operation of power flow controllers --computational

OperationofPowerFlowControllers:ComputationalEfficiencyandMarket

Participation

Mostafa [email protected]

1EPRITechConference

SummaryofResearchProjects

• PowerSystemOperationDuringWindstorms– CollaborativeResearchwithDepartmentofCivilEngineering

• Computationally-EfficientAlgorithmDesignforOperationofPowerFlowControllers– TransmissionSwitching(ARPA-EProject)– ControllableReactance(TCSC,SmartWireGrid)

• MarketDesignforFlexibleTransmission

2EPRITechConference

Motivation

3

Economicsizeoftheindustry:$350billion

Transmissionsystemisunderstress

Transmissionbottleneckscreateeconomicinefficiency

Transmissionsystemneedstobeupgraded• Improvedeconomicefficiency• Reliability-motivatedupgrades

EPRITechConference

TransmissionBottlenecks

EPRITechConference 4

• Option1:buildmorelines• Option2:powerflowcontrol

Congested

NotCongested

CongestionCostinUSISO/RTOs

5

00.20.40.60.81

1.21.41.6

ISOCongestionCosts– 2015

CAISO ERCOT ISO-NE MISO NYISO PJM SPP

$B

EPRITechConference

Choices

BuildingNewTransmission

Lines

MoreEfficientUtilizationoftheExistingGrid– PowerFlowControl


Moreefficientutilizationoftheexistingnetworkischeaperandparamount!

ResearchandDevelopmentEfforts

• ARPA-EGENIinitiative:Over40milliondollarsforpowercontrolhardwareandsoftware

Hardware:• Smartwiregriddevice• FlexibleACTransmissionSystem(FACTS)

Software:• Transmissionswitching(TS)

– Fastconvergence– QualityACsolution– Dynamicstabilityanalysis

• EnhancedFACTSadjustment(notsupportedbyARPA-E)– Samebenefits– Moreorlessthesameconcerns

7EPRITechConference

PowerFlowPhysics

Vj∠θ jVi∠θi B

EPRITechConference

F = B(θ j −θi )DCPowerFlowEquation

ThisisalinearapproximationofACpowerflowequation:• Relativelyaccurate• Facilitatesefficientcomputation

Susceptance

Electricityflowsaccordingtothelawsofphysics,noteconomics!

F

8

VariableImpedanceFACTSBmin ≤ B ≤ Bmax PowerElectronicsFk = Bk (θ j −θi )

EconomicExample


1 2G1:Cheap G2:Expensive

Load:250MW

Capacity:100MW,X

Capacity:150MW,X

100MW

100MW

200MW

50MW

100MW

140MW

240MW

10MW

CostReduction!

Technology– TCSC

• Thyristor-ControlledSeriesCompensator

10

8 Thyristor control | Thyristor Controlled Series Compensation

In a TCSC, the whole capacitor bank or alternatively, a section of it, is provided with a parallel thyristor controlled inductor which circulates current pulses that add in phase with the line current so as to boost the capacitive voltage beyond the level that would be obtained by the line current alone. Each thyristor is triggered once per cycle and has a conduction interval that is shorter than half a cycle of the rated mains frequency. By controlling the additional voltage to be proportional to the line current, the TCSC will be seen by the transmission system as having a virtually increased reac-tance beyond the physical reactance of the capacitor.

The thyristor valve is integrated in the capacitor overvoltage protection scheme. It replaces the Fast Protective Device and allows a reduction of the rating of the protective parallel varistor.

Thyristor control

Thyristor-controlled segment of a series capacitor.

Xv

a) b)

uc

uc

iL xc

iLiv iv

TCSC in steady-state, a) circuit b) waveforms.

ABB– TCSCbrochure EPRITechConference

Technology– SmartWireGrid

• SmartWireGridDevice

11

PowerRouterbrochure

EPRITechConference

EconomicImpacts


Congested

Not Congested

Withpowerflowcontrol,cheaperresourcescanreplacethelocalexpensiveresources.

ResearchObjective


• Challenges:1. Computationalcomplexity(limitedtime)2. Powerflowcontrollersareapartofthe

transmissionnetwork• Regulated• Noincentivetooperateinasociallyoptimalway

• Goal:Designamarketmechanismthatwouldallowpowerelectronicstoparticipateinthemarket!

COMPUTATIONALCOMPLEXITY

14EPRITechConference

ComputationalComplexity– DCOPF

• DCOPF– LinearProgram(LP)𝑚𝑖𝑛∑ 𝑐'𝑃'' (1)

𝑃')*+ ≤ 𝑃' ≤ 𝑃')-. ∀𝑔 (2)−𝐹3456≤ 𝐹3 ≤ 𝐹3456 ∀𝑘 (3)𝐹3 − 𝐵9 𝜃+ − 𝜃) = 0 ∀𝑘 (4)∑ 𝑃99∈>? + − ∑ 𝑃99∈>@ + + ∑ 𝑃''∈' + = 𝑑+ ∀𝑛 (5)

3/8/17 EPRITechConference 15

LinearProgram

VariableImpedanceFACTS

• VariableimpedanceFACTS

• Providepowerflowcontrol• CreatenonlinearitiesinDCoptimalpowerflow

LinearProgramè Non-LinearProgram(MixedIntegerProgram)


Vn∠θn Vm∠θm

Rk + jXk jXmin ≤ jXv ≤ jXmax

NonlinearequationBmin ≤ B ≤ Bmax Susceptance isavariableFk = Bk (θ j −θi )

ComputationalBurden

NoFACTSsetpointadjustmentwithinEMSorMMSsoftware

Infrequentadhocadjustments

ComputationalComplexity–NLP/MIP

NonConvex(MIP)

Convex(LP)

Convex(LP)


Fk = Bk (Δθk )Bkmin ≤ Bk ≤ Bk

max

Fk

Fkmax

Fkmin

Δθk

WhatifweknewwhichB&Btreenodeistheoptimalnode?


EngineeringInsight

• Weonlyneedtoknowthedirectionofthepowerflow

• Weknowthisdirectionformajorlines(COI)

• Evenifwedonotknowthedirection,wecanrunatwo-stageDCOPFandidentifyit.


Convex(LP)

Convex(LP)

19

Fk = Bk (Δθk )Bkmin ≤ Bk ≤ Bk

max

Fk

Fkmax

Fkmin

Δθk

KnowingthedirectionwouldreducethecomplexitytoaLP

Thisisaheuristic

Optimalityisnotguaranteed!

SCEDCostSavingsIEEE118-BusSystem


0 10 20 30 401200

1400

1600

1800

2000

2200

Number of Lines With FACTS

Cos

t ($/

h)

2%5%

10%

20%30%

70%90%

50%

0%10%20%30%40%50%60%70%80%90%

0% 50% 100%

Saving

s

FACTSCapacity

5 10 15 20Number ofFACTS:

OptimalFACTSPlacement:>98%Optimal

LocatedonMoreHeavilyUtilizedLines:100%Optimal

Savingsarecalculatedcomparedtoatransportationmodel

SCEDCostSavingsPolishSystem


0

10

20

30

40

50

60

70

80

90

0% 20% 40% 60% 80% 100%

%ofP

oten

tialSavings

FACTSReactanceControlRange

5 10 15 20Number ofFACTS:

LocatedonMoreHeavilyUtilizedLines:100%Optimal

Savingsarecalculatedcomparedtoatransportationmodel

~2,400buses

~2,900branches

ComputationalTime


0 100 200 300 400 500 600

LPMIP

ComputationalTime(ms)

MIPAverage

LPAverage

Max:4630s

CorrectiveAdjustments

• Incorrectiveadjustmentswehaveevenbetterinsightaboutthedirectionofthepowerflow:pre- orpost- contingencyflows

• Goal:minimizationofpost-contingencynetworkviolations

• OptimalutilizationofFACTSinrecoursestateonly

EPRITechConference 23FACTS Adjustment

Contingency Analysis

SCUC

Contingency Analysis

Calculate the difference in Network Violations

CorrectiveResultsIEEE118-BusSystem


25 10 20 30 50 70 900

20

40

60

80

100

Reactance Change (%)

Viol

atio

n R

educ

tion

(%)

LPMILP

5 Lines10 Lines

15 Lines20 Lines LocatedonMore

HeavilyUtilizedLines:100%Optimal

ShiftFactorStructure

• IndustryimplementationsofSCUCandSCEDdonotuse𝐵𝜃structure;theyusePTDFs.– Noneedtomodelallthevoltageangles– Noneedtocalculatealltheflows– Significantlyfastercomparedto𝐵𝜃


from to𝑏9 + 𝛥𝑏9

from to𝑏9

𝑓9𝛥𝑏9

𝑏9 𝑓9

𝛥𝑏9

𝑏9

InjectionModelofReactanceControl

• Again,weendupwithaMixed-IntegerLinearProgram!• Wecanusethesameengineeringinsighttoconvertthis

toaLP.• Similarmethodcanbeusedtogeneratecontingency

constraints.


from to𝑏9 + 𝛥𝑏9

from to𝑏9

𝑓9𝛥𝑏9

𝑏9 𝑓9

𝛥𝑏9

𝑏9

Results– PolishSystem


𝑩𝜽 versusPTDF 𝐅𝐢𝐱𝐞𝐝𝐯𝐞𝐫𝐬𝐮𝐬𝐀𝐝𝐚𝐩𝐭𝐢𝐯𝐞𝐓𝐡𝐫𝐞𝐬𝐡𝐨𝐥𝐝𝐬

MARKETPARTICIAPTION


O’Neill’sCompleteMarketProposal

29

1 2G1:Cheap G2:Expensive

Load:250MW

Capacity:100MW,X

Capacity:150MW,X

100MW

200MW

50MW

100MW

• PositiveexternalityinDr.O’Neill’scompletemarketproposal:• Paymenttoline:(Flow)x(LMPDifference)

• Nomatterwhichlinechangesthereactance,itisalwaysthesecondlinethatwillcarrymorepowerandgetpaid!

EPRITechConference

ProposedPaymentSystem

30

Fk = Bk (θ j −θi ) (Sk )

Sk (θ j −θi )×ΔBkMarginalValue:Price Quantity

• Usethesusceptance pricetocalculatethemarginalvalueofsusceptance:

EPRITechConference

TwoNodeSystem


G1 G2

-700p.u.,400MW

-700p.u.,450MWd2

MC2=P2+50($/MWh)MC1=$30/MWh

FACTScontrolrange:2%

MarginalValue

32

SAHRAEI-ARDAKANI AND BLUMSACK: TRANSFER CAPABILITY IMPROVEMENT 3711

Fig. 10. Cost savings due to the improved transfer capability offered by theFACTS devices.

Fig. 11. Congestion rent in thousands of dollars with and without FACTSdevices.

payments are much smaller than the congestion rent shown inFig. 11, making the market revenue adequate.Fig. 12 shows the payments to the FACTS owners. FACTS

revenue is clearly smaller than the congestion rent shown inFig. 11. According to the proof presented in Section III-A, pay-ments to the owner of should be less than the con-gestion rent collected by line, 2 since the FACTS adjustmentaims at increasing the flow of this line by increasing the abso-lute value of its susceptance. However, revenue adequacy is notguaranteed for , since the susceptance adjustment isin the opposite direction. Despite the absence of proof, FACTSpayments are much smaller than the congestion rent shown inFig. 11, making the market revenue adequate.Fig. 13 provides additional insight into how the market would

work. The marginal value of FACTS capacity for the device in-stalled on line one is depicted in the figure. This is depicted ac-cording to (8). It shows how the price is set at different levelsof demand. In this example, each per unit change in the sus-ceptance of the line would decrease the marginal value forminga negatively sloped curve. Note that the slope may very well

Fig. 12. Payments to the FACTS owners. Solid lines indicate perfect competi-tion, while dashed lines show Cournot results.

Fig. 13. Marginal value and supply functions for FACTS capacity installed onthe line one at different levels of load.

be positive due to the non-convexities of the market. In a per-fectly competitive market, FACTS owners would submit a bidof $0/p.u., which would be a horizontal line at zero until theircapacity is exhausted; then, it would be a vertical line, meaningthat they cannot offer more adjustment at any price. When theload is low and FACTS capacity is enough to relieve the conges-tion, the price would be zero. For example the market results ina price of $0 per p.u. for demand of 805MW. However for largeenough demand, that FACTS capacity is not enough for removalof the congestion, the marginal value of the FACTS adjustmentsets the price. For example, for the load of 830 MW, the pricewould be $18.11 per p.u. change in the susceptance of the firstline.Under Cournot competition, the players find their optimal ca-

pacity to offer to the market based on the marginal value func-tion. Thus, even when the FACTS capacity is enough to relievethe congestion, the device owners would strategically withholdsome of their capacity to keep the marginal value positive. If thecongestion is removed this value would go down to zero.

EPRITechConference

𝑆9(𝜃* − 𝜃[)

RevenueAdequacy

• Congestionrentisthepaymentsource

• Revenueadequateiftheadjustmentsleadtoincreasedloading!

• Notnecessarilyguaranteedinallcases

• Itishighlyunlikelythatthemarketisrevenueinadequate


IEEE118BusSystem2FACTSDevices


Conclusions

• MathematicalrepresentationofOPFwithFACTS:NLP

• WereformulatedtheNLPtoaMILP;usingourknowledgeofelectricityflowphysics,wereformulatetheproblemtoanLP

• TheLPheuristicisextremelyeffective:itfoundtheoptimalsolutionmorethan98%ofthetime.

• Theheuristicisextremelyfast(LP)andwouldnotaddtothecomplexityoftheOPFproblem

• Wedesignedacompensationmechanismtosignalenhancedoperationofthedevices.


Thankyou!Questions?

36

Mostafa [email protected]

• M.Sahraei-ArdakaniandK.Hedman,“AFastLPApproachforEnhancedUtilizationofVariableImpedanceBasedFACTSDevices,”IEEETransactionsonPowerSystems

• M.Sahraei-ArdakaniandK.Hedman,“Day-AheadCorrectiveAdjustmentofFACTSReactance:ALinearProgrammingApproach,”IEEETransactionsonPowerSystems

• M.Sahraei-ArdakaniandS.Blumsack,“TransferCapabilityImprovementthroughMarket-BasedOperationofSeriesFACTSDevices,”IEEETransactionsonPowerSystem

• M.Sahraei-ArdakaniandK.Hedman,“ComputationallyEfficientAdjustmentofFACTSSetPointsinDCOptimalPowerFlowwithShiftFactorStructure,”IEEETransactions onPowerSystems

EPRITechConference

operation of power flow controllers --computational

Documents