OperationalAwareInvestmentsinTransmissionSystems:ScenariosGeneration,SecurityAnalysis,FACTSDevices
InstallationsforSystemReinforcement
1
VladimirFrolov1,Priyanko Guha Thakurta1,MichaelChertkov2,ScottBackhaus2,Janusz Bialek1
(1- Skoltech,Moscow,2– LANL,LosAlamos,NM)
FACTSdevices– flexiblealternatingcurrenttransmissionsystemdevices
EPCC14,May14– 17,2017,Wiesloch
• Operationalawareinvestments• FACTSdevicesinstallations- Singletime-frameFACTSinvestments- Multitime-framesFACTSinvestments• Futureloadingscenariosgeneration(usingLoadDurationcurve)• InvestmentexampleforPolishsystem• Discussion- Currentlyobtainedresults- Dataanalysisforimprovedinvestmentdecisions- Operationalaware+securityconstrainedplanning- Practicalapplications
Contents
Investment decision is made taking into account futuretransmission system operations with new equipment installed:1. Investment and operational variables are considered2. CAPEX + OPEX is optimized3. Multiple loading conditions are considered (with probabilities)4. Exact AC modeling5. Single of multiple time frames (decision or plan)6. Security analysis, Security constraints*
This is in contrast with single (usually worst case) scenario planningwhen only investment cost is minimized to resolve specific problem
BUT:Problemiscomputationallyhard.Scalableoptimizationalgorithmsshouldbedevelopedforresolution.
OperationalAwareInvestments
SingleTime-FrameFACTSInvestments
SCdevices– modificationoflineinductance(atedge)SVCdevices– injection/consumptionofreactivepower(atloadnode)
𝜋 transmissionlinemodel
𝑔𝑒𝑛: 𝑆() = 𝑃(
) + 𝑗𝑄()
𝑙𝑜𝑎𝑑: 𝑆(3 = 𝑃(3 + 𝑗𝑄(3
Investmentmotivation:• Generationcostreduction• Reliabilityimprovements• Congestionreduction
Operationalobjectives:• Oper.costminimization• Regimeexistence• Absenceofoverloads
Improvedflexibilityofthe systemreinforcingtransmissiongridforthefuturesystemloadsandpostponehugeinfrastructureinvestmentsImportant:Scalabilityoftheapproachforpracticalsizesystems
Applications:• Shorttermplanning• Longtermplanning• ControlofFACTS
• Optimally place and size SCs and SVCs• Consider multiple loads configurations (scenarios) with their rates• Minimize capital investment and system operational costs• Given service period• Exact AC-modeling paradigm• Find optimal settings for the installed devices for each scenario• Develop practical planning methodology (scenarios sampling)
Features
ProblemStatement
Min(CAPEX+OPEX)s.t.:1.Operationalconstraintsforeachscenario2.Connectionofinvestmentandoperationalvariables
OptimizationModel
OptimizationModel
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Objectivefunction:• Investmentcostandoperationalcost
summarizedovergivenscenariosConstraintsmeaning:• Stateforeachscenarioisdefinedbyvectors
oflineinductances,voltages,phases,activeandreactivepowerinjectionsatnodes
• ActuallineinductanceisequaltoitsinitialvalueplusSCcorrectionadjustedtoascenario,howevermaintainedwithintheinstalledcapacitybounds
• ActualreactivepowerdemandforaloadisequaltoitsinitialvalueplusSVCadjustedtoascenario,howevermaintainedwithintheinstalledcapacitybounds
• Limitsforvoltagesandpowergeneration
• Linethermallimits
• Activeandreactivepowerbalanceconstraintsatnodes
Why:1. Recedinghorizonoptimization2. Lifetimeofequipment3. Uncertaintygrowswithtime4. Evolutionofprices
MultiTime-FramesFACTSInvestments
12t– decisionpoint
0NyearsMscenarios(t),a=1..M
T– numberofdecisionpointsN=TM– totalscenarios
min∆8,∆:,;<=
>𝐶@ABB ∆𝑥(D
<�
(D∈G
+ 𝐶;HIB B ∆𝑄(<
�
(∈JKL>M
+ 8760𝑁𝑦𝑒𝑎𝑟𝑠BB𝑝𝑟 ∗ 𝐶(𝑃<Y)
[
Y\]
^
<\]
^
<\]
^
<\]
S.t.:1. 𝑠𝑡<Y = 𝑥, 𝑉, 𝑇ℎ, 𝑃, 𝑄 <
Y
2. ∆𝑥< <f<Y3 = ∑ ∆𝑥h<h\]
3. ∆𝑄< <f<Y3 = ∑ ∆𝑄h<h\]
4. ∆𝑥< ≥ 0∀𝑡, ∆𝑄< ≥ 0∀𝑡5. 𝑥<Y − 𝑥(o(< ≤ ∆𝑥< <f<Y36. |𝑄𝑙𝑜𝑎𝑑<Y − 𝑄𝑙𝑜𝑎𝑑(o(<| ≤ ∆𝑄< <f<Y37. ∀𝑡, ∀𝑎: VoltageandGenerationconstraints8. ∀𝑡, ∀𝑎: Apparentpowerlimitsonlines9. ∀𝑡, ∀𝑎: ActiveandReactivepowerbalanceatnodes10. ∀𝑡, ∀𝑎: Slackbusconstraints11. +BudgetlimitationorCapacityconstructionlimitation
OptimizationModel
12t– decisionpoint
0NyearsMscenarios(t),a=1..M
T– numberofdecisionpointsN=TM– totalscenarios
Features|OperationalVarsConsideration
Additionaldegreesoffreedom(whichavailableatoperations)allowtosignificantlyreduceinvestmentcosts
Setting: Optimizationisdonefor5%overloadedbasecasescenario(infeas.)forhorizonof0years.0meansthatonlyinvestmentcostisminimized
Investmentcostcomparisonfor30bussystem
Investmentcostcomparisonfor2736bussystem
Features|MinimizationofCAPEX+OPEX
Case30:
Nyears at optimization
Investment Cost, $
Operational Cost, $/hour
Usage for # of years: 1 year, M$ 10 years, M$
Cost difference for 10 years, M$
Cost difference for 10 years, %
0 55618,76 698,24 total cost: 6,172 61,722 7,864 14,601 121838,27 616,25 total cost: 5,520 55,202 1,343 2,49
10 248860,59 611,98 total cost: 5,385 53,858 0,00 0,00
Polish:
Nyears at optimization
Investment Cost, $
Operational Cost, $/hour
Usage for # of years: 1 year, M$ 10 years, M$
Cost difference for 10 years, M$
Cost difference for 10 years, %
0 188138,62 1949816,70 total cost: 17080,6 170805,8 4330,1 2,601 402179,51 1911233,78 total cost: 16742,8 167428,1 952,4 0,5710 742509,22 1900399,40 total cost: 16647,6 166475,7 0,00 0,00
Forpracticalplanninghorizonsoperationalcostismuchbiggerthaninvestment.Importanttooptimize
forsumofCAPEX+OPEX
Setting: Optimizationisdonefor5%overloadedbasecasescenario(infeas.)forhorizonsof0,1and10years.0meansthatonlyinvestmentcostisminimized
Features|ScenarioDependentOperationalSettingsSetting:Numberofscenarios:10Eachoccurrencerate:10%Stddevfactor:0.1alpha:1.1Serviceperiod:1yearACOPF(AlternatingCurrentOptimalPowerFlow)feasibleandinfeasibleloadingconditions
Optimalsolutionfor2of10sc.
FACTS- additionaldegreesoffreedom,adjustedtogetherwithother
operationalvariables
Features|UpperBoundOptimality
IPOPTsolutionofnonlinearproblem1. Solution – build SVC2. SVCcapacity:2.436MVar3. Objectivefunction:5.520094e6$
Solutionobtainedbyalgorithm1. Solution – build SVC(atsamebus)2. SVCcapacity:2.437MVar3. Objectivefunction:5.520159e6$
Algorithmdiscoversupperboundsolutionwithsimilarstructureandobjectivefunctionvalue
Setting:30bussystem5%overloadedbasecaseACOPFinfeasible
Features|Scalability
Solutiontimedependingonproblemsize,30bussystem.Green(IPOPT),black(Alg)
Developedalgorithmallowstosolveplanningproblemsforpracticalsizesystems
Solutiontimedependingonproblemsize,2736bussystem
y = 1,896x
y = 0,6367e0,1143x
0
1000
2000
3000
4000
5000
6000
7000
0 500 1000
Tim
e, se
c
Number of scenarios
y = 4,943x3 - 28,965x2 + 282,85x - 101,22
02000400060008000
100001200014000160001800020000
0 5 10 15 20
Tim
e,se
c
Number of scenarios
ScenariosSamplingUsingLDCurve
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1. 𝑁 ∗ 𝑀𝑙𝑜𝑎𝑑𝑖𝑛𝑔𝑐𝑜𝑛𝑓𝑖𝑔𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝑠2. 𝛼 ∶ ∀𝑖 = 1. .𝑀𝑙𝑜𝑎𝑑𝑠(z = 𝛼( ∗ 𝑙𝑜𝑎𝑑𝑠z3. ∀𝑗 = 1. . 𝑁: 𝑙(
D = 𝑙(z + 𝑛𝑚𝑟𝑑 𝑠𝑡𝑑𝑑𝑒𝑣 ∗ 𝑙(z
4. 𝑝(D = 𝑤(/𝑁
ExampleofLDcurveapproximation
Long-termPlanning|PolishsystemSetting:Totalscenarios:16Beta:0.5%/yearServiceperiod:10yearsComp.time(CPLEX):10397sFeas.+infeas.conditions
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Solution:Investment:350k$Aver.economy:3369.4$/hMax.economy:61840$/hSVC:3.30MVarSC:14.4%,70.4%(l-->r)Feasibilityobtained:yes
Costanalysisforthesystem
Convergenceofthesolution Optimalinvestment
ScenariosGenerationfromRealData
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Measureddataisimportantnotonlyforoperationsbutforimprovementofinvestmentdecisionsaswell
1. Forexamplenodalgeneration/consumptionisknownforeachhourforseverallastyears
2. Hourlyregimescanbeanalyzedandclassified3. Nodescanbeclassifiedbyload/generationprofiles4. Trendsinthepastshouldbedeterminedtomakepredictions
aboutthefuture:- Levelsofuncertaintyandfluctuations- Dynamicsofload/generationprofiles(nodesbehavior)- LayoutoffutureLDcurves5. Accordingtopredictionsrepresentativefutureloading
conditionswillbedetermined
SecurityConstrainedPlanning
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Addition of all N-1 security constraints to optimization problemwill make it impossible to resolve.
Possible approaches:1. Perform security analysis. Try to find important contingencies2. Develop optimization model which performs N-k securityConstrained planning
Modelling:• Singleormultipletimeframes• Multipleloadingscenarios• ConsideringACOPFforoperationsExternalfactors:• Plannedgenerationretirement,amountofreserves• Policies(climate)• Lifetime(e.g.howmuchenergyitcanproduce)Questions:• Whichtypetobuild• Placementandcapacities• Whentobuild(plandependsonusageofothergens)
Applications|GenerationConstruction
• Investorlookingforbuildinga(e.g.)generator• Budgetislimited• Wantstomaximizepayout
𝑃IY�(oH�;<- buildcapacity
𝑃;�<(oH�;<- operationalsettingforparticularscenarioOperationalsettingsaredefinedbyACOPF:𝑃;�<(oH�;<=ACOPF(𝑃IY�(oH�;<,scenario)
Problem: max��>������=
GY�o��[fo��@��o<[fo��
s.t.:
1.𝑃;�<(oH�;<=ACOPF(𝑃IY�(oH�;<,scenario)2.Budgetconstraint
Applications|InvestorProblem
ResultsandWorking/FuturePlansResults:• Improvedplanning
methodology• Solutionalgorithm• Justifiedoptimality• Scalabilityofapproach• Sparsity+non-locality• Singleofmultitimeframes
Applications:• FACTSinvestmentplanning• Optimalcontrolofthe
installeddevices• Extensionsofmethodology
tootherinvestments
Futurework:• Algorithmperformanceandconvergenceimprovements• Modelingimprovements• Statementandsolutionofgenerationconstructionproblem• Consideringextensions
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