142661965-stabilitatea-tensiunii

7/28/2019 142661965-stabilitatea-tensiunii

1/8

AMPLASAREA OPTIMA DISPOZITIVELOR FACTS

PENTRU A MBUNTII STABILITATEA STATICA TENSIUNII

OPTIMAL PLACEMENT OF FACTSTO IMPROVE STATIC VOLTAGE STABILITY

Mahdad BELKACEM* Tarek BOUKTIR** Kamel SRAIRI** Department of Electrical Engineering, University of Biskra, Algeria.

** Department of Electrical Engineering, University of Oum El Bouaghi, Algeria.*Email: [email protected], **Email: [email protected]

Rezumat: Mai multe avarii majore de sistem, pretutindeni n lume,

au fost asociate direct cu colapsul tensiunii; utilizarea dispoziti-velor FACTS n sistemele electronergetice este realizat pentrucontrolul circulaiei de puteri, mbuntirea stabilitii, manage-mentul tensiunii, corecia factorului de puterei reducerea pierde-rilor. Lucrarea investigheaz utilizarea dispozitivelor conectaten serie (TCSC) i a dispozitivelor conectate n paralel (SVC),din punctul de vedere al sensibilitii sarcinii i pierderilor deutere reactiv, pentru a crete stabilitatea tensiunii. Studiul aost realizat pe sistemul test IEEE 30 pentru a verifica corectitu-

dinea i eficiena metodei propuse. Lucrarea evideniaz faptulc dispozitivele FACTS amplasate optim n sistem mresc semni-icativ limitele puterii i stabilitatea sistemului.

Cuvinte cheie: Circulaie de putere, Stabilitate static a tensiunii,FACTS, SVC, TCSC, Bifurcaie, Vectori proprii.

Abstract: Several major blackouts throughout the world have been

directly associated to the voltage collapse, the application of FACTSin electric power system is intended for the control of power flow,improvement of stability, voltage profile management, power factorcorrection, and loss minimisation. This paper investigates the useof the series device(TCSC) and the parallel device (SVC) from theoint of load margin and reactive power loss sensitivity index to

increase voltage stability. The study has been carried out on theIEEE 30 Test System to verify the validity and efficiency of the pro-

osed method. It reveals that incorporation of FACTS devices withoptimal location significantly enhance load margin as well as systemstability.

Keywords:Powerflow,StaticVoltageStability,Facts,SVC,TCSC,Birufcation, Eigenvectors.

1. IntroducereScopulreelei de transport este conecteze centralele i

centrele de sarcin pentru a alimenta sarcina cu o fiabilitateceruti eficien maxim, la un pre sczut. Pe msur cecrete puterea transferat, sistemul electroenergetic poatedeveni tot mai ncrcat i mai nesigur pentru circulaiilede puteri neprogramate i piederile mari. n acest context,a fost introdus un concept denumit sistem flexibil de trans-mitere a curentului alternativ. Conceperea dispozitivelorFACTSca o filosofie de control total al reelei a fost intro-dus de ctre N.G. Hingorani [1] de la Electric PowerResearch Institute (EPRI) din SUA n 1988, dei dispo-

zitivele cu electronic de putere au fost folosite de muli anin reeaua de transport. Dispozitivelor FACTS se folosescn sistemele electroenergetice pentru controlul circulaieide puteri, mrirea stabilitii, managementul tensiunii,corecia factorului de putere i minimizarea pierderilor.

Problema colapsului tensiunii n sistemul electroenergetica devenit una din cele mai importante pentru a fi rezol-vat, mai multe avarii majore de sistem, pretutindeni nlume, fiind asociate direct cu acest fenomen.

De altfel, datorit avariilor de sistem care au aprut nAmerica i Canada n 2003, cercettorii ncearc s desco-

pere metode alternative pentru a mri stabilitatea tensiunii.Stabilitatea regimului permanent se refer la rspunsul

dinamic al sistemului la perturbaii mici care apar n modcurent n timpul funcionrii sistemului. Aceast problempoate fi studiat utiliznd ecuaiile dinamice liniarizate alesistemului ntr-un punt de funcionare. Un sistem se afl n

1. IntroductionThepurposeofthetransmissionnetworkistopoolpower

plantsandloadcentersinordertosupplytheloadatarequiredreliabilityandmaximumefficiencyatalowercost.Aspowertransfergrow,thepowersystemcanbecome increasinglymoredifficult tooperate,and thesystembecomesmoreinsecurewithunscheduledpowerflowsandhigherlosses.Inthiscontext,aconceptcalledaflexiblealternativecurrenttransmission systemwas introduced.TheconceptionofFACTSasatotalnetworkcontrolphilosophywasfirstintro-ducedbyN.G.Hingorani[1]from theElectricpowerresearchinstitute(EPRI)intheUSAin1988,althoughthepower

electroniccontrolleddeviceshadbeenusedinthetransmissionnetworkformanyyearsbeforethat.TheapplicationofFACTSinelectricpowersystemisintendedforthecontrolofpowerflow,improvementofstability,voltageprofilemanagement,

power factor correction, and loss minimisation.Theproblemofvoltagecollapseinpowersystemisnow

becomingoneofthemostimportantpredicamentstoresolve,asseveralmajorblackouts throughout theworldhavebeendirectlyassociated to this phenomenon.

Moreover,becauseof the blackout thatoccurred inAmericaandCanadain2003,researchesareattemptingtodiscoveralternativemethodstoimprovingvoltagestability.Steadystatestabilityreferstodynamicsystemresponseto

small disturbances that continuouslyoccurduring theoperationofthesystem.Thisproblemcanbestudiedbylookingatthelinearizeddynamicequationsofsystematanoperationpoint.Thus,apowersystemissteadystatestable


2/8

The 6th International Power Systems Conference52

regim stabil pentru o anumit condiie de funcionare, dacn urma unor mici perturbaii, el revine la regimul staionar [2].

Condiia de stabilitate se determin calculnd valorileproprii ale sistemului liniarizat; dac toate prile reale alevalorilor proprii sunt negative, sistemul este stabil; altfel,sistemul este instabil. Circulaia de putere pe o linie de c.a.este o funcie de modulul i faza tensiunii i impendanaliniei. Consecinele lipsei controlului pentru oricare dinaceste variabile sunt probleme cu stabilitatea, circulaii de

puteri nedorite, circulaii de puteri reactive nedorite, pier-deri mari, tensiune ridicat sau sczut, printre altele. Cudispozitivele FACTSputem controla faza tensiunii, mrimeasa n nodul ales i impedana liniei [3].

Condensatoarele Serie Controlate cu Tiristoare (TCSC)i Compensatoarele Statice de Putere Reactiv (SVC) suntcele mai populare dispozitive FACTS. Obiectivul principalal SVC este de a regla tensiunea ntr-un nod ales controlndinjecia de putere reactiv n locaia respectiv. Menine-rea nivelelor tensiunii este important din punctul de vedere

al consumatorilor. Valorile sczute ale tensiunii provoacdereglri ale performanelor sarcinilor cum ar fi motoarede inducie, lmpi cu incandescen etc., n timp ce valorileridicate ale tensiunii provoac saturaie magnetici gene-reazarmonici,precumiproblemecuizolaia.Acestedispo-zitive sunt caracterizate printr-un rspuns rapid, domeniumare de aplicare i fiabilitate ridicat.

Compensarea capacitiv longitudinal este o alt metodpentru a mbunti limitele de stabilitate i de a crete ca-pacitatea de transport. Puterea transportat pe o linie esteinvers proporional cu impedana de transfer. De exemplu,considernd ali parametrii constani, o compensare seriede 50 % dubleaz aproximativ puterea transmis n regim

stabil, n timp ce o compensare serie de 75 % va crete pu-terea transportat aproximativ de patru ori. Din perspectivaunui regim stabil, structura dispozitivului este echivalentcu cea a unuiFC-TRC SVCprezentat n figura 1.

2. Prezentarea problemeiSe discut pe scurt unele concepte fundamentale referi-

toare la analiza stabilitii tensiunii i regulatorul FACTS.A. Stabilitatea tensiuniii teoria bifurcaiei

Fenomenele neliniare, mai ales anumite tipuri de bi-furcaii, s-au dovedit a fi responsabile de o varietate de

probleme de stabilitate n sistemele electroenergetice. nparticular, lipsa punctelor de echilibru postavarie n mod

curent asociate cu punctele singulare de birfucaiile (SNB)i anumite tipuri de bifurcaii produse la limit (LIB), s-adovedit a fi motivul principal al colapsului de tensiune.Explicaii i exemple detaliate ale acestor bifurcaii n sis-temele electroenergetice i asocierea lor cu stabilitatea ten-siunii pot fi gsite n [11]. n general, punctele de bifurcaie

pot fi definite ca puncte de echil ibru unde se schimbcantitatea i / sau calitatea echilibrului, asociate cu unsistem neliniar de ecuaii dinamice, n condiiile variaieilente a parametrilor sistemului.B. Principiul compensrii

Circulaia de putere pe o de transport este direct propor-ional cu diferena unghiului de fazi invers proporionalcu mrimea reactanei. Condensatoarele serie reduc reac-tana total a liniei de transport.

foraparticularoperatingcondition iffollowinganysmalldisturbance, the system reaches a steady-state condition [2].

Thestabilityconditionisdeterminedbycalculatingtheeigenvaluesofthelinearizedsystem,ifallrealpartsoftheeigenvaluesarenegative,thesystemisstable;otherwise,itisunstable.Powerflowthroughanaclineisafunctionof

phaseangle,lineand voltagesand lineimpedance.Theconsequencesoflackcontroloveranyofthesevariablesare

problemswithstability,undesirablepowerflows,undesirablevarflows,higherlosses,highorlessvoltage,amongtheothers,WithFACTdeviceswecancontrolthephaseangle,the magnitude at chosen bus and line impedance [3].

ThyristorControlledSeriesCapacitors(TCSC)andStaticVarCompensators(SVC)are themostpopulardevicesoftheFACTS.ThemainfunctionalityoftheSVCistoregulatethevoltageatachosenbusbycontrollingthereactivepowerinjectionatthelocation.Maintainingtheratedvoltagelevelsis importantforproperoperationandutilizationof loads.Undervoltagecausesderegulationin theperformanceof

loadssuchas inductionmotors, lightbulbs,etc.,whereasovervoltagecausesmagneticsaturationandresultanthar-monicgeneration,aswellasequipmentfailuresduetoinsu-lationbreakdown.Thisdevicesarecharacterisedby rapidresponse, wide operational range and high reliability.

Seriescapacitorcompensationisanotherapproach toimprovestability limitsand increasetransfercapabilities.Thetransmittedpowerthroughalineisinverselyproportionaltothe transfer impedance.Forexample,consideringother

parametersconstants,50%seriescompensationapproxi-matelydoublesthesteady-statetransmittedpower,whereas75%seriescompensationwouldincreasethetransferedpowertoaboutfourtimestheoriginalvalue.Fromasteady-state

perspective,thestructureofthedeviceis equivalent to aFC-TRC SVCpresented in figure 1.

2. Background reviewSome fundamental concepts behind voltage-stability

analysis andFACTScontroller area briefly discussed.A. Voltage Stability and Bifurcation Theory.

Nonlinearphenomena,especiallycertaintypesofbifurca-tions,havebeenshown toberesponsibleforavarietyofstabilityproblemsinpowersystems.Inparticular,thelackofpostcontingencyequilibriumpoints,typicallyassociatedwithsaddlenodebifurcation (SNB)and certain typesoflimitinducedbifurcations(LIB),havebeenshowntobethe

main reasonbehind severalvoltage-collapseproblemsthroughouttheworld.Detailedexplanationsandexamplesofthesebifurcationsinpowersystemsandtheirassociationwithvoltagestabilitycanbefoundin[11].Ingeneral,bifur-cationpointscanbedefinedasequilibriumpointswherechange in thequantityand /orqualityof theequilibriaassociatedwithanonlinearsetofdynamicequationsoccurwith respect to slow varying parameters in the system.B. Principle of Compensation

The power flow along the transmission line is directlyproportional to the difference of the phase angle and inverselyproportional to the magnitude of the reactance

Series capacitors reduce the total reactance of the trans-mission line, which is often the main reason for their

application.

P = )sin( 2121

cl XX

VV(1)


3/8

03-04.11.2005, Timioara, Romania 53

Fig. 2. Principiul compensrii condensatoare serie i unt

Fig. 2. Principle of compensation - series and Shunt

3. Modelarea regulatoarelor FACTSB.1. Compensatoare statice de putrere reactiv

nc din 1980, progrese n regulatoarele pentru sistemeleflexibile de transport n curent alternativ (FACTS) n sis-temele electronergetice au condus la utilizarea lor pentru amri stabilitatea reelelor electroenergetice. n literaturade specializate s-au publicat mai multe studii analiznd uti-lizarea dispozitivelorFACTSpentru tensiuni i stabilitateaunghiului. Efectul regulatorului SVC asupra exploatriieconomice i stabilitatea tensiunii reelei este principalulmotiv n spatele ncorporrii SVCn diferite formule.

Modelul pentru regimul stabil prezentat n [3] este folositaici pentru a ncorpora SVCn problemele PF. Acest modeleste bazat pe reprezentarea regulatorului ca o impedan

variabil, presupunnd o configuraie SVCcu un conden-sator fix (FC) i o bobin de reactan controlat cu tiristoare(TCR), dup cum este descris n figura 1. Trimind nacelai timp un impuls de poart tuturor tiristoarelor unuiredresor, se comand redresorul s intre n conducie. El seva bloca aproximativ la trecerea prin zero a curentului, nabsena semnalelor de amorsare. Deoarece elementul decontrol este redresorul cu tiristoare, tiristoarele sunt amor-sate simetric, cu un domeniu de control al unghiului de 90la 180 tensiunea condensatorului (bobinei). Legea de controla regimului stabil pentru SVCeste o caracteristic tipicde curent tensiune, ilustrat n figura 2.

Fig. 1. Componentele circuitului principal SVCFig 1. SVC main circuit components

Fig. 3. Reprezentarea circuitului SVC pentru regim stabilFig 3. SVC steady-state circuit representation.

3. Modeling of FACTS controllersB.1. Static VAR Compensator

Sincetheearly1980s,advancesinflexibleactransmissionsystems(FACTS)controllers inpowersystemhave led totheirapplicationinimprovingstabilityofpowernetworksSeveralstudiesanalyzingtheapplicationofFACTScontrollersforvoltageandanglestabilityhavebeenreported in theliterature.TheeffectoftheSVCcontrollerontheeconomicoperationandvoltagestabilityofthenetworkistheprinciplemotivationbehind incorpora ting the SVC into variousformulations.

Thesteady-statemodelproposedin[3]isusedheretoincorporatetheSVConPFproblems.Thismodelisbased

onrepresenting the controllerasavariable impedance,assuminganSVCconfigurationwithafixedcapacitor(FC)andThyristor-controlledreactor(TCR)asdepictedinfigure1.Applyingsimultaneouslyagatepulsetoallthyristorofathyristor valvebrings the valve into conduction. The valvewillblockapproximatelyatthezerocrossingoftheaccurrent,intheabsenceoffiringsignals.ThusthecontrollingelementistheThyristorvalve.thethyristorsarefiredsymmetrically,inananglecontrolrangeof90to180withrespecttothecapacitor (inductor) voltage. The steady-state control lawfor theSVC is the typicalcurrent-voltage characteristic,illustrated in figure 2.

V = Vref+ Xsl I (2)

Xsl sunt n domeniul 0.02 la 0.05 u.r. n raport cu bazaSVC. Panta este necesar pentru a evita nclcarea limitelor.La limitele tensiunii SVC este transformat ntr-o reactanfix. Impedana total echivalentXe a SVC poate fi repre-zentat de

Xslareintherangeof0.02 to0.05p.u.withrespecttotheSVCbase.Theslopeisneededtoavoidhittinglimits.Atthevoltage limits theSVC is transformedintoafixedreac-tance.The total equivalent impedance Xe ofSVCmay berepresented by

)/12(22sin

/

X

XCe

k

kXX

+=

(3)

unde where

/x C Lk X X=

SVC este conectat de obicei la sistemul de transport prinintermediul unui transformator cobortor, care este tratatntr-o manier similar ca i alt transformator din sistem.

The SVCis usually connected to the transmission systemthrough a step-down transformer, which is treated in a similarmanner as other transformers in the system.

Vref-XslVkBe + Vl = 0 (4) Qsvc -

2k

V Be =0 (5)

0)/2(2sin =++ CLeLC XXBXX (6)


4/8


unde where

ee XB /1= .

Limitele de regim stabil ale unghiului de amorsare sunt900 < < 1800, unde se obine conducia parial. Unghiurilede amorsare mai mici de 900 nu sunt permise, deoarece ele

produc curent nesimetric cu o component continu ridicat.B.2. Condensatoare serie controlate cu tiristoare (TCSC)

Diferena principal fa de SVCo reprezint faptul cTCSCeste conectat n serie cu linia de transport, n timpce SVCeste conectat n unt ntr-un nod. O alt diferenmajor o reprezint faptul cTCSCeste conectat direct lalinie, iarSVCprintr-un transformator cobortor.

Fig. 4. Caracteristicile pentru regim permanent V-I al SVCFig. 4. Typical steady state V-I characteristics of SVC

Fig. 5. Componente circuitului principal al TCSCFig. 5. TCSC main circuit components

Fig. 6. Compensare serie a linieiFig. 6. Series Compensator Line

Steady-state limits of the firing angle are 900 < < 1800,where partial conduction is obtained. Firing angles less than900 are not allowed, as they produce unsymmetrical current

with a high dc component.B-2. Thyristor Controlled Series Capacitors (TCSC)

The main difference from SVC is that the TCSCis seriesconnected to the transmission line, whereas the SVCis shuntconnected to a bus. Another major difference is that TCSCis directly connected to the line, as opposed to the SVCwhichtypically requires a step-down transformer.

Fig. 7. Impedana de frecven fundamental pentru uncondesator conectat n serie comandat de tiristoare

Fig. 7. Thyristor-controlled series capacitor (TCSC) fundamentalfrequency impedance.

Fig. 8. Circulaia de putere pe o linie de transportFig.8. Power flow in a transmission line

4. Amplasarea optim a TCSC i SVCA.Amplasarea optim a TCSCA.1. Indicele de sensibilitate al pierderii de putere reactiv

Unul din rezultatele importante ale compensrii serieeste reducerea pierderilor de putere reactiv. Scopul estegsirea liniei pe care se va amplasa TCSC, determinnd

indicii de sensibilitate ai pierderilor de putere reactiv nfiecare linie. Indicele de sensibilitate reprezint rata deschimbare n pierderi de putere reactiv datorit reactaneiliniei. Dup acest indice poate fi gsit cea mai convena-

bil linie pentru cazul compensrii serie.

4. Optimal placement of TCSC and SVCA. Optimal placement of TCSCA.1. Reactive power loss sensitivity indexes

Oneoftheimportantresultsofseriescompensationisthereductionofthereactivepowerlosses.ThegoalistofindthelinetoplacetheTCSC,byfindingreactivepowerloss

sensitivityindexesineachline.Theindexsensitivityistherateofchangeinreactivepowerlossduetolinereactance.Bythisindexthemostsuitableline,fromthereductionofreactivepowerlossespointofview,fortheseriescompen-sation can be found.

Ecuaia pierderilor de putere pe linia dat n figura 6,poate fi scris astfel:

Loss power equation of the line, given in figure 6, canbe written as:

++

+=+

2222 XR

Xj

XR

RKQjP (7)

unde where

)cos(222 mnmnmn VVVVK += (8)

Apoi indicele de sensibilitate (SI) este Then the sensitivity index SIis

SI= 222

22

)()(

XR

XRK

X

Q

+

=

(9)


5/8


B. Amplasarea optim a SVCMai nti scriem ecuaia sistemului electroenergetic:

B. Optimal placement ofSVCFirst we can write equation of the power system like this:

F(y, , p) = 0 (10)unde y reprezint vectorul variabilelor de stare, cores-

punde vectorului puterilor reale i reactive ale sarcinilorip

reprezint orice parametru al sistemului care este directcontrolabil, cum ar fi nivelele de compensare unt i serie.n orice regim stabil al aceast ecuaie este satisfcut.

Aceasta nseamn c la punctul de nceput al funcio-nrii (y0, Q0, p0) i punctul singular al nodului de bifurcaie(yb, Qb, pb) sunt dou ecuaii:

wherey represents the vector of state variables, corre-spondstothevectorofrealandreactiveloadpowersandp

meansanyparameterofthesystemthataredirectlycontrol-lable,suchasshuntandseriescompensationlevels.In anysteady state of the system this equation is satisfied.

That means at the beginning point of the operating (y0,0, p0) and saddle node bifurcation point (yb, b, pb) thereare two equations:

F(y0, 0,p0) = 0 (11)F(yb, b,pb) = 0 (12)

Aici exist o relaie ntre Q0 indicnd puterile active ireactive la punctul iniial de funcionare i Qb indicnd celsingular al nodului de bifurcaie. n punctul singular al no-dului de bifurcaie, matricea jacobian bfy | este singular.

Pentru un set dat de parametrii controlabilip0, cderea ten-siunii studiaz de obicei concentrat pe determinarea cderiisau punctului de bifurcaie (yb, Qb), unde corespunde deobicei nivelului maxim de sarcin sau coeficientului desiguran al ncrcrii.

5. Analiza simulrilorAmbele TCSCi SVCsunt separat testate pe un sistem

text cu 30 noduri IEEE i rezultatele folositoare suntobservate i discutate.

A. Rezultate SVCnainte de inserarea dispozitivelor SVC, sistemul a fost

mpins n punctul su de prbuire crescnd att sarcina activ,

ct i reactiv direct folosind circulaia continu a sarcinii.n cadrul acestui sistem test conform rezultatelor obi-nute din circulaia continu a sarcinii, putem afla faptul cnodul 30 i 26 sunt cele mai bune locuri pentru amplasat(figura B1, B2, B3, B4). Pentru a confirma acest rezultatteoretic presupunem SVC cu valorile tehnice indicate ntabelul 3, instalate n noduri diferite. Figura B1 arat clarrezultatul su cu coeficientul de siguran al sarcinii n celmaibunnod.Putemconcluzionadinrezultateledintabelul1,faptul c nodul 30 ar trebui s fie selectat.

B. Rezultatele TCSCPentru acest caz, n concordan cu ecuaia 9 care indic

indicele de sensibilitate (SI), putem obine valoarea lui SI

dup cum se indic n figura (A1, A2, A3). Se arat n linia[1-2], cantitatea SIatinge valoarea cea mai mare. Aceastanseamn c n momentul n care reactana ramificaieiselectate se schimb va avea cel mai mare efect asupra per-formanei circulaiei puterilor. Prin urmare, liniiile [1-2]ar trebui s fie selectate prima dat pentru TCSC. Liniile(2-5), (1-3) vor schimba de asemenea mult sistemul. Liniile(3-6), (4-6) i (2-6) vor oferi o contribuie mic asupra

performanei circulaiei de putere.Cnd instalm TCSCpe o linie diferit, folosind indi-

cele de sensibilitate n condiii normale i folosind circulaiacontinu a sarcinii, valoarea numeric menionat n ta-

belul 2 arat clar faptul c ramificaia [1-2] cu 2.3137 ncondiii normale i 2.9529 n condiii anormale (factor de

ncrcare egal cu 1.1) reprezint locul optim de amplasareal TCSC. Indic de asemenea c aceast abordare bazat

pe indicele de sensibilitate este o metod folositoare pentrua gsi locul optim de amplasare al TCSC.

Here there is a relationship between 0 indicating the realand reactive powers at the beginning point of operating andb indicating the saddle node bifurcation point.

At the saddle node bifurcation point, the jacobian matrix

bfy | issingular.Foragivensetofcontrollableparametersp0,voltage collapse studies usually concentrate on determiningthe collapse or the bifurcation point (yb, b), where typicallycorresponds to the maximum loading level or loadabilitymargin.

5. Simulation analysisBothTCSCandSVCareseparatelytestedonIEEE30bus

testsystem, and useful results are observed and discussed.A. SVC results

Before the insertion ofSVCdevices, the system waspushed to its collapsing point by increasing both active andreactive load discretely using continuation load flow.

In this test system according to results obtained from thecontinuation load flow, we can find that bus 30 and 26 arethe best placement point (figure B1, B2, B3, B4). To affirmthis theoretical result we suppose the SVC with technicalvalues indicated in table.3 installed on a different bus. FigureB1 shows clearly its result with the load margin of the best

bus. We can conclude from results in table 1, that the bus30 should be selected.

B. TCSC results

Forthiscase,accordingtoequation9whichindicatethesensitivityindexesSI,wecanobtainthevalueofSIasindicatedinfigure(A1,A2,A3).Itshowsinline[1-2] thatthequantityofSIreachesthegreatestvalue.Thatmeanswhenthereactanceofthisbranchselectedischangeditwillhavethelargestaffectonthepowerflowperformance.Therefore,lines[1-2]shouldbeselectedfirstforTCSC.Lines(2-5),(1-3)willalsochangethesystemgreatly.Lines(3-6),(4-6)and(2-6)will provide small contribution to the power flow

performance.WhenweputTCSConadifferentline,usingthesensi-

tivityindexinnormalconditionandusingcontinuationloadflow,thenumericalvaluementionedintable.2showsclearlythatbranch[1-2]with2.3137innormalconditionand2.9529inabnormalcondition(Loadfactorequal1.1)representtheoptimalplacementofTCSC.Italsoindicatesthatthisapproach

based insensitivity index isausefulmethod tofind theoptimal placement ofTCSC.


6/8


0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

Lines

Valueofindex

sensitivitySI

SI in Normal

Voltage

Fig. A1. Indicele de sensibilitate n condiii normaleFig. A1. Index Sensitivity in Normal Condition

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

Lines

ValueofindexsensitivitySI

SI with 1.1%load

Voltage

Fig. A3. Indicele de sensibilitate cu o cretere a sarcinii de 1.1 %Fig.A3. Index sensitivity with 1.1 % load Incrementation

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

Lines


SI with 65%Serie Compensation Line 2-5

Voltage

Fig. A5. Indicele de sensibilitate cu o compensare serie de 65 %pe linia [2-5]

Fig. A5. Index Sensitivity with 65 % Serie Compensation in line [2-5]

0 0.5 1 1.5 2 2.50.75

0.8

0.85

0.9

0.95

1

1.05

1.1

Loading coefficient

VoltageMagnitude[pu]

SVC in BUS 30

v30

v26

v10

v14

v28

Fig. B1. Mrimea tensiunii cu continuitatea circulaiei de putere

SVC n nodul 30Fig. B1. Voltage Magnitude with load Fow Continuation SVC in

bus 30

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

Lines


SI with 1.03%load

Voltage

Fig. A2. Indicele de sensibilitate cu o cretere a sarcinii de 1.03 %Fig. A2.Index Sensitivity with 1.03 % load Incrementation

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4

Lines

Valueofindexsens

itivitySI


Voltage



0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5

3

Lines



Voltage



0 0.5 1 1.5 2 2.5-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Loading coefficient

QsvcandBsvc[pu]

SVC in BUS 30

Bsvcmax

Bsvcmin

QSVC

BSVC

Fig. B2. Puterea reactiv injectati susceptana cu continuitatea

circulaiei de putere SVC n nodul 30Fig. B2. Reactive Power Injected and Susceptance with load

Fow Continuation SVC in bus 30


7/8


0 0.5 1 1.5 2 2.50.75

0.8

0.85

0.9

0.95

1

1.05

1.1

Loading coefficient

VoltageM

agnitude[pu]

SVC in BUS 26

v30

v26

v10

v14

v28


SVC n nodul 26Fig. B3. Voltage Magnitude with load Fow Continuation SVC

in bus 26

0 0.5 1 1.5 2 2.50.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Loading coefficient

VoltageMagnitude

[pu]

SVC in BUS 10

v30

v26

v10

v14

v28


SVC n nodul 10Fig. B5. Voltage Magnitude with load Fow Continuation SVC

in bus 10

0 0.5 1 1.5 2 2.50.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Loading coefficient


SVC in BUS 28

v30

v26

v10

v14

v28


SVC n nodul 28Fig. B7. Voltage Magnitude with load Fow Continuation SVC in

bus 28

0 0.5 1 1.5 2 2.50.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Loading coefficient


SVC in BUS 14

v30

v26

v10

v14

v28

Fig. B9. Mrimea tensiunii cu continuitatea circulaiei de putereSVC n nodul 14

Fig. B9. Voltage Magnitude with load Fow Continuation SVC inbus 14

0 0.5 1 1.5 2 2.5-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Loading coefficient

QsvcandBsvc[pu]

SVC in BUS 26Bsvcmax

Bsvcmin

QSVC

BSVC


circulaiei de putere SVC n nodul 26Fig. B4. Reactive Power Injected and Susceptance with load

Fow Continuation SVC in bus 26

0 0.5 1 1.5 2 2.5-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Loading coefficient

QsvcandBsvc[p

u]

SVC in BUS 10

Bsvcmax

Bsvcmin

QSVCBSVC


circulaiei de putere SVC n nodul 10

Fig. B6. Reactive Power Injected and Susceptance with loadFow Continuation SVC in bus 10

0 0.5 1 1.5 2 2.5-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Loading coefficient

QsvcandBsvc[pu]

SVC in BUS 28

Bsvcmax

Bsvcmin

QSVC

BSVC


circulaiei de putere SVC n nodul 28


0 0.5 1 1.5 2 2.5-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Loading coefficient

QsvcandBsvc[pu]

SVC in BUS 14

Bsvcmax

Bsvcmin

QSVC

BSVC

Fig. B10. Puterea reactiv injectati susceptana cucontinuitatea circulaiei de putere SVC n nodul 14



8/8


Tabelul 1. Rezultatele principale ale sistemului cu 30 de noduri IEEE cu un TCSC instalatTable 1. Main Results of IEEE 30 Bus System With One TCSC Installation

Load Incrementation0 % 5 % 10 % 0 % 5 % 10 % 0 % 5 % 10 %

B(pu) P VminSVC in 30 0.0777 0.0854 0.0933 17.8623 19.9781 22.2354 0.9689 0.9654 0.9620

SVC in 26 0.0690 0.0763 0.0838 17.8381 19.9534 22.2112 0.9638 0.9603 0.9567SVC in 10 0.0934 0.1251 0.1572 17.8019 19.8790 22.0930 0.9511 0.9471 0.943SVC in 14 -0.0206 -0.0061 0.0086 17.9142 20.0211 22.2718 0.9467 0.9417 0.9367SVC in 28 -0.1098 -0.0863 -0.0622 17.9859 20.0891 22.3316 0.9425 0.9381 0.9337

Tabelul 2. Valoarea SI pentru diferite l iniiTable 2. SI Values for different lines

Normal Abnormal

)(X

Q

Lines 1.03 * Sload 1.1 * Sload

2.3137 1-2 2.4924 2.95290.6372 2-5 0.6775 0.77890.5894 1-3 0.6308 0.61970.4965 3-4 0.5314 0.6197

0.4612 4-6 0.4901 0.56210.3109 2-6 0.3305 0.3807

Tabelul 3. Datele modelului SVCTable 3. DATA of the SVC Model

Model Bi BLo BHi0.02 -0.25 0.25FAi FAmin Famax140 90 180

6. ConcluziiSVCi TCSCau fost modelate i au fost studiate efectele

lor asupra stabilitii tensiunii. Testele realizate pe sistemultestIEEE30 sunt pe deplin ncurajatoare i promitoare.

Ambele dispozitive arat faptul c instalarea lor n sistemulelectroenergetic pot eventual s creasc limita de putere,puterea transportat pe linie i capacitilor de ncrcare areelei la fel ca i mrirea stabilitii sistemului. Totui, n

practica pe scar larg a sistemelor de putere, se solicitstudii mai aprofundate pentru a lua n considerare limitrileliniei i stabilitii generatorului.

6. ConclusionsSVCandTCSChasbeenmodeledandtheireffecton

voltagestabilityarestudied.FortheSVCplacementweareusedaloadmarginsensitivity,andforTCSCplacementa

reactivepowerlosssensitivityindexisimplemented.ThetestsperformedontheIEEE30testsystemarefoundtobequiteencouragingandpromising.Bothdevicesexhibitsthefact that insertion of thesedevices inpowersystemcaneventuallyincreasethepowerlimit,linepowerandloadingcapabilityofthenetworkaswellasenhancingthesystemstability.However,inthelargepowerpracticalsystem,furtherstudiesarerequiredtotakeinconsiderationlineandgeneratorstability limitation.

References (Bibliografie)[1] N.G. Hingorani, High Power Electronics and Flexible AC Transmission System ,IEEE Power Engineering review, july 1988[2] Tarek Bouktir, Application de la programmation Oriente Objet loptimisation de lcoulement de puissance , thse de doctorat,

Universit de Batna, 2004.

[3] William D.Rosehart, Claudio A, Canizares, and Victor H.Quintana. Effect of detailed Power System Models in Traditional andVoltage Stability Constrained Optimal Power Flow Problems, , IEEE Transactions on Power Systems, Vol.18, NO 1,FEBRUARY 2003.

[4] Ge Shaoyun, T S Chung, Coupled Active Dispatsh with FACTS Devices and Specified Power Flow Control Constraints , Proceedingsof the 4th International Conference on Advances in Power System Control, APSCOM 97, HONG KONG, November 1997.

[5] M. Moghavvemi, M.O.Faruque, Effects of Facts Devices on Static Voltage Stability ,IEEE 2000.[6] Mohammad A.S. Masoum, Marjan Ladjevardi, Akbar Jafarian, and Awald F.Fuchs, Optimal Placement, Replacement and Sizing Of

Capacitor Banks in Distribution Networks by Genetic Algorithm,IEEE Transactions On Power Delivery, Vol 19, N4, October 2004.[7] Fernando L. Alvardo Solving Power Flow Problems with a Matlab implementation of the Power System Application Data dictionary ,

Proceeding of FACTS devices, Electrical Power and Energie Systems 2003.[8] Yunqiang Lu, Ali Abur, Static Security Enhancement via Optimal Utilization of Thyristor Controlled Series Capacitors,

IEEE transactions on Power Systems, VOL 17, N2, May 2002.[9] Abdel-Moumen .M.A, Narayana Prasad Padhy, Pwor Flow Control and Transmission Loss Minimisation Model With TCSC

for Practical Power Networks. 2003 IEEE.[10] R.J. Nelson, J.Bian, S.L.Williams, Transmission Series Power Flow Control, IEEE transactions on Power Delivery, Vol.10, N1,

January 1995.[11] Claudio A. Canizares , Power Flow and Transient Stability Models Of FACTS Controllers for Voltage And Angle Stability Studies,2000IEEE.

[12] Mohammad A.S.Masoun, Marjin Ladjevardi, Akbar Jafarin, and Awald F. Optimal Placementn, Replacement and Sizing of CapacitorBanks in Distribution Networks by Genetic Algorithms , IEEE Transactions on power Delivery, Vol, 19, N04, October 2004.

142661965-stabilitatea-tensiunii

Documents

Transcript of 142661965-stabilitatea-tensiunii