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    614

    APPLICATION

    P. Kundur, Fellow

    IEEE

    IEEE Transact ions on Powe r Sys tems Vol. 4, No. 2 M a y 1989

    OF POWER SYSTEM STABILIZERS FOR ENHANCEMENT

    OF

    OVERALL SYSTEM STABILITY

    M.S. Zywno

    .

    Klein G.J. Rogers Member

    IEEE

    System Planning Division Ontario Hydro

    Toronto

    Abstr act

    Thi s paper provi des a det ai l ed account of

    anal yti cal work carr i ed out t o determ ne t he

    par ameters of power system st abi l i zers for a l arge

    gener ati ng stat i on. Smal l si gnal and t r ansi ent

    st abi l i t y st udi es are r eport ed whi ch demonst r ate the

    eff ecti veness of the stabi l i zers i n enhanci ng the

    stabi l i ty of i nt er- area as wel l as l ocal pl ant modes

    of

    osci l l ati on. Per f ormance of t wo al t ernati ve

    schemes, one w t h and t he other w t h no t r ansi ent

    exci ter gai n reducti on, are i nvesti gated.

    Kevwor ds

    Exci t ati on Contr ol Power System Stabi l i zers

    -

    Steady Stat e

    Stabi l i ty Transi ent Stabi l i ty .

    I NTRODUCTI ON

    For over 25 years, Ontari o Hydr o has r el i ed on

    hi gh i ni t i al response exci t ati on systems equi pped

    w th power system stabi l i zers ( PSS) as an ef f ecti ve

    means of enhanci ng overal l system stabi l i ty. Thi s

    has contr i b- ed si gni f i cant l y t o i ncreased

    f l exi bi l i t y i n t he desi gn and operati on of t he power

    system[l].

    The i ni t i al devel opment and appl i cati on of PSS

    were i n the ear l y 1960s on f our hydraul i c pl ant s on

    t he Moose Ri ver i n Nort her n Ont ari o. St abi l i zers

    usi ng shaf t speed ( Del t a-Omega) as i nput si gnal s were

    successf ul l y desi gned and appl i ed t o t hese uni t s and

    subsequentl y t o several other hydraul i c uni t s [2].

    Fourt een of t hese are curr ent l y i n operati on. I n

    1969, Del t a- Omega st abi l i zers were devel oped f or

    t her mal uni t s and 16 of t hese have been appl i ed

    successf ul l y. However, due t o the necessi t y of usi ng

    torsi onal f i l ters, this type of stabi l i zer was f ound

    to suff er f rom a number of l i mt ati ons whi ch

    compl i cate i ts desi gn and restri ct i ts

    eff ect i veness

    [ 3 ] .

    I n 1978, Del t a- P- Omega

    st abi l i zers, whi ch use shaf t speed and el ect r i c power

    as i nput si gnal s. were devel oped to over come t hese

    l i mtat i ons

    [ 4 ] .

    They have been used on 10 new uni t s

    and have been r etr of i t t ed on 8 uni t s t hat had

    previ ousl y used Del t a-Omega stabi l i zers.

    The contr ol desi gn and tuni ng procedures of power

    system stabi l i zers have a very si gni f i cant i nf l uence

    on t hei r eff ect i veness i n enhanci ng overal l system

    st abi l i t y. The advancement s i n har dware desi gn and

    methods of der i vi ng i nput si gnal s have been

    accompani ed by i mprovement s i n anal yti cal t echni ques

    and t uni ng procedur es. These i mprovements have, t o a

    l arge measure, cont r i but ed t o the successf ul

    58

    SY 669 4

    by t h e

    I X E E

    Power System Engineer ing Committee of

    t h e

    I E Y E

    Power Engineer ing Socie ty

    or

    p r e s e n t a t i o n

    a t t h e t E E E / P E S 1988 S um e r Y e e t i n g P o r t l a n d

    Oregon

    J u l y

    4 29 1938 . Manus cr ip t s ubmi t t ed

    Tanuary 29 1988; made avai Lab le

    Ear

    p r i n t i n g

    4 p r i l 2 8 1988.

    paper reconmended and approved

    Ontar io

    appl i cati on of stabi l i zers f or the sol uti on of

    st abi l i t y probl ems i ntr oduced by t he changi ng

    charact eri st i cs of t he power system

    Thi s paper descr i bes r ecent anal yti cal work

    carr i ed out f or t he det erm nati on of PSS cont rol

    par ameter s f or t he Darl i ngt on nucl ear gener ati ng

    st ati on presentl y under const r uct i on i n eastern

    Ontari o. The r esul t s present ed her e ar e, however, of

    gener al i nterest and pr ovi de a comprehensi ve anal ysi s

    of the ef f ects of the di f f erent stabi l i zer paramet ers

    on t he over al l dynamc per f ormance of t he power

    system They show how stabi l i zer sett i ngs may be

    sel ect ed

    so

    as to enhance t he st eady- st ate and

    tr ansi ent st abi l i t y of l ocal pl ant modes as wel l as

    i nter - area modes i n l arge i nterconnect ed systems. I n

    addi t i on, i t i s shown t hat t he sel ected par ameter s

    resul t i n sat i sf act ory perf ormance dur i ng system

    i sl andi ng condi t i ons, when l arge f r equency excursi ons

    are experi enced.

    DARLI NGTON GS

    Darl i ngt on nucl ear gener ati ng st ati on i s l ocated

    on

    t he shor e of Lake Ontar i o about 65

    km

    east of

    Toronto. When compl eted, i t w l l compri se f our

    1100 MVA, 0. 85 p. f. , 1800 RPM t urbi ne gener ator s w t h

    CANDU- PHW r eactors, moderat ed and cool ed by heavy

    water. The f our uni t s w l l be pl aced i n servi ce

    between 1989 and 1992. The st at i on w l l be

    i ncorporated i nt o the 500 kV net work t hrough t hree

    doubl e- ci rcui t l i nes.

    The uni t s w l l be equi pped w t h t ransf ormer- f ed

    t hyr i st or exci t ati on syst ems and Del t a- P- Omega

    stabi l i zers.

    A s

    i n the case of al l nucl ear uni ts i n

    Ontari o, dupl i cat e vol t age regul ators and st abi l i zers

    w l l be used i n order to achi eve hi gh rel i abi l i ty.

    I n such an ar r angement , one vol t age r egul ator w t h

    t he associ ated PSS i s i n-servi ce at any one t i me,

    w t h the other tracki ng i t. Transf er to t he

    al t ernat e regul ator and PSS i s i ni t i at ed by vari ous

    protecti ve f eatures, f or detectabl e mal f uncti ons.

    EXCI TATI ON CONTROL SYSTEM MODEL

    A bl ock di agr am r epr esent ati on of t he thyri stor

    exci t ati on system i ncl udi ng an aut omati c vol t age

    regul at or, a power system stabi l i zer, and a t erm nal

    vol tage l i mt er i s shown i n Fi gur e 1.

    The ti me const ant s necessary f or f i l t eri ng the

    r ect i f i ed t erm nal vol t age waveform can be r educed to

    a si ngl e t i me const ant , TR. i n t he r ange

    0.01

    t o

    0 . 0 2

    s.

    Ot her t i me const ant s t hrough to t he exci t er

    out put , i ncl udi ng any associ ated w t h the exci t er

    i t sel f , are negl i gi bl e and the mai n path can be

    r epr esent ed si mpl y by t he gai n

    KA.

    The f i gure al so

    shows a t r ansi ent gai n reduct i on (TGR) bl ock.

    The power syst em st abi l i zer model consi st s of t wo

    phase- l ead compensati on bl ocks, a si gnal washout

    bl ock, and a gai n bl ock. The i nput si gnal t o the

    stabi l i zer i s t he equi val ent rot or speed devi ati on

    fw

    .

    For a Del t a-P-Omega stabi l i zer, thi s i s

    der f zed f rom shaf t speed and i nt egral of change i n

    t erm nal el ect r i cal power. For anal ysi s i n whi ch

    t orsi onal modes are not of i nt erest , t he i nput si gnal

    i s equi val ent t o t he r otor speed devi ati on comput ed

    usi ng a l umped si ngl e mass r epresent ati on of t he

    t urbi ne-generator rotor [I].

    0885-8950/89/0500-0614 01

    .WO

    1989 IEEE

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    E J

    F MN

    WASHOUT P H A S E L F A D

    N B

    b DERI VED F RO M T ERMI NAL

    PO WER

    AND

    S H A F T S P E E D

    P O W E R SYSTEM STABlLlZEFI

    SMN

    Fi gure 1 Bl ock D agramof Thyri stor Exci t at i on Syst emW t h

    PSS.

    PSS

    PERFORMANCE OBJ ECTI VES

    An i nterconnect ed power system dependi ng on i t s

    si ze, has hundr eds to t housands of modes of

    osci l l at i ons. I n t he anal ysi s and cont rol of system

    stabi l i ty, two di sti nct t ypes of systemosci l l ati ons

    are usual l y recogni zed. One t ype i s associ ated w t h

    uni t s at a generati ng st ati on sw ngi ng w t h respect

    t o t he r est of t he power system Such osci l l at i ons

    are ref err ed t o as l ocal pl ant mode osci l l at i ons.

    The fr equenci es of t hese osci l l at i ons are t ypi cal l y

    i n t he range 0.8 to

    2. 0

    Hz. The second t ype of

    osci l l ati ons i s associ at ed w t h the sw ngi ng of many

    machi nes i n one par t of t he system agai nst machi nes

    i n other part s. These are referr ed to as i nter- area

    mode osci l l ati ons. and have f requenci es i n t he range

    0.1 t o 0 .7 Ha. The basi c f unct i on of t he PSS i s t o

    add dampi ng t o both t ypes of systemosci l l ati ons.

    Ot her modes whi ch may be i nf l uenced by PSS

    i ncl ude tor si onal modes, and cont rol modes such as

    t he exci t er mode associ ated w t h t he exci t at i on

    systemand the fi el d ci rcui t [ 3 ] .

    The overal l exci t at i on cont rol system i s desi gned

    so

    as to:

    - maxi m ze the dampi ng of t he l ocal pl ant mode as

    wel l as i nt er- area mode osci l l at i ons w t hout

    compromsi ng t he st abi l i t y of other modes;

    - enhance systemt ransi ent stabi l i t y;

    -

    not adversel y aff ect system perf ormance duri ng

    maj or system upsets whi ch cause l arge f requency

    excursi ons; and

    - mni mze t he consequences of exci t ati on system

    mal f unct i on due t o component f ai l ures.

    GENERAL PROCEDURE FOR SELECTI ON OF

    PSS

    PARAMETERS

    The bl ock di agram of t he PSS used to achi eve the

    desi red per f ormance obj ecti ves i s shown i n Fi gure 1.

    The f ol l ow ng i s a descri pt i on of t he consi derati ons

    and procedures used i n the sel ecti on of PSS

    parameters .

    To provi de dampi ng. t he st abi l i zer must produce a

    component of el ect r i cal t orque whi ch i s i n phase w t h

    speed var i ati ons. Therefore, t he PSS t ransf er

    f uncti on shoul d have an appropr i ate phase- l ead

    character i st i c t o compensat e f or t he phase l ag

    bet ween t he exci t er i nput and the el ect r i cal t orque.

    The phase characteri st i c t o be compensated

    changes w t h system condi ti ons. Theref ore, a

    compromse must be made and a characteri st i c

    acceptabl e f or a desi red range of f requenci es

    ( normal l y

    0. 1

    t o

    2. 0

    Hz) and f or di f f erent system

    condi t i ons i s sel ect ed. Thi s may resul t i n l ess than

    opt i mum dampi ng at any one fr equency. General l y,

    sl i ght undercompensati on i s preferabl e t o

    overcompensat i on so t hat bot h dampi ng and

    synchroni zi ng t orque components are i ncreased.

    The frequency response bet ween the exci t er i nput

    and generator el ect r i cal t orque, needed for

    det erm ni ng the phase compensati on, shoul d be

    cal cul ated assumng the generator angl e to remai n

    constant . Thi s i s done to el i mnat e t he f eedback

    ef f ect due t o rot or angl e var i ati ons caused by

    changes i n el ect r i cal t orque [5]. The phase

    characteri st i c i s obt ai ned usi ng a mul t i machi ne

    ei genval ue program [ 3 , 71. The el ectr i cal

    characteri st i cs of the generati ng uni t s under

    consi derati on are r epresent ed i n detai l as one

    equi val ent uni t w t h i t s i nert i a assumed to be very

    l arge ( say 100 t i mes t he act ual i nert i a). The

    dynamcs of al l other machi nes are negl ected. For

    adj acent machi nes, t he generati on i s r epresented as

    negat i ve l oad whi l e t he remai ni ng ones are

    represent ed as i nf i ni t e buses. Thi s ensures t hat the

    Theveni n equi val ent i mpedance at the t erm nal s of t he

    machi ne under st udy i s cor rect. The resul t i ng phase

    characteri sti c has a rel ati vel y si mpl e form f ree from

    the ef f ect s of nat ural f r equenci es due to i nt eracti on

    w t h external machi nes. The adequacy of t he phase

    compensati on determ ned i n t hi s manner i s checked, as

    descr i bed l ater, by a detai l ed st udy of

    PSS

    perf ormance under a w de range of syst em

    condi t i ons usi ng a f ul l systemr epresent at i on.

    Stabi l i zi ng Si gnal Washout

    The si gnal washout f unct i on i s a hi gh pass fi l t er

    whi ch removes dc si gnal s, and w t hout i t st eady

    changes i n speed woul d modi f y t he t erm nal vol t age.

    From t he vi ewpoi nt of washout f unct i on, t he val ue of

    t he associ at ed ti me constant TW i s not cri t i cal and

    may be anywhere i n the range of 1 t o

    20

    seconds. The

    mai n consi derati on i s that i t be l ong enough t o pass

    st abi l i zi ng si gnal s at t he f requenci es of i nt erest

    rel ati vel y unchanged, but not

    so

    l ong t hat i t l eads

    to undesi rabl e generator vol t age excursi ons as a

    resul t of stabi l i zer acti on duri ng system i sl andi ng

    condi t i ons. For l ocal mode osci l l ati ons, a washout

    of

    1

    t o

    2 s

    i s sati sfactory. From the vi ewpoi nt of

    l ow f r equency i nter - area osci l l ati ons a washout t i me

    const ant of 10 s or hi gher may be requi red i n order

    t o reduce phase l ead at l ow f requenci es. The over

    compensati on, whi ch resul t s f rom t oo l ow a val ue of

    TW reduces dampi ng as wel l as synchroni zi ng t orque

    components at i nter - area f requenci es.

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    St abi l i zer Gai n

    The st abi l i zer gai n ( K~TAB) i s chosen by

    examni ng t he ef f ect f or a w de r ange

    of

    val ues. I n

    t hese t ests al l uni t s t o be equi pped w t h PSS are

    represented i ndi vi dual l y i n detai l . I deal l y, t he

    st abi l i zer gai n shoul d be set at a val ue

    cor r espondi ng to maxi mum dampi ng. However, t he gai n

    i s of t en l i mt ed by other consi derati ons. I t i s set

    to a val ue whi ch resul t s i n sat i sf act ory dampi ng of

    t he cri t i cal s ystemmode(s) w t hout compromsi ng t he

    st abi l i t y of ot her modes,

    or

    tr ansi ent stabi l i t y, and

    whi ch does not cause excessi ve ampl i f i cati on of

    stabi l i zer i nput si gnal noi se. Our past exper i ence

    has been t hat, w t h a Del t a-P- Omega st abi l i zer,

    sati sf act ory dampi ng of l ocal pl ant mode osci l l ati on

    can be achi eved at a val ue of st abi l i zer gai n wel l

    bel ow the l i mt i ng val ue due to t he other

    consi derati ons. We have t herefore been conservati ve

    i n sett i ng t he gai n, and probl ems associ ated w t h

    very hi gh st abi l i zer gai ns have not been f ul l y

    i nvesti gat ed.

    St abi l i zer Out put Li mt s

    I n or der t o restri ct the l evel of generat or

    t erm nal vol t age f l uctuat i on duri ng t ransi ent

    condi t i ons, l i m t s are i mposed on t he PSS out put . To

    ensur e maxi mum cont r i but i on of t he st abi l i zer, i t has

    been Ontar i o Hydro' s pr acti ce t o use a rel ati vel y

    l arge posi ti ve output l i mt of 0. 1 t o 0. 2 pu. Thi s

    i s compl ement ed by a vol t age l i mt er ci r cui t whi ch

    prevents t he gener ator t erm nal vol t age f rom

    exceedi ng a set l evel of t ypi cal l y

    1.12

    t o 1.15 pu.

    W t h t he hi gh l i mt er gai n KL requi red, and

    TD must be chosen w t h consi derat i on of ::mte

    l oop st abi l i t y and stabi l i t y of t orsi onal modes. The

    ef f ect of t he two l i mt s i s to al l ow maxi mum f orci ng

    capabi l i t y whi l e mai nt ai ni ng t he t erm nal vol t age

    w thi n the desi red l i mts.

    On

    t he negati ve si de, a

    l i mt of -0.05 to - 0. 1 i s used. Thi s val ue i s chosen

    so as to al l ow suf f i ci ent cont rol range, t o provi de

    sat i sf actor y t ransi ent response, and to reduce t he

    probabi l i t y of a uni t t r i p as a consequence of

    s tabi l i zer fai l ure.

    Check

    On

    Sel ect ed Sett i nss

    The f i nal st age i n stabi l i zer desi gn i nvol ves

    determ ni ng i t s eff ect on t he overal l system

    perf ormance. Here, t he eff ect s of stabi l i zer

    on

    var i ous modes of osci l l ati ons are determ ned f or a

    w de range of syst em condi t i ons usi ng ei genval ue

    programs. Two programs of di f f erent types are used.

    Fi rst a program cal l ed MASS [7], whi ch comput es al l

    ei genval ues, i s used t o check l ocal pl ant modes,

    cont r ol modes and i nt eracti on w t h other generat i ng

    uni t s. Then, a speci al program cal l ed PEALS [7, 8],

    whi ch has been devel oped speci f i cal l y f or the

    ei genval ue anal ysi s of very l arge power syst ems, i s

    used t o check i nter- area modes and sel ected l ocal

    modes.

    Af t er checki ng i t s perf ormance under smal l

    pert urbati ons, the ef f ect on tr ansi ent stabi l i ty i s

    examned t o establ i sh out put l i mt s and to check the

    adequacy of other PSS sett i ngs.

    DESI GN OF PSS FOR DARLI NGTON GS

    At Ontar i o Hydr o, st abi l i zers have i n t he past

    been used pri mari l y t o damp l ocal pl ant modes of

    osci l l at i ons. I t has been our practi ce to set t he

    exci t er gai n ( KA) to about 200 [1,3]. A common

    i ndust ry pract i ce i s to r educe t he gai n of t he

    exci t er by use of t ransi ent gai n reduct i on [5.6].

    Except i n speci al ci r cumst ances, we have not s o fa r

    f ound i t benef i ci al to use TGR [l ].

    W t h the changi ng characteri st i cs of t he

    i nterconnect ed syst em the emphasi s at present i s t o

    enhance stabi l i t y of both i nt er- area modes and l ocal

    pl ant modes. Theref ore, two al t ernat i ve exci t ati on

    cont rol schemes, one w th no TGR and the other w t h

    TGR, were i nvest i gated f or Darl i ngt on GS. I n bot h

    cases t he gai n KA was set t o 200. For t he scheme

    w t h TGR, TA of

    1.0

    and Tg of 10. 0 were used.

    A summary of Dar l i ngt on generator and exci t er

    dat a used i n the desi gn and eval uat i on of t he PSS i s

    gi ven i n t he Appendi x.

    Phase Compensat i on

    The basi s f or t he sel ecti on of t he phase- l ead

    char acter i st i c of t he PSS f or t he scheme w t h

    no

    TGR

    i s i l l us t rated i n Fi gure 2. Curve 1 of t he f i gure

    shows the phase l ag bet ween t he exci t er i nput and t he

    el ect r i cal t orque as a f unct i on of f requency. Thi s

    cur ve was computed usi ng the MASS ei genval ue program

    w t h t he f our Darl i ngt on generators represent ed

    in

    detai l as a si ngl e equi val ent generator havi ng a

    l arge i nert i a and t he generators at al l ot her

    st ati ons represent ed as i nf i ni t e buses. Curve 2 of

    t he f i gure shows t he phase- l ead compensat i on provi ded

    by t he PSS w t h the fol l ow ng parameters:

    Phase- l ead: T1=T~=O. 118s, T3=T4=0. 044 s

    Washout : TW= O O

    s

    i IA S E LAG

    TO BE

    COMPENSATED

    @

    PSSPH ASE

    LEAD WlTH T

    - 20.0

    FREQUENCY

    ( n z )

    Fi gur e

    2

    Phase Characteri sti cs W t h

    NO

    TGR.

    Curves

    3

    and 4 show t he ef f ects of usi ng

    TW

    of

    1. 5 s and 20. 0

    s

    respecti vel y. I t i s seen t hat a

    of 1. 5

    s

    resul t s i n consi derabl e overcompensa-

    Z o n at l ow f requenci es, whi ch i s undesi rabl e f rom

    the vi ewpoi nt of i nt er- area osci l l ati ons. I ncreasi ng

    TW f r om 10

    s

    t o 20

    s

    resul t s i n onl y a smal l

    i mprovement i n t he phase character i st i c. The

    char acter i st i c of Curve 2 was t herefore chosen as an

    accept abl e compromse.

    I t shoul d be noted that si nce Curve 1 i s a pl ot

    of phase & bet ween exci t er i nput and el ectr i cal

    t orque, i t f al l s on the posi ti ve si de of the

    hori zont al axi s al ong w t h the phase

    compensat i on characteri st i cs.

    Fi gure 3 i l l ustr ates the basi s f or the sel ecti on

    of t he phase charact eri st i c f or t he scheme w t h TGR.

    Curve

    1

    shows t he exci t er- generator phase- l ag

    char acteri st i c requi red to be compensat ed. Curve 2

    shows the phase- l ead compensat i on provi ded by t he PSS

    w th:

    Phase- l ead: T1=T2=0. 27 s , T3=T4=0. 036 s

    Washout: TW=1. 5 s

    Curves 3 and 4 show t he ef f ect s of i ncreasi ng

    TW t o 5. 0

    s

    and 10. 0

    s ,

    respecti vel y. I t i s seen

    t hat a l ow val ue of TW

    i n t he order of 1.5 s i s

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    617

    ei genvect or associ ated w t h the speeds of al l

    machi nes. and i s shown i n Fi gure 4. The ei genvector

    el ement s f or Onl y a f ew r epresent ati ve machi nes are

    shown i n t he f i gure. The machi nes havi ng posi t i ve

    ei genvect or r eal par t s osci l l ate agai nst t hose havi ng

    negati ve real part s, across a weak tr ansm ssi on

    i nterf ace. The l ocat i on of t he i nterf ace i s

    i ndi cated by t hose gener ator s whi ch have smal l

    ei genvect or magni t udes.

    I t i s evi dent f rom t he mode shape t hat t he change

    i n speed of Darl i ngt on uni t s i n t hi s mode i s

    si gni f i cant. Thi s, together w th the l arge si ze of

    t he generators, i ndi cat e t hat PSS on Darl i ngt on uni t s

    can be used to enhance t he st abi l i t y of t hi s mode.

    Tabl es 1 and 2 show t he ef f ects of t he two

    al t ernat i ve exci t ati on cont rol schemes on the dampi ng

    of t he l ocal pl ant and i nter- area modes, f or

    di f f erent val ues of the stabi l i zer gai n, K s T ~.

    The resul t s shown are f or one set of syst em

    condi t i ons w t h 4 Darl i ngt on uni ts and al l ci rcui t s

    i n servi ce. The resul t s f or other system condi t i ons

    showed si m l ar general ef f ect s of PSS on dampi ng of

    system osci l l at i ons. I t i s seen fr om the resul ts

    t hat i ncr easi ng t he st abi l i zer gai n i mproves dampi ng

    of both modes of i nt erest. I n order t o achi eve

    comparabl e l evel s of dampi ng, t he st abi l i zer gai n f or

    t he scheme w t h TGR has t o be near l y tw ce that w t h

    no TGR.

    An

    examnati on of t he compl ete resul t s of t he

    MASS

    progr am ( not present ed here) showed t hat nei t her

    of t he t wo schemes had adverse ef f ect s on any other

    sat i sf actory when TGR i s used, and t hat Curve 2

    r epr esents an accept abl e phase characteri st i c f or t he

    PSS.

    @

    PHASE LAG

    TO

    BE COMPENSATED

    @ PSS PHASE LEAD WITH Tw 1.5

    @

    PSS

    PHASE LEAD WITH

    Tw ~

    5 8

    @

    PSS PHASE LEAD WITH

    T -

    10 0

    000 0 2 2 044

    067

    089 1 1 1

    133

    3 5 6

    178 2

    FREOUENCV

    ( H I )

    Fi gur e 3 Phase Char acteri st i cs W t h TGR.

    Smal l Si anal St abi l i t v Perf ormance

    An ext ensi ve ei genval ue anal ysi s, usi ng MASS and

    PEALS smal l si gnal st abi l i t y programs, was carr i ed

    out i n or der t o est abl i sh t he ef f ect of t he t wo

    al t ernat i ve exci t ati on contr ol schemes on the dampi ng

    of

    system modes under di f f erent syst em condi t i ons.

    PEALS si mul at i ons used a 3000 bus, 300 gener ator

    r epr esentat i on of t he i nt erconnected system A

    reduced system r epr esentat i on consi st i ng of 1500

    buses and 98 generat ors was used f or

    MASS

    si mul at i ons.

    The MASS programwas used to st udy the ef f ects of

    t he PSS on al l modes, i ncl udi ng cont r ol modes, and t o

    ensure t hat t here were no adver se i nt eracti ons w t h

    t he cont r ol s of ot her pl ant s. The Del t a- P- Omega

    st abi l i zer does not i nt eract w t h t or si onal modes

    and, consequentl y, t hi s i nteract i on was not

    i nvesti gat ed.

    The PEALS program comput es ei genval ues associ ated

    w t h one rot or angl e mode at a t i me and was used to

    st udy t he st abi l i t y of onl y sel ect ed modes such as

    t he dom nant i nter - area mode and t he l ocal Darl i ngt on

    mode.

    For t he range of syst em condi t i ons consi der ed,

    t he l ow f r equency i nter- area mode of i nt erest has a

    f r equency of about 0. 2 Hz. Al l machi nes i n t he

    system par t i ci pat e i n t hi s mode. The mode shape i s

    descr i bed by t he el ement s of the corr espondi ng

    GEN MAG PHASE -1 0

    _ _ - -

    + +

    GEN

    1 1 0

    -2 5

    GEN

    2 1 0 5 0

    GEN 3 1 0

    2 9

    GEN

    4 0 9 9

    DARLlNG T O N+G EN 5

    B 9 -2

    4

    GEN

    150 0 6

    I4 2

    GEN

    151 0 5 10 9

    GEN 152

    0 5 9 8

    GEN 153 0

    5

    13 9

    GEN

    154 0

    5 12 0

    GEM 520 0

    0

    91 6

    GEN

    521 0

    0 133

    8

    GEN 522

    0

    0 142 7

    GEN

    523

    0 0 -137 4

    GEN

    524 0

    0 142 3

    GEN 750

    0 3 161 2

    GEN 751

    0 3 161 4

    GEN

    752 0 3 161 2

    GFN 751 0

    3

    152

    5

    GEN

    754 0 3 161

    8

    GEN 950 0

    5

    161 6

    GEN 951

    0 5 161

    GEN 952 0 5 161 6

    GEN

    953 0 5

    161

    5

    GEN 954 0 5

    161

    6

    R

    R

    R

    R

    R

    TABLE 1

    Ef f ect of I ncreasi ng KSTAB on Dampi ng

    NO

    TGR, TW= O. O sec

    PSS Local Pl ant Mode I nter - Ar ea Mode

    Fr eq Dampi ng

    ai n Fr eq Dampi ng

    ( HZ) Rati o (HZ) Rati o

    0 0.855 0. 090

    0.192 0. 009

    10 0.864 0. 163

    0.187 0. 059

    15 0. 857 0.201 0.184 0. 082

    20 0. 844 0.239 0.182 0. 103

    0. 179 0. 1225 0.823 0. 274

    5 0 0.716 0.383 0.167 0. 193

    +

    0 0

    +

    I

    I

    I

    I

    I

    I

    I

    I

    I

    I

    R I

    R I

    R I

    R I

    I

    I

    I

    I

    1

    I

    I

    I

    I

    R

    R

    R

    R

    GROUP A

    ~

    S E L E C T E D M A C H I N K

    NORTH OF THE INTERFA CE

    GROUP B

    SELECT ED MACHI NES NEAR T HE I NT ERF ACE

    GROUP

    C

    SELECT ED MACHI NES

    SOUTH OF THE INTERFACE

    R

    REAL PART OF EIGENVECTOR ELEMENT

    I IMAGINARY PART OF EIGENVECTOR ELEMENT

    MAG

    ~

    MAGNITU DE OF EIGENVECTOR ELEMENT

    6

    e

    PHASE PHASE (DEG) OF EIGENVE CTOR ELEMENT

    Fi gur e 4

    Mode Shape of I nter- area Mode.

  • 7/26/2019 Kun Dur 1989

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    618

    TABLE 2

    Ef f ect of I ncreasi ng KsTAB on Dampi ng

    w t h TGR, TW=1.5 sec

    PSS

    Gai n

    0

    15

    25

    50

    70

    100

    Local Pl ant Mode I nter - Ar ea Mode

    Fr eq Dampi ng Fr eq Dampi ng

    (HZ) Rati o

    [ Hz) Rat i o

    0.843 0.102 0.187 -0.057

    0.849 0.140 0.183 0 009

    0.849 0.168

    0.180 0.050

    0.833 0.242

    0.170 0.138

    0.805 0.299

    0.161 0.186

    0.739 0.362

    0.152 0.227

    modes even at t he very hi gh val ues of gai ns

    consi der ed i n Tabl es 1 and 2. Thi s conf i r ms t hat

    t her e ar e no probl ems due t o cont rol modes l ocal t o

    Darl i ngt on uni t s

    or

    due to i nt eracti on w t h cont r ol s

    of uni t s at ot her generati ng stati ons. A s di scussed

    earl i er, t here are ot her consi derati ons i n usi ng very

    hi gh val ues of stabi l i zer gai n that need furt her

    i nvest i gati on. Fi el d t esti ng woul d be requi red

    bef ore t he l i m t i ng val ue can be establ i shed. I n

    order t o ensure maxi mum cont r i but i on to the dampi ng

    of

    i nt er- area osci l l ati ons, we propose to set t he

    gai n to as hi gh a val ue as possi bl e. I t i s expect ed

    t hat t he stabi l i zer gai n used woul d be not l ess than

    25 f or t he scheme w t h no TGR and 50 f or t he scheme

    w t h TGR.

    From t he resul t s of Tabl es 1 and 2, i t can al so

    be seen t hat w t hout PSS ( KSTAB = 0 . t he TGR

    i mproves l ocal mode dampi ng but decr eases i nter - area

    mode dampi ng. Thi s i s of i nt erest si nce reduct i on of

    t r ansi ent gai n i s of t en recommended as a means of

    i mpr ovi ng smal l si gnal stabi l i t y i n the absence of

    PSS.

    As di scussed ear l i er, w t h no TGR, a rel at i vel y

    hi gh val ue of washout t i me const ant TW has to be

    used to m ni m ze overcompensat i on at l ow

    f requenci es. The eff ect of varyi ng TW on l ocal and

    i nter - area modes i s present ed i n Tabl e 3. A s i s to

    be expected, t he l ocal mode i s l argel y unaf f ected by

    changes i n

    Tw.

    The dampi ng of t he i nter - area mode

    i ncreases si gni f i cant l y when TW i s i ncreased f rom

    1.5

    s

    t o 10.0 s . Furt her i ncrease i n TW has a

    negl i gi bl e ef f ect.

    I n vi ew of t he approxi mat i ons i nvol ved i n t he

    det erm nat i on of phase- l ead compensat i on due to t he

    si mpl i ci t y of external system representati on, the

    ef f ects of i ncreasi ng or decreasi ng t he phase

    compensati on were i nvesti gat ed. The resul t s

    TABLE 3

    NO TGR

    Ef f ect of I ncreasi ng

    TW

    on Dampi ng

    Local

    Pl ant Mode I nter - Ar ea Mode

    KSTAB TW Freq

    Dampi ng Fr eq Dampi ng

    Hz)

    Rat i o ( Hz) Rat i o

    15 1.5 0.847

    0.201 0.181

    0.056

    15 10. 0.857

    0.201

    0.184 0.082

    15 20.

    0.858

    0.201

    0.185 0.083

    25 1.5 0.809

    0.267 0.175

    0.081

    25 10

    0.823 0.274

    0.179 0.122

    25 20.

    0.825 ~0.274

    0.180 0.124

    conf i r med t hat t he phase- l ead ci r cui t chosen f or each

    scheme was sat i sf act ory. The i nvest i gati ons al so

    conf i r med t hat , when stabi l i zers were l ost on one or

    mor e Darl i ngt on uni t s, t here were no adverse

    i nt eracti ons between uni t s w t h and w t hout PSS.

    Transi ent St abi l i t y Per f ormance

    Ti me domai n si mul ati ons were carr i ed out to

    eval uat e the ef f ects of t he t wo al t ernat i ve

    exci t ati on cont r ol schemes on t ransi ent stabi l i t y and

    to veri f y some of t he resul t s of ei genval ue anal ysi s

    w t h regard to the ef f ect s on t he dampi ng of system

    osci l l ati ons. A 3000 bus, 300 gener ator syst em

    r epresent at i on was used, and a number of

    cont i ngenci es i nvol vi ng di f f erent t ypes of f aul t s and

    f aul t l ocat i ons were consi dered. Sel ected resul t s

    i l l ustr ati ng the ef f ects of varyi ng the stabi l i zer

    gai n, washout t i me constant and PSS out put l i mt s are

    shown i n Fi gures 5 t o 8. The resul t s shown are f or a

    cont i ngency i nvol vi ng a three- phase f aul t cl ose to

    Darl i ngt on GS on one 500 kV ci rcui t, w th another

    ci rcui t i ni t i al l y out- of - servi ce. They are, however,

    r epr esent ati ve of resul t s f or ot her cont i ngenci es

    consi dered.

    I n vi ew of t he l arge number of var i abl es and

    cases i nvol ved, onl y t he r otor angl e r esponses are

    shown and the overal l ef f ect s of t he PSS parameters

    on system t ransi ent stabi l i t y and dampi ng are

    di scussed.

    The resul ts of t he tr ansi ent st abi l i t y

    si mul ati ons show that:

    For t he syst em condi t i ons consi dered, t he 0.2 Hz

    i nter - area mode domnat es t he rotor angl e

    response of Darl i ngt on uni t s;

    For t he PSS scheme w t hout TGR, an i ncrease i n

    st abi l i zer gai n resul t s i n an i mprovement of

    f i r st sw ng stabi l i t y as wel l as dampi ng of r ot or

    osci l l ati ons (Fi gure 5):

    For t he PSS scheme w t h TGR, an i ncrease i n

    st abi l i zer gai n resul t s i n an i mprovement of

    dampi ng and a deteri orati on of f i r st sw ng

    stabi l i ty (Fi gure 6).

    A

    compromse i s t herefore

    necessary i n sel ect i ng t he val ue of t he gai n.

    I n t he absence of

    a

    PSS ( KSTAB = O , the ef f ect

    of t he TGR i s t o cause a det eri orat i on of t he

    dampi ng of rotor angl e osci l l ati ons ( Fi gures 5

    and

    6)

    dom nat ed by t he i nter - area mode. Thi s i s

    I

    I

    I

    I

    0 0 2

    4 3 6 8 0

    T l U E

    (

    SECS 1

    Fi gure 5

    Ef f ect of Changi ng St abi l i zer Gai n;

    PSS Scheme Wt hout TGR.

    Tw=lO, V s m = O . 2 , V s m = - O . O 6

  • 7/26/2019 Kun Dur 1989

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    619

    i n agr eement w t h t he resul t s of ei genval ue

    anal ysi s.

    For bot h schemes, t here i s a noti ceabl e

    i mpr ovement i n f i r st sw ng stabi l i t y when t he

    washout t i me const ant ( TW i s i ncr eased f r om

    1.5

    s t o 10. 0 s; f urt her i ncrease i n TW has

    negl i gi bl e eff ect (r esul t s shown i n Fi gur e

    7

    for

    t he scheme w t hout TGR).

    I n the case of t he scheme w t h TGR, expandi ng the

    PSS out put posi t i ve l i m t Vs+ fr om 0. 1 to

    0 3 pu causes an i mprovement I n f i r st sw ng

    st abi l i t y ( r esul t s not shown) wher eas, expandi ng

    t he negat i ve l i m t ( Vsm) f rom - 0. 06 to - 0. 3 pu

    causes a deteri orati on of f i rst sw ng stabi l i ty

    ( Fi gur e 8).

    I n t he case of t he scheme w t hout TGR, t he PSS

    out put remai ns w t hi n 0. 1 and - 0.06 pu and hence,

    expansi on of t he l i m t s has no ef f ect on system

    stabi l i t y (r esul ts not shown).

    I I I I

    100

    AI

    20

    4 0

    6 0

    B O

    TlME

    ( SECS

    1

    Fi gur e

    6

    Ef f ect

    of

    Changi ng St abi l i zer Gai n;

    PSS Scheme Wt h TGR.

    TW=1. 5, Vsm=O. 2, Vsm=- O. O6

    I

    1 1

    I I

    n o 2 0 1 5 0

    , , M E , S E C S ,

    Fi gur e I

    Ef f ect of Changi ng Washout Ti me

    Const ant : PSS Scheme Wt hout TGR.

    Ks TAB=~~,sm=O. 2,

    Vsm=-O.O6

    I

    I I I

    ~i l

    .-i

    I I I

    I I I

    100

    I

    z o 1 0 6 B O

    TlME

    S E C S 1

    Fi gure 8

    Ef f ect of Changi ng Negati ve PSS Output

    L i m t ; PSS Scheme Wt h TGR.

    KSTAB=~O, sm=0. 2

    Per f ormance Duri nu SystemI sl andi ng

    The per f ormance of t he Darl i ngt on st abi l i zers

    dur i ng condi t i ons of l arge f r equency excursi ons was

    examned by si mul ati ng an overgenerat ed i sl and f ormed

    as a r esul t of separati on of east ern Ont ar i o f r omt he

    rest of t he system The total l oad w t hi n t he ar ea,

    pr i or to t he f ormati on of t he i sl and, was

    3605 MW1409 Mvar and t he total generat i on was

    6695 MW2369 Mvar . The resul t i ng i sl and thus had

    about 400 excess generat i on. The gener ator s,

    exci t ers and pri me-movers of al l uni t s w t hi n t he

    i sl and were r epr esent ed i n detai l , i ncl udi ng

    overvol t age and overspeed cont rol s. Of par t i cul ar

    i nt erest i n these si mul ati ons was t he i nf l uence of

    Darl i ngt on PSS on the generator term nal and net work

    vol tages.

    Fi gures 9 and

    10

    show t he responses of Darl i ngt on

    t erm nal vol t age w t h the two stabi l i zer schemes.

    The over al l exci t ati on cont r ol i ncl uded a t er m nal

    vol tage l i mt er (See Fi gure 1). set t o l i m t the

    maxi mumval ue of t he t erm nal vol t age to 1. 13 pu. I n

    each case, t he washout t i me const ant ( Tw) was

    vari ed bet ween 1. 5

    s

    and

    20. 0 s .

    Both schemes are seen t o r esul t i n acceptabl e

    t er m nal vol t age response duri ng system i sl andi ng.

    The termnal vol tage l i mt er i s ef f ecti ve i n l i mt i ng

    t he maxi mum r i se i n vol t age to 1.13 pu i n bot h cases

    w t hout much overshoot. The subsequent vol t age

    sw ngs are, however , more pronounced i n t he case of

    t he scheme w t h TGR.

    For

    ei t her scheme, t he ef f ect of i ncreasi ng TW

    fr om 1.5 s t o 20. 0 s i s t o i mprove the overal l

    response. Al t hough the durat i on of t he i ni t i al

    maxi mum vol t age i s i ncreased sl i ght l y w t h a hi gher

    val ue of TW t he ampl i t udes of t he subsequent

    sw ngs are reduced consi derabl y. Thi s i s si gni f i cant

    si nce a hi gher val ue of TW i s al so desi rabl e f rom

    t he vi ewpoi nt of smal l si gnal and t ransi ent

    stabi l i ty, part i cul arl y w thout TGR.

    Ot her r esul t s ( not shown) of t he anal ysi s of

    i sl andi ng condi ti on i ndi cate t he f ol l ow ng:

    w t hout t he term nal vol t age l i m t er , t he maxi mum

    vol t age i ncreases to about 1. 18 pu f or bot h

    schemes. The absence of t he vol t age l i m t er had

    ver y l i t t l e eff ect on t he rest of t he response;

    t he ef f ect of i ncr easi ng t he PSS output upper

    l i mt i s to make the termnal vol t age l i mt er

  • 7/26/2019 Kun Dur 1989

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    620

    sl i ght l y l ess ef f ecti ve. Wt hout any upper

    l i m t , t he maxi mum t erm nal vol t age i ncreases to

    about 1.19 pu, w t h ei t her scheme.

    ~ ~~ ~

    ~

    : 7

    ' b . 0 0 1 0 0 I l i . 0 0 7 ' 1 .0 0 2 8 . 0 0 3 5 0 r i o o

    TIME ( SECS 1

    Fi gur e 9 PSS Scheme Wt h No TGR

    KSTABz25, Vsm=O. 2, Vsmz-0.06

    RELATI VE PERFORMANCE

    OF PSS

    SCHEMES

    W TH AND WTHOUT TGR

    W t h appropr i atel y desi gned phase- compensat i on

    and proper sel ecti on of parameters, i t i s seen t hat

    bot h schemes provi de sati sf act ory over al l

    per f ormance. Our pr ef erence i s f or t he scheme

    w t hout TGR for t he f ol l ow ng reasons:

    The scheme w t hout TGR requi res l ower PSS gai n

    and output l i m t s t han t hose f or t he scheme w t h

    TGR, i n order to provi de t he same over al l

    per f ormance.

    I n the case of t he scheme w t hout TGR, an

    i ncrease i n stabi l i zer gai n i mproves dampi ng as

    wel l as tr ansi ent stabi l i ty. I n contr ast, f or

    t he scheme w t h TGR, an i ncrease i n PSS gai n,

    whi l e i ncreasi ng dampi ng, resul t s i n a

    det eri orat i on of tr ansi ent stabi l i ty. Thi s may

    r equi r e a compromse to be made i n the sel ect i on

    of stabi l i zer gai n.

    Loss of

    PSS

    on one or more uni t s i s l ess

    det r i ment al t o i nter - area mode dampi ng, w t hout

    TGR than w t h TGR.

    The use

    of

    di scont i nuous exci t at i on cont r ol to

    enhance tr ansi ent stabi l i t y i s mor e eff ecti ve and

    l ess compl i cat ed w t hout TGR. Thi s t ype of

    cont r ol i s at present used on 16 l arge uni t s on

    o u r system

    [ l ] .

    FI ELD TESTI NG AND CALI BRATI ON

    Pri or to the i nstal l ati on of

    PSS,

    we pl an to

    per f orm f r equency response test s on one of t he

    Darl i ngt on generators t o det erm ne t hei r

    characteri st i cs more accuratel y. Duri ng the i ni ti al

    f i el d comm ssi oni ng, the on- l i ne t i me response of t he

    gener at i ng uni t w t h PSS w l l be measured and used

    to ver i f y some of t he anal yti cal r esul t s and to

    i dent i f y maxi mum al l owabl e stabi l i zer gai n. I f there

    are di scr epanci es bet ween comput ed and measured

    responses, t he model s w l l be appr opr i atel y modi f i ed

    and revi sed PSS sett i ngs w l l be determ ned.

    Dur i ng f i el d commssi oni ng, we do not f i nd i t

    practi cal to f i ne t une t he set t i ngs or eval uat e

    st abi l i zer per f ormance under a w de range of syst em

    condi t i ons. The pri mary val ue of on- l i ne t est i ng i s

    i n i dent i f yi ng equi pment characteri st i cs and

    val i dati ng si mul ati on resul t s, rather

    t han

    PSS

    t uni ng.

    GENERAL COMMENTS ON THE

    PSS

    CONTROL DESI GN

    St abi l i zers desi gned as descri bed i n t hi s paper,

    provi de robust decent ral i zed cont rol l er s f or t he

    dampi ng of el ect romechani cal osci l l ati ons i n power

    syst ems. The method used f or est abl i shi ng t he phase

    characteri sti cs of the stabi l i zer i s si mpl e and

    r equi r es onl y t he dynamc characteri sti cs of t he

    concer ned machi nes to be model l ed i n detai l .

    Detai l ed anal ysi s of t he per f ormance of t he power

    syst emi s used to est abl i sh other parameters and to

    ensure adequacy of t he overal l per f ormance of t he

    stabi l i zer. The resul t i s a stabi l i zer whi ch

    enhances t he overal l stabi l i t y of t he syst em under

    di f f erent operati ng condi t i ons. Si nce t he PSS i s

    t uned so as t o i ncrease t he dampi ng t orque component

    f or a w de r ange of f requenci es, i t cont r i but es t o

    t he dampi ng

    of

    al l system modes i n whi ch the

    r especti ve generator has a hi gh part i ci pati on. Thi s

    i ncl udes any new mode that may emerge as a r esul t

    of

    changi ng syst emcondi t i ons. Si nce we have been abl e

    to sat i sf y the requi rement s f or a w de range of

    system condi t i ons w t h f i xed parameters t here i s

    l i t t l e i ncent i ve to consi der an adapt i ve cont rol

    sys em

    Ot her methods f or deter mni ng t he PSS parameters

    have been suggest ed whi ch

    use

    mul t i vari abl e st ate

    space t echni ques i n order to meet a speci f i ed

    per f ormance cr i t eri on. Methods whi ch tr eat t he PSS

    desi gn as a pol e pl acement probl em [9] can be readi l y

    appl i ed to i ncrease dampi ng of

    a

    gi ven syst em mode

    when onl y one system condi t i on i s of i nterest and t he

    power syst em model i s known accuratel y. However,

    t her e i s no di rect way of i dent i f yi ng a uni que set of

    parameters accept abl e f or w del y di f f eri ng syst em

    condi t i ons. Al so, t he pol e pl acement probl embecomes

    extr emel y compl ex when deal i ng w t h i nter- area modes

    associ ated w t h l arge systems.

    I n a recent paper [lo] t he i ssue of robust ness of

    st ate space desi gned cont rol l ers was i nvest i gated. A

    number of PSS desi gns (i ncl udi ng ful l stat e f eedback

    and f ul l order observer) were compared on the basi s

    of t hei r f r equency response characteri sti cs. A

    si mpl e system consi sti ng of a si ngl e gener ator

    connected to an i nf i ni t e bus was used to compare t he

    methods. The most sati sf actor y

    of

    t hese desi gns

    showed a f r equency r esponse of a si m l ar nat ure t o

    t hat of t he st abi l i zer desi gned by t he method

    out l i ned i n t hi s paper. The other desi gn methods

    produced phase character i st i cs whi ch were

    sat i sf actory onl y for t he osci l l at ory mode f r equency

    associ ated w t h the system condi t i on consi dered and

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    621

    unsati sf act ory at other f requenci es. Thi s i ndi cat es

    t he need for r ecogni zi ng t he gl obal requi rement s of

    t he PSS and the advantages of basi ng i t s desi gn

    on

    an

    approach, such as t hat descri bed i n t hi s paper, whi ch

    can ef f ecti vel y deal w t h l arge compl ex syst ems and

    changi ng syst emcondi t i ons.

    SUMMARY AND CONCLUSI ONS

    Thi s paper has descr i bed the det ai l s of power

    system stabi l i zer contr ol desi gn f or a maj or

    generati ng st ati on i n Ont ar i o.

    I n

    sel ecti ng the

    stabi l i zer and other exci tati on system contr ol

    paramet ers, emphasi s was pl aced

    on

    t he enhancement of

    overal l syst em stabi l i t y. Speci al consi derat i on has

    been gi ven to the st abi l i t y of a l ow f requency

    i nter - area mode i n whi ch al l t he machi nes i n t he

    i nt erconnect ed systempar t i ci pat e.

    Two al t ernati ve exci t ati on cont rol schemes were

    consi der ed, one w t h and the ot her w t hout t ransi ent

    exci t er gai n reducti on. I t has been shown t hat , w t h

    appr opr i ate sel ecti on of stabi l i zer parameters, bot h

    schemes provi de sat i sf actor y overal l perf ormance, t he

    scheme w t hout TGR havi ng a number of advant ages.

    The i mpor t ance of appropr i ate choi ce of washout t i me

    const ant and stabi l i zer out put l i mt s, i n addi t i on to

    phase- l ead compensati on ci r cui t parameter s, has been

    demonst rated.

    APPEND X

    Darl i nat on Generat or and Exci t er Data

    Gener at or Parameters i n pu on Machi ne Rati ng:

    X =0. 188 R =0. 002

    1

    =1. 58 X =1. 56

    d q

    T' =8.75

    s

    Ti o=O. l l S

    do

    =o.

    33 X =O. 25

    d

    H=10. 2

    MWs/MVA

    Exci t er parameters:

    K =200

    T =0.01

    Em=6. 6 EFM N=- 5 5

    VLs=1. 13 T =0. 025 T =1. 212

    C

    =17

    T ~1. 0

    T

    =10.0 ( W t h TGR)

    T

    = O O

    T

    ~ 0 . 0

    (Wth No TGR)

    ACKNOWLEDGMENT

    The authors w sh to thank Messrs. L. J . Rubi no,

    D C. Lee and R. E. Beaul i eu f or thei r hel pful

    suggest i ons

    i n t he pr eparati on of t hi s paper.

    REFERENCES

    [l ] D C. Lee and P. Kundur , Advanced Exci t ati on

    Cont r ol f or Power System St abi l i t y Enhancement ,

    CI GRE Paper 38- 01, 1986.

    [2] P. L. Dandeno, A. N Karas, K. R. McCl ymont and

    W Watson, Ef f ect of Hi gh Speed Recti f i er

    Exci t ati on Syst ems on Generator St abi l i t y

    Li m t s , I EEE Trans. , Vol . PAS- 87, J an. 1968,

    pp 190-201.

    [3] P. Kundur , DC Lee and

    H M

    Zei n El - D n, Power

    System Stabi l i zers f or Thermal Uni ts:

    Anal yti cal Techni ques and On- si t e Val i dati on ,

    I EEE Trans. , Vol . PAS- 100, J an. 1981, pp. 81-95.

    [4] D C. Lee, R. E. Beaul i eu and J . A. R. Ser vi ce, A

    Power SystemStabi l i zer Usi ng Speed and El ectr i c

    Power I nputs- Desi gn and Fi el d Experi ence , I EEE

    Trans. , Vol . PAS-100, Sept. 1981, pp. 4151- 4167.

    [ 5] E. V. Lar sen and D. A. Swan, Appl yi ng Power

    System St abi l i zers, Part s I , I 1 and 111 , I EEE

    Trans. , Vol . PAS- 100, J une 1981, pp. 3017- 3046.

    [6] F.P. DeMel l o and C. Concordi a, Concept s of

    Synchronous Machi ne Stabi l i t y as Af f ected by

    Exci t ati on Cont rol , I EEE Trans. , Vol . PAS- 88,

    Apri l 1969, pp. 316- 329.

    [7] Smal l Si gnal St abi l i t y Anal ysi s Program

    Package , EPRI Proj ect RP2447- 1, Fi nal Report

    prepar ed by Ontari o Hydro, November 1987.

    [ 8] D Y. Wong,

    G. J .

    Rogers, B. Por r et t a and

    P. Kundur , Ei genval ue Anal ysi s of Very Large

    Power Syst ems , paper

    no .

    87WMO97- 9, I EEEI PES

    Wnter Meeti ng, New Orl eans, Loui si ana, Feb.

    1987.

    [ 9] C. N Chen and Y. Y. Hsu, Coordi nat ed Synt hesi s

    of Mul t i machi ne Power Syst emSt abi l i zer usi ng an

    Ef f i ci ent Decent ral i zed Model Cont rol

    Al gori thm, I EEE Trans. Vol . PWRS- 2, August

    1987, pp. 543-551.

    [l o] J . H Chow and J . J . Sanchez- Gasca, Frequency

    Response Eval uat i on of State Space Desi gned

    Cont rol l ers f or Systems w t h Li ght l y Damped

    Osci l l atory Modes A Power Syst em St abi l i zer

    Exampl e . Proceedi ngs of t he 26t h Conf erence

    on

    Deci si on and Cont r ol , Los Angel es, CA, December

    1987.

    Pr abhashankar Kundur r ecei ved t he M A. Sc and

    Ph. D. degrees f r om t he Uni versi t y of Tor ont o, Canada

    i n 1965 and 1967 respect i vel y. He taught at Mysore

    and Bangal ore Uni ver si t i es dur i ng 1967- 1969. I n

    1969, he j oi ned Ontar i o Hydro where he i s cur rent l y

    t he head of t he System Cont rol s and Transi ent s

    Secti on i n the System Pl anni ng D vi si on. He al so

    hol ds the posi t i on of Adj unct Prof essor at the

    Uni ver si t y of Tor ont o.

    Dr . Kundur was el ect ed a Fel l ow of t he I EEE i n

    1985 and i s a member of several I EEE worki ng groups

    and task f orces.

    Mei r Kl ei n recei ved the B. A. Sc and M A. Sc degr ees

    f rom t he Uni ver si t y of Tor ont o i n 1978 and 1983

    respecti vel y. He j oi ned Ontar i o Hydro i n 1978 and

    worked unt i l 1983 as a System Pl anni ng Engi neer on

    var i ous aspects of pl anni ng bul k power t r ansm ssi on

    l i nes and t ransf ormer st ati ons. Si nce 1983 he has

    been worki ng as a System Desi gn Engi neer, where he i s

    i nvol ved i n vari ous power syst em stabi l i t y studi es

    and i n codi ng, t est i ng and document i ng comput er

    programs.

    Graham Rogers graduated i n El ect r i cal Engi neer i ng

    w t h f i r st cl ass honour s f rom Sout hampton Uni ver si t y

    i n 1961. Fr om 1961 t o 1964 he was empl oyed as a

    consul t ant mathemat i ci an by AEI ( Rugby) Ltd. From

    1964 t o 1978, he was Lect urer i n El ectr i cal

    Engi neeri ng at Southampton Uni versi t y. Si nce 1978 he

    has been empl oyed by Ontari o Hydro where he i s

    curr ent l y System Desi gn Engi neer Speci al i st

    Cont r ol s i n t he System Pl anni ng D vi si on. He al so

    hol ds t he posi t i on of Associ at e Prof essor ( part - t i me)

    at McMaster Uni versi t y. He i s a Fel l ow of t he

    I nst i t ute of Mat hemat i cs and i ts Appl i cat i ons.

    Mal sorzata

    S.

    Zywno has an M Eng. degree ( 1977)

    f rom the Uni versi t y of Lodz, Pol and. Bef ore

    i mmgrat i ng to Canada she had worked at t he I nsti t ute

    of Heat Technol ogy, Lodz, devel opi ng sof t ware f or

    power syst em model l i ng. I n 1982, MS. Zywno j oi ned

    t he f acul t y of El ectr i cal Engi neer i ng at Ryer son

    Pol ytechni cal I nst i t ute, Toront o, wher e she curr ent l y

    t eaches i n t he area of Cont rol Syst ems.

    Si nce 1986, she has worked duri ng t he summers f or

    t he System Pl anni ng Di vi si on of Ont ari o Hydr o, where

    she has been i nvol ved i n power system st abi l i t y and

    cont rol studi es.

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    DI SCUSSI ON

    J . F. HAUER ( Bonnevi l l e Power Adm ni st r ati on,

    Por t l and, Oregon): Thi s i s an excel l ent exampl e of

    r ecommended pract i ce i n cont r ol syst emdesi gn, and i t

    may wel l become a benchmark i n the l i t erat ure f or

    power system stabi l i zers. The expl i ci t att enti on

    t hat t he aut hors gi ve to cont rol l er robust ness i s

    especi al l y wel come.

    Many quest i ons and i nferences can be drawn f r omt hi s

    paper . TGR i s a case i n poi nt . Lag/ l ead cont r ol i n

    a si t uati on wher e phase l ag i s al ready excessi ve

    demands caref ul examnati on, especi al l y when a

    cont rol l er pol e must be l ocat ed i n a regi on where

    model i ng i s poor and anal ysi s di f f i cul t . Can the

    aut hor s recommend quanti f i ed gui del i nes concerni ng

    TGR use?

    A robust cont rol l er , broadl y defi ned, i s one t hat

    per f orms wel l under an appropri atel y w de range of

    system condi t i ons. Str ong concl usi ons as to whether

    a contr ol l er has thi s very i mpor t ant pr opert y usual l y

    requi r e di rect examnat i on of t he contr ol envi r onment

    ( i e, f i el d measurement s and tests) . The aut hor s are

    dr aw ng upon experi ence gai ned at si m l ar si t es, and

    i t appears that thei r cont rol l er i nput i s bot h wel l

    behaved and wel l underst ood. Stabi l i t y enhancement

    by other means may r equi r e much cl oser at t ent i on to

    such i ssues [1,2].

    The authors make ver y br oad cl ai ms about t he abi l i t y

    of t hei r st abi l i zer desi gn to accommodate new modes

    and operati ng condi t i ons. I t r emai ns t o be shown, I

    t hi nk, t hat broad-band dampi ng enhancement f or a

    part i cul ar machi ne can, i n no ci r cumst ances,

    adversel y af f ect t he dampi ng of ot her machi nes. Does

    not t he TGR case pr ovi de a counter - exampl e t o t hi s?

    I t i s not abl e t hat t he PSS i s desi gned to compensate

    a par t i al - der i vat i ve ef f ect. Si nce t he associ ated

    f r equency response cannot be di r ectl y measured i n the

    f i el d, one must i nst ead val i date t he model f r omwhi ch

    i t i s cal cul at ed. I t woul d add cont ext t o the paper

    i f t he aut hor s were t o show t he ful l t r ansf er

    f unct i on response, i n a f orm enabl i ng compari son w t h

    f ut ure t est r esul ts.

    [l] J . F. Hauer, Robust Dampi ng Cont rol s f or Large

    Power Systems, t o appear i n t he I EEE Cont rol

    Systems Magazi ne, J anuary 1989.

    [2]

    J . F. Hauer, React i ve Power Cont r ol as a Means

    f or Enhanced I nterarea Dampi ng i n t he West ern

    U S. Power Syst em- A Frequency-Domai n Perspect i ve

    Consi der i ng Robustness Needs, i n Appl i cat i on of

    St at i c Var Syst ems f or Syst em Dynam c

    Per f ormance, I EEE Publ i cati on 87TH0187- 5-PWR,

    pp. 79- 92.

    Manuscr i pt recei ved August 18, 1988 .

    YAKOUT MANSOUR (B. C. Hydro, Vancouver , Canada) : The

    aut hors have present ed an i nval uabl e addi t i on to t he

    art and sci ence of t uni ng power system st abi l i zer s.

    Thi s di scusser woul d ' l i ke to make t he f ol l ow ng

    comment s:

    Studi es done at B. C. Hydro usi ng t he WSCC system

    model proved t he ei genval ue- ei genvector sof t ware

    package, whi ch the aut hors ref err ed to as

    MASWPEALS package, t o be an i nval uabl e

    anal yti cal tool f or determ ni ng t he degree of

    part i ci pat i on of vari ous machi nes i n part i cul ar

    modes of osci l l ati on, t he shape of vari ous modes

    of concern and the r espect i ve dampi ng factors.

    These are essenti al par ameter s to ensure proper

    t uni ng of power syst emst abi l i zers.

    Si nce t he earl y i mpl ement ati on of st ati c exci t ers

    and power system st abi l i zer s, t he benefi t of t he

    t ransi ent gai n r educti on (TGR) has been debat ed.

    Earl i er st udi es done at B.C Hydro showed t hat

    cl ear benef i t can be gai ned by i mpl ement i ng TGR

    i n cases wher e a si ngl e-i nput si mpl e-l ead/or

    si mpl e- l ag PSS (dependi ng on t he i nput. si gnal ).

    Wt h such PSS' i t was al ways di f f i cul t t o obt ai n

    reasonabl e dampi ng at bot h area and l ocal modes

    of osci l l ati on. I n those cases t he stabi l i zer

    woul d be tuned pr i mari l y to f ul l y compensat e the

    phase l ag at t he area mode whi l e t he TGR woul d

    hel p i mprove t he dampi ng at t he hi gher l ocal

    mode. The l att er was usual l y achi eved at t he

    expense of some deteri orati on of t r ansi ent

    st abi l i t y. The aut hor s showed, and t hi s

    di scusser agrees, t hat there i s l i tt l e benef i t i n

    appl yi ng TGR i f t he PSS i s desi gned such t hat

    proper compensati on i s achi eved over t he range of

    f r equenci es between t he area and l ocal modes.

    Agai n t he aut hor s are to be congrat ul ated f or a wel l

    wr i t t en document .

    Manuscri pt recei ved August

    18,

    1988.

    MA. PA1 ( Uni versi t y of I l l i noi s, Urbana): The

    aut hors have pr esented extr emel y i nterest i ng r esul t s

    on t he appl i cati on of a modi f i ed PSS ( i n t he sense

    t hat t he i nput i s not j ust h t o damp out both

    el ect romechani cal and tor si onal modes. The t uni ng of

    PSS parameter s i s done f or both l ocal

    el ect romechani cal and area modes. To accompl i sh

    t hese several obj ecti ves they have had to consi der

    ef f ect s of both TGR and wash out t i me const ant s. I n

    convent i onal PSS w t h

    h

    si gnal , t he washout t i me

    const ant i s si mpl y set at a f i xed val ue f or dampi ng

    out l ocal modes. Through t hi s paper t he aut hors have

    rai sed some i nt eresti ng theoreti cal possi bi l i ti es.

    1. Can some sensi ti vi ty anal ysi s (i e, sensi ti vi ty of

    ei gen val ues t o syst em parameter ) be used as a

    t ool f or systemati c t uni ng f or bot h l ocal and

    t ors i onal modes?

    2. Si nce the f eedback si gnal i s no more output

    f eedback but rat her part i al st at e f eedback i e,

    basi cal l y A6, Am ( si nce Ape = ( K1A6

    + K ~A E )

    can

    some other st ates be used al so as i nput si gnal t o

    PSS? I s t here any report ed pr acti cal experi ence

    i n thi s r egard besi des t he academ c l i t erature?

    I n t he past f ew year s mul t i vari abl e cont rol

    syst emdesi gn t echni ques have matured qui t e a bi t .

    The di scusser seeks t he f ol l ow ng mnor cl ari f i cat i on

    i n Fi g. 1. I t i s stated that I heq i s der i ved

    f r om t erm nal power and shaf t speed. By t erm nal

    power do t he aut hors mean t he accel erat i ng power i e,

    (AP, Ape)? I n an ear l i er paper [ l ] that

    seems t o be t he case.

    I n some desi gns [2] t he f ol l ow ng t ype of PSS

    conf i gur ati on and si gnal condi t i oni ng i s empl oyed

    ( see f i gure bel ow). I t appear s to be a P-I

    contr ol l er w t h accel erati ng power as i nput. I s i t

    9

    q I 1

    +sT2

    U

    Fl gure 1 .

    An

    al ternat i ve PSS conf i gurat i on [ Z ]

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    623

    i n some sense equi val ent to t he aut hor ' s

    Del t a-P- Omega st abi l i zer? I woul d appreci ate

    comment s and any suggest i ons r egardi ng t uni ng of

    par ameters on such a stabi l i zer . TI i s the washout

    t i me const ant .

    J . P. Bayne, D C. Lee and W Watson, A power

    system st abi l i zer f or t hermal uni ts based on

    deri vat i on of accel erat i ng power, Paper

    F77- 137-3, I EEE PES Wnter Power Meet i ng, New

    Yor k, J an. 30- Feb. 4, 1977.

    P.G Murt hy and R. K. Si nghal , Rol e of power

    system stabi l i zers i n the operati on of

    i nterconnect ed power syst ems, Paper #11- 85,

    CI RGE Symposi um 1985.

    Manuscr i pt r ecei ved August 18 1988.

    J . R. SM TH and D A. PI ERRE ( El ect r i cal Engi neer i ng

    Dept . , Mont ana State Uni vers i t y, Bozeman) : We

    congratul ate the author s f or a very i nt erest i ng and

    i nsi ght f ul paper on PSS t uni ng w t h robustness

    consi der ati ons. There are a f ew poi nt s on whi ch we

    woul d l i ke to sol i ci t some fur t her comment s.

    1) I f ot her exci tati on contr ol l ers i n t he

    i nt erconnected system are to be t uned f or

    robustness i n a si m l ar f ashi on to what you have

    descr i bed, f or other modes or f or t he 0. 2 Hz

    mode, w l l i t be necessary to recheck or possi bl y

    r eadj ust the Darl i ngt on exci t er parameters? I t

    appears t hat t he Dar l i ngt on exci t ati on cont rol l er

    desi gn i s ver y r obust but i t al so seems t hat t he

    ext ensi on of t hi s desi gn method t o other

    machi nes, f or several l ocal and i nterarea modes,

    over a w de range of operat i ng condi t i ons coul d

    become qui t e compl i cated. Do you have any pl ans

    to extend thi s desi gn procedure to ot her

    gener ati ng st ati ons and do you have any i nsi ght s

    or comment s about t he necessi t y of rechecki ng or

    r eadj usti ng one set of exci t ers when another set,

    somewher e el se i n the syst em i s bei ng tuned?

    2

    As t he i nt erconnected power system dynam c

    character i st i cs change over the years w t h

    di f f erent l oad patt erns and network connect i ons

    do you t hi nk i t w l l be necessar y to per i odi cal l y

    check and possi bl y r eadj ust t he Darl i ngton

    exci t er parameters, and i f s o how of t en?

    3) For t he case of Darl i ngt on exci t ers , we woul d be

    i nterest ed to know r oughl y how many di f f erent

    operati ng condi t i ons of your system do you f eel

    i t i s necessar y to check before you are conf i dent

    t hat t he exci t er parameter sett i ngs resul t i n a

    suf f i ci ent l y r obust cont r ol l er ? Do you check

    onl y t hose oper ati ng condi t i ons whi ch are known

    to have a st rong 0. 2 Hz mode or are operat i ng

    condi t i ons w t h ot her cri t i cal modes al so checked?

    Manuscr i pt recei ved August 19 1988.

    CARSON W. TAYLOR ( Bonnevi l l e Power Admni st r ati on,

    Port l and, Oregon) : I commend t he aut hors f or an

    out st andi ng paper descr i bi ng Ontar i o Hydro' s power

    system stabi l i zer appl i cati ons. The authors'

    exper i ence i s much bet t er t han exper i ence i n t he

    western i nterconnect i on wher e stabi l i zers are oft en

    out of ser vi ce, and where there are somet i mes l ong

    del ays i n comm ssi oni ng.

    The aut hor s di scuss t r ansi ent gai n reduct i on at

    l ength. I n the l i t erature, the reason f or tr ansi ent

    gai n reduct i on, or equi val ent r at e f eedback

    ( exci t at i on system stabi l i zer) , seems to be mai nl y

    open ci r cui t perf ormance. For exampl e a wel l - damped

    response fol l ow ng l oad r ej ecti on i s desi rabl e.

    Al t hough open ci r cui t per f ormance i s cl ear l y much

    l ess of a probl em w t h a stati c exci ters (see

    ref erence A f or a si mpl e textbook exampl e), deMel l o

    and Concordi a [6], st at e t hat l ow t r ansi ent gai n i s

    desi r abl e even f or st at i c exci ters. Coul d t he

    authors comment on t he open ci r cui t per f ormance of

    thei r machi nes? Wt h st ati c exci t ers ar e t here cases

    of l ong open ci r cui t f i el d ti me const ant s wher e l ower

    t r ansi ent gai ns are necessary?

    The authors emphasi ze t he i mpor t ance of good model s

    and model val i dat i on. Thi s cont r asts w t h t he

    emphasi s of t he wel l known Farmer/ Agrawal paper [B]

    wher e the st atement i s made that . . . i t was

    det erm ned that exci t ati on syst ems cannot be

    adequat el y model l ed to al l ow opt i mum PSS t uni ng by

    si mul ati on. Theref ore, PSS t uni ng must be done i n

    t he f i el d. Coul d the authors di scuss thei r

    experi ences at other generat i ng pl ant s r egardi ng how

    cl ose model predi cat i ons are to f i el d tests?

    I n t he oral di scussi ons f ol l ow ng t he paper

    present at i on, Dr . Kundur ment i oned that they pr efer

    st ati c exci t ers over hi gh response rotati ng exci t er s

    part l y because of t he compl exi t i es associ ated w t h

    anot her synchronous machi ne- model l i ng and PSS desi gn

    are greatl y si mpl i f i ed w th stati c exci ters.

    El aborat i on on these poi nts by t he authors woul d be

    val uabl e.

    [A] 0. 1. El ger d, El ect r i c Energy Syst ems Theory: an

    i nt r oducti on, McGr aw- Hi l l , 1982.

    [B] R. G Farmer and B. L. Agrawal , State-of - t he Art

    Techni ques f or Power System Stabi l i zer Tuni ng,

    I EEE Transact i ons on Power Apparatus and Systems,

    Vol . PAS-102, No. 3, pp. 699-709, March 1983.

    Manuscr i pt recei ved September

    16,

    1988.

    P. KUNDUR, M KLEI N, G J . ROGERS and MS.

    ZWYNO:

    We

    t hank the di scussers f or t hei r ki nd comment s and

    quest i ons, and f or provi di ng us an oppor t uni t y to

    el aborate on some of t he aspects of our approach to

    power system st abi l i zer desi gn and appl i cat i on.

    Si nce several di scussers have ref err ed to our

    examnat i on of t he use of t ransi ent gai n r educti on

    (TGR) i n t he f orward path of an AVR, i n thi s cl osure

    we w l l consi der t hi s aspect f i r st and then ret urn

    to answer t he ot her poi nts r ai sed by t he i ndi vi dual

    di scussi ons.

    M . Car son Tayl or cor rectl y poi nt s out t hat one

    of t he i mpor t ant r easons f or usi ng TGR i s t o ensure

    sati sf actory per f ormance of the uni t on open

    ci rcui t . Wth thyri stor excit ers, t hi s i s l i kel y to

    be t he case onl y i n si t uat i ons wher e the t erm nal

    vol t age sensi ng ci r cui t t i me const ant ( TR) i s

    l arge. Al l our uni ts have smal l val ues of TR ( i n

    t he r ange 0.01 t o

    0.02

    s ) and are very st abl e on

    open ci r cui t w t hout TGR. I n f act , we per f or m l oad

    r ej ect i on t est s and open- ci rcui t st ep response tests

    on our uni t s as part of acceptance t est s, and the

    measured t r ansi ent vol t age r esponses duri ng such

    t ests ar e very wel l damped. Fi gure A shows t he

    measured ter m nal and f i el d vol t age r esponses of one

    of

    our t hermal uni t s f ol l ow ng a st ep change i n AVR

    ref erence i nput, w t h the uni t on open ci rcui t.

    Thi s uni t has a T' do of about 6.0

    s ,

    a vol t age

    sensi ng ci rcui t t i me const ant TR of

    0.01 s ,

    and an

    exci t er gai n KA of 200 w t h no TGR. As can be

    seen f rom t he f i gure the open ci r cui t r esponse i s

    wel l damped. Thi s t ype of r esponse i s typi cal of

    al l our uni t s w t h thyri stor exci ters, some of whi ch

    have T' do as hi gh as 10 S On the other hand,

    uni t s w t h rotati ng exci t ers normal l y requi re a

    reduct i on of vol t age r egul ator gai n at hi gh

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    624

    2 3 . 8

    d c

    I

    f r equenci es

    Fi gur e

    A

    Open-c i r cui t Response

    to ensur e sat i sf actor y exci t er

    response. Thi s i s usual l y achi eved by usi ng a rat e

    f eedback.

    I n t he l i t erature on PSS appl i cat i on, t he use of

    TGR i s al so w del y r ecommended f romt he vi ewpoi nt of

    over al l syst em dynam c perf ormance. For exampl e,

    see r eferences

    5

    and 6 and di scussi on by

    F. P. DeMel l o of r eference 3 . Such recommendati ons

    are based on overl y si mpl i f i ed anal ysi s of

    l i neari zed perf ormance. I n our paper, we have

    att empted to eval uat e t he ef f ects of usi ng TGR on

    t he over al l st abi l i t y perf ormance. A s shown i n t he

    paper, by proper sel ecti on of phase l ead ci r cui t

    parameters , si m l ar smal l si gnal perf ormances can be

    achi eved w t h and w t hout TGR. I t i s, however,

    i mpor t ant t o r ecogni ze the need t o use a hi gher

    val ue of st abi l i zer gai n when TGR i s used. The

    resul t i ng stabi l i zer out put si gnal i s l arger and i s

    more l i kel y to hi t i ts l i mt s duri ng

    a

    t ransi ent

    condi t i on. Thi s compl i cat es t he l arge si gnal

    perf or mance, oft en resul t i ng i n l ess t han

    sat i sf act ory perf ormance. I t i s al so i mport ant to

    r ecogni ze t hat, w t h t he PSS out of servi ce, TGR has

    a det r i ment al ef f ect on dampi ng of l ow f requency

    i nter- area osci l l ati ons.

    We agree w t h Mr . Yakout Mansour t hat w t h a

    f i r st order phase compensat i on ci r cui t tuned to

    provi de the desi r ed compensat i on corr espondi ng to

    one domnant mode of osci l l ati on, t he TGR coul d be

    ef f ect i ve i n i mpr ovi ng t he phase char acter i st i cs

    corr espondi ng t o other modes.

    A s

    noted by M r .

    Mansour, t here i s no need to use TGR when t he PSS i s

    desi gned t o have pr oper phase charact eri st i c over a

    w de range of f r equenci es.

    I t i s not easy to pr oduce the quanti f i ed gui de

    l i nes on t he use of TGR requested by Dr . J ohn

    Hauer. As di scussed i n refer ence 1 of our paper , we

    have had to r esor t t o the use of TGR onl y to sol ve

    pr obl ems associ ated w t h i nteract i ons between

    adj acent generati ng uni ts. one of whi ch had sl ow

    rot ati ng exci t er and the other a t hyri st or exci t er.

    We now return to repl y to t he i ndi vi dual

    di scussi ons.

    Dr

    J F

    Hauer: We agree t hat t he enhancement of

    st abi l i t y by ot her contr ol means, such as dc l i nk

    curr ent modul ati on or SVC modul ati on, i s not as wel l

    under st ood as i s t he eff ect of power system

    stabi l i zers. The reason, i n our opi ni on, i s t he

    l ack of a di rect connecti on bet ween t he act i on of

    t he contr ol l i ng devi ce and t he addi t i on of dampi ng

    to a syst em mode. Provi ded t hat t he machi ne to

    whi ch a power system stabi l i zer i s fi tt ed

    part i ci pat es str ongl y i n t he mode t o be st abi l i zed,

    t he stabi l i zer can be desi gned to i ncr ease t he modal

    dampi ng. Dependi ng on t he syst emcondi t i ons, i t may

    not add suf f i ci ent dampi ng to compl etel y st abi l i ze

    t he mode. I n such a case, st abi l i zers on addi t i onal

    uni t s may be necessary to obt ai n t he r equi red syst em

    perf ormance. We have not exper i enced any si t uat i ons

    wher e the appl i cati on of a properl y t uned st abi l i zer

    has had an adverse ef f ect on the dampi ng of other

    machi nes. I t i s, however, i mport ant to ensur e t hat

    t he cont r ol s on cl osel y coupl ed uni t s and ot her

    devi ces such as HVdc l i nks and SVCs are properl y

    coordi nat ed. Thi s i s one of t he mai n reasons why we

    car ry out detai l ed si mul ati ons usi ng the

    MASS

    program

    i

    \

    \

    \

    ?S

    r

    ~

    no ?5

    I

    5

    F 7

    on z

    s

    L L L 2

    7

    C

    ~ ~

    1 7

    Fi gur e

    B

    Cal cul ated Frequency Response

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    625

    As noted by Dr . Hauer and for t he r easons

    expl ai ned i n the paper, t he phase char act er i st i c t o

    be compensated by PSS ci r cui t r y has to be deter m ned

    w t h t he f eedback ef f ect of t he rotor angl e

    el i m nated. Whi l e thi s characteri sti c can be

    comput ed by assumng a l arge i ner t i a const ant , i t

    cannot be di r ect l y measured. The f r equency r esponse

    of t he ful l t ransf er f uncti on ( i ncl udi ng the rotor

    angl e f eedback ef f ect ) between el ect r i cal power and

    t he AVR ref erence f or a Darl i ngt on uni t comput ed

    usi ng t he PEALS program i s shown i n Fi gur e

    B.

    For

    pur poses of val i dat i on, we have i n t he past measured

    on- l i ne f r equency response charact eri st i cs of

    t ransf er f unct i ons rel ati ng pert urbed val ues of

    speed, f i el d vol t age, el ect ri cal power out put and

    t er m nal vol t age. Reference

    3

    of

    our

    paper shows

    compari sons between computed and measured on- l i ne

    f r equency r esponses as wel l as t i me r esponses f or

    some of our PSS i nstal l ati ons.

    M.

    Y.

    Mansour : We are pl eased to know about t he

    good exper i ence B. C. Hydro has had w t h MASSI PEALS

    programs i n t he WSCC syst em st udi es. As

    Mr.

    Mansour

    i s aware, under a j oi nt ef f ort by EPRI and Ontar i o

    Hydro, t hese programs are bei ng f urt her devel oped i n

    order to enhance thei r model l i ng and anal yti cal

    capabi l i t i es.

    Professor M.A. Pai : We agree t hat i t woul d be

    possi bl e to empl oy ei genval ue sensi t i vi t i es t o

    devel op a method of deter m ni ng some of t he PSS

    par ameter s. However, i t i s unl i kel y t hat such a

    desi gn al gor i t hm woul d be more syst emat i c t han t he

    procedure we have descr i bed. Mode shapes and

    f r equenci es al t er w t h l arge changes i n system

    condi t i ons. The ef f ect s of such changes cannot be

    account ed f or by anal ysi s of sensi t i vi t y to smal l

    changes i n system paramet ers. Theref ore st abi l i zer

    desi gn based on ei genval ue sensi t i vi t y techni ques

    cannot ensure sati sf actory perf ormance under w del y

    di f f eri ng systemcondi ti ons.

    We are not f aml i ar w t h any pr act i cal PSS

    appl i cat i on based on mul t i var i abl e cont rol system

    desi gn.

    As

    di scussed i n our paper , such approaches

    t o PSS desi gn have i nherent l i mt at i ons. One of t he

    probl ems w t h most publ i shed st abi l i zer desi gn

    pr ocedures, based on l i near mul t i var i abl e cont rol

    t echni ques, i s t hei r l i m t ed r obust ness t o changi ng

    systemcondi t i ons.

    Prof essor Pai appears t o have msunders t ood the

    basi s and f unct i on of our del t a P- Omega stabi l i zer.

    Ref erences

    1

    and 4 of our paper provi de a good

    descri pti on of t he stabi l i zer. I n ef f ect, t hi s

    stabi l i zer uses onl y one stabi l i zi ng si gnal whi ch i s

    pr oport i onal to speed devi at i on. Thi s si gnal i s

    deri ved usi ng shaf t speed and t erm nal el ect r i c

    power so as t o el i m nat e t orsi onal modes. I n

    Fi gure

    1

    of t he paper, t he t erm nal power r efers to

    t he el ectr i cal power out put of t he gener ator and not

    t he accel erat i ng power.

    The stabi l i zer conf i gur at i on gi ven by Professor

    Pai can be compar ed to a speed i nput st abi l i zer w t h

    A

    Pa, =

    SMAU

    At l ow f requenci es there woul d be a phase shi f t of

    180 degrees pr oduced by the ef f ecti ve deri vat i ve of

    speed i n t he power i nput and by t he washout. The

    phase shapi ng ci r cui t , whi ch basi cal l y pr ovi des a

    phase l ag charact eri st i c, shoul d enabl e t he i deal

    phase char act er i st i c t o be mat ched over a nar r ow

    f r equency range about that of t he l ocal mode. I t i s

    unl i kel y that t hi s st abi l i zer conf i gurati on coul d be

    used successf ul l y t o add t o the dampi ng of l ow

    f requency i nter - area modes.

    J.B.

    S m i t h

    and

    D.A. Pi err e: The PSS on ou r

    exi st i ng uni t s were ori gi nal l y t uned pr i mari l y to

    damp l ocal pl ant modes. I n vi ew of

    our

    r ecent

    concern f or dampi ng of l ow f r equency i nter - area

    modes, we have i n fact revi ewed PSS set t i ngs for al l

    our l arge uni t s usi ng t he approach descr i bed i n t he

    paper f or desi gni ng Darl i ngt on PSS. The phase l ead

    ci r cui t par ameters were f ound t o be sati sf act or y.

    The onl y changes we are consi der i ng are i ncreasi ng

    t he washout t i me const ant s f r om about 1. 5 s t o about

    10. 0 s and usi ng sl i ght l y hi gher stabi l i zer gai ns.

    The procedure used for Darl i ngt on PSS desi gn has

    been appl i ed to these uni ts w th l i tt l e di f f i cul ty.

    We have conf i r med t hat nei t her t he changes t o

    t he set t i ngs of PSS on exi st i ng uni t s nor t he

    addi ti on of PSS on ot her uni ts w l l requi re

    readj ust ment of Darl i ngt on PSS set t i ngs.

    I t i s not normal l y necessary t o change t he PSS

    set t i ngs as syst em condi t i ons change, si nce t he

    approach we have descr i bed resul t s i n a robust

    desi gn. The phase char act er i st i c between st abi l i zer

    out put and the gener ator ai r - gap t orque r emai ns

    w t hi n a narr ow band as system condi t i ons change.

    Wt h the PSS phase compensat i on char acteri st i c

    chosen so as t o pr ovi de a sati sf actory compromse

    under di f f eri ng systemcondi t i ons, t here i s normal l y

    no need t o peri odi cal l y modi f y PSS set t i ngs.

    For

    Darl i ngt on PSS desi gn, we consi der ed several

    system condi t i ons to check t he ef f ects of cri ti cal

    out ages and changi ng the number of Darl i ngt on uni t s

    i n servi ce. I n addi t i on, we al so l ooked at t he

    ef f ect s of some of t he maj or r ei nforcement s to t he

    EHV t r ansm ssi on syst emt hat have been pl anned. The

    obj ecti ve was t o check f or t he robustness of PSS

    desi gn t o maj or changes i n syst em condi t i ons, and

    not t o examne the st abi l i zer per f ormance f or every

    possi bl e condi t i on.

    CW

    Tayl or: We have i ndeed had good exper i ence

    w t h our appl i cat i on of power system stabi l i zers.

    We r el y heavi l y on thyri stor exci t ers equi pped w t h

    PSS to mai nt ai n system stabi l i t y and t hi s has

    contr i buted si gni f i cantl y to the fl exi bi l i ty of

    syst em desi gn and operat i on. Speci al measures are

    t aken t o ensure that stabi l i zers perf orm rel i abl y.

    Stati sti cs col l ected i n

    1982

    showed a mean- t i me- t o-

    f ai l ure of about 5. 4 years i n near l y 107

    stabi l i zer- years of operati on. New stabi l i zer

    desi gns have bui l t - i n moni t ori ng and protect i on

    ci rcui t s t o mt i gat e the consequences of f ai l ures.

    Dynamc test faci l i ti es bui l t i nto the stabi l i zers

    al l ow routi ne testi ng by stati on personnel i n order

    t o avoi d undetect ed f ai l ures.

    We f eel t hat on- l i ne t uni ng of PSS to deter m ne

    opt i mumsett i ngs i s pract i cal onl y when t here i s one

    dom nant mode to be st abi l i zed and t he

    characteri st i cs of t he mode does not change

    si gni f i cantl y w th systemcondi ti ons. I n si tuati ons

    wher e t her e ar e many modes t o be st abi l i zed, not al l

    t he modes are l i kel y to be pr esent at t he t i me of

    comm ssi oni ng the stabi l i zer and on- l i ne t uni ng of

    stabi l i zer t o provi de sat i sf actory dampi ng of al l

    cr i t i cal modes woul d be i mpossi bl e. Thi s i s

    part i cul arl y true of i nt er- area osci l l at i ons whose

    character i st i cs and mode shapes change si gni f i cant l y

    w t h system condi t i ons. Even i f al l modes are

    present, i t woul d be a Hercul i an t ask t o det erm ne

    opti mum val ues of t he di f f erent stabi l i zer

    par ameter s by moni t ori ng t he responses of a sel ected

    number of l ocal pl ant vari abl es. We have devel oped

    a consi der abl e amount of conf i dence i n t he model s we

    use f or PSS desi gn. I n t he appl i cat i on of

    st abi l i zers at other pl ant s, we have been very

    successf ul i n matchi ng the resul t s of si mul ati ons

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    6 6

    w t h f i el d measurement s. Reference 3 of t he paper

    presents some of our exper i ences i n t hi s r egard.

    Good model l i ng capabi l i t y i s essent i al not onl y f or

    desi gni ng t he

    PSS

    sati sfactori l y, but f or si mul ati ng

    i ts perf ormance properl y i n system stabi l i ty

    studi es. W t hout such a capabi l i t y, we f ai l to see

    how t he stabi l i t y perf ormance can be determ ned

    accur atel y and the systemoperated w t h conf i dence.

    Practi cal l y al l generati ng uni t s we have

    i nstal l ed w thi n the l ast 2 0 years have stati c

    exci t ers and our experi ence w t h t hese exci t ers has

    been very good. They are rel i abl e, si mpl e to

    mai ntai n, easy to modi f y and str ai ght f orward to

    model . Rotat i ng exci t ers on t he other hand

    i nt r oduce dynamc charact eri st i cs of t hei r own

    addi ng to the model l i ng compl exi t y and t he

    di f f i cul ty of stabi l i zer desi gn.

    Manuscr i pt recei ved Sept ember 22 1988.