAccuracy,becauseitwill
Theorem 1, properly tuning the penalties ↵ ,↵ is critical
consider the EV arrivals and departures as well as a forecast 2 3
for satisfying the pc pd 0 constraint.
of the AGC signal when deciding how to update the SoC of k k
The constraints consider (1) the dynamics of the batteries
the vehicles.
(Eq.13),(2)thepresentandfutureerrorinfollowingtheAGC
signal (Eq. 14) and (3) the feasible set for both the power
A. Trajectory Following with Model Predictive Control
variables and the energy state (Eqs. 15 to 18). The purpose
(TFMPC)
of Eq. 18 is twofold. First, it is needed to ensure that the
A first approach to use MPC with TF would be to sum up task’s minimum energy requirements are fulfilled. Second, it
the objective function values, while interpreting the bounds acts as a terminal constraint to ensure the feasibility of the
�ik, as functions of the SoC. Including the upper bound MPC controller, regardless of the length of Fk.
6
B. AGC signal forecast Accuracy, ⌘= 0.92
1
Asmentionedearlier,thegenerationsignalgk hasarandom 0.98
component gFR. As this paper handles uncertainty with the 0.96 EDF
k 0.94 LLF
MusPinCgaapnpAroRacIMh,AseqaupepnrotiaaclhfowreicthastthsearienfcoornmsaidtieornedavfoarilgabkFlRe ubpy Accuracy000..89.982 TTTFFFAMPPPCR AORXIMA Fcast
toeachtimestep.ThisassumesthatgFRisazero-meansignal, 0.86 TFMPC Perfect Fcast
whichmaynotbetrueinrealapplications(whendefiningdrive 0.84 Oracle
0.82
cycles,non-zeromeanscanbecompensated[38]).Tocompare
0.8
0 50 100 150 200 250
results, a comparison was made between simulations with an
AGC Magnitude (kW)
(1) an ARIMA forecast and a (2) a perfect forecast. Accuracy, ⌘= 0.85 Accuracy, ⌘= 0.8
1 1
0.98 0.98
C. Operational capacity limits 0.96 0.96
0.94 0.94
oLfeTtthhCeekrfle,eC¯aekrtemsaoym0,be1ecladimseenistoetidenbtwhyeheixclohowgteehrneoauinnsdpsuuytps/otpeuemtrpuoctpoencrdaaipttiaioocnnitasyl. Accuracy0000...889.9682 Accuracy0000...889.9682
¯
capacity limit at time step k, respectively, as a fraction of the 0.84 0.84
0.82 0.82
originalregulationcapacityofthefleet.Inordertoaccountfor 0.8 0.8
0 50 100 150 200 250 0 50 100 150 200 250
this limitation in the MPC problem, the following constraint AGC Magnitude (kW) AGC Magnitude (kW)
is included for each time step k:
Fig.4. Accuracyfordifferentalgorithms,AGCsignalmagnitudesandbattery
C m pc pd C¯ m (19) efficiencies⌘ 0.92,0.85,0.8 .Meanforallseeds.
¯k i ik ik k i
i 1,...,V i Tk i 1,...,V
TABLEII
V. NUMERICALRESULTS AVERAGEACCURACYFOREACHALGORITHM,RELATIVETOORACLE
The data set used in our numerical simulations is the
Oracle TFMPCPerfect TFMPCARIMA TF TFAPPROX LLF EDF
same as in [30], with a fleet of 18 EVs, with a maximum
100% 99.38% 99.31% 99.03% 98.43% 95.87% 94.61%
regulation capacity of 15 kilowatts [kW] per vehicle, and a
runtimeoftwodayswithtimestepseveryfiveminutes,during
which the number of available vehicles changes according
⌘ 0.92, the effective plugged in power capacity of each EV
to a fixed task schedule. TFMPC used a forecast horizon of
is 13.8 [kW], and sorting the performance of the algorithm
N 10. Simulations were run using the MATLAB toolbox
and its benchmarks gives the following list: (1) Oracle, (2)
YALMIP[39]alongwiththesolverGurobi[40].Thevariable
TFMPC Perfect Forecast, (3) TFMPC ARIMA Forecast, (4)
component of the generation signal, gFR, was simulated as
k TF, (5) TFAPPROX, (6) LLF, and (7) EDF. The Accuracy
an ARIMA time series for simulation purposes, based on
resultsforLLFandEDF,theonlyalgorithmsthatdonottrack
historicaldataforPJM’sregd testsignal,meanttobeusedfor
predefined SoC trajectories, are noticeably worse than for the
fast regulation resources such as EV batteries [41]. For each
other algorithms, for all the magnitudes of the AGC signal;
time step, a forecast was made with the information of past
fortheremainderofthealgorithmstheperformanceissimilar.
realizations of the AGC signal.Input data were obtained from
When the efficiency of the batteries is decreased to ⌘
PJM’sASwebsite[42],wherenormalizeddynamic(regd)and
0.85, the effective plugged in power capacity of each EV is
traditional (rega) regulation signals are provided from seven
reduced to 12.75 [kW], and the performance of all the algo-
daysinMay2014.Thedynamicregulationsignalwasusedfor
rithmsdegradesbutkeepsthesameorder.Inpercentageterms,
thisexperiment.Intermsofcomputationtime,thesimulations
EDF and LLF are farther from the rest for low magnitudes of
wereruninona2.5GHzIntelCorei5-3210Mprocessor,and
theAGCsignal,andcloserforhighmagnitudes.Thishappens
theTFMPCalgorithmwithN 10(themostcomputationally
because the benefits of trajectory following are greatest when
expensive) took always less than 0.1 seconds to be solved.
real SoC trajectories are close to the reference trajectories –
whichhappenstobewhentheAGCmagnitudeissmallest.On
A. Accuracy results the other hand, when the AGC signal is large, the difference
All of the proposed versions of the algorithms were tested between real and reference trajectories is inevitably large –
with six different test AGC signals and the Accuracy results therefore reference trajectory following provides little benefit
were averaged. These represent the performance of each relative to EDF and LLF.
algorithm. Figure 4 shows the results for different magni- Finally, when ⌘ 0.8, the effective plugged in power
tudes of the AGC signal and different battery efficiencies capacity of each EV is reduced to 12 [kW], and the
(⌘ ⌘ ⌘). Note that the AGC Magnitude value is a tendency described in the former paragraph is confirmed:
higher bound for the signal’s absolute value. Table II shows a Earliest Deadline First (EDF) and Least Laxity First (LLF)
comparison of the accuracy performance of each controller, show bad performance for low Automatic Generation Control
relative to the Oracle case. The results must be discussed (AGC)magnitudes,buttheirperformanceforhighmagnitudes
separately depending on the efficiency of the batteries. When comparedtotheotheralgorithmsissimilar,duetothelimited
7
benefits to reference trajectory following when real trajecto-
ries are substantially different (as described in the previous 1 1
Oracle
paragraph). Note that both TFMPC options achieve Accuracy 0.95 MMPPCC ffccaasstt ApeRrIfMecAt 0.95
TF
results that dominate over all the non-predictive algorithms. 0.9 TFAPPROX 0.9
Timhpesroevaer,ewclhoiscehtcootuhledObreacdloen’se,bwuitththleornegiesrsftiolrlescoamstehrooroimzontos Accuracy00.8.85 ELLDFF Accuracy00.8.85
and more accurate forecasts. Without delay
0.75 0.75 With delay (improved)
1) Effect of exogenous system limitations: A case study With delay
was performed for the TFMPC ARIMA controller with the 0.70 50 A1G00C Mag1n5i0tude (k2W00) 250 0.70 50 A1G00C Magn15it0ude (k2W00) 250
additional constraint (Eq. 19), where Ck C¯k 0.5 k (a) Accuracy of different algorithms (b) Accuracy of anticipative TFMPC
¯
20,80 , for ⌘ 0.92. The results in Figure 5 show how the withdelay ARIMAwithdelay
controllerstrugglestotracktheAGCsignalduringanepisode Fig. 6. Delay effect on the response of the fleet. (a) Results for different
of system limitations which translates into a tracking error. algorithms, AGC signal magnitudes and fixed battery efficiency ⌘ 0.92.
Meanforallseeds.(b)AccuracyachievedbyMPCfcastARIMAalgorithm,
Mild congestion episodes for short periods of time could be
for different AGC signal magnitudes and fixed battery efficiency ⌘ 0.92.
Meanforallseeds.
W)
200 200 k
kW) mit ( B. Regulation capacity results
AGC Signal (-200 0 -02 0 0Congestion Li rthanaWtgeteheodfeflfipenoewetcetarhneinpfrewoavhsiiidbcehleraergeggueulnaletairtoaiontinownrietshgiginononalergRrkokr,s,hwRohkuilldealbsieeitnhsgoe
able to fulfill the minimum energy requirements.
20 40 60 80 100 120 140
Outside the feasible region, the algorithms with a myopic
approach behave differently than TFMPC. For myopic algo-
Without congestion
200 With congestion rithms, their behavior is easy to understand: in that situation,
W) all the difference between g and the fleet’s capacity to
k
k
or ( 0 provide regulation results in error. In contrast, the look-ahead
Err characteristic of the latter provides other possibility. TFMPC
-200 algorithms may choose to save battery energy in a given
time step, resulting in avoidable error in the short run in
20 40 60 80 100 120 140
favor of reducing long-run error to minimize total error. This
Time steps (x5 min)
emphasizes the relevance of properly tuning the parameters
↵ ,↵ ,↵ inawaythatthesystemmakesdesirabledecisions
Fig.5. Effectofexogenoussystemlimitations.Limitingthecapacityofthe 1 2 3
fleettorespondtotheAGCsignalreducesaccuracyintheresponse. in the face of these trade-offs. The results for R and R are
shown in Figure 7.
anexampleofexogenoussystemlimitationsthattheproposed When sorting the algorithms by the width of the mean
AGC controllers can handle. However, in general, limitations feasibleregulationregiontheyachieved,ingeneraltheorderis
associated with distribution congestion should be addressed the same as in the ranking shown for Accuracy (not including
by modifying the reference signal (gEM), before the action Oracle).
of the AGC controller. In the case of the LAAF project, this As for R results (charging capacity), TF approaches
task should be performed by the DER-CAM stage, as shown achieve better levels than EDF and LLF in all cases, which is
in Figure 1. another benefit of tracking SoC trajectories. As the system
2) Effect of delay: Figure 6a shows the accuracy of the receives AGC signals with higher magnitude or uses less-
different control algorithms for the case with a delay of 1/10 efficient batteries, batteries get drained, and therefore R
of an AGC time-step. It can be observed that the accuracy increases because there is more room for the batteries to get
is reduced between 10-15% for all the algorithms, and for charged.
different magnitudes of the AGC signal, when compared with On the other hand, R (discharging capacity) is the real
thecasewithoutdelay(seeFigure4).Nevertheless,theresults bottleneck of the system for large AGC signals, because the
still show a superior performance of MPC-based controllers battery SoC is typically well below what is required to follow
over non-predictive algorithms for the case of delayed fleet the AGC signals. Furthermore, minimum energy requirements
response. An improved performance can be obtained using atatask’sdeparturealsoconstrainthedischargingcapacityof
the predictive feature of MPC controllers to anticipate the each EV. Results for R are similar to the Accuracy results
AGC signal for a known, constant delay. In particular, Figure when sorting the performance of the algorithms, except for
6b shows the case in which the TFMPC ARIMA controller TFAPPROX when ⌘ 0.8; the bad quality of the p x
ik ik
anticipates the delay of the response to the AGC signal by approximationdirectlyimpactsthedischargingcapacityofthe
implementing its predicted response, achieving approximately batteries. It is clear that implementing MPC improves the
a 3% increase in accuracy with respect to the non-anticipative capacity of the EV fleet to discharge its batteries, and this
case. effect is magnified and therefore can be seen more clearly