Aspects of Wide-Area Damping Control Design using Dominant Path Synchrophasor Signals

using Dominant Path Syn hrophasor Signals

YUWACHOMPOOBUTRGOOL

Do toral Thesis

ISSN 1653-5146

ISBN 978-91-7595-522-3

SE-10044Sto kholm

SWEDEN

AkademiskavhandlingsommedtillståndavKunglTekniskahögskolanframlägges

till offentliggranskningföravläggandeavAkademiskavhandling 7May2015isal

F3, Lindstedtsvägen28,KungligaTekniskaHögskolan,Sto kholm.

Abstra t

The presen e of inter-area os illations has long ae ted stability on-

straints,andtherefore,limitedthepowertransfer apa ityofinter onne ted

power systems. Adequate damping of these inter-area os illations is, thus,

ne essarytose uresystem operationandensuresystem reliabilitywhile in-

reasing powertransfers. Powersystemstabilizers(PSS)arethe most om-

mondevi esusedtoenhan ethedampingofsu hos illations. Manystudies

havedemonstratedthatPSSsusing remotesignalsmayperformbetterthan

usinglo alsignals.

Theadventof phasormeasurementunits(PMU)makesremoteorwide-

areasignalsbe omeavailable,whi henablesvariousimportantappli ations.

Ofparti ularinterestiswide-area damping ontrol(WADC),whi haimsto

utilizeremoteorwide-areameasurementstodamptheinter-areaos illations.

However, two main hallenges in WADC designare (1)feedba k ontroller

input signal sele tion (whi h PMU signal is best to use?), and (2) laten y

(whi hisinherentinthetransmissionofthemeasurements) onsiderations.

In response to the rst hallenge, this thesis proposesa on ept alled

dominant inter-areaos illation path,whi h servesto pinpoint a setof an-

didatesignalsthat anbeusedasthefeedba k ontrollerinputsbylo ating

theinter onne ted orridorswheretheinter-areamodal ontentsarethemost

observable. Derivation,identi ation,anduseofthedominantinter-areaos-

illationpathsaredemonstratedthroughoutthethesis.Extensiveanalysison

the relationshipsbetweenthe proposedset ofsignals andsystem properties

regarding stability and robustness is presented. Tota kle the se ond hal-

lenge,theimpa tsoftimedelaysonthesystemperforman e whenusingthe

dominantpathsignalsareinvestigated.

To date,several studieshave proposed dierent ontrol designmethods

using various os illation dampers to designWADC.Nevertheless, neither a

systemati methodnora on ept thaten ompasses fundamentalknowledge

onpowersystemdynami shasyetbeenoered. Theobje tiveofthisthesisis,

thus,toproposeananalyti alframeworkbasedonthedominantpath on ept

whi hisbuiltuponfundamentalprin iplesforfeedba k ontrollerinputsignal

sele tioninWADC.Withthisframework,aproperandsystemati approa his

developed.Theproposedmethodallowstosele tappropriatesignalsanduse

themto ee tively mitigatethe inter-area os illationsthat onstrain power

This thesis work is an out ome after numerous inputs all of whi h I am grateful

for: the nan ial support from Elforsk/Energimyndigheten, the fa ility and help

supports from EPS department, and the friendly support from EPS olleagues.

Moreimportantly,Iamindebtedtomysupervisor,Dr. Luigi Vanfretti,forallthe

inputsintothiswork: his guidan e,en ouragement,help andsupport. Espe ially,

his attentiveness (in going throughall of my works meti ulously), dedi ation (as

a role of supervisor), and are (for my and other students' sake) are gratefully

appre iated. Thisthesiswouldnothavebeen ompleted withouthim.

ThroughoutmyPhDstudyinSweden,throughalltheimpermanen eand on-

tinuous hangesbothoutsideandinside,andthroughalltheupsanddowns,there

areanumberofpeople towhomI amgratefulforbeingimportantandinvaluable

inputsto mylife.

ManythankstoAngela, Wei,Ezgi,Maxime,Camille, Yalin, Fran is o,Almas,

Rujiroj,Ri hard,and Fredrik, forall thetimeswehavehad together,for making

mydaysatKTHdierentfromtheothers,andforhavingsu hamiable hara ters

¨

⌣

Many thanks to Sakonvan, Thiansin, Pranpreya, Nisarath, Kittipong, Artita,

Kasinee, Surasin, Gunyarath, Cheevarat, and Rerngvit for all the supports you

havegiven,forallthemoments(andfood)wehaveshared,forallthe arethathas

neverbeenmissed,andfortheassistinpolishingmylanguageskill:-).

ManythankstoPat hanittha,Potjamon,Yuwalak,ThipnateeandWaiYee for

their ontinualwirelesssupports, forthe omforts Ifeelwheneverwe onverse,for

themirthandjoyweneverpart,despitethelongdistan eapart.

Spe ial thanks to Dr. Juliette Soulard, Kittipong, Wai Yee and Afshin for

proofreadingand ommentingthethesis.

Mostimportantofall,innumerablethanksto myparents(towhomI ameter-

nallyindebted),mysister,andmyauntsfortheiruna ountableandindes ribable

inputsthatasmu hasItrytoin reasemye ien y,theoutputwillalwaysbefar

lessthan100%.

This work mayamount[℄to no morethan onedropin a[riverof knowledge℄.

Yetwhatisany[river℄,butamultitudeofdrops?

1

1

DavidMit hell,CloudAtlas(2004).

Contents 6

1 Introdu tion 11

1.1 Resear hBa kground . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 Obje tive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 ThesisOrganization . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.6 ListofPubli ations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

I Theory: Con ept of Dominant Inter-Area Os illation Paths 19 2 DominantInter-AreaOs illationPaths 21 2.1 BasisoftheCon ept . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1.1 LinearizedPowerSystemModel . . . . . . . . . . . . . . . . 21

2.1.2 NetworkSensitivities. . . . . . . . . . . . . . . . . . . . . . . 22

2.1.3 NetworkModeshape . . . . . . . . . . . . . . . . . . . . . . . 22

2.2 Denition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Con eptIllustration . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Persisten e ofMultipleIntera tion Paths 25 3.1 Se ondaryInter-AreaOs illationPaths. . . . . . . . . . . . . . . . . 25

3.2 AssumptionandHypothesis . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 StudySystem: KTH-NORDIC32 . . . . . . . . . . . . . . . . . . . . 26

3.3.1 Small-SignalStabilityAnalysis . . . . . . . . . . . . . . . . . 26

3.3.2 MainIntera tionPathsoftheStudySystem. . . . . . . . . . 26

3.4 Contingen yStudies . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5 SimulationResultsandDis ussions . . . . . . . . . . . . . . . . . . . 30

3.5.1 LossofaFAR orridor. . . . . . . . . . . . . . . . . . . . . . 30

3.5.2 LossofaNEAR orridor . . . . . . . . . . . . . . . . . . . . 30

3.5.3 LossofanON orridor. . . . . . . . . . . . . . . . . . . . . . 31

3.5.4 Dis ussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.6 Con eptValidation throughNonlinearTime-Domain Simulations . . 33

3.6.1 AnalysisofTime-DomainSimulationResponses. . . . . . . . 33

3.6.2 Re onstru tion of the Intera tion Pathsfrom the Nonlinear Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

II Identi ation of Dominant Inter-Area Os illation Paths 35 4 DominantPath Identi ationAlgorithms 37 4.1 Model-basedAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1 AlgorithmDemonstration . . . . . . . . . . . . . . . . . . . . 38

4.2 Measurement-basedAlgorithms . . . . . . . . . . . . . . . . . . . . . 40

4.2.1 TransientMeasurements . . . . . . . . . . . . . . . . . . . . . 41

4.2.2 AlgorithmDemonstration . . . . . . . . . . . . . . . . . . . . 41

4.2.3 AmbientMeasurements . . . . . . . . . . . . . . . . . . . . . 44

4.2.4 AlgorithmDemonstration . . . . . . . . . . . . . . . . . . . . 45

4.3 Dis ussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3.1 AlgorithmComparison. . . . . . . . . . . . . . . . . . . . . . 48

4.3.2 ChallengesandLimitationsoftheAlgorithmsUtilizingMea- surements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.2.1 Referen eSele tion . . . . . . . . . . . . . . . . . . 49

4.3.2.2 Window Sele tion . . . . . . . . . . . . . . . . . . . 49

4.3.2.3 Abundantvs. S ar eMeasurements . . . . . . . . . 50

4.3.3 ConsiderationsforImplementation . . . . . . . . . . . . . . . 50

III ControlImplementingtheDominantInter-AreaOs illation Paths Con eptand Analyses 53 5 Analysis ofInput Signalsfor DampingControllerDesign 55 5.1 DampingControllerDesign . . . . . . . . . . . . . . . . . . . . . . . 55

5.1.1 SimulationApproa h. . . . . . . . . . . . . . . . . . . . . . . 55

5.1.2 ControllerStru ture . . . . . . . . . . . . . . . . . . . . . . . 55

5.1.3 ControllerDesignIllustration . . . . . . . . . . . . . . . . . . 57

5.2 Justi ationofSignalInputTypes . . . . . . . . . . . . . . . . . . . 57

5.2.1 VoltageMagnitudeasInputSignals . . . . . . . . . . . . . . 58

5.2.2 VoltageAngleDieren esasInputSignals. . . . . . . . . . . 59

5.2.3 RotorSpeedsasInputSignals. . . . . . . . . . . . . . . . . . 61

5.2.4 InputSignalComparison . . . . . . . . . . . . . . . . . . . . 62

6 Impa tsofTimeDelayonControllersusingDominantPathSig- nals 63 6.1 PadéApproximationofaTimeDelay . . . . . . . . . . . . . . . . . 63

6.3 DelayMargin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.4 AnalysisofDominantPathSignalsConsideringTimeDelays . . . . 65

6.4.1 Impa tsonFrequen yResponses . . . . . . . . . . . . . . . . 65

6.4.2 Impa tsonTimeResponses . . . . . . . . . . . . . . . . . . . 67

6.4.3 ComparisonAmongDominantPathSignals . . . . . . . . . . 67

6.4.4 DelayMarginValidation. . . . . . . . . . . . . . . . . . . . . 70

6.5 Veri ationthroughNonlinearTime-DomainSimulations . . . . . . 70

6.5.1 PSSVeri ation . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.5.2 Closed-LoopResponses subje ttoDelays . . . . . . . . . . . 71

6.5.3 DelayMarginsAssessment. . . . . . . . . . . . . . . . . . . . 72

6.5.4 TimeDelayCompensation . . . . . . . . . . . . . . . . . . . 73

7 UsingDominant Path Signalsin WADC 75 7.1 StudySystem: 3-AreaSystem . . . . . . . . . . . . . . . . . . . . . . 75

7.1.1 SystemDes riptions . . . . . . . . . . . . . . . . . . . . . . . 75

7.1.2 CaseStudiesandSmall-SignalStabilityAnalysis . . . . . . . 75

7.1.3 DominantInter-AreaOs illationPaths. . . . . . . . . . . . . 76

7.2 ControllerDesignApproa hes . . . . . . . . . . . . . . . . . . . . . . 77

7.3 PropertiesofDominantPathSignals: LinearAnalysis . . . . . . . . 77

7.3.1 Open-LoopPropertiesofDominantPathSignals . . . . . . . 77

7.3.2 Study1: FixedPSS . . . . . . . . . . . . . . . . . . . . . . . 78

7.3.2.1 Frequen yDomainResponses. . . . . . . . . . . . . 78

7.3.2.2 TimeResponses . . . . . . . . . . . . . . . . . . . . 80

7.3.2.3 LoadingEe ts. . . . . . . . . . . . . . . . . . . . . 80

7.3.3 Study2: RetunedPSS . . . . . . . . . . . . . . . . . . . . . . 82

7.3.3.1 Frequen yDomainResponses. . . . . . . . . . . . . 82

7.3.3.2 LoadingEe ts. . . . . . . . . . . . . . . . . . . . . 83

7.4 Veri ationthroughNonlinearTime-DomainSimulation . . . . . . . 84

7.4.1 ControllerDampingPerforman e . . . . . . . . . . . . . . . . 84

7.4.2 TimeDelayImpa tonDominantPathSignals . . . . . . . . 85

7.4.3 DelayMarginAssessment . . . . . . . . . . . . . . . . . . . . 85

7.4.4 TimeDelayCompensation . . . . . . . . . . . . . . . . . . . 86

7.5 Con eptDemonstrationonaLargeSystem . . . . . . . . . . . . . . 87

7.5.1 SystemDes ription&Open-LoopProperties . . . . . . . . . 87

7.5.2 FixedPSS:Frequen yResponseProperties . . . . . . . . . . 88

7.5.3 RetunedPSS:Frequen yResponseProperties . . . . . . . . . 88

7.6 ConsiderationsforSignalSele tionand WADC Design . . . . . . . . 89

7.6.1 SignalCombination . . . . . . . . . . . . . . . . . . . . . . . 89

7.6.2 ControllerLo ation . . . . . . . . . . . . . . . . . . . . . . . 91

7.6.3 ProposedGuidelines forWADC. . . . . . . . . . . . . . . . . 91

8 Challengesand Limitations ofWACS Design Tools 93 8.1 ModelingApproa hes . . . . . . . . . . . . . . . . . . . . . . . . . . 93

8.2.1 Continuousvs. HybridModels . . . . . . . . . . . . . . . . . 94

8.2.2 Impa tsofSamplingRate . . . . . . . . . . . . . . . . . . . . 95

8.2.3 Impa tsofTimeDelay. . . . . . . . . . . . . . . . . . . . . . 96

8.3 Impli ationsforPowerSystemControlDesign. . . . . . . . . . . . . 99

8.3.1 Continuousvs. HybridModels . . . . . . . . . . . . . . . . . 99

8.3.2 Impa tsofSamplingRates . . . . . . . . . . . . . . . . . . . 100

8.3.3 Impa tsofTimeDelay. . . . . . . . . . . . . . . . . . . . . . 101

9 Con lusion 103 9.1 Con lusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

9.1.1 Con epts&Identi ation . . . . . . . . . . . . . . . . . . . . 103

9.1.2 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

9.1.3 ModelingandSimulationLimitations . . . . . . . . . . . . . 104

9.2 FutureWorks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

A Justi ation ofPadé Order for TimeDelay Approximation 107 A.1 Mean-SquareErrors . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

A.2 Impa tsofthePadéOrderinPowerSystemStudies . . . . . . . . . 108

B PSSand TimeDelay Software Implementationin PSAT 113 B.1 VoltageMagnitudeand VoltageAngleDieren esImplementation . 113 B.2 Filters andTimeDelayImplementation . . . . . . . . . . . . . . . . 114

C Dampingratio and Loadings Relationship 125

Bibliography 127

Introdu tion

1.1 Resear h Ba kground

Powersystemos illationdampingremainsasoneofthemajorproblemsforse ure

and reliable operation of power systems. In response to a ontinual in rease in

ele tri itydemandand thetrendformoreinter onne tions[1℄,powersystemsare

driven loser to their physi al operation limits, espe ially those of transmission

apa ity. Consequently, one issue of on ern is the mitigation of low-frequen y

inter-areaos illations(LFIO).

Inter-area os illations refer to the dynami s of the swing between groups of

ma hines in one areaagainstgroups of ma hines in another area, intera ting via

thetransmissionsystem. Typi ally,thesetypesofos illationso urin largepower

systemsinter onne ted by weak transmission lines [2℄ that transfer heavy power

ows. They are possibly aused by in remental hanges (hen e the term small-

signal)su has hangesinloadsandhavethe riti al hara teristi ofpoordamping

ormayo urasanaftermathoflargedisturban es.

Forthe aseofLFIOs,theymayberesultfromsmalldisturban esofwhi htheir

ee tsmightnotbeinstantaneouslynoti ed. Whena ertaintypeofswingo urs

in su h system, insu ient dampingof LFIOs may leadto alimitation of power

transfer apabilityor,worsethanthat,agrowthinamplitudeoftheLFIOswhi h

ouldpossibly ause asystem to ollapse [3℄. As su h, enhan ing powertransfer

apability, while keeping the system stable, is one of the main goals for system

operators.

Toenhan e transfer apa itywhile preventingthe systemfrombreaking up,a

ommon ountermeasure is to install power system stabilizers (PSS) [4℄, [5℄, [6℄,

whi h provide additional damping to the system through generators. PSSs are

the most ommon and ost ee tive damping ontrol devi es in power systems.

Generally, these devi es relyon lo al measurementsand are ee tive in damping

lo almodes.

Su essfuldamping,however,reliesheavilyonthelo ationsandtypesofinput