Smart refrigerators: a distribution-referred … refrigerators: a distribution-referred ... (t) P(t)...
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Smart refrigerators: a distribution-referred approach to decentralised control Simon Tindemans, Vincenzo Trovato, Michael Evans, Goran Strbac [email protected] Probabilistic methods for energy networks King’s College London, 14 March 2017
Transcript of Smart refrigerators: a distribution-referred … refrigerators: a distribution-referred ... (t) P(t)...
Smartrefrigerators:adistribution-referredapproachtodecentralisedcontrol
SimonTindemans,VincenzoTrovato,MichaelEvans,GoranStrbac
ProbabilisticmethodsforenergynetworksKing’sCollegeLondon,14March2017
Outline
1. Opportunitiesforflexibleloadcontrol2. Distribution-referredcontrol3. Applicationtorefrigerators4. Systemusesofaggregatecontrol
Flexibilityinthefuturepowersystem
electricitygridin=out
CO2CO2
CO2
+-flexibility
+flexibility+flexibility
Theflexibilityspectrum
Flexiblegenerators
Gridscalestorage
IndustrialandcommercialDR
+-
residentialDR
10-100MW 1-1000MW 100kW- 1MW 10W– 1kW
source
individualmagnitude
number 100 10- 1000 1000- 10000 10sofmillions
‘Longtail’ofdemandresponse
Unlocking the longtail
Constraints/challenges• Flexibilityisaby-productofotheractivities,whichwill
affectserviceavailability.• Smallper-deviceflexibilitycontribution,socostand
attentionbudgetissmall• Privacyconcerns• Significantheterogeneity
Opportunity• Verylargenumberofdevices,sostatisticaldiversity
canbeanasset.
Flexiblerefrigeration
1000 2000 3000 4000 5000 6000 7000t [s]
20
40
60
80P [W]
0
Pon
P
0 1000 2000 3000 4000 5000 6000 7000t [s]
2
4
6
8
T [°C]
Tmin
Tmax
T
sourceofflexibility
Powerconsumption
Temperature
≅( )
Flexiblerefrigeration:from‘what’to‘how’
Theopportunity• Refrigeratorsrepresent5-15%of
systemload(est.2-3GWinGB)*• Loadshiftingfor~30minutesis
free*secondaryuse
0
20000
40000
60000
potentialzerocostflexibility!
Thechallenge• Maintaincoolingperformance: Secondaryuse(flexibility)shouldnot
compromisetheprimaryuse(cooling)ofdevices.• Robustnessandscalability:Relianceonreal-timecommunication
mayresultinbottlenecksandsinglepointsoffailure• Controllability:Ensuresufficientcontroloverpowerconsumption,
andavoidunwantedinteractions.
DISTRIBUTION-REFERREDCONTROL
Controlrequirements
Aim:controltheaggregatepowerconsumptionofacollectionofappliances𝒜:𝑃$%$&' 𝑡 = ∑ 𝑃&(𝑡)�
&∈𝒜
Constraints:• Useonly aglobalcontrolsignalΠ(𝑡),suchthat𝑃$%$&' 𝑡 ≅ Π 𝑡 𝑃0$%$&'
• Applianceshavelimitedcontrollability• Discretepowerlevels• Localqualityofservice
𝑃$%$&' 𝑡 ≅1𝑃&(𝑡)�
&
= 𝑃0$%$&'×Π 𝑡Π(𝑡)
Complexpopulationconstraints
thermalmodels
states
(temperature,on/off*)
shouldnotswitchoff
shouldnotswitchon
x
x
x
Distribution-referredcontrol
𝐸 𝑃$%$&' 𝑡 = 𝑁𝐸 𝑃 𝑡 |Π7$
= 𝑁𝐸8 𝐸9(8) 𝑃(𝑆) 𝑀, Π7$ lawoftotalexpectation
= 𝑁 11𝑁𝐸9(>
?) 𝑃(𝑆) 𝑚&, Π7$�
&∈𝒜
= 1 𝐸9(>?) 𝑃(𝑆) 𝑚&, Π7$�
&∈𝒜
Assumptions• State𝑠 ofafridgewithmodel𝑀 isarandomrealisationof𝑆(𝑀)• ThedistributionofSissufficientlydiversetopermitvariationin𝑃(𝑆)• Independencebetweenappliances(O 𝑁CDE convergence)
𝐸9(>?) 𝑃(𝑆) 𝑚&, Π7$ = 𝑃0&Π 𝑡
= 1 𝑃0&Π 𝑡�
&∈𝒜
Controlconstraint
= 𝑃0$%$&'Π 𝑡
Distribution-referredcontrol
thermalmodels
states
(temperature,on/off*)
x
Howcanweoperatetheaggregatewithoutreal-timecommunication?
designcontrolstrategybasedonall statesforaspecificmodel
x
x
DISTRIBUTION-REFERREDCONTROLFORREFRIGERATORS
• Decentralisedcontrolofthermostaticloadsforflexibledemandresponse.SimonTindemans,VincenzoTrovato,GoranStrbacIEEETransactionsonControlSystemsTechnology(2015)
• Nondisruptive decentralizedcontrolofthermalloadswithsecondorderthermalmodelsSimonTindemans,GoranStrbac2016IEEEPESGeneralMeeting,Boston.
Constructingapopulation
𝑑𝑇(𝑡)𝑑𝑡 = H −𝛼(𝑇(𝑡) − 𝑇%K)
−𝛼(𝑇(𝑡) − 𝑇&>LMNK$)(on)(off)
0 1000 2000 3000 4000 5000 6000 7000t [s]
2
4
6
8
T [°C]
Tmin
Tmax
T
cabinet𝑇R(𝑡)
[on/off]
𝑇S>LMNK$environment
Refrigeratordynamics
0 2 4 6 8T [°C]
0.05
0.10
0.15
0.20
0.25
0.30probability
Tmin TmaxT
Steadystatetemperaturedistribution
Distribution-referredcontrol
Chooseone-parameterfamilyoftransformations:• Compatiblewithtemperaturelimits• Sufficientlyslowtoberealisable• Distributionknownatalltimes
𝑣 𝑇, 𝑡 = 𝛼𝛽(𝑡)(𝑇 − 𝑇>&V) 0 2 4 6 8T [°C]
0.05
0.10
0.15
0.20
0.25
0.30probability
Tmin TmaxT
𝑑𝑇W(𝑡)𝑑𝑡 = −𝛼 𝑇W 𝑡 − 𝑇%XX + 𝑇%XX − 𝑇W0 Π(𝑡)
Relateaveragetemperatureandpower
DesiredpowerconsumptionΠ 𝑡
Populationaveragetemperature𝑇W 𝑡
one-to-oneTransformationofpopulationdensity(parametrisedby
𝑣 𝑇, 𝑡 )
one-to-many
continuityequation𝜕𝜕𝑡 𝑓 𝑇, 𝑡 = −
𝜕𝜕𝑇 𝑣 𝑇, 𝑡 𝑓 𝑇, 𝑡
Computeswitchingactions
2 3 4 5 6 7 8T [°C]
0.05
0.10
0.15
0.20
2 3 4 5 6 7 8T [°C]
0.05
2 3 4 5 6 7 8T [°C]
0.05
0.10
0.15
on
off
-4000 -2000 0 2000t [s]
2
4
6
8
T [°C]
Tlow
Thigh
θ
stochastic switching event
desiredcollectiveresponse
device-levelactions
2 3 4 5 6 7 8T [°C]
0.05
0.10
0.15
0.20
requiredflux
computeswitchingactions1. Deterministicswitching2. Stochasticswitching
Π(𝑡)
Controllerimplementation(summary)
2 3 4 5 6 7 8T [°C]
0.05
0.10
0.15
0.20
-4000 -2000 0 2000t [s]
2
4
6
8
T [°C]
Tlow
Thigh
θ
stochastic switching event
2. Constructahomogeneous ’virtualpopulation’withrandomtemperatures.
4. Determinedevice-specificactions,basedontheactualdevicetemperature
2 3 4 5 6 7 8T [°C]
0.05
0.10
0.15
0.20
3. Manipulatethe‘virtualpopulation’tocontrolits(virtual)powerconsumptioninlinewithΠ 𝑡 .
𝑑𝑇(𝑡)𝑑𝑡 = H −𝛼(𝑇(𝑡) − 𝑇%K)
−𝛼(𝑇(𝑡) − 𝑇&>LMNK$)(on)(off)
1. Eachapplianceknowsitsstate andmodel
Π(𝑡)
Controllerimplementation(summary)
2 3 4 5 6 7 8T [°C]
0.05
0.10
0.15
0.20
-4000 -2000 0 2000t [s]
2
4
6
8
T [°C]
Tlow
Thigh
θ
stochastic switching event
2. Constructahomogeneous ’virtualpopulation’withrandomtemperatures.
4. Determinedevice-specificactions,basedontheactualdevicetemperature
2 3 4 5 6 7 8T [°C]
0.05
0.10
0.15
0.20
3. Manipulatethe‘virtualpopulation’tocontrolits(virtual)powerconsumptioninlinewithΠ 𝑡 .
𝑑𝑇(𝑡)𝑑𝑡 = H −𝛼(𝑇(𝑡) − 𝑇%K)
−𝛼(𝑇(𝑡) − 𝑇&>LMNK$)(on)(off)
1. Eachapplianceknowsitsstate andmodel
Π(𝑡)Eachapplianceconsidersitselfasarandom
representativeofapopulation...
...andtakesactionsinlinewithpopulationobjectives
Aggregateresponse
0 1000 2000 3000t
Π(t)
Collectively,heterogeneousfridgestrackthereferencesignal𝛱 𝑡
N=1000domesticrefrigerators
Nextsteps:labtesting
• ModifyfridgewithtemperaturesensorsandRaspberryPitocontrolthecompressor
• ...• Profit!
Challenges• Howmanytemperaturemeasurementstoinclude?• Sensitivitytomodelmisspecification• Howtotestastochasticcontrollerinasmall-scalelabtrial?
AGGREGATESERVICEPROVISION
• TheLeakyStorageModelforoptimalmulti-serviceallocationofthermostaticloads.VincenzoTrovato,SimonTindemans,GoranStrbacIETGeneration,Transmission&Distribution(2016)
• UnderstandingtheAggregateFlexibilityofThermostaticallyControlledLoadsVincenzoTrovato,SimonTindemans,GoranStrbacPowerTech 2017(submitted)
High-levelapproach
Aggregator
AggregateloaddispatchModelofcollectiveflexibility
controlsigna
l
resourceavailability
flexibilityproducts
Markets
Theleakystorageunit
Six-parametermodeltodescribetheflexibilityofahomogeneouspopulation
𝑑𝑆(𝑡)𝑑𝑡 = −
𝑆 𝑡𝜏 + 𝑃(𝑡)
withconstraints:
𝑃>MK ≤ 𝑃 𝑡 ≤ 𝑃>&V𝑆>MK ≤ 𝑆(𝑡) ≤ 𝑆>&V
_ 𝑆 𝑡 𝑑𝑡 = 𝑆0`
0
P(t)
αS(t)
Smax
S0Smin
S(t)
preservethefood!
𝑑𝑇W(𝑡)𝑑𝑡 = −𝛼 𝑇W 𝑡 − 𝑇%XX + 𝑇%XX − 𝑇W0 Π(𝑡)
𝜏
Aggregationofleakystorageunits
Heterogeneousmodelsaremergedintoaconservativeenvelopeflexibilitymodel.
Themodelissufficientandlinear,foreasyembeddingindispatchmodels.
P(t)
αS(t)
Smax
S0Smin
S(t)
P(t)
αS(t)
Smax
S0Smin
S(t)
P(t)
αS(t)
Smax
S0Smin
S(t)
P(t)
αS(t)
Smax
S0Smin
S(t)
P(t)
αS(t)
Smax
S0Smin
S(t)
Propertiesofapplianceclasses
𝑑𝜎(𝑡)𝑑𝑡 = −
𝜎 𝑡�̂� + Π(𝑡)
Πc>MK ≤ Π 𝑡 ≤ Πc>&V𝜎d>MK ≤ 𝜎(𝑡) ≤ 𝜎d>&V
_ 𝜎 𝑡 𝑑𝑡 = 1`
0
(heterogeneous)
Suitabilityofapplianceforservicedelivery
a b c
a b c
Powermodulation≅ Πc>&V- Πc>MK
30-minserviceprovision Energyarbitrage≅ 𝜏 𝜎d>&V − 𝜎d>MK
Firstorderanalysisofsuitabilityfordifferentservices
AggregatorAggregateloaddispatchModelofcollective
flexibility
controlsigna
l
resourceavailability
flexibilityproducts
Markets
P(t)
αS(t)
Smax
S0Smin
S(t)
Casestudy:Optimaluseofdifferentdeviceclasses
domestic commercial
OptimalserviceallocationinapproximateGBsystem• Energyarbitrage• Shortterm(30sec)frequency
services• Mediumterm(30min)
frequencyservices
Serviceallocationsreflectphysicalcharacteristics:• Slowthermaltimeconstants
aregoodforenergyarbitrage• Lowdutycyclesindomestic
appliancesleaveheadroomforhighfrequencyresponse.
Simulation:optimalallocationofflexibility59,524refrigerators(1MW);24-hourallocation
simulationofheterogeneous
refrigerators
Usingrefrigeratorstoprovideenergyarbitrageandfrequencyservices,makingoptimaluseofdeviceflexibility
deliveryoffrequencyresponse
Simulation:Clusteringofsimilarappliancesforbetterserviceallocation
Leakystoragemodelforflexibilityislimitedbylowestcommondenominator.
Flexibilitycanbeimprovedbycreatingclustersofappliancesaccordingtotheircapabilities.
WRAPPINGUP
Thedemandresponsecontrolspectrum
Ourapproach:distribution-referredcontrol• Devicesaresemi-autonomous• Collectivegoals aresetcentrally• Actions aredecidedlocally,withreference
toexpectedgroupbehaviour
Indirectcontrolusingincentives
Decentralised actionsonthebasisofanon-localcontrolsignals.
UsefultaxonomyofindirectcontrolinHeussen etal.,IEEEPESISGTEurope2012
Goalsandactionsaredecidedcentrally,orinadistributedfashion
Directdispatchofflexibleresources
• Requiresreal-timecommunication• Limitedautonomy• Privacyconcerns
V • Controllability
CommunicationrequirementsRobust‘semi-autonomous’operation
aggregator
responsedesigncycle
operationalcycle
1. Measuretemperature2. Updatemodel3. Switchon/off
realtime
aheadoftime
Significantchangesin:• thermalmodel• constraints
real-timecontrolsignalΠ(𝑡)
or
powerresponsemodel
Summaryandoutlook
Wehavedevelopedanend-to-endcontrolschemeforTCLsthatis• Nondisruptive: fridgesrespectlocalconstraintsatalltimesandarefree
torespondtoindividualcoolingrequirements• Decentralised:(semi-)autonomousoperationdoesnotrequirereal-time
commandandcontrolinfrastructure• Accurate:accuratecontroloveraggregatepowerconsumption,despite
on/offcharacteroffridgesandpopulationheterogeneity
Openquestionsandfurtherdevelopment• Robustness: Howsensitiveisthisschemetomodelmisspecification?• Thelimitoflargebutnotinfinitenumbers:meanfieldfeedbackeffects• Complexconstraints:lockout,temperaturevariations• Labtesting:firstsmallscale,thenlarge.• Optimaldispatchofleakystorageunits.
Wanttoknowmore?
• Decentralisedcontrolofthermostaticloadsforflexibledemandresponse.SimonTindemans,VincenzoTrovato,GoranStrbacIEEETransactionsonControlSystemsTechnology (2015)
• TheLeakyStorageModelforoptimalmulti-serviceallocationofthermostaticloads.VincenzoTrovato,SimonTindemans,GoranStrbacIETGeneration,Transmission&Distribution(2016)
• Nondisruptive decentralizedcontrolofthermalloadswithsecondorderthermalmodelsSimonTindemans,GoranStrbac2016IEEEPESGeneralMeeting,Boston.
• UnderstandingtheAggregateFlexibilityofThermostaticallyControlledLoadsVincenzoTrovato,SimonTindemans,GoranStrbacPowerTech 2017(submitted)
