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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