Frequency Control Ancillary Service Provided by Efficient Power Plants Integrated in Queuing

21 Pages·2017·4.38 MB·English

energies
Article
Frequency Control Ancillary Service Provided
by Efficient Power Plants Integrated in
Queuing-Controlled Domestic Water Heaters
YebaiQi1,DanWang1,*,HongjieJia1,TianjiaoPu2,NaishiChen2andKaixinLiu1
1 KeyLaboratoryofSmartGridofMinistryofEducation,TianjinUniversity,Tianjin300072,China;
[email protected](Y.Q.);[email protected](H.J.);[email protected](K.L.)
2 ChinaElectricPowerResearchInstitute,HaidianDistrict,Beijing100192,China;[email protected](T.P.);
[email protected](N.C.)
* Correspondence:[email protected];Tel.:[phone]
AcademicEditors:LeiFengandJohnKessels
Received:20December2016;Accepted:13April2017;Published:19April2017
Abstract: Frequency is an important parameter of a power system. It is of great significance to
maintainitsstability,especiallyinthecurrentdevelopmentscenariooflarge-scaleinterconnected
powersystems. Thermostaticallycontrolledappliances(TCAs)aregoodcontrollableresourcesfor
demandresponseowingtotheirrapidresponsecapabilitiesandrelativelywidecontrollableranges.
Inthisstudy,domesticwaterheaters,whichhavewiderdeadbandscomparedwithothertypical
TCAs,suchasheatpumps,areusedasfrequencyregulationresources. Themaincontributionofthis
paperisthatitproposesaqueuing-controlledstrategywithlock-onandoffconstraintsforcontrolling
an efficient power plant consisting of water heaters (EPP-WH). The queuing-controlled strategy
enablesTCAstoprovidefrequencyregulationancillaryserviceforthenormaloperationofthepower
system. The thermal dynamic process of the water heater and the formation of the EPP-WH are
firstdiscussed. Basedonthedevelopedmodel,aseriesofstrategiesareproposed,includingload
sheddingcalculation,toplayeroptimization,andimprovedtemperatureprioritylist(TPL)strategy
withlock-onandoffconstraints. Finally,typicalcasestudiesarediscussedtoillustratethefrequency
regulationeffectsandtheeffectsoftwocharacteristicparameters—users’willingnessandlocktime
limits. Reasonabletargetsaregeneratedbasedonvariousconsiderationfromtoplayeroptimization
module. Theresultsindicatethatusingthemodelandproposedstrategies,theEPP-WHhasgood
frequencyregulationperformance.
Keywords: frequency control; demand response; thermostatically controlled appliance (TCA);
efficientpowerplant(EPP);temperatureprioritylist(TPL)strategy
1. Introduction
Frequencyisacriticalparameterthatindicatesthebalancebetweenpowergenerationandload
consumptioninpowersystems. Whenthereisaseveredisturbanceoradrasticchangeinloading
conditions, the operating state of the system may change from the normal state to the emergency
state. Traditionally,thefrequencyisprimarilycontrolledbyadjustingresourcesonthegenerationside,
includingextracapacityfromlargegeneratorsandinterconnection[1]. Ifthesystem’sfrequencyisstill
outofthenormalrange,effectivemeasuresmustbetakentomaintainthefrequencystability,such
asloadsheddingandmodifyingdemandresponse. Insuchconditions,loadsheddingisregarded
asoneeffectiveemergencycontrolmethod,whichhasbeenanestablishedpracticetobringsystems
backtotheirnormaloperatingstate. Itisalong-termmeasureoftenusedaftertheprimaryfrequency
regulationfails. Themainobjectiveofloadsheddingistobringthesystem’sfrequencybacktoan
Energies2017,10,559;doi:10.3390/en10040559 www.mdpi.com/journal/energies
Energies2017,10,559 2of21
acceptable range. This type of scheme is called under frequency load shedding (UFLS), which is
an effective control measure for preventing frequency collapse after a large disturbance occurs or
foraddressingpowershortages. Manystudieshavebeencarriedoutinthisfield. Therearemainly
threecategoriesofcontrolmethodsinthetraditionalUFLSschemes: themaximumavailablecapacity
methods,thelinearmethods,andtechniquestoenablesystemfrequencyrecovery. Inaddition,fuzzy
andbinarycontrolmethodshavealsobeenimplementedinfrequencyregulation[2]. Thestudyin[3]
proposed a frequency-based control strategy, taking into account renewable energy resources and
energystorage. Theimpactsofemulatedinertiafromwindpowerwerestudiedin[4]. Inaddition,
somedispatchstrategieswereproposedusingtheaggregatedelectricvehiclestoparticipateinthe
ancillaryfrequencyregulation[5–9]. Withthedevelopmentofadvancedmeteringinfrastructure(AMI)
andautomaticmeterreading(AMR),thecontrolcenterofthepowersystemcanacquiremoredetailed
consumptioninformationabouttheelectricalloads. Forexample,asimplelowcostsmartsocketwas
proposedtoswitchoffhouseholdappliancessuchasfansinordertoprovideaprimaryfrequency
response[10].
With respect to load control, studies have been carried out on providing energy market and
ancillaryservices,suchasloadshifting[11],primaryfrequencyresponse[12],andvoltagestability
enhancement[13]. Frequencycontrolancillaryserviceprovidedbyawindfarmdualbatteryenergy
storagesystemwasstudiedin[14]. AcontrolstrategyforV2Gaggregatorsparticipatinginfrequency
regulationwasstudiedin[15]. In[16],anautomaticgenerationcontrol(AGC)algorithmwithEVs
wasproposedandthedynamicpowersystemcharacteristicsduetoagivenloaddisturbancewere
analyzed. In addition, a comprehensive central DR algorithm for frequency regulation in a smart
microgridwaspresentedin[17]. In[18],useoftheelectricitydemandasfrequencycontrolledreserve
(DFR)hasbeeninvestigatedtoprovidefrequencyreservetopowersystems. Adynamicdemand-side
controlalgorithmispresentedtoimprovethefrequencystabilityofthepowersystem,andtoreduce
thedemandforsystemreservecapacityin[19]. In[20],amulti-stagedemandresponsetechnologyis
introducedtoparticipateintheprimaryfrequencyregulationofthesystemthroughdirectloadcontrol.
An adaptive scheme is studied in [21] for coordination of demand response and system spinning
reservesforquickfrequencyrecovery. In[22],thefrequencyregulationofdemandresponseandwind
poweronpowersystemisdiscussedinsingleareapowersystem.
Due to the presence of considerable thermal inertia in thermostatically controlled appliances
(TCAs), their short-term operation changes will not have too much impact on users’ comfort.
Asaconsequence,TCAsaregoodcontrollableloadresourcesforfrequencyregulationinpowersystems.
In[23],adirectloadcontrolalgorithmwasdevelopedtoaggregatethewaterheaterloadforthepurpose
of frequency regulation. In [24], a supplementary load frequency control algorithm considering a
number of EVs and the heat pump water heaters as controllable loads was proposed. A dynamic
frequencyregulationalgorithmwhichusedresidentialTCAstoalleviatefrequencydeviationscaused
byhighpenetrationofrenewableenergysourcesinthepowersystemwasproposedin[25]. In[26],
anoveldecentralizeddemandcontrolstrategyforfamily-friendlycontrollablerefrigeratorsconsidering
customercomfortlevelisproposedtoregulatethefrequencyofautonomousmicrogridincoordination
withtheenergystoragesystem(ESS).Combiningsmartdemandresponsetechnologywithunder
frequencyloadsheddingmeasuresisinvolvedinthethirdlineofdefensespecifiedinatechnicalguide
forelectricpowersystemsecurityandstabilitycontrol,wherebycoordinatedcontrolcouldbecarried
outbyusingquickresponseresourcesandthethirdlineofdefense,andanewunderfrequencyload
sheddingschemeconsideringtheresponseofsmarthouseholdapplianceswasproposedin[27].
Traditionally,UFLSinvolvestwomainsteps: relativelymoreloadsheddingatthebeginningof
powerdeficitandlessloadsheddingwhenthefrequencyisclosetothelowerlimitofthenormal
operatingrange. However,afterthesecondstep,thefrequencymayriseovertheupperlimitofthe
normalrange. Asaresult,along-termmethodaimedatmaintainingthesystem’sfrequencyshould
becontinuouslyimplemented. Consideringthetimescaleofcontrol,TCAsaresuitableresourcesfor
Energies2017,10,559 3of21
frequencyregulation. Owingtotheuniquefeaturesofthermostaticinertia,TCAshavelessinfluence
ontheusers’comfortablelevelswhentheyparticipateinfrequencyregulation.
In this paper, a type of adaptive UFLS scheme is proposed, which is established based on a
frequency differential and system frequency response model. The required load shedding to be
implementedwasacquiredaccordingtotherateofchangeoffrequency. Waterheaters,asatypical
example of TCAs, were selected as the load shedding resource. The proposed strategy takes full
advantageofthethermostaticenergystoragecharacteristicofTCAs,demonstratingthefrequency
regulationcapabilityofwaterheaters.
This paper is organized as follows: models of water heaters, efficient power plants with and
withoutconsideringlock-onandoffconstraintsarepresentedinSection2. Relatedcontrolstrategies
areintroducedinSection3. CasestudiesandsimulationresultsarediscussedinSection4. Conclusions
andfutureworkaresummarizedinSection5.
2. ModelingMethodologies
Adetailedunderstandingofthethermaldynamicprocessofwaterheatersisnecessarytoevaluate
theimpactsofdifferentfactorsonwaterheaters’potentialcontrollability. Thissectionwilldiscussthe
thermalmodelofwaterheatersdevelopedbasedontheETPapproach.
2.1. SingleWaterHeaterModel
Asinglewaterheater’sthermaldynamicprocesscanbedescribedbyEquation(1). Assumingthe
watertemperatureinthetankisθt1 attimet . After∆t,thewatertemperatureinthetankattime
temp 1
t +∆tiscalculatedby:
1
 θθttte11m++p∆∆tt == (cid:104)θatθ1t1+QMR−−θ(cid:16)t1θatm1t+1 +ut1θQt1mRt−1(cid:105)/θtM1(cid:17)e−∆t/RC uθtt11+∈∆t{>0,1θ}t1 (1)
temp temp set n a n temp set
 θtte1m+p∆t = (cid:104)θtte1mp(cid:16)M−mtn1(cid:17)+θat1mtn1(cid:105)/M θtte1m+p∆t ≤ θst1et
Inthispaper,itisassumedthatuserscanusehotwaterwhenwaterheatersareinbothmodes.
Whenthereishotwaterdemandfromahousehold,hotwaterisdrawnfromthetank,andcoldwater
isaddedtoitsbottom;itswatertemperaturecanbeexpressedbythelastlineofEquation(1). Misthe
tankvolume,mt1 standsforwaterconsumptionattimet ,θt1 istheambienttemperature. Byfitting
n 1 a
the observed performance data, including user’s water demand and water temperature, thermal
parameters,suchasR,C,andQcanbedetermined.
AsshowninFigure1,thetemperatureinthetankdevelopsbetweenθ andθ . θ represents
high low set
thesetpointsofthewaterheater. Whenthewaterheaterison,thetemperatureincreasesalongwith
powerconsumption,whilewhenthewaterheaterisoff,itdecreases. Thecurveintheellipsesimulates
thetemperaturetrendwhentheuserdemandsalargequantityofhotwater. Theshadedrectangles
belowrepresentthepowerconsumption. Thereisauniquecorrespondencebetweenthetemperature
risingandthepowerconsumption. Therelationshipofθ ,θ ,θ ,andδcanbedefinedasfollows:
high low set

 θhigh = θset+ 2δ
θ = θ − δ (2)
low set 2
 δ = θ −θ
high low
Energies2017,10,559 4of21
Energies 2017, 10, 559 4 of 21
Energies 2017, 10, 559 4 of 21
Hot water huge
Temperature
consumption
Hot water huge
Temperature
θhigh consumption
θhig h

θset deadband
θset deadband
θlow
θlow
time
Power oonn time
Power
consumption
consumption
ooffff
timetime
WWaateter r
cocnosnusummpptitoionn
timetim e
FFiigguurree 11.. TThheerrmmaal ld dyynnaammici cp rporcoecses sosf osifn sginleg wlea wtera theera hteera. ter.
Figure1.Thermaldynamicprocessofsinglewaterheater.
2.2. Efficient Power Plant Consisting of Water Heaters
2.2. Efficient Power Plant Consisting of Water Heaters
2.2. EfficientPowerPlantConsistingofWaterHeaters
Based on the single water heater’s thermal dynamic process, a group of water heaters can be
Based on the single water heater’s thermal dynamic process, a group of water heaters can be
reBgaasreddedo ans tahne esfifnicgielnet wpoawteerr hpelaantet r(’EsPtPh).e rItms aoultdpyunt apmowicerp lriomcietss sP, at+Δgt,r oPutp+Δto fatw ta+teΔrt, hceaant ebres canbe
rergeagdraedrsedcdreidbae sads aa nsa nfoe leflfifofcwiciesie:n ntt ppoowweerr ppllaanntt ((EEPPPP)).. IIttss oouutptpuut tppoowwere rlimlimitsim tisnPmPt+intΔ+tm∆, atx,PmPt+axΔt+t ∆att att+tΔ+t,∆ cta,nc abne be
described as follows: min max
describedasfollows: Pt+Δt ≤Pt+Δt ≤Pt+Δt
Pmti+nΔt ≤PEPtP+Δt ≤mPatx+Δt
 PPPmmmttt+++iiannx∆∆∆ttt =≤= PPPEEEtttPPP+PPPmmmttt∆PPP++a+iaxnΔΔxΔt−+ttt≤===∑∑PPPPEttEEPPPmttPPP+wwiiPPa-+x∆hh+t((θθPiiPm,,ittwPai++xh wi ∆∆( h(θ θtt i(,i∈∈θt,t++ΔΔi,t((tt+∈θθΔ∈tllii(,,oo(∈ttθθww++lii(o,,∆∆twθt++ttΔΔlio,,,ttwtθθ+,,θθΔhhii,,thiiiitt,,igg,++ttgθ++hhhΔΔ∆∆hitt,itttg))+)),h,Δ,,t)uu,iiuu,,ttii==u,,tti10,==t))= 010))) (3) (3) (3)
 min EPP wh low high
Pt+Δt =Pt -Pi (θi,t+Δt∈(θi,t+Δt,θi,t+Δt), ui,t =1)
 min EPP wh low high
InFigure2, theshadedtrianglerepresentstheenergyreducedasaresultofadoptingcontrol
In Figure 2, the shaded triangle represents the energy reduced as a result of adopting control
stratsetrgaIintee sgFidiegsuu drriuen rg2in, tgth htehee ps peheraridoioeddd ∆ tΔrtti,a,t nthhgeel egg rrraaeyyp drdeoostettetndetd sl intlhienese resenprererepgsreyen srt eetdhneut cEthePdeP ’Eas sPo Pua t’rpseuostuu llittmp oiutf,t aalndimdo pittht,iena dgna dcrkot nhterodla rk
positnrpatosteiangrtisee sas rodemu sroeimnpgeo ptshoseisb spilbeelreoi oopdpe erraΔatttii,nn tggh esst tgaatrtuausys. .dotted lines represent the EPP’s output limit, and the dark
points are some possible operating status.
Pt+△t
max
Pt+△t
EPP upper limit max
Rising capacity
EPP upper limit Pt+△t
EPP_u
Rising capacity
Pt+△t
Pt EPP_u Controlled capacity
EPP
Pt+△t
Pt EPP
Controlled capacity
EPP
Pt+△t
Energy reduced
EPP
Shedding capacity
Energy reduced Pt+△t
min
Shedding capacity
EPP lower limit
Pt+△t
min
Figure2.Efficientpowerplantmodel.
Figure 2. Efficient power plant model.
EPP lower limit

There are four main parameters: Pt and Pt , which are logically equivalent to the users’
max min
comfortable level constraints; uFingcuorne t2r. oElflfeicdienEt PpPowsetra ptleanPt mt odel;. and controlled EPP state Pt .
EPP_u EPP
From Figure 2, it can be observed that if EPP-WH has a large feasibility range, and the operating
pointisneartheupperlimit,ithasbetterconditionstobecomeagoodcandidateforloadshedding.
Usingthesebasicparameters,othermaintechnica lparameterscanbedefinedas:
Energies2017,10,559 5of21
 ∆PEt+P∆Pt = PEt+P∆Pt−PEt+P∆P_tu
∆Pt+∆t = Pt+∆t−Pt+∆t (4)
up max EPP
 ∆Pt+∆t = Pt+∆t−Pt+∆t
down min EPP
The controlled capacity ∆Pt+∆t represents the capacity of the energy storage or the energy
EPP
releasingcapacity,thatistosaythatwaterheaterscanabsorborreleaseenergywhentheEPP-WH
is under control; ∆P and ∆P represent the feasible regions of the EPP’s state, which are the
up down
feasibleboundariesoftheenergystorageortheenergyreleasingcapacityatthismoment. Inparticular,
thesheddingcapacity∆P representstheEPP’sbiggestpowersavingability.
down
2.3. LockOnandOffConstraints
Topreventwaterheatersfrombeingcontrolledtoooften,lock-onandofffunctionswereincluded
intheTPL[28]strategy. Thebasiclogicofthisconstraintistosetminimumtimelimitston ortoff .
limit limit
When a water heater is on or off, it should maintain its status for at least ton or toff . The water
limit limit
heatersinlock-onandoffstatusshouldnotbecontrolled. Usingparameterli,t andli,t ascontrolling
on off
index,usingtri,t+1andtri,t+1aslock-onandofftimertorecordthelocktime:
on off

 ttrroii,,ntt++11 ==0troi,nt +1 ((lloii,,ntt ==10))
on on
tri,t+1 = tri,t +1 (li,t =1) (5)
 troi,tf+f1 =0off (loi,tff =0)
off off
(cid:40)
1 tri,t < ton , tri,t (cid:54)=0
li,t = on limit on (6)
on 0 tri,t ≥ ton
on limit

 1 tri,t < toff , tri,t (cid:54)=0
li,t = off limit off (7)
off  0 tri,t ≥ toff
off limit
Ifawaterheaterisbeinglocked,thetimerwillkeepcounting,andduringthisperiod,EPP-WH
cannotbecontrolled. Afterthetimerreachesitstimelimits,theEPP-WHcanbeavailableagainas
showninEquations(5)–(7). WhencalculatingthelimitsofEPP-WH,Equation(3)needstobeupdated:
 Pt+∆t ≤ Pt+∆t ≤ Pt+∆t
 Pmmt+ianx∆__tll = PEEtPPPP__ll+∑mPawx_hl,i (θi,t+∆t ∈ (θli,otw+∆t,θhi,itg+h∆t), ui,t =0,loi,nt =0) (8)
 Pt+∆t = Pt −∑P (θi,t+∆t ∈ (θi,t+∆t,θi,t+∆t), ui,t =1,li,t =0)
min_l EPP_l wh,i low high on
ThecontrolledcapacityPt+∆t representsthecapacityoftheenergystorageortheenergyreleasing
EPP_l
capacity,thatistosaythatwaterheaterscanabsorborreleaseenergywhentheEPP-WHisunder
control; ∆P and ∆P represent the feasible regions of the EPP’s state, which are the feasible
up down
boundaries of the energy storage or the energy releasing capacity at this moment. In particular,
thesheddingcapacity∆P representstheEPP’sbiggestpowersavingability:
down
 ∆Pt+∆t = Pt+∆t −Pt+∆t
 EPP_l EPP_l EPP_u
∆Pt+∆t = Pt+∆t −Pt+∆t (9)
up_l max_l EPP_l
 ∆Pt+∆t = Pt+∆t −Pt+∆t
down_l min_l EPP_l
Figure3showstheoperatingpointsoftheEPP-WH,wherethegraypointsrepresentthestate
without lock-on and off constraints. The upper and lower limits of the EPP-WH have shrunk.
Compared with the uncontrolled point Pt , the total energy restored can be seen as Section A
EPP_u
Energies 2017, 10, 559 6 of 21
feasible boundaries of the energy storage or the energy releasing capacity at this moment. In
particular, the shedding capacity ΔP represents the EPP’s biggest power saving ability:
down
ΔPt+Δt =Pt+Δt -Pt+Δt
 EPP_l EPP_l EPP_u
ΔPt+Δt =Pt+Δt -Pt+Δt (9)
up_l max_l EPP_l
ΔPt+Δt =Pt+Δt -Pt+Δt
 down_l min_l EPP_l
Figure 3 shows the operating points of the EPP-WH, where the gray points represent the state
wEitnheroguiest 2l0o1c7k,1-0o,n55 9and off constraints. The upper and lower limits of the EPP-WH have shru6nokf.2 1
Compared with the uncontrolled point Pt , the total energy restored can be seen as Section A plus
EPP_u
section B. Taking lock-on and off constraints into account, some water heaters cannot be controlled
plussectionB.Takinglock-onandoffconstraintsintoaccount,somewaterheaterscannotbecontrolled
even if they are within reasonable temperature ranges. Therefore, the target generation of the EPP-
eveniftheyarewithinreasonabletemperatureranges. Therefore,thetargetgenerationoftheEPP-WH
WiHs b ies cboemcoimngin“gc o“ncosenrsvearvtiavteiv”e,”le, aledaidnigngto toa ah higighheerro oppeerraattiinngg ppooiinntt ∆ΔPPEtEtPPPP__ll,, aanndd ththee eneenregryg yrersetsotroerde d
dedcerceraesaesde dtot oonolnyl ythteh earaerae aini nsescetciotino nAA. T.hTeh elolaoda dcacpaapcaictiietise osfo tfhteh erirsiisnign,g d,edcerceraesaisnign,g a,nadn dcocnotnrtorlolellde d
wwereer ealal lrlerdeudcuecde.d B.uBtu wtwithit hthtihs icsocnosntsrtarianitn, tt,hteh eusuesresr’ sc’ocmomfofrotartbalbel leelveevles lwswereer emmaianitnatianiende,d w,whihchic his ias a
mmajaojro ardavdavnatnatgaeg eofo tfhtihsi aspapprporaocahc.h .
Pt+△t
max
EPP upper limit
Pt+△t Rising capacity reduced
EPP upper limit max_l
with lock constrains Pt+△t
EPP_u
Pt A Pt+△t Controlled capacity
EPP EPP_l
B
Controlled capacity reduced
Pt+△t
EPP
EPP lower limit Pt+△t
with lock constrains min_l
Shedding capacity reduced
Pt+△t
EPP lower limit min

Figure3.Changesinlimitstakinglock-onandoffconstraintsintoaccount.
Figure 3. Changes in limits taking lock-on and off constraints into account.
2.4. Users’WillingnessModel
2.4. Users’ Willingness Model
Users’willingnessγcanbedefinedasthedegreeofinitiativeforwaterheateruserstoparticipate
Users’ willingness γ can be defined as the degree of initiative for water heater users to
intodemandresponse. Itisaffectedbymanyfactors,likeeducationallevel,familyincome,family
participate into demand response. It is affected by many factors, like educational level, family income,
members’age[29,30]andsoon. Generally,familymembershavingacollegeoraboveeducationlevel
family members’ age [29,30] and so on. Generally, family members having a college or above
havestrongerwillingnesstoparticipateindemandresponse;familieswithhigherincomeincrease
education level have stronger willingness to participate in demand response; families with higher
theirinitiative;iftheaverageageoffamilymembersisbetween35–45,itismorelikelytohaveastrong
income increase their initiative; if the average age of family members is between 35–45, it is more
willingnesstoparticipateindemandresponse. Inthispart,threefactors—educationallevel,income
likely to have a strong willingness to participate in demand response. In this part, three factors—
influenceandfamilymembers’age—aretakenintoaccount. Figure4showstherelationshipofrelated
educational level, income influence and family members’ age—are taken into account. Figure 4 shows
factorsanduses’willingness. Asthediversityofeducationallevelisnotasabundantasthatoffamily
the relationship of related factors and uses’ willingness. As the diversity of educational level is not as
incomeandfamilymembers’age,threelevelsaresetuptodescribetheinfluencesofeducationallevel
abundant as that of family income and family members’ age, three levels are set up to describe the
onusers’willingness,ELstandsfortheeducationlevel.
influences of educational level on users’ willingness, EL stands for the education level.

γELγ=EL=bbbbbb11223 aaaa00121<<<<<<EEEELEELLLLL≤≤≤≤≤≤aaa123aaa 12 (10()10)
3 2 3
Thelowandmiddleincomegroupaccountforthemajorityofthetotalgroup. Thisgroupof

peoplehaverelativelyweakerwillingnesstoparticipateindemandresponseactivitiescomparedwith
thehighincomegroup,soanexponentialmodelissetuptodescribetheinfluenceofeducationallevel
onusers’willingness. HereFI standsforthefamilyincome:
(cid:40)
eFI 0< FI ≤ a
γ = 4 (11)
FI ea4 FI > a4
wherea standsforthemaximuminput,ifFI ismorethana ,theinfluencestaysthesame.
4 4
Energies 2017, 10, 559 7 of 21
The low and middle income group account for the majority of the total group. This group of
people have relatively weaker willingness to participate in demand response activities compared
with the high income group, so an exponential model is set up to describe the influence of educational
level on users’ willingness. Here FI stands for the family income:
eFI 0<FI ≤a
γFI =ea4 FI >a 4 (11)
4
where a stands for the maximum input, if FI is more than a ,the influence stays the same.
Energies20147,10,559 4 7of21
The influence of family members’ average age on users’ willingness can be described as follows:
Theinfluenceoffamilymembers’averγage=age1one(-u(FsA2e-σar25s)2’)w illingnesscanbedescribedasfollo(w12s):
FA
2π
The influences of family members’γ aFvAer=ag√e1 2aπgee( −o(bFeA2−yσ2a 5a) 2n)ormal distribution with expectation( 1a2)
5
σ
and standard deviation , which means children and the aged are not the main participants in
Theinfluencesoffamilymembers’averageageobeyanormaldistributionwithexpectationa
5
demand response programs. People aged between a and a (usually 35–45) will have more
andstandarddeviationσ,whichmeanschildrenandthe6agedaren7otthemainparticipantsindemand
interest.
responseprograms. Peopleagedbetweena anda (usually35–45)willhavemoreinterest.
6 7
BasBeads eodno tnhet haenaalnyasliyss aisboabvoe,v aen,a inntiengtreagtreadte udseursse’r ws’iwlliinllginngensse smsomdoedl ecalnca bneb seets eutpu: p:
γγ ·γ⋅γ ·⋅γγ
γ γ= = ELEL FIFI FFAA ((1133))
wh wh mamxa(xγ(γ ·γ⋅γ ·⋅γγ ))
ELEL FIFI FFAA
wwhheerreeγγwwhh h hasast aktaekneend uedcautcioatniaolnlaelv elel,vfealm, iflayminilcyo minecoamnde faamndil yfammeimlyb emrse’mavbeerras’g eavagereaignet oaagcec oiunntot.
aγcwchocuhnatn. gγesf rocmhan0gtoes1 fraoftmer 0n toor m1 aaflitzear tnioonrm. alization.
wh
Users’ Users’
willingness
willingness
b3 ea4
b2
b1
Educational
Family
Level
Income
0 a1 a2 a3 0 a4
(a) (b)
Users’
willingness
1
2π
Family Members’
Average Age
0 a6 a5 a7
(c)
Figure 4. The relationships of related factors and uses’ willingness. (a) Educational level influence; (b)
Figure4. Therelationshipsofrelatedfactorsanduses’willingness. (a)Educationallevelinfluence;
Family income influence; and (c) Family members’ age influence.
(b)Familyincomeinfluence;and(c)Familymembers’ageinfluence.
3. Optimization and Strategies
3. OptimizationandStrategies
This section will discuss the main optimization methods and strategies. Figure 5 illustrates the
This section will discuss the main optimization methods and strategies. Figure 5 illustrates
different periods of frequency response and the corresponding resources. When the system is
the different periods of frequency response and the corresponding resources. When the system is
running normally, the frequency of the system is kept within a reasonable range, which is usually a
runningnormally,thefrequencyofthesystemiskeptwithinareasonablerange,whichisusuallya
±0.2 Hz deviation of the system standard frequency (50 or 60 Hz). When there is a system disturbance,
±0.2Hzdeviationofthesystemstandardfrequency(50or60Hz). Whenthereisasystemdisturbance,
the frequency of the system may immediately drop out of the normal range. The first part of the

UFLSwillbeginwhenthesystemfrequencyisbelow f ;thispartcanberegardedas“emergency
epp
adjustment”,whichundertakesthemostloadsheddingtask,withtheEPP-WH,EV,andstorage(such
asbatteries)asthefrequencyresponseresources.
Energies 2017, 10, 559 8 of 21
Energies 2017, 10, 559 8 of 21
the frequency of the system may immediately drop out of the normal range. The first part of the UFLS
the frequency of the system may immediately drop out of the normal range. The first part of the UFLS
will begin when the system frequency is below f ; this part can be regarded as “emergency
epp
will begin when the system frequency is below f ; this part can be regarded as “emergency
epp
aEdnejrugsietsm20e1n7,t”10, ,w55h9ich undertakes the most load shedding task, with the EPP-WH, EV, and sto8roafg2e1
adjustment”, which undertakes the most load shedding task, with the EPP-WH, EV, and storage
(such as batteries) as the frequency response resources.
(such as batteries) as the frequency response resources.
fnor UFLS
fnofrn_olr UFLS
fnor_l
Emergency
Regulation adjustment
adEmjusetrmgeenncty
Regulation adjustment
adjustment
Frequency
cForlleaqpuseens cy
fepp collapses
fepp
EV
EV
Storage
Storage EPP-WH
EPP-WH
0 time
Figure 5.0 Different periods of frequency response and corresponding retismoeurc es.
FFiigguurree 55.. DDiiffffeerreenntt ppeerriiooddss ooff ffrreeqquueennccyyr reessppoonnsseea annddc coorrrreessppoonnddininggr reessoouurcrceess..
When the frequency changes back to f , which is the lower limit of the system frequency,
WWhheenn tthhee ffrreeqquueennccyy cchhaannggeess bbaacckk ttoo fnfor_l,, wwhhiicchh iiss tthhee lloowweerr lliimmiitt ooff tthhee ssyysstteemm ffrreeqquueennccyy,,
regulation adjustment begins in order to mainnnotorar__liln the system frequency. A long-term approach will
rreegguullaattiioonna addjujussttmmeenntt bbeeggiinnss iinn oorrddeerr ttoom maaiinnttaaiinn tthhee ssyysstteemm ffrreeqquueennccyy..A Al olonngg--tteerrmma apppprrooaacchhw wiillll
be implemented, which includes load shedding and rising, different from the emergency adjustment.
bbeei immpplleemmeenntteedd,,w whhiicchhi inncclluuddeess llooaadd sshheeddddiinngg aanndd rriissiinngg,, ddiiffffeerreenntt ffrroomm tthhee eemmeerrggeennccyy aaddjjuussttmmeenntt..
Figure 6 illustrates the control structure and strategies.
FFiigguurree6 6i lillulussttrraatteesst htheec coonntrtroolls strtruucctuturerea anndds strtarateteggieiess..
Frequency perturbation
Frequency△ pferturbation
△f
△f>fnor -fepp
△yef>sfnor -fepp
The rotor speed of yes
Emergency adjustment
Theg ernoetorra tsopresed of
Emergency adjustment
generators
Center of inertia System frequency
Cefnreteqru oefn icnyertia System frequency
frequency
no
The input mechanical torque no △f<fnor -fnor_l
The inpouf tg meneecrhaatonricsal torque △f<fnor -fnor_l
yes
of generators update
yes
update
Target optimal Regulation adjustment
Tdairsgpeatt cohpitnigmal Regulation adjustment
dispatching
EV target (*) storage target (*)
EPP-WH target (*)
EV target (*) storage target (*)
EPP-WH target (*)
EPP-WH strategy EV storage
EPP-WH strategy EV storage
EPP-WH EV status storage status
EPP-WH EV status storage status
EPP-WH operating information
Switch Status EPP-WHT oempepraetriantug rien formatLioonck on&off (Flag)
Switch Status Temperature Lock on&off (Flag)
Figure 6. Flowchart of control structure and strategies.
Figure 6. Flowchart of control structure and strategies.
Figure6.Flowchartofcontrolstructureandstrategies.
By analyzing the status of the generators, the frequency deviation of the system Δf and the
requiBrBeyyd a alnonaaaldlyy ztzoiin nbgge t tshhheee sdst taatΔtuuPss oocffa tnthh ebee g gceeannleceruraaltatotoerrsds,,. tWthheeit fhfrr eteqhqueu eeenvncacyylu dadeteivoviniaa ttoiiofo nnΔ ofof,f ttthhheee fsrsyeysqsttueeemmnc ∆yΔ ffr eaasnpndodn tthsheee
rrreeesqqouuuiirrreceedd w llooialald db tetoo d bbeeeci sdshheeeddd. U∆ΔsPiPncg ac niannbfo ebrcema calactulicolunalt aeotdne. dth.W eWi gtihethnt hetrheaeet overva’aslu louapatietoironantoi nofgf∆ pΔfof,i,t nhtthe, etf hrfereeq tquouteaenlnc tcyayrr greeesstp poΔonnPssee
rreessoouurrccee wwiillll bbee ddeecciiddeedd.. UUssiinngg iinnffoorrmmaattiioonn oonn tthhee ggeenneerraattoorr’’ss ooppeerraattiningg ppooinint,t ,ththee tototatal ltatargrgeet tΔ∆PP
can be calculated through a series of analyses which will be elaborated in more detail in the following
ccaannb beec caallccuullaatteeddt thhrroouugghha as seerrieiesso offa annaallyysseessw whhicichhw wililllb beee ellaabboorraatteeddi innm moorreed deettaailili innt thheef foolllloowwiinngg
section. The EPP-WH, EV, and storage receive their targets based on their percent power
sseeccttioionn..T hTeheE PEPP-WP-HW,HEV, ,EanVd, satnorda gsetorercaegiev ertehceeiirvtea rgtheetsirb atsaerdgeotns tbhaesiredp erocnen tthpeoiwr eprecrocnesnut mppotwioenr

inthesystem. Inthisstudy,wefocusedontheperfo rmanceoftheEPP-WH,assumingEVandstorage
hasgoodandstableperformance. Toensurethatappropriatetargetsaredispatched,severalelements
Energies2017,10,559 9of21
weretakenintoaccount,includingtheEPP-WH“users’willingness”andoperatingpoints. Duringthe
periodofemergencyadjustment,eachtypeofresourcesdecreasesitspowerconsumptiontohelppull
thesystemfrequencybacktothenormalrange. Whileintheregulationadjustmentperiod,response
targetsgeneratedfromthesystemincludesbothloadincreasingandloadshedding.
3.1. LoadSheddingCalculation
Whenadisturbanceoccursinamulti-machinepowersystem,withthemeasureddynamicsystem
response,changesinrotorspeedofsynchronousgeneratorscanbedetectedfirst. Intheprocessof
dynamicfrequencychange,differentgeneratorshavedifferentinfluencesonthesystemfrequency.
Therefore,thedefinitionofthecenterofinertia(COI)frequencyisputforward. Inthispaper,therate
ofchangeoftheCOIfrequencyisregardedastherateofchangeofthesystemfrequency. Basedon
this,therotorspeedandthemotionequationoftheCOIareexpressedasfollows:
 N
 ω = 1 ∑ T ω
COI TJi=1 Ji i (14)
 T dwCOI = ∆P
J dt
N
whereω istherotorspeedofthecenterofinertia(rad/s),T = ∑ T ,T istheinputmechanical
COI J Ji Ji
i=1
torqueoftheithgenerator(kW·s·rad−1), f isthefrequencyofthecenterofinertia(Hz)basedon
COI
therelationshipω =2πf ,inperunitvalue,ω = f :
COI COI COI COI

N
 f = 1 ∑ T f
COI TJi=1 Ji i (15)
 T dfCOI = ∆P
J dt
UsingEquation(15),thetargetloadshedding∆Pisachieved. Usinginformationonwaterheater
users’willingnessandtheoperatingpoint, f canbeobtainedas:
epp
 f = f −γ× f
 γeipp=kN∑=i1nγorwi,kh× PPEiwiP,khPP
 γPEi=PPi_∑=mto1taγli=×∑PmEiPPPEPiP_EitPoPtaPl (16)
i=1
whereγi,k standsforthekthwaterheateruser’swillingnessinthei-thEPP-WH,rangingfrom0to1,
wh
Pi,k is the power consumption of the k-th water heater. γi can be calculated through a method of
wh
weightingconsideringusers’actualpowerconsumption,andγcanbegeneratedbyweightingallthe
γi insystem. f representsthemaximumfrequencyrangeoftheregulationfrequencyadjustment,
P
whichcanbeestimatedbyEquation(16). Usinginformationfromthesystem, appropriatetargets
canbeidentifiedtotheexecutionunitsunderdifferent ∆f conditions. Equation(15)describesthe
relationshipbetweentherateoffrequencyandtheloadsthatneedtobedecreasedorincreased. Before
thefrequencyreturnsbackto f ,∆Pisanegativeparameter;duringthisemergencyadjustment
nor_l
period,thesystemcontinuesloadshedding. Whileintheregulationadjustmentprocess,∆Pmaybea
positiveornegativeparameterdependingonthesystemoperatingstatus,thesystemhasdemandsof
sheddingandincreasingloads.
Energies2017,10,559 10of21
3.2. TargetAssignmentMethod
Assumingthereisaloadsheddingdemandattimet,theEPP-WHsathigheroperatingpointswill
besuitabletoundertakemoretask,astheyhavelarger∆P todecreasetheirpowerconsumption.
down
Similarly,ifoneEPP-WHisoperatingatalowerpoint,itcanbeagoodresourcetoresponseloadrising
target. ToevaluatetheinfluencesofEPP-WH’soperatingstatus,parameterλisdefinedtocalculate
the degree of suitability for an EPP-WH to participate into demand response. λ can be obtained
throughanalysisoftheoperatingstatusofEPP-WH.Consideringthelock-oneffectsanddiversitiesof
EPP-WHs,eachEPP-WHhasdifferentoperatingstatusandpowerlimitswhicharealltime-varying,
thedegreeofsuitabilityforanEPP-WHtoparticipateintodemandresponseattimetcanbedefined
asfollows:
(cid:40)
∆Pt /(Pt −Pt ) loadshedding
λk,t = up_l max_l min_l (17)
∆Pt /(Pt −Pt ) loadrising
down_l max_l min_l
Conclusioncanbedrawnthatthelargerthevalueofλk,tis,themoretargetsshouldbedistributed
tothisEPP-WH,andthemoreithEPP-WHislikelytobeagoodresponseresource. Basedonthe
analysisabove,theobjectivefunctionandconstraintscanbewrittenasfollows:
m (cid:12) (cid:12)
objmin{ ∑ (1−λk,t)(cid:12)∆P∗k,t(cid:12)}
(cid:12) (cid:12)
k=1
m
st ∑ ∆P∗k,t = ∆Pt
total (18)
(cid:40) ∆Pt+∆t k<=1∆P∗k,t <0 loadshedding
down_l
0< ∆P∗k,t < ∆Pt+∆t loadrising
up_l
where∆P∗k,t standsforthetargetdistributedtoithEPP-WH,∆Pt isthetotaltargetwhichcanbe
total
generatedbyEquation(15). TheequationconstraintmeansalltheEPP-WHsundertakethetotaltarget
∆Pt . Besides, every EPP-WH should satisfy its upper and lower limits considering the lock-on
total
andoffeffects. Byusing1−λk,t asweightingfactor,thetargetgeneratedfromobjectivefunctionhas
consideredtheinfluencesofusers’willingnessλk,t andthelock-onandoffconstraints. UsingPSO
methodtosolvethisoptimalproblem,generating∆P∗k,t foreachEPP-WH.
3.3. EPP-WHOptimizationStrategies
Inthisstudy,anewTPLmethodwithlock-onandoffconstraintswasusedtocontroltheEPP-WH.
First,ateachtimestep,takingintoaccountthestatusofthewaterheaters,thecontrolledgroup
werescreenedout,theupperandlowerlimitswerecalculatedusingEquation(3),theEPP-WHwas
developed,inwhichwaterheatersin“lock”statushavebeeneliminated. Second,thewaterheaters
weredividedintotwopartsbasedontheirswitch’sstatus,makinguptwocontrolledgroupsasshown
inFigure7andEquations(19)–(20):
Ot = (Ot,Ot,Ot,...,Ot ), (19)
open 1 2 3 n1
Ct = (Ct,Ct,Ct,...,Ct ). (20)
closed 1 2 3 n2
InOt ,waterheatersweresortedaccordingtotheirtemperatureindescendingorder. Whilein
open
Ct ,waterheatersweresortedaccordingtotheirtemperatureinascendingorder.
closed