NEW APPROACHES FOR STATIC STATE ESTIMATION IN POWER SYSTEMS

8/14/2019 NEW APPROACHES FOR STATIC STATE ESTIMATION IN POWER SYSTEMS

1/11

WEC REGIONAL ENERGY FORUM FOREN 2010Neptun, 13-17 June 2010

Reference no:

NEW APPROACHES FOR STATIC STATE ESTIMATION IN

POWER SYSTEMS

Mihai Gavrilas, Gh. Asachi Technical Universit !" #asi

$vi%iu #van!v, Gh. Asachi Technical Universit !" #asi

Abstract& 'tatic state esti(ati!n plas an i(p!rtant r!le in the real ti(e c!ntr!l an% !perati!n !"

(!%ern p!)er sste(s. #n present %a %ispatch an% c!ntr!l centers the assess(ent !" sste( state

an% the (aintenance !" the %esire% relia*ilit an% c!ntr!lla*ilit !" the p!)er sste( are "ul"ille%

* the +ner Manae(ent 'ste( +M', )h!se *ac/*!ne is "!r(e% * the 'tate +sti(at!r '+.

Tra%iti!nal '+s use !nl active an% reactive *ranch p!)er "l!)s !r *us inecti!ns an% v!ltae

(anitu%e (easure(ents, as )ell as !ther in"!r(ati!n li/e tap p!siti!ns an% circuit *rea/er status.ertain li(itati!ns c!ntinue t! eist in the use !" tra%iti!nal '+s, especiall relate% t! the

(easure(ent inaccurac an% s!(e lac/ !" in"!r(ati!n a*!ut neih*!rin sste(s. ecentl,

a%vances "r!( the 'nchr!ni4e% 5has!r Measure(ent '5M techn!l! has pr!vi%e% the

!pp!rtunit t! inclu%e hihl accurate anle (easure(ents as a%%iti!nal '+ inputs that, in the

previ!us 'A6A "ra(e)!r/, c!ul% n!t *e c!nsi%ere% %ue t! i(precise snchr!ni4ati!n. This paper

presents a set !" ne) appr!aches t! the pr!*le( !" static state esti(ati!n in p!)er sste(. Three

tpes !" '+ applicati!ns )ill *e presente%. The ne) appr!aches are *ase% !n '5M techn!l! an%

static net)!r/ euivalents !r !n h*ri% s!luti!n that use *!th techn!l!ies.

1. Intr!"ct#n

As p!)er sste(s *ec!(e larer an% (!re c!(ple, their secure an% e""icient !perati!n

reuires %evel!pin an% %esinin cl!ser an% (!re accurate real ti(e (!nit!rin an% c!ntr!l

pr!ce%ures. #n a%%iti!n, the last t)! %eca%es )itnesse% t! the transiti!n !" the electric p!)er

in%ustr all !ver the )!rl% t! %ereulati!n. The "un%a(ental chanes pr!%uce% since then )ere

*ase% !n the *elie" that li*erali4e%, c!(petitive electricit (ar/ets )ill *e the %rive t!)ar%s a (!re

e""icient enerati!n sect!r, an% eventuall t! l!)er electricit prices.

#n the ne), %ereulate% c!ntet, trans(issi!n an% c!((ercial !perat!rs are "ace% )ith the nee%

"!r (!nit!rin an% c!ntr!llin electricit transacti!ns *et)een re(!te l!cati!ns in the p!)er

sste(. This tpe !" c!ntr!l an% !perati!n !" electricit net)!r/s an% (ar/ets is hihl %epen%ent

!n the access t! real ti(e in"!r(ati!n a*!ut the state !" the sste(. $n the !ther han%, a"ter%ereulati!n, "!r(er (!n!p!lies have *een replace% * (!re plaers i.e. enerat!rs, %istri*ut!rs,

trans(issi!n !perat!rs etc, )hich can s!(eti(es "eel reluctant t! share in"!r(ati!n )ith !ther

c!(petit!rs. This "ra(entati!n !" the p!)er sste( has (a%e the !n-line (!nit!rin an% c!ntr!l

!" the ri% even (!re c!(ple an% "!rce% the ne) plaers t! !perate it cl!ser t! its (arins.

Un%er the ne) c!n%iti!ns, p!)er sste( !perat!rs nee% c!(putati!nall e""icient t!!ls t!

assess sste( state an% (aintain the %esire% relia*ilit an% c!ntr!lla*ilit !" the sste(, an% t!

prevent the !ccurrence !" events li/e the *lac/!uts in #tal !r !n the N!rtheastern !ast !" U'A in

2003 81,29.

#n present %a %ispatch an% c!ntr!l centers such "uncti!ns are "ul"ille% * the +ner

Manae(ent 'ste( +M', )h!se *ac/*!ne is "!r(e% * the 'tate +sti(at!r '+. Thus, static

state esti(ati!n plas an i(p!rtant r!le in the real ti(e c!ntr!l an% !perati!n !" (!%ern p!)er

sste(s, its results *ein use% * !ther +M' "uncti!ns such as net)!r/ analsis, securit analsis,

1


2/11


ec!n!(ic l!a% %ispatch an% !ther !pti(i4ati!n applicati!ns, as )ell as a supp!rt "!r p!)er sste(

%ispatchers in %ecisi!n (a/in pr!cesses.

'tate esti(ati!n is a (eth!% )hich esti(ates the state !" the p!)er sste( at a iven (!(ent

usin a set !" availa*le (easure(ents pr!vi%e% * %e%icate% c!((unicati!n sste(s at the sa(e !r

ver cl!se (!(ent. The state !" the sste( is c!(pletel %escri*e% * a set !" )ell ch!sen

varia*les, calle% state varia*les. A )i%el use% set !" state varia*les is the v!ltae phas!rs %e"ine%

* (anitu%e an% anle at all *uses !" the p!)er sste( un%er c!nsi%erati!n. A"ter the '+c!(putes the state varia*les, !ther %epen%ent varia*les, such as active an% reactive p!)er "l!)s,

line currents, l!sses etc can *e %eter(ine t! c!(pletel %escri*e the state !" the sste(.

Tra%iti!nal '+s use !nl active an% reactive *ranch p!)er "l!)s !r *us inecti!ns an% v!ltae

(anitu%e (easure(ents, as )ell as !ther in"!r(ati!n li/e tap p!siti!ns an% circuit *rea/er status.

ertain li(itati!ns c!ntinue t! eist in the use !" tra%iti!nal '+s, especiall th!se relate% t!

nu(erical %i""iculties an% epansive c!(putati!nal e""!rts inv!lve% in pr!%ucin su""icientl

accurate esti(ates, *ase% !n tra%iti!nal (easure(ent %ata pr!vi%e% * 'A6A sste(s.

#n this c!ntet, the usae !" %irect (easure(ents !" v!ltae an% current phas!rs, t!ether )ith

tra%iti!nal (easure(ents, is c!nsi%ere% t! *e !ne !" the (!st pr!(isin an% e""icient appr!aches t!

the state esti(ati!n pr!*le(. The (ain vect!r !" this appr!ach is the techn!l! !" 'nchr!ni4e%

5has!r Measure(ent '5M *ase% !n 5has!r Measure(ent Units 5MUs snchr!ni4e% * ti(e-

tae% G5' sinals. The '5M techn!l! pr!vi%es the !pp!rtunit t! inclu%e hihl accurate anle

(easure(ents as a%%iti!nal '+ inputs that, in the previ!us 'A6A "ra(e)!r/, c!ul% n!t *e

c!nsi%ere% %ue t! i(precise snchr!ni4ati!n.

$n the !ther han%, )hen esti(atin the state !" a iven p!)er sste(, essential in"!r(ati!n

a*!ut !ther neih*!rin sste(s can help in a reat etant t! i(pr!ve the esti(ati!n accurac.

:!)ever, since present %a sste( !perat!rs can *e reluctant t! share !n-line in"!r(ati!n a*!ut

their sste( t! !ther sste( !perat!rs, c!nsi%ere% as c!(petit!rs, %etaile% in"!r(ati!n a*!ut these

sste(s (a *e scarce an% %i""icult t! !*tain. ;!r such cases, applicati!n !" static net)!r/

euivalents, currentl use% in c!ntinenc analsis, is an e""ective )a !" (!%elin neih*!rin

sste(s. M!re!ver, events in the neih*!rin sste( can *e re(!tel (!nit!re% usin the sa(enet)!r/ euivalents, )hich (a !r (a n!t *e supple(ente% )ith '5M units.

#n this paper a set !" ne) appr!aches t! the pr!*le( !" static state esti(ati!n in p!)er sste(

)ill *e presente%. The ne) appr!aches are *ase% !n '5M techn!l! an% static net)!r/ euivalents

!r !n h*ri% s!luti!n that use *!th techn!l!ies. Three tpes !" '+ applicati!ns *ase% !n the ne)

appr!aches )ill *e presente%. ;irst a h*ri% 'A6A-'5M s!luti!n "!r an in%epen%ent p!)er

sste(, )ith !pti(al place(ent !" 5MUs, is presente%. The sec!n% applicati!n appr!aches the

interacti!n !" t)! neih*!rin sste(s in ter(s !" the '+ * c!nsi%erin p!ssi*le c!ntinencies in

the eternal sste(. ;inall, the last applicati!n a%%resses issues relate% t! the pr!*le( !" (ulti-

area state esti(ati!n t! assess the l!a%in c!n%iti!ns !" intertie lines.

2. W$#%&t$! L$ast S'"ar$ Stat$ Est#(at#n

'tate esti(at!r, as the (ain "uncti!n !" the +M' in p!)er sste( c!ntr!l centers, enerates

esti(ates !" un(easure% uantities, * pr!cessin %ata c!llecte% at %i""erent l!cati!ns in the p!)er

sste(. "ine-tune the

state varia*les usin a least suares (eth!%, *ase% !n the (ini(i4ati!n !" the su( !" resi%ual

suares 8?9. #n p!)er sste( analsis, the "irst state esti(ati!n (eth!% )as !riinall pr!p!se% *

'ch)eppe et al 839 as a )eihte% least suares pr!*le(.

M!st present %a '+ (!%ules !" +M's )ere "!r(ulate% as nu(erical s!luti!ns t!

!ver%eter(ine% sste(s !" n!nlinear euati!ns, appr!ache% usin the (!%el !" @eihte% =east'uares @=' 839. $ther (athe(atical techniues use% t! s!lve state esti(ati!n in p!)er sste(s

are the =east A*s!lute alue =A 8B9 an% the #terativel e)eihte% =east 'uares

2


3/11


i(ple(entati!n !" @eihte% =east A*s!lute alue #='-@=A 8C9. M!re!ver, present %a '+s

are i(ple(ente% )ith a%%iti!nal "uncti!ns %esine% t! supp!rt the *asic '+ (!%ule, such as

t!p!l! pr!cess!rs, %ata prepr!cessin, *a% %ata %etecti!n, !r t! c!(ple(ent it, such as para(eter

esti(ati!n an% !*serva*ilit analsis.

This secti!n )ill "!cus !n the *asic @=' state esti(ati!n (eth!%, )hich )ill *e use% as the

al!rith(ic t!!l in the net secti!ns. The calculati!n that "!ll!)s is *ase% !n lineari4ati!n !" p!)er

sste( euati!ns that %escri*e the relati!nship *et)een (easure% uantities an% state varia*les&

[ ] 989-8...

,...,,-

...

,...,,-

,...,,-

...

2

1

21

212

211

2

1

exh

e

e

e

xxxh

xxxh

xxxh

z

z

z

z

mnm

n

n

m

+=

+

=

= 1

)here 8z9 D z1,z2, E,zm is the vect!r !" (easure% uantities, 8x9 D x1,x2, E,xn is the vect!r !"

state varia*les, h1, h2, E, hnare n!nlinear "uncti!ns !" (easure(ents )ith respect t! state varia*les,

an% 8e9 D e1, e2, E, em is the vect!r !" n!r(all %istri*ute% n!ise !r (easurin err!rs. The stat

varia*les vect!r 8x9 c!nsists !" v!ltae (anitu%es U1, U2, E , UNan% v!ltae anles F2, F3, E , FN,

)hereNis the nu(*er !" in%epen%ent *uses in the sste( un%er c!nsi%erati!n an% F1D0 is the anle

!" phas!r U1, c!nsi%ere% as re"erence.

The @=' esti(ati!n ai(s t! (ini(i4e the !*ective "uncti!n&

9.9-8988989.9-89889.9-889.-81

2xhzWxhzwxhzxJ

Tm

i

iii ===

2

)here 8W9 is a %ia!nal (atri )ith n!n-4er! ele(ents eual t! )eihts wi ass!ciate% t! each

(easure(entzi. The *est ch!ice !" the )eiht (atri 8W9 is the inverse !" the c!variance (atri 8R9

)h!se %ia!nal ele(ent2

i is the stan%ar% %eviati!n !" err!r "!r (easure(entzi.

Mini(i4ati!n !" "uncti!n 2 is %!ne iterativel startin "r!( an initial uess 8x90, )hich is

repeate%l c!rrecte% usin&kkk

xxx 989898 1 +=+ 3

)here c!rrecti!n 8x9kis c!(pute% as s!luti!n !" the linear euati!ns sste(&

kkTkkzRxHxxG 9898.9-898.9-8 1 = ?

:ereH 8x9k is the Jac!*ian (atri !" (easure(ent "uncti!ns hian% G 8x9k c!(pute% as&

.9-8.9-898.9-8 1 knot

kkT xGxHRxH = B

is the ain (atri. The c!nverence !" the iterative pr!cess is c!ntr!lle% * c!n%iti!n&

kxMax 98 C

A %isa%vantae !" the @=' al!rith( is the nee% t! appl re-evaluati!n an% re-"act!ri4ati!n !"

the ain (atri G 8x9k at each iterati!n. This is a ti(e c!nsu(in reuire(ent )hich can *e

av!i%e% * c!nsi%erin an appr!i(ate *ut c!nstant ain (atri. This appr!ach is c!nsistent )ith

the !*servati!ns acc!r%in t! )hich the ain (atri ele(ents are slihtl (!%i"ie% %urin the

iterative pr!cess, )hile the sensitivit !" active reactive p!)er euati!ns t! chanes in the

(anitu%e anles !" *us v!ltaes is ver l!).


4/11


stan%ar% %eviati!ns. The pr!*le( )ith this /in% !" *alancin (easure(ent i(p!rtance is that ver

hih c!n"i%ence %erees ass!ciate% t! !ne !r (!re (easure(ents can lea% t! a ain (atri cl!se t!

sinularit 8H9. :ence, the pr!*le( !" %e"inin the )eihtin (atrices 8W9 !r 8R9 (ust *e

appr!ache% )ith cauti!n.

Other specific features of the WLS algorithm that must be considered arethe need for system observability, the statistical assumption of zero meansmeasurement values and the deviation of the measurement noise from thenormal distribution [9,10

3. State estimation with traditional and PMU measurements

!ecently, "#S synchronized phasor measurement data $ere proposed to beused as ancillary input data to traditional S% modules& #'(s at the busbars oftransmission substations measure voltage and current phasors& )ompared $ithother metering systems, #'(s are more accurate and allo$ even moreaccurate results due to the synchronization procedure&

State estimators based only on #'( measurements can be devised& *n thiscase, the estimation model becomes linear, and simpler solution procedure canbe applied [1+& o$ever, using state estimators based only on S#'s can provea very e-pansive solution, especially for large po$er systems& .herefore, ahybrid solution $hich uses both traditional and S#'s must be ta/en intoconsideration as an effective one&

.his section presents an original approach to the problem of optimal #'(slocation for S%, applied to develop an e-isting traditional measurementconfiguration through the placement of additional #'(s& .he algorithmicapproached is based on "enetic lgorithms "2& .he optimization algorithmaims to find the optimal placement of a given set of #'(s at the buses of a

po$er system $ith a /no$n initial measurement configuration&'i(ulati!ns )ere carrie% !ut usin the #+++ 1? *us test sste( ;i. 1 an% a li(ite% nu(*er

!" tra%iti!nal v!ltae an% p!)er "l!) (easure(ents that lea% the sste( t! the vere !"

!*serva*ilit.


5/11


are. 'tartin "r!( the re"erence case )here there arenIt an 5MU place% an% the FFvalue "!r the

MVclass is 7.CC, the GA en%s up t! aFFvalue !" 1C.1C )hen 5MUs are place% at *uses ? an% C

that lea%s t! *etter esti(ate% values. 'i(ilar results are !*taine% "!r the !ther (easure(ents classes,

as sh!)n in Ta*le #.

;i. 1. The #+++ 1? *us test sste(. ;i. 2. 'ur"ace pl!t "!r M class.

Ta*le #. ;itness "uncti!n values "!r %i""erent

hp!theses.

N. PMU L) M) S)

0 ?.B7 7.CC .33

2 1C.H 1C.1C 1C.22

3 17.B2 17.B1 17.B2

? 17.3 1H.12 17.B

;i 3. hr!(!s!(es ev!luti!n %urin GA

runnin, "!r the 30-th enerati!n.

6ata "r!( Ta*le # re"lects a p!sitive e""ect !" usin 5MUs as %ata-s!urces "!r the '+. As !ne

can see, )hen the '+ uses !nl tra%iti!nal (easure(ents the "irst line in Ta*le #, the variance !"

the (easure(ent err!rs in"luence in a reat etant the esti(at!r accurac "uncti!n ;; varies "r!(

si(ple t! %!u*le. $n the !ther han%, usin 5MUs as %ata-s!urces "!r the '+ the last three lines in

Ta*le #, the esti(ati!n accurac i(pr!ves sini"icantl the "itness "uncti!n increases * 2 t! ?

ti(es, )hile, "!r a iven nu(*er !" 5MUs, the esti(ati!n accurac re(ains appr!i(atel

unchane% )hen (easure(ent err!r variances varies "r!( = t! '. 6ata "r!( Ta*le # als! sh!)that * increasin the nu(*er !" 5MUs t! *e place% in the sste(, the esti(at!r accurac als!

increase, *ut )ith a %ecreasin rate.

*. Stat$ $st#(at#n +#t& stat#c n$t+r, $'"#-a$nts

@hen esti(atin the state !" a iven p!)er sste(, essential in"!r(ati!n a*!ut !ther

neih*!rin sste(s can i(pr!ve esti(ati!n accurac. :!)ever, such in"!r(ati!n (a *e scarce !r

%i""icult t! !*tain, especiall )hen sste( !perat!rs (ust share partial in"!r(ati!n a*!ut their

sste(s. ;!r such cases, static net)!r/ euivalents, currentl use% in c!ntinenc analsis, (a *e

use% t! (!%el neih*!rin sste(s. The literature re"erences certain tpes !" net)!r/ euivalents,

such as @ar%, +# an% #T+ #%eal Trans"!r(er +uivalent euivalents 8119. A(!n these, the +#

euivalent (!%el )ill *e use% in this paper.

B


6/11


The "un%a(entals !" the pr!p!se% state esti(ati!n (!%el )ill *e %escri*e% usin the particular

case !" t)! neih*!rin sste(s, !ne !" )hich is the su*sste( un%er stu% the internal

su*sste( #', an% the !ther is the eternal su*sste( +', !n )hich the !perat!r has li(ite%

in"!r(ati!n, restricte% t! its static +# euivalent ;i. ?.

;i. ?. Transiti!n "r!( t)! su*sste(s #' an% +' t! !ne su*sste( #' an% a +# euivalent !"

the !ther !ne +'.

a *

;i. B. 'i(ple +#K5MU euivalent a an% (ultiple +#-5MU euivalent.

;!r such a sste( it is a c!((!n !*servati!n that static net)!r/ euivalents are )i%el use%

"!r real-ti(e c!ntinenc analsis, )hen c!ntinencies are l!cate% in the internal p!)er sste(.

!ntinencies in the eternal p!)er sste( i.e. the sste( that is replace% * the net)!r/

euivalent cann!t *e ta/en int! c!nsi%erati!n since the euivalent net)!r/ )as *uilt "!r re"erence

!peratin c!n%iti!ns, )ith "ie% net)!r/ structure an% inecti!ns in the eternal sste(.

T! enhance eternal su*sste( sensitivit )ith respect t! its resp!nse t! chanes in the

net)!r/ structure !r enerati!n L c!nsu(pti!n patterns "r!( the internal su*sste(, the literature

has pr!p!se% t! use (ultiple +# euivalents, )ith t)! !r (!re +# *uses 5, 5U !r h*ri%

*uses 8119.

The auth!rs !" this paper pr!p!se a ne) appr!ach t! (!%el the eternal p!)er sste( usin

+# euivalents an% phas!r (easure(ents, %en!te% as the +#-5MU euivalent. This s!luti!n is

*ase% !n three principles&

- M!nit!rin !" certain *uses "r!( the eternal sste( usin 5MUs, an% representin these*uses as in%epen%ent +# *uses ;i. B.a.

- Transiti!n "r!( +# euivalents )ith !ne *us t! (ultiple +# euivalents )ith t)! (!re

h*ri% *uses ;i. B.*

- $pti(i4ati!n !" the +#-5MU euivalent structure, t! %eter(ine the !pti(al l!cati!ns !"

5MUs in the eternal su*sste( an% the !pti(al areati!n !" eternal *uses int! h*ri%

+# *uses.

The a*!ve !pti(i4ati!n pr!*le(s have *een appr!ache% *ase% !n ev!luti!nar c!(putati!n

techniues, na(el enetic al!rith(s GAs. #(ple(entati!n !" GA "!r the !pti(al l!cati!n !"

5MU at the *uses !" the eternal su*sste(, t! *uil% the *asic +#-5MU euivalent, )as %!ne

*ase% !n the (!%el %escri*e% in the previ!us secti!n. ;!r the !pti(al eternal *us areati!n int!h*ri% +# *uses that %e"ine the (ultiple +#-5MU euivalent, an appr!ach si(ilar t! the !ne

%escri*e% in paper 8129 )as use%.

C

#' +' #' +#

#' #'

+#-1

+#

5MU-1

5MU-2

5MU-1

5MU-2

+#-3

+#-2


7/11



8/11


s(all R up t! 0.02H ra% 1.C %e. R an% (a *e even neative the esti(ate et )!rse R up t! -

0.01 ra% 0.C %e. $pti(i4ati!n analsis *ase% !n 5MU l!cati!n sh!)s that the *est result,

c!nsi%ere% in ter(s !" i(pr!ve(ents in *!th v!ltae (anitu%e an% anle, )as !*taine% )hen t)!

5MUs )ere installe% in the eternal su*sste(, at *uses 2 an% H. At the sa(e ti(e, this s!luti!n

pr!%uces the larest i(pr!ve(ents in *!th v!ltae (anitu%e an% anle 1.3 an% 0.02H ra% 1.C

%e. respectivel. As t! the nu(*er !" +# *uses use% in the (ultiple +#-5MU euivalent,

nu(erical tests have sh!)n that a%%in (!re h*ri% +# *uses lea%s t! hiher i(pr!ve(ents in the

(ean a*s!lute err!rs Ta*le ###, as c!(pare% t! the case !" si(ple +#-5MU euivalent.

/. #str#b"t$! stat$ $st#(at#n

A"ter %ereulati!n, the "!r(er (!n!p!lies "r!( the p!)er in%ustr have *een replace% * (!re

entities )hich pla in a c!(petitive envir!n(ent. #n such an envir!n(ent c!(petiti!n is !"ten the

s!urce !" %i""icult access t! real ti(e in"!r(ati!n a*!ut the state !" the sste(s. #n "act,

"ra(entati!n !" the p!)er sste( has (a%e the !n-line (!nit!rin an% c!ntr!l !" the ri% even

(!re c!(ple an% "!rce% the ne) plaers t! !perate it cl!ser t! its (arins.;!r )i%e area p!)er sste(s, each sste( !perat!r (a run its !)n state esti(ati!n (!%ule t!

pr!cess l!cal (easure(ents, )hile the /n!)le%e !" the )i%e sste( state nee%s an interatin

appr!ach. Generall, "!r l!cal esti(at!rs, classical al!rith(s are use%, )hich (a !r (a n!t

inclu%e pr!cessin !" snchr!ni4e% phas!r (easure(ents. The (ain %i""erences a(!n these

(eth!%s lies in the )a in )hich the l!*al esti(ate is %!ne, *ase% !n l!cal esti(at!rs results.

Thus, (!st (eth!%s an% appr!aches presente% in the literature 81?, 1B9, use a central state

esti(at!r, )hich c!!r%inates l!cal esti(ati!ns t! i(pr!ve their results, an% especiall several

sste( state varia*les at certain critical l!cati!ns "!r instance, active an% reactive p!)er "l!)s !n

intertie lines. :!)ever, s!lvin lare scale state esti(ati!n pr!*le( is a c!(ple an% ti(e

c!nsu(in tas/, )hich (a "ace hue pr!*le(s relate% t! nu(erical e""icienc. $n the !ther han%

in%epen%ent sste(s !perat!r (iht *e reluctant t! chane !r a%apt their state esti(ati!n (!%ulest! (eet speci"icati!ns i(p!se% * the central !perat!r.

This secti!n a%%resses issues relate% t! the pr!*le( !" (ulti-area !r %istri*ute% state esti(ati!n

an% pr!p!ses a ne) appr!ach t! in%epen%entl assess the state !" l!cal p!)er sste(s. The ne)

(eth!% re(!ves the nee% "!r a central state esti(ati!n c!!r%inat!r, usin +# euivalents t! (!%el

eternal sste(s, %urin the areati!n stae !" l!cal esti(ati!ns. T)! particular "eatures !" the

(eth!% )!rth (enti!nin&

- c!rrelati!n !" l!cal esti(ati!ns )ith respect t! v!ltae aru(ents is %!ne usin a net)!r/ !"

5MUs installe% in the slac/ *uses !" in%ivi%ual su*sste(sS

- each in%ivi%ual su*sste( has access t! the +# euivalents !" the !ther su*sste(s *uilt

usin as supp!rt *uses the internal *!r%er *uses !" each su*sste(.The (ain phases !" this (eth!% are %escri*e% *el!)&

'tep 1. The l!*al sste( is %ivi%e% int! in%ivi%ual L l!cal su*sste(s.

'tep 2. =!cal esti(ati!ns are c!(pute% "!r each in%ivi%ual su*sste(, usin a l!cal t!p!l!,

)hich inclu%es *!r%er *uses *ut eclu%es intertie *ranches. #n this phase the results pr!vi%e% *

l!cal esti(at!rs are v!ltae phas!rs an% *ranch p!)er "l!)s "!r each su*sste(. #ntertie *ranch

p!)er "l!)s are n!t esti(ate% at this step.

'tep 3. +ach su*sste( is eten%e% t! inclu%e *!r%er *uses "r!( the neih*!rin su*sste(s

an% the +# euivalents !" these su*sste(s are use% t! replace the(.

'tep ?. Gl!*al esti(ati!ns, inclu%in p!)er "l!)s !n intertie *ranches, are per"!r(e% in each

su*sste( usin +# euivalents t! replace eternal su*sste(s.The (ain a%vantaes !" this (eth!% are& i the central esti(ati!n c!!r%inat!r is n! (!re

nee%e%S ii each sste( nee%s a (ini(al v!lu(e !" in"!r(ati!n a*!ut the neih*!rin su*sste(sS

H


9/11


iii the (eth!% can *e applie% "!r c!ntinenc analsis t!!, applin +# euivalents up%ates

*ase% !n the (!%el presente% in the previ!us secti!n.


10/11


P#

P#P#< ?#P#< ?#

NEW APPROACHES FOR STATIC STATE ESTIMATION IN POWER SYSTEMS

Documents

Transcript of NEW APPROACHES FOR STATIC STATE ESTIMATION IN POWER SYSTEMS