Self-regulating Supply-Demand Systems

2.9 MB·

by  Evangelos Pournaras

Self-regulating Supply-Demand Systems
EvangelosPournarasa,MarkYaob,DirkHelbinga
aProfessorshipofComputationalSocialScience
ETHZurich,Zurich,Switzerland
{epournaras,dhelbing}@ethz.ch
bSmartEnergy
IBMT.JWatsonResearchCenter
YorktownHeights,NYUSA
[email protected]
Abstract
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1Supply-demand systems in Smart City sectors such as energy, transportation, telecommunication and others, are subject of rev-
0olutionary technological transformations with implications for the effectiveness of traditional regulatory practices. Can existing
2regulatory actions capture the new dynamics and opportunities that Internet of Things technologies bring to supply-demand sys-
n tems? Regulatorydecision-makingbygovernmentalofficers,policymakersorsystemoperatorsisusuallylong-term,operationally
aoffline and top-down. Such decisions may turn out to be ineffective or may even come in conflict with automated, online and
J
bottom-up decisions nowadays performed, on behalf of people, by software agents embedded in the physical assets of modern

6supply-demand systems, e.g. Smart Grids. This paper contributes a generic decentralized self-regulatory framework, which, in
1
contrast to related work, is shaped around standardized concepts and Internet of Things technologies for an easier adoption and

applicability. An evaluation methodology, integrated within this framework, is introduced that allows the systematic assessment
]
Yof optimality and system constraints, resulting in more informative and meaningful comparisons of different self-regulatory set-
Stings. Evidence using real-world datasets of energy supply-demand systems confirms the effectiveness and applicability of the
.self-regulatory framework. It is shown that a higher informational diversity in the options, from which agents make local selec-
s
ctions, results in a higher system-wide response and savings under different regulatory scenarios. Several strategies with which
[agentsmakeselectionscomealongwithstrikingmeasurabletrade-offsbetweenresponseandsavingscreatingavastpotentialfor

1 radicalonlineadjustmentsincentivizedbyutilities,systemoperatorsandpolicymakers.
v
Keywords: self-regulation,supply,demand,SmartCity,InternetofThings,SmartGrid,optimization,agent,tree
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41. Introduction supply and demand in different regulatory scenarios by steer-
0 ingthepriceelasticityofdemandinafullydecentralizedfash-
. Regulating supply-demand systems in techno-socio-
1 ion? (ii) How to continuously measure and evaluate this self-
0economic sectors of Smart Cities, such as energy, trans- regulatorycapabilityindifferentregulatoryscenariosofsupply-
7portation, telecommunication, financial markets and others,
demand systems? Regulatory scenarios refer to the mitigation
1is a complex, yet critical endeavor for societal development
of imbalances in supply-demand originated from varying gen-
v:and sustainability. Regulation usually implies government- eration and/or consumption, system failures, system reforms,
iimposed controls on business activities and infrastructural
X etc. Thispaperstudiesthebalanceofsupplyanddemandwith
operations [1], in which decison-making by the involved
a fundamental, yet highly applicable approach by introducing
ractors is often centralized and operationally offline. However,
a a minimal and standardized information exchange. This ap-
the introduction of Internet of Things technologies [2] in
proach does not require major system interventions and can
supply-demand systems suggests a new required type of
makeaself-regulationmechanismapplicableinvariousSmart
participatory regulation, designed to operate in an automated,
Citysectors.
online and distributed fashion as a result of the inter-temporal
nature of supply and demand [3]. For example, the regulation How to balance supply-demand or how to design efficient
of electricity prices used to be a result of institutional and computational markets remains a fascinating challenge for a
legalpolicydesignsstrictlyimposedinatop-downfashion. In very broad range of scientific communities. Most remarkably,
contrast,SmartGridtechnologiesenableregimeswithinwhich game-theoretical approaches in combinatorial games are rele-
bottom-up price formation can be automated via real-time vant in systems in which agents have a finite number of op-
pricing schemes and tariffs that continuously balance supply tions to choose from and each choice influences the evolution
anddemand[4,5,6,7]. and outcome of the game. Although mathematical tools ex-
This new type of online bottom-up self-regulation imposes ist for solutions to particular problems [8], there is no uni-
twograndscientificchallenges: (i)Howtoeffectivelybalance fied theory or framework addressing combinatorial elements
PreprintsubmittedtoFutureGenerationComputerSystems January18,2017
inthesegames. Thisobservationusuallycharacterizesmatch- awell-establishedstandardizedconceptandimplementedtech-
ing mechanisms [9] and learning techniques that have at least nology in real-world supply-demand systems of Smart Cities.
the following limitations in applied contexts: (i) long con- Table A.1 in Appendix A outlines all mathematical symbols
vergence times [10, 11] that can make them inapplicable in usedinthispaperintheordertheyappear.
practice due to technological limitations, e.g. communication
bandwidth or computational capacity. (ii) Solutions have of- 2.1. Overview
tenalimitedscope,meaningthatequilibriumisnotguaranteed
Figure 1 introduces a framework for the self-regulation of
with a minor problem modification or when adding/removing
supply-demandsystemsinvarioustechno-socio-economicsec-
aconstraint[12]. Forexample, theliteratureoncertaingame-
torsofSmartCities. Eachphysicalassetofsupplyanddemand
theoreticalapproachesinSmartGridsrevealsthelimitedappli-
isrepresentedandmanagedbyasoftwareagent. Theagentfa-
cabilityofcooperativegamesanddynamicmodelstotacklethe
cilitatestheself-regulationlogicandrepresentssocialoroper-
pervasivepresenceoftime-varyingparameterssuchasgenera- ationalrequirementssuchasthetype/amountofresourcessup-
tionanddemand[12]. Moreover,itisalsoshownthatnetwork
pliedanddemanded.
delays may lead to incorrect price inquiries. A similar con-
clusionissharedwithinotherrelatedwork[13]claimingthata
Provision Evalua.on
highlyresponsiveandnon-disruptiveregulatorysystemforload (5) UB
requiresdirectcentralizedcontrolbyutilities[13]. - CoMnsetarna ints in Demand --   RSaevsipnogns se
-  Mean & vola2lity -  Mean & vola2lity error
This paper contributes a novel and generic self-regulatory
framework for supply-demand systems. A single-commodity (4) TIS (4) iTFS (5) iTFS (5) eTFS
resource-oriented equilibrium market [9] resembles the opera-
(6) Metrics
Incen.viza.on
tionsoftheproposedself-regulatedsupply-demandsystemthat
- TIS genera2on
interacts with a loop of (i) incentive signals that communicate
(1) iTFS
supply costs and (ii) feedback signals that communicate the
Supply
(3) eTFS
demand acquired. Agent-based bilateral interactions are per- Feedback
formedinthebackgroundofabottom-upcomputationalmech- Loop (2) TIS Demand
anismadvancedtooperateinthisgenericcontextofdistributed Self-reg ula.on . . .
supply-demand systems. This mechanism self-regulates the EPOS
balanceofsupplyanddemandinasimilarfashionwiththein- --   SPelalenc g2eonne fruan2co2no n . . .
tuitiveparadigmofAdamsSmith’s‘invisiblehand’[15]. Reg-
Figure1:Aself-regulatoryframeworkforsupply-demandsystems.
ulation becomes an emergent system property [16], originated
fromreconfigurableinteractionsandadaptivedecision-making
Self-regulation aims at balancing supply and demand under
structured over a self-organized tree topology. Earlier work
various operational scenarios and constraints, such as keep-
motivatestheadoptionoftreestructuresincomputationalmar-
ing demand within a certain range, distributing demand fairly
ketsandsupply-demandsystems[17,14,18],however,thepro-
among consumers, or supplying a minimum amount of re-
posedframeworkdoesnotexcludetheadoptionofothermech-
sources to each consumer. Self-regulation is based on two
anismsandstructures[19].
typesofinformationsignals: (i)incentivesignalsand(ii)feed-
Evidenceusingreal-worlddatasetsofenergysupply-demand
backsignals. Theincentivesignalisthepriceforeachunitof
systems confirms the effectiveness and applicability of the
resource supplied. The feedback signal is the amount of de-
framework in a broad spectrum of regulatory scenarios. The
mand requested based on the incentive signal provided. Self-
implications of informational diversity in consumers’ options
regulation is governed by a feedback loop: agents coordinate
but also the actual consumers’ selections are studied by quan-
demand in a fully decentralized fashion to collectively form a
tifyingtheregulatorycapabilitywithtwometricsreferredtoas
feedback signal as a response to a given incentive signal. A
‘response’ and ‘savings’. A novel characteristic of these met-
new incentive signal is potentially formed to further steer an
rics is that they are relative to different upper bounds. This
improvedfeedbacksignal.
allows the systematic evaluation of optimality and constraints
resulting in more informative and meaningful comparisons of
different self-regulatory settings. Findings show striking mea- 2.2. Transactivecontrol
surabletrade-offsbetweenresponseandsavingscreatingavast This framework is far beyond conceptual. Regulating sup-
potentialforradicalonlineadjustmentsincentivizedbyutilities, plyanddemandwithincentiveandfeedbacksignalsistheba-
systemoperatorsandpolicymakers. sisoftransactivecontrol,awell-establishedstandardizedcon-
cept and implemented technology in the real world [20, 21].
Theterm‘transactive’referstotheuseofeconomicandcontrol
2. Self-regulatoryFramework techniquestoimprovesystemreliabilityandefficiency. Trans-
active control defines the minimal interaction types and infor-
This section introduces a self-regulatory framework for mation exchange in the domain of Smart Grids. However, it
supply-demand systems. It is shown how this framework can does not define any computational logic or formal methodol-
berealizedasadecentralizedtransactivecontrolsystemthatis ogyfortheregulationofsupplyanddemand,ortheevaluation
2
oftheregulatorycapability. Theproposedframeworkfillsthis the result of incentivization performed based on the outcome
gap by introducing a decentralized regulation mechanism and of previous operational cycles and the current system require-
anevaluationmethodologythatmotivatesthefurtheradoption ments.Incentivizationisperformedbysystemoperators,policy
of transactive control in other Smart City applications such as makersorevenautomatedsoftwaresystemsthatchoosehowto
gasnetworks,waternetworks,trafficsystems,supplychainsys- optimizeandregulateasupply-demandsystem[22]. Theprice
tems,etc. informationintheTISsignaliscomputedbyusinginformation
Atransactivesignalisasequence1S =(s )T ofnumeri- about the available supply or constraints in the characteristics
TS TS,t t=1
calvalues,wheres ∈R .Thispaperassumesthatallsignals offuturedemand,e.g. themeanand/orvolatility.
TS,t >0
aretimeseries,andtherefore,T isafuturetimehorizon. How- In the third signaling, depicted by Arrow 3 in Figure 1, an
ever, there is no limitation to other signal types applicable to eTFSsignalisprovidedbydemandtosupplyasaresponsetothe
severalcomputationalproblems[11,10]. Asequenceprovides receivedTISsignal. TheeTFSsignaliscomputedbytheadopted
a computational degree of freedom in self-regulation: in the self-regulation mechanism. At this stage, supply has all in-
caseoftimeseries,temporaladjustmentsscheduledinthetrans- formation to provision and evaluate the regulatory capability
activesignalscanbeusedasregulatorytools,e.g. load-shifting achievedinthisoperationalcycleasoutlinesbelow.
inpowergrids, load-balancingbetweenvehiclesintransporta- In the fourth signaling, depicted by Arrow 4 in Figure 1, a
tionsystems,etc. hypotheticaloptimumTFSsignaliscomputed,theupperbound,
Thetypesoftransactivesignalsaredefinedasfollows: giventheTISandiTFSsignals,alongwithconstraintsincharac-
teristicsofdemand. Suchconstraintsmayconcernthecompu-
• Transactive Incentive Signal (TIS): A time series with the tation of an upper bound signal with the same mean or, mean
priceincurrencyperunitofresourcessupplied. andvolatility,withtheiTFSsignal.
In the fifth signaling, depicted by Arrow 5 in Figure 1, the
• TransactiveFeedbackSignal(TFS):Atimeserieswiththe
evaluationoftheeTFSsignalistriggeredinthelightoftheiTFS
unitsofresourcessuppliedordemanded. Thispaperaddi-
signal and the UB signal. Evaluation measures the response,
tionallydistinguishesthefollowingTFSsignals: savingsandthemean/volatilityerror.
– InelasticTransactiveFeedbackSignal(iTFS):Anon- Finally, in the sixth signaling, depicted by Arrow 6 in Fig-
regulatedhistoricorforecastTFSsignal. ure1,anoperationalcyclecompletesbyprovidingthevaluesof
themeasuredmetricsasinputtoincentivization.Thenextoper-
– Elastic Transactive Feedback Signal (eTFS): A regu-
ationalcycleinitiatesthegenerationofanimprovedTISsignals
latedTFSsignal.
that can potentially achieve a higher response and savings but
– UpperBoundSignal(UB):AreferenceTFSsignalfor lowermeanandvolatilityerror.
theevaluationofself-regulation. The rest of this paper illustrates the self-regulation frame-
workindetail.
All interactions within the proposed framework are entirely
basedontheabovetransactivesignalsasshowninFigure1.
3. Incentivization
2.3. Operationallifecycle
Incentivization concerns the construction of TIS signals that
Theself-regulatoryframeworkofFigure1performsthefol- accurately reflect the costs of supply, costs of infrastructure,
lowing four operations: (i) incentivization, (ii) self-regulation, operationalconstraintsandcertainregulatoryactionsrequired.
(iii) provision and (iv) evaluation. Each of these operations For instance, when a power generator fails, costs increase as
may be performed at either supply or demand-side depending theavailablesupplyislower, infrastructuremayrequiremain-
on how a supply-demand system is institutionalized. For con- tenance and complex operational constraints should be met,
sistency and an intuitive understanding of the framework, the i.e. ramp up times for the activation of operational power re-
rest of this paper positions the operation of self-regulation at serves[22]. Moreover,systemoperatorsandutilitiesmayiniti-
demand-sideandallotheroperationsatsupply-side. Sixtrans- atecostlydemand-responseeventssothatconsumerslowerde-
activesignalingsareperformedtocompleteanoperationalcy- mand. Thecostsofalltheseactionssumupandformtheprices
cle. of a TIS signal. Forecasting is a critical component of incen-
Inthefirstsignaling,depictedbyArrow1inFigure1,aniTFS tivization as cost information is not always available [23, 24].
signalisprovidedbydemandtosupply. Thissignalisusedasa For example, the availability of energy supply generated by
historicorforecastbaseinformationbytheotheroperationsof renewables is highly stochastic. Therefore the accuracy of
theframework. weatherforecastingtechniquesinfluencetheeffectivenessofa
In the second signaling, depicted by Arrow 2 in Figure 1, a TISsignal.
TISsignalisprovidedbysupplytodemand. ATISsignalmaybe These observations suggest that incentivization is a highly
domain-dependent process. Implementations of the proposed
self-regulatoryframeworkcanmakeuseofexistingtechniques
1Thispaperassumespositivesignalsforsimplifyingtheillustrationofthe adoptedbyvariousapplicationdomainsforconstructingTISsig-
frameworkandresults. Negativesignalsarepossibleaswellandcorrespond
nals. However, the framework introduces the option to con-
tosupply-demandsystemsinwhichanagentmayactasboth,consumerand
producer. structincentivesignalsinanevolutionaryfashion. Themetrics
3
measured at the stage of evaluation can be used as feedback UpperBound1. GivenaTISsignalSTISandaniTFSsignalSiTFS,
informationtoconstructmoreeffectiveTISsignals,whereeffec- anupperboundS isgivenasfollows:
UB1
tivenessismeasuredbytheproposedmetrics. Inotherwords,
a weighting scheme of the costs or an elasticity function [25]
µ(S )
based on the metrics of evaluation can be used to compute a s = iTFS n(t,S ),∀t∈[1,T]
new incentive signal to improve the self-regulatory capability UB1,t µ(STIS) TIS (2)
of a supply-demand system. This paper focuses on evaluating subjecttoµ(SUB1)=µ(SiTFS)
asingleoperationalcyclebyusingreal-worldTISsignalscom-
Proof. The average cost of one demand unit during the time
putedviatoolkitfunctionsbasedonadvancedpredictiveanalyt-
horizon T is given by µ(S ). Subject to µ(S ) = µ(S ),
ics.Section7illustratestheTISsignalsstudiedinthispaper.The TIS UB1 iTFS
the average demand acquired for one cost unit of demand is
evaluation of an evolutionary operation of the self-regulatory
µ(S )/µ(S ).Then,byproportionality,forn(t,S )costunits
frameworkispartoffuturework. iTFS TIS TIS
ofdemand, µ(SiTFS)n(t,S )unitsofdemandareacquiredforthe
µ(STIS) TIS
upperbounds .
UB1,t
4. Provision
UpperBound2. GivenaTISsignalSTISandaniTFSsignalSiTFS,
anupperboundS isgivenasfollows:
UB2
This section shows how to construct hypothetical eTFS sig-
nals representing an optimally regulated supply-demand given
thhyepiontcheentitcivaelssiiggnnaallsSarTeISraenfderaresdettooafsduemppaenrdbcoounnsdtsra.iTnhtse.iTnhceense- sUB2,t =σ(SiTFS)r(t,SσTIS()S−µ)(STIS) +µ(SiTFS),∀t∈[1,T] (3)
TIS
tive signal is assumed to have a reversed linear2 relation with subjecttoµ(S )=µ(S )andσ(S )=σ(S )
UB2 iTFS UB2 iTFS
thefeedbacksignal,meaningthatahigherpriceinsupplyshall
result in lower demand. In other words, the incentive signal Proof. Let r(t,S ) − µ(S ) represent the price difference at
TIS TIS
seemsmoreappropriatetoconstructalowerboundsignal. One timetfromtheaveragepriceµ(S ). Thisdifference,measured
TIS
waytoovercomethismathematicalhurdleistocreateareflec- in units of price, can be measured in units of price volatility
tionoftheincentivesignalS asfollows: oftheTISsignalas r(t,STIS)−µ(STIS). Thedemanddifferencefrom
TIS σ(STIS)
the average demand µ(S ) at time t can be constructed using
TIS
r(t,STIS)=2µ(STIS)−sTIS,t (1) tσh(eSdem)a=ndσv(Solati)l.itGyiσve(SnitThFSa)taµs(σS(Si)TF=S)rµ(t(,SSTσIS(S)−T)Iµ,S()tShTeIS)fisnuabljuepctpteor
UB2 iTFS UB2 iTFS
where the mean of the incentive signal µ(S ) is used as the bound signal is constructed by summing the average demand
hyperplanefortheflip. TheisometryoftherTeISflectionr(t,STIS) µ(SiTFS)asσ(SiTFS)r(t,STσIS(S)−TIµS()STIS) +µ(SiTFS3).
and the selection of the mean µ(S ) as hyperplane result in a
TIS
price signal with the same total cost for one unit of resources
Althoughthesehypotheticalupperboundsareconstrainedto
compared to the initial incentive signal S . An undesired ef-
TIS
fectofareflectionisthatitmayresultinasignalwithnegative aggregatedemandcharacteristicsoftheiTFSsignal,othermore
complex operational constraints can be captured as well, de-
values. AnormalizationisillustratedinAppendix Bthatguar-
pending on the application domain considered. For example,
anteesasignaln(t,S )withpositivevalues. Itisusedforthe
TIS
inSmartGrids,operationalconstraintsoftheindividualhouse-
computationoftheUB1.
hold devices or the availability of renewable energy resources
Thispaperintroducestwoupperboundsdistinguishedbytwo
canbeconsidered[26,27,28].
demandconstraints:
• Themeanµ(SUB)oftheUBsignalequalsthemeanµ(SiTFS) 5. Evaluation
of the iTFS signal. This constraint keeps the total amount
of demand equal to the one of the iTFS signal, however This paper studies three factors that measure the effective-
demand is distributed more effectively as defined by the ness of self-regulation: (i) response, (ii) savings and (iii)
reflectediTFSsignalr(t,STIS). mean/volatilityerror. GivenaninitialfeedbacksignalSiTFS and
afeedbacksignalS computedbyaregulationmechanismaf-
eTFS
• The mean µ(S ) and volatility σ(S ) of the UB signal ter applying an incentive signal S , response and savings are
UB UB TIS
equal the mean µ(SiTFS) and volatility σ(SiTFS) of the iTFS computedasfollows:
signal. Thisconstraint keepsthetotalamount ofdemand
equaltotheoneoftheiTFSsignaland,additionally,itlimits R= (cid:80)Tt=1|siTFS,t−seTFS,t| (4)
thestandarddeviationofthevaluestotheleveloftheiTFS (cid:80)T |s −s |
t=1 iTFS,t UB,t
signal.
(cid:80)T s ∗s −(cid:80)T s ∗s
P= t=1 TIS,t iTFS,t t=1 TIS,t eTFS,t (5)
(cid:80)T s ∗s −(cid:80)T s ∗s
2Thisstrongassumptioncanbeovercomewithempiricaldataordomain- t=1 TIS,t iTFS,t t=1 TIS,t UB,t
specificmodelsofsupply-demandsystems. whereS isanupperboundsignal.
UB
4
Response measures the distance |s − s | of the two Thispaperfillsthisgapbyintroducingtwonewselectionfunc-
iTFS,t eTFS,t
feedbacksignalsS andS inrelationtothemaximumdis- tions without any change in the algorithm and architecture of
iTFS eTFS
tancethatthesetwosignalscanhypotheticallyhave. Thismax- EPOS.
imum distance is computed using the upper bound signal as TheplansofEPOSandthetransactivesignalsarebothmath-
|s −s |. ematicallyequivalentsequences. Thismakesatransactivecon-
iTFS,t UB,t
Savingspayoffmeasuresthecostreductionbetweenthefeed- trolsystemfullyinteroperablewiththeEPOSmechanism. The
back signals SiTFS and SeTFS in relation to the maximum hypo- supply-sideprovidestoEPOSaTISsignal3andreceivesbackan
thetical cost reduction between the feedback signal SeTFS and eTFSsignalcomputedinEPOSasfollows:
the upper bound signal S . Cost is computed by multiplying
UB (cid:88)n
theincentivesignal(price)withthefeedbacksignal(quantity), s = d (7)
for example, s ∗ s provides the cost of s amount of eTFS,t i,s,t
TIS,t eTFS,t eTFS,t i=1
resourceswithprices attimet.
TIS,t wherenisthetotalnumberofagentsconnectedinthetreeover-
An upper bound S is required to compute both response
UB laynetworkofEPOSandd istheselecteddemandofagenti
andsavings. Withthesetwometricsbasedonanupperbound, i,s,t
attimet.
different self-regulation strategies can be meaningfully com-
Plan generation computes the possible plans. Each one can
pared. Forexample,aself-regulationstrategy‘A’maydecrease
beexecutedbytheagentlocallyifselected. Thepossibleplans
thedemandcost5%morethananotherstrategy’B’.Thisfind-
represent a degree of freedom in the operation of the physical
ingisnotsoinformativecomparedtoknowingamaximumpos-
assetsthattheagentregulates. Therefore,thephysicalcharac-
sible cost reduction of demand that indicates the actual effec-
teristics and the parameterization of these physical assets can
tivenessofthesestrategiescomparedtoahypotheticaloptimal
makethecomputationofpossibleplansfeasibleinvariousap-
case. This evaluation methodology is especially useful in de-
plication domains. For example, possible plans can be opera-
centralized self-regulation mechanisms that capture objectives
tionallyequivalent,andthereforealternatives,whenhousehold
withoptimumsolutionsbeingcomputationallyintractable.
appliancespermitthis[29,13]. Moreover, possibleplansmay
Thecapabilityofaregulatorymechanismtosatisfythecon-
represent social preferences, such as comfort levels [32? ] or
straintsoftheupperboundscanbemeasuredbythemeanand
even recommendations extracted from historic data [30]. This
volatilityerrorsasfollows:
paperstudiestheroleofinformationaldiversityinthepossible
planswiththreegenerationschemesthatcanbeappliedinsev-
µ(S ) σ(S )
(cid:15)µ =|1− µ(SeTFS)|,(cid:15)σ =|1− σ(SeTFS)|, (6) eral application domains and scenarios: (i) SHUFFLE, (ii) SHIFT
iTFS iTFS and (iii) SWAP. In SHUFFLE, each possible plan is a random per-
where(cid:15)µ istherelativeerrorofthemeanintheeTFSsignalrel- mutationoftheotherones. Thisschemerepresentsscenariosin
ative to the mean of the iTFS signal, and (cid:15)σ is the respective whichagentshaveasignificantcontrollabilityintheoperation
relativeerrorofdemandvolatility. oftheregulatedassets. InSHIFT,thevaluesofaplanarerotated
bypushingvaluescertaintimestepsaheadintime.Thisscheme
represents load-shifting scenarios or future resource realloca-
6. Self-regulation tion and rescheduling. In SWAP, a number of values in a plan
interchange their positions. This scheme represents scenarios
in which scheduled operations can be interchanged within the
This paper advances the EPOS mechanism [29] to employ
futurehorizon.
it as a highly generic self-regulation mechanism for supply-
Each scheme generates plans that contain the same values
demand systems. EPOS is earlier studied in the Smart Grid
and,therefore,theyhavethesamemean,volatilityandentropy
domainasafullydecentralizedmechanismtoimprovethero-
that is useful for the interpretation of the measurements per-
bustnessofSmartgridsbystabilizingenergydemand,lowering
formed. Inthisway,thegenerationschemesarenothighlydis-
power peaks and other regulatory actions. Loads, represent-
ruptiveforconsumers[13]anddonotinfluencethetotalamount
ing electrical household devices or even the consumption of a
ofsupplyscheduledwithintheperiodT. Moreover,theelastic-
household as a whole [30], are regulated by software agents
ity of volatility is exclusively governed by EPOS and not by
self-organized [31] in a tree topology for structuring their in-
teractions. A tree overlay network provides a cost-effective the generation schemes that would bias the measurements of
responseandsavings.
aggregation of the demand level required for coordinating the
Theinformationaldiversityis definedbytheEuclideandis-
decision-making: each agent generates p number of possible
plansD =(d )p andcollectivelyselectsthepland thatfits tance between the positions of the demand values after apply-
i i,j j=1 i,s ing a generation scheme. Let d being a seed possible plan
besttoanobjective. Decision-makingisperformedwithselec- i,1
and d the diversified possible plan with one of the proposed
tion functions [30] that evaluate characteristics of the demand i,2
generation schemes. The informational diversity is measured
plan,e.g. howuniformlydistributeddemandisovertime,how
largethedemandpeaksare,etc.
ThemainlimitationofEPOSisthatitdoesnotinteractwith
3TheTISsignalcanbedistributedtoallagentsofthetreeoverlaynetwork
supply and, therefore, it cannot be used for balancing supply
viaapplication-levelbroadcastingsupportedinEPOSfordistributingtheglobal
and demand under a broader range of operational scenarios. plan[29].
5
as (cid:80)T |t−tˆ|, where t refers to the time point of demand d
t=1 i,1,t
and tˆ=d(t) refers to the new time point of demand di,2,tˆ after (cid:115)
diversificationwithafunctiond(t)suchthatdi,1,t ≡di,2,tˆ. s=argpmk in (cid:80)Tt=1(ci,j,t−sUB,t)2
Figure 2 illustrates the probability density functions of in- j=1 T (9)
formational diversity for the five generation schemes4. SHUF- subjecttos =c
FLEhasthehighestinformationaldiversityfollowedbySHIFT(20). iTFS,t i,j,t
SHIFT(10),SWAP(30)followverycloselyandSWAP(15)hasthelowest This relation gives the combinational plan, and therefore the
diversity.
selectedplanofeachchild,withtheminimumrootmeansquare
error. Thisisthecombinationalplanwiththehighestmatching
�� ����������������������������� to the upper bound. The upper bound is recomputed for each
�������
��������� combinational plan given that s = c . This condition is
���� ������������������������� necessary as it makes collectiveiTdFSe,tcisioni-,jm,taking possible6. It
actually means that when a number of agents have a selected
������������������� pthlaenr,esmtoeafnthinegagtheentasgneenetdstionbthinedbtrhaenirchdeucnisdieornn-ematahkienagchtocthhielsde,
existingchoices.
���� ThethirdselectionfunctionMIN-COSTisdevisedtominimize
thecostofdemand:
���� ����� ����� ����� ����� ������ ������
�����������������������
pk (cid:88)T
s=argmin s ∗c (10)
Figure2: Probabilitydensityfunctionofinformationaldiversityforthefive TIS,t i,j,t
generationschemes. j=1 t=1
where the price of supply sTIS,t in the TIS signal multiplied by
Decision-makingisperformedbottom-upandlevel-by-level: the planned demand ci,j,t in the combinational plan at time t
children interact with their parents and collectively decide providestherespectivecostofdemand.
whichplantoexecutebasedon(i)theirowndemandplansand The generation schemes, selection functions and number of
(ii) the selected plans of the agents connected to each of their possible plans are all configurations that influence the perfor-
branchunderneath. Selectioniscomputationallyperformedby manceofself-regulations. Theycanbeincentivizedbysupply-
theparentofthechildrenthatcomputesthecombinationalplans demandserviceprovidersviasomepayoff.
asfollows:
7. ExperimentalFrameworkEvaluation
Ci =(ci,j)pj=k1 =b(Au,...,Au+k) (8)
Thissectionillustratestheapplicabilityandevaluationofthe
where the parent agent i performs a brute force operation self-regulatoryframeworkinfourscenariosofbalancingenergy
b(Au,...,Au+k) to compute all combinations between the se- supplyanddemand: (i)rampdown,(ii)generationfailure,(iii)
quences of aggregates plans Au,...,Au+k received by its k chil- maximum entropy and (iv) minimum entropy. Each regulatory
dren. Thechilduofagentiisassumedtobethefirstoneand scenario corresponds to a TIS signal of size 144 as standard-
thechildu+kthelastone. Anaggregateplana ∈ A iscom- ized in transactive control for Smart Grids7 [33, 21]. Eval-
u,j u
putedbysummingthedemandpland andallselectedplans uation is based on both simulated and real-world Smart Grid
u,j
oftheagentsreceivedthroughthebranchunderneathchildu. datasources: (i)thesimulatedzonalpowertransmissioninthe
Three selection functions are introduced with the following PacificNorthwest8 (SIM),(ii)theE´lectricitee´ deFrance9 utility
self-regulation objective: match the actual demand to any de- (EDF)and(iii)thePacificNorthwestSmartGridDemonstration
sireddemandcurve. Thisisanespeciallychallengingobjective Project8(PNW).
tofulfillgiventhatdecision-makingisperformedinafullyde- A ramp down scenario concerns a situation in which power
centralizedfashion. Thethreeselectionfunctionsusedifferent supply suddenly drops due to, for example, a low availability
mathematical approaches to achieve the same self-regulation of renewable energy resources, e.g., wind generation. In this
objective.
ThefirsttwoselectionfunctionsMIN-RMSE-UB1andMIN-RMSE-
6Severalotherversionsofselectionfunctionsareexperimentallyevaluated,
UB2aredevisedtomaximizeresponse5. Theycomputetheroot however,itisthisfunctionthatresultsineTFSsignalswithimprovedresponse
meansquareerrorbetweenthecombinationalplansandoneof andsavings.
theupperboundsillustratedinSection4: 7Thiscorrespondstoa72hoursforecastingofvariablegranularitywithina
marketoperatingevery5minutes.
8Available upon request at http://www.pnwsmartgrid.org/
participants.asp(lastaccessed:November2015)
4ThetestisimplementedinJavausingrandomizationmethodsofJDK1.8. 9Available at https://archive.ics.uci.edu/ml/datasets/
5Theyarealsoexpectedtodecreasethecostgiventhatareflectionofthe Individual+household+electric+power+consumption (last accessed:
TISsignalisusedforthecomputationoftheupperbounds. November2015)
6
case, operating reserves with high operational costs are acti- Thethreefollowingsettingsvaryineachexperiment:(i)gener-
vated such as backup diesel generators. Figure 3a shows that ationscheme,(ii)selectionfunctionand(iii)dataset. EacheTFS
during the time period [40,80] the generation costs in the TIS signalisgeneratedbyaprocesspipelineoffourstagesasillus-
signaloftheSIMdatasetdoublesreflectingthelowavailability tratedinFigure4. Thefirststageinthispipeline,thedisaggre-
ofcheaprenewableenergyresourcesduringthisperiod. gation, is applied in the SIM and EDF datasets that only contain
the aggregate base load of all residential consumers. In con-
�� ����� trast,thePNWdatasetcontainsthebaseloadforeachindividual
������������� �������������������
���������������������� ������������������� household.
�� ������
�� ����� 1( Planning( 1( 2( …( p(
��� ���
���������� �� ���������������� (1)$ 2( Planning( 1( 2( …( p(
�� ����� ...((( ...(((
iTFS(
�� ������ n( Planning( 1( 2( …( p(
(2)$
�� ��� ��� ��� ��� ���� ���� ���� ����� ���� ����� ����� ����� Evalua2on( Disaggregated( Possible(plans(
����������� ����������� base(load(
(a) TIS signals from the SIM (b) TIS signals from the PNW eTFS( 2(1...((((p( (3)$
dataset. dataset. ...((( ...(((
(4)$ 2(1(p( .(.(.( 2(1(p(
Figure3: TheTISsignalscorrespondingtothefourregulatoryscenarios: (i) ...((( ...(((
rampdown,(ii)generationfailure,(iii)minimumentropyand(iv)maximum 2(1(p( .(.(.( 2(1(p(
entropy.
Selected(plans(by(EPOS(
The generation failure scenario concerns the unexpected Figure4: TheexperimentalsetupforgeneratinganeTFSsignal: (1)Theag-
damageofanoperationalpowergeneratoratthesametimein gregatedbaseloadfromdifferentreal-worldSmartGriddemonstrationprojects
which the ramp down scenario occurs as well. Further expen- isdisaggregatedtonindividualhouseholdbaseloads. (2)Anagentineach
householdgeneratespnumberofalternativedemandplansbasedonagenera-
siveoperatingreservesneedtobeactivatedfollowedupbyur-
tionschemethatreceivesasinputthebaseloadofahousehold.(3)Theagents
gent repair costs to meet demand. This scenario is illustrated areself-organizedinatreetopologyoverwhichthedecentralizedalgorithmof
inFigure3awiththeTISsignalfromtheSIMdatasetthatshows EPOSrunstoselectthedemandplanforexecution. (4)Theagentsperforma
the increase in the price of generation during the time period treeaggregationthatcomputestheeTFSsignal.
[60,80].
Each regulatory scenario is applied in two project sites13
Theminimumentropyscenarioconcernsasituationinwhich
thatbelonginasingletransmissionzone14. Theloadsineach
the availability of power generation is highly dispersed over
project site are regulated by the EPOS agents that are self-
time. This dispersion is measured with the entropy of Shan-
organized in an overlay network with a 3-ary balanced tree
non’s information theory [34]. This scenario assumes that a
topology. Self-organization is performed with the AETOS
low entropy in the incentive signal corresponds to a high dis-
overlay service [31]. Each EPOS agent generates 4 possible
persion in power generation. Therefore, matching demand to
the available supply is more challenging. The opposite holds plansusingthefollowinggenerationschemes: (i)SHUFFLE,(ii)
for the maximum-entropy scenario that assumes a low disper- SHIFT(10), (iii) SHIFT(20), (iv) SWAP(15) and (v) SWAP(30). Plan se-
sioninthepowergenerationovertime. Whendemandisregu- lection is performed with the MIN-RMSE-UB1, MIN-RMSE-UB2 and
lated to have a maximum entropy, the required adjustments in MIN-COST selection functions of EPOS. The iTFS signal of the
thegenerationareminimizedasdemandismoreuniformlydis- SIM dataset is disaggregated in 5600 and 2374 loads for each
projectsiterespectively,emulatinginthiswaytheloadsofthe
tributedcomparedtotheminimumentropyscenario. Figure3b
‘Flathead, Libby’and‘Flathead, Haskill’projectsites. Disag-
illustratesaseriesofconsecutiveTISsignalsusedfromthePNW
dataset10. Anexhaustiveheuristicalgorithmisappliedoverall gregation is performed as illustrated in Appendix C with pa-
consecutiveTISsignalsofsize144todiscovertheoneswiththe rameter ε = 0.20. The iTFS signal of the EDF dataset is disag-
gregated, as illustrated in Appendix C, in 724 loads for each
minimumandmaximumentropyasshowninthisfigure.
Experimental evaluation is performed for each regulatory projectsiterespectively. ThePNWdatasetcontainstheresiden-
tialbaseloadofapproximately1000residentialconsumerson
scenariobymeasuringandcomparingtheresponse,savingsand
volatilityerror11oftheeTFSsignalsusingtheupperboundUB212. the date 23.07.2014. It is split in two subsets referred to as
PNW-MORNINGandPNW-EVENING.TheiTFSsignalforPNW-MORNING
concerns the duration 01:00-13:00, whereas the iTFS for PNW-
10TheTISsignalsconcernthetransmissionzone12atprojectsite14forthe EVENINGconcernstheduration11:00-23:00.
periodstartingon30/07/13at09:45to06/08/13at09:30.
11Themeanerrorisnotillustratedasthepossibleplansforeachagenthave
thesamemeanandtherefore,foranyselectionperformed,µ(SeTFS)=µ(SiTFS) resultsarenotshowninthispapergiventhespacelimitationsandthefactthat
is satisfied. Experimental evaluation confirms an average (cid:15)µ = 0.09 for all theyindicatesimilarfindings.
performedexperiments. 13Theyareenumeratedasprojectsite12and14.
12ResponseandsavingsarealsomeasuredwiththeupperboundUB1.These 14Itisenumeratedastransmissionzone14
7
7.1. Response,savingsandvolatilityerror of14.75%inPNW-MORNING.Theinfluenceofadatasettotheper-
Figure 5 illustrates the performance of the self-regulatory formanceconcernsthecomplexityoftheiTFSsignalincompar-
framework in the light of four studied aspects: (i) generation isontoUB2. Forexample,whenbothsignalsaremonotonously
schemes, (ii) selection functions, (iii) datasets and (iv) regu- increasing,theymayrequirealowerdegreeofadjustmentcom-
latory scenarios. Performance is evaluated by averaging the paredtothecaseinwhichtheoneismonotonouslyincreasing
response, savings and volatility error in each experiment that andthesecondmonotonouslydecreasing15. Thecomplexityof
involvesthechoiceofagenerationscheme,selectionfunction, thesignalsineachdatasetisshowninthefiguresofSection7.2.
dataset and regulatory scenario. Figure D.13, D.14 and D.15 Thehighestvolatilityerrorof40.37%isobservedinSIMandthe
inAppendix Dillustratetheindividualresultsineachexperi- lowestoneof18.82%inPNW-EVENING.
mentperformed. Figure5dillustratestheresponseandsavingsunderthefour
differentregulatoryscenarios. Theminimumentropyscenario
has the highest response of 44.14%, whereas generation fail-
���� ����
������������ ������������
����������� ����������� urehasthelowestresponseof31.05%. Themaximumentropy
��������� ���������
��� ��� hasthehighestsavingsof40.22%,incontrasttothegeneration
failurescenariowiththelowestsavingsof17.51%.Thehighest
����� ��� ����� ��� volatilityerroris31.61%formaximumentropyandthelowest
������ ��� ������ ��� oneis23.55%forgenerationfailure.
Figure 6 visualizes the agent selections under the genera-
��� ���
tion failure scenario for the PNW-MORNING dataset. Figure 6a-c
�� �� providequalitativecomparisonsabouttheselectionmadewith
����������������������������������������� ������������ ������������ �������� MFLIEN.-RAMgSeEn-UtBs2aadnodptMinINg-CthOeSTSuHsUiFnFgLEthgeegneenraetriaotniosncshcehmemeeunodfeSrHtUhFe-
(a) GenerationSchemes (b) SelectionFunctions MIN-RMSE-UB2 and MIN-COST selections functions make 50.91%
different selections. Figure 6d-f show selections made with
���� ������������ ���� ������������ MIN-RMSE-UB2,thoughusingthegenerationschemesSWAP(15)and
����������� �����������
��� ��������� ��� ��������� SWAP(30). Agents adopting the MIN-RMSE-UB2 selection function
under the SWAP(15) and SWAP30 generation schemes make 67%
����� ��� ����� ��� differentselections. Finally, Figure6g-ishowselectionsmade
������ ��� ������ ��� withMIN-COST,thoughusingthegenerationschemesSWAP(15)and
SWAP(30). AgentsadoptingtheMIN-COSTselectionfunctionunder
��� ��� theSWAP(15)andSWAP30generationschemesmake64.59%dif-
ferentselections.
�� ��
��� ��� ���������������������� ��������� ������������������������������������������������ volGativileitny ethrreorp,earfpolramusainbcleeqrueessutlitosnotfharteasrpiosenssei,s isfatvhiensgesmaentd-
rics are correlated in practice. Intuitively, a high response can
(c) Datasets (d) RegulatoryScenarios
be incentivized via reducing the demand cost. Similarly, high
savingsrequireasignificantresponse. Finallyahighresponse
Figure5: Response,savingsandvolatilityerrorineachstudiedaspectofthe
self-regulatoryframework. can originate from adjustment in demand volatility. How cor-
related are these metrics in the empirical findings illustrated?
Figure5ashowsthatSHUFFLEandSHIFT(20)havethehighestre- Which system parameter can be used to make trade-offs be-
sponseof60.06%and38.02%respectively.Theseschemesalso tweenresponseandsavings,whileminimizingvolatilityerror?
have the highest savings of 47.63% and 32.67%. In contrast, The total number of experiments performed are a popula-
thelowestperformanceisobservedinSWAP(15)with18.01%re- tiononwhichthecorrelationbetweenresponse-savings,error-
sponseand19.3%savings. SHUFFLEandSWAP(30)causethehigh- response and error-savings can be measured. In this case, the
est volatility error of 53.72% and 28.15%, while SHIFT(10) the correlation coefficient is 0.3, 0.44 and -0.08. However, not all
lowest one of 12.32%. These results confirm that a higher in- experimentsvarythesameparameter. Fourdifferentaspectsas
formationaldiversityresultsinhigherperformance. studiedasshowninFigure5. Forthisreason,itismeaningful
Figure5bshowsthattheMIN-RMSE-UB1selectionfunctionhas torestrictthecorrelationmeasurementsforeachstudiedaspect.
thehighestresponseof38.12%,thoughMIN-RMSE-UB2alsohasa Figure 7 illustrates the correlation coefficient for each stud-
significant response of 38.09%. In contrast, MIN-COST achieves iedaspectoftheself-regulatoryframework. Thethreemetrics
thehighestsavingsof56.67%andMIN-RMSE-UB1thelowestsav- appearhighlycorrelatedwhenmeasurementsareperformedfor
ings of 7.99%. The highest volatility error is 29.79% by MIN- the experiments that vary the generation scheme and regula-
RMSE-UB1andthelowestoneis18.2%byMIN-COST. tory scenario. For example, the correlation range [0.69,0.93]
Figure 5c illustrates that the highest response of 48.06% is indicatesthatresponse,savingsandvolatilityerrorarelikelyto
observedinthePNW-EVENINGdatasetandthelowestresponseof
28.02%atthePNW-MORNINGdataset. Similarly,thehighestsav- 15Forexample, Figure11dshowsaniTFSandanUB2withaverysimilar
ingsof52.31%areobservedinPNW-EVENINGandthelowestones complexity.
8
1 2 3 4 1 2 3 4
SelectedPlan SelectedPlan DifferentSelection
SameSelection
(a) SHUFFLE,MIN-RMSE-UB2 (b) SHUFFLE,MIN-COST (c) SHUFFLE,MIN-RMSE-UB2vs.MIN-COST
1 2 3 4 1 2 3 4
SelectedPlan SelectedPlan DifferentSelection
SameSelection
(d) SWAP(15),MIN-RMSE-UB2 (e) SWAP(30),MIN-RMSE-UB2 (f) SWAP(15)vs.SWAP(30),MIN-RMSE-UB2
1 2 3 4 1 2 3 4
SelectedPlan SelectedPlan DifferentSelection
SameSelection
(g) SWAP(15),MIN-COST (h) SWAP(30),MIN-COST (i) SWAP(15)vs.SWAP(30),MIN-COST
Figure6:AgentselectionsunderthegenerationfailurescenarioforthePNW-MORNINGdataset.
increaseordecreasesimultaneouslybyonlychangingthegen- error-responsehaveacorrelationof0.45anderror-savingshave
eration scheme. This is a desired property of the framework asignificantnegativecorrelationof-0.995.
asthechoiceofthegenerationschemeandregulatoryscenario
The correlation results under different selection functions
shouldnotgovernthedynamicsbetweenthethreemetrics. Un-
der different datasets, response-savings have a correlation of have two striking implications. The first implication is that
0.56,error-responsehaveacorrelationof0.29anderror-savings thedesign ofselectionfunctions isempiricallyvalidated: MIN-
haveanegativecorrelationof-0.33. Finally,underdifferentse- COST maximizes the savings while MIN-RMSE-UB1 and MIN-RMSE-
lectionfunctions,response-savingshaveacorrelationof-0.44, UB2 maximize the response. Trade-offs between response and
savingscanbeperformedbychoosingtherespectiveselection
9
��
�������������������������������������������� ����������������������������������������������
������ ���� �������� ����
�������������������������������� ��������������������� ������� ����������������������������� �������
���������������� �������� ��
��������������������������� ��������
��
������������������������������������������ ������������������� ������������ ��� ��� ��� ��� ���� ���� ���� ������������� ��� ��� ��� ��� ���� ���� ����
����������� �����������
Figure7:Correlationcoefficientbetweenresponse,savingsandvolatilityerror (a) SIM,SHIFT(20),MIN-COST (b) EDF, SHUFFLE, MIN-RMSE-
foreachstudiedaspectoftheself-regulatoryframework. UB2
��������������������������������������������� ������������������������������������������
����� �����
���� ����
function. In practice, these trade-offs can be incentivized by ���� ������� ���� �������
systemoperatorsorpolicymakers[35,36,37]: eachconsumer ����
����
of the supplied resources may change its selection function in ����
ewxhcehnanthgeeovfolaatmiloitnyeetarrryorpsahyoouffl.dTrhemesaeincosntdricimtlyplmiciantiimonali,sitthaist ��������� �������� ��������� ��������
�� ���� �� ����
more likely for the self-regulatory system to increase the sav- ����
����
ingsratherthantheresponse. ����
���� ����
�� ��� ��� ��� ��� ���� ���� ���� ���� ��� ��� ��� ��� ���� ���� ����
7.2. Signalswithmaximumresponse ����������� �����������
(c) PNW-MORNING, SHUFFLE, (d) PNW-EVENING, SHIFT(20),
This section illustrates the resulting eTFS signals with the MIN-RMSE-UB2 MIN-COST
maximum response in each dataset and regulatory scenario.
TheeTFSsignaliscomparedtoiTFSandUB2. Figure8:eTFSsignalswithmaximumresponseundertherampdownscenario.
Forcomparison,theiTFSandUB2signalsareshown.
Figure8illustratestherampdownscenario. Themaximum
responseis96.61%,55.98%,59.38%and60.73%forSIM,EDF,
PNW-MORNINGandPNW-EVENINGrespectively.Itisshownthatdur- 31.29%. Giventhatresponseandsavingsarerelativemeasure-
ing the period [40,80] in which the cost generation is maxi- ments,lowdifferencesresultinsignificantchangesinthemag-
mized,themajorityofthevaluesintheeTFSsignalsisdecreased nitudeofresponseandsavings. Thisexplainsthemoreextreme
comparedtotherespectivevaluesoftheiTFSsignal. Figure8d valuescomputedwiththePNW-EVENINGdataset.
shows a significant match of the eTFS signal with UB2. In the
case of Figure 8a and 8d that maximum response is achieved
8. DiscussionandConclusion
withSHIFT(20),asignificantlylowervolatilityerrorof9.14%and
3.3%isobserved. This paper illustrates extensive experimental findings using
Figure9illustratesthegenerationfailurescenario. Themax- data from real-world operational supply-demand systems that
imum response is 61.68%, 58.03%, 55.57% and 65.27% for confirmthefeasibilityofanewtypeofbottom-up,onlineself-
SIM, EDF, PNW-MORNING and PNW-EVENING respectively. Similarly regulation. Incontrasttoearlierwork,thispapercontributesa
totherampdownscenario,themajorityofthevaluesintheeTFS genericself-regulatoryframeworkshapedaroundstandardized
signalsduringtheperiod[60,80]isdecreasedcomparedtothe conceptsandimplementedtechnologiesforaneasieradoption
respectivevaluesoftheiTFSsignal. andapplicabilityinSmartCityapplications.
Figure 10 illustrates the maximum entropy scenario. The An evaluation methodology, integrated within this frame-
maximum response is 65.49%, 66.47%, 95.72% and 74.28% work, allows the systematic assessment of optimality and sys-
for SIM, EDF, PNW-MORNING and PNW-EVENING respectively. A re- tem constraints, resulting in more informative and meaningful
sponsewithahigherdemandatthebeginningandattheendof comparisons of different self-regulatory settings. For exam-
theeTFSsignalisachievedduringwhichgenerationcostislow. ple, thecomparisonofdifferentagentselectionsbymeasuring
Figure 11 illustrates the minimum entropy scenario. The response, savings and volatility error shows that purely cost-
maximum response is 99.11%, 67.57%, 61.8% and 122.57% based metrics, such as savings, on which earlier work mainly
for SIM, EDF, PNW-MORNING and PNW-EVENING respectively. The relies on, cannot adequately quantify the dynamics and capa-
maximum response in SIM is achieved with MIN-COST that re- bilities of regulatory mechanisms to adjust demand. Instead,
sults in a low volatility error of 16.58% confirming the sig- comparisons between response and savings suggest trade-offs
nificant negative correlation between error-savings as shown thatopenupnewpathwaystoevaluatemultipledimensionsand
in Figure 7. Note that in Figure 11d, the iTFS signal and the engineer multi-objective self-regulatory systems. The correla-
UB2 signal have a very similar trend with a volatility error of tion results of the three metrics empirically validate the effec-
10