kun dur 1989
TRANSCRIPT
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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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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.
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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
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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
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7/26/2019 Kun Dur 1989
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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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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
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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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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.