On-Line Observability Determination in Electric Power Network

Copyrighl (J, IFAC Rnl Tirn~ Digita l Conuol Applications Guadalljara. Mui,o 198'

ON· LINE OBSERVABILITY DETERMINATION IN ELECTRIC POWER NETWORK P. Albertos* C. Alvarez** andJ . A. de la Pue nte* 'A u/omalie COlllrol Depl., E. T. 5, 1.1., Um'vew'dad Politeeniea , Valencia , Spain •• Elect rie Power Dept., E. T. 5. 1. 1., UniveTsidad Politeeniea. Valencia, Spain

,\b«tl'>ll't . Th .. "bs~·n·abilit~· determInation in electric pO"'e r net;.;oJ'ks is dl s ,' ussed In the pape !' , ,\ rl,,·ic ... IIf the di f ft'rent approaches is pre sent ed and tlw de~i"abl~' fC;l l Ul'l' S f,,,' a I'cal-time alg o l' ithm 31'e pointed out , Deletion of measu rl'mt;!lts ,I>, "ell as gene r al l" polui,.v changes ask fOI' ;.;c 11 adapted a lgo " ithms , Thl' s"lu t ion PI"'posed in the paper takes advantages of but h tupologi ,'al and nume"it'al alg"I'ithms. The upera tlonal pro"edu l'e IS applie d to an e xpCI'imental reuuc,·d ",'del' ]aboratol'jI ne t ,,'or k . KeY"' ol"ds , r.iectr'ic po;.;c r net"'ol'ks , state estimation, Observab ility , On- li ne "pC !'atlon ,

INTRODl:CTIO N

Re a l - ti me da tll -a cqu i sit j on

In the base of mod{'rn electric pl' ....·er system monitoring and COn CI'''] , state estimati()f"l tech nique s a,'c fundamental fur se~'u ,'i t y and co ntingen cy evaluation. Slate esti ma tion algorithms require a good net;.;ork mode l and the o bservability conditiun in th e mea su r ement s y st em, That is , t he availa b le se t of me asurement s mus t alia ....· the unique determina tion of the system state va .-iab les , i , e , t he comple x bU l> \'oltag"s in all the bu ses hf the net"'ork , wh en a (,ontingency happens , cu mputer aided di s _ patch for elecll'ic po;.;er systems needs a fa st and re I iable o b se r vab ll i ty algo r l thm before state estimati(>f"l algorithms can be applied ,

1

I

,"d

Filte ring validation chec k

1

Ne t . topolog . de t erm, and model pa"ameter retrieval

1

Observa b i]i~y check n ~

lp,

u 0 Meas , additi o n

J, Sta te estimati on

An o bservabi lity algorithm is a lso needed f o r design purposes . In this ('ase ti.me sa\'ing is not so i mp ortant bu t a good kn o"' ledge ab o ut the relevan ce o f each measurement device i n the estimated state co mpu ta ti on is convenient , ~loreover o bservabi 1 i ty is lands mus t be de tected and the suggestion of additional mea sure men ts to h e i mp le mented in o rder t o achieve complete net ~o rk o b servability is required .

J, Bad da ta detecti o n and me as , deletion

1

Branch fl O,,'s & injeetion Computat io n

'"'

Finally , anothe r p oint o f vie ,,· in pO"'er ne t wo rk obse r vability determinat io n is the effect o f bad data measurement detection . rn fact a cr itical o r fund a me ntal measuremen t , as later defined, is necessary for network o bservability

601

J, DATA BASE UPDATI NG

Fig.I, Real-time state estimation process

602

P . Alber tos , C. Alvarez and J. A. de la Puent e

computation but slat ... estimatj'm algo ri thms cannot give us info r mation "bout the correct v pcratiuo (I f the corresponding eithe r' measurt.-ment device or telcmcterlng station . Then at any moment , 11 is YCl'y important to kno w the set of cri t leal measu,'ement5 . So j r a mca _ S\lrement deyi.:,," is turned "ff , the set <.I f measut'crnents that bccnmc crItical must be knolo.'n , if any . Since thi!; pap,'r is ma in ly a discussion of the suitability of (,","0 different approaches to on -line (,bscr>ubility determination . a genet' a l \I\'('I'\"i"" of the real-lime measu r e ment processi ng in "rder to p{·!'r",'m a data base up dal ing is pn,\j"usly pl'cs,,;ntcd . '\s Sh"Ianple "f the tclcmeter.,d measuI'ements is prol'es'wd . ,\ filtc l'ing and \ali d atiun check is pC I'f"l'Illed at fil'5t . The \'alidtly check is very simple but ne(ess,lI'Y in IJI'del' to u\"oid a bad 5tntus duta s(>t to be prllcessed by the sta te r5timntion alguI'i t hm , F(lI' instance , nu fl ('1<;5 .,n' a I I "".. cd tu rl u"" "vel' ,'pen lines or to transf""mc~' prc5entcd as "ut " f servicc . The status u f br'eak"'rs and disconnects must be con_ si!
a ny inte r nal va r iable in the net work can b e computed i f so r equired. The ne w co mputed vari ab les are the entries to update t he d ata base . Secur ity monituring . opf' r at{)rs guidano;:e and r efer'ency to any further cumputation un the net ...·or k , suc h as cos t opti mization 01' mo d el verification . are pe l'furmed (m the base f some r equired concepts and approaches tu determine the obsel'vabll i ty condi tion of a netl<;"rk . Then the main chn r acteristics uf t ...·o ulgurith ms pn:> posed by thi' auth.., r s are presented . lhe; r use in the fl'amework of electric po,", e r system central dispatch is described in t he fo\lo,",ing sectivn . Finally some resu l ts and conclusions ar'c pl'cscnted .

OBSERVABILITY Numerical Observabili t y condition Let us considl'lr an electric pU"'er net l<;or k Wit h non li near l"easurement functions h( , J z - h( x ) . v

Frum the information nbullt the status of brea _ kers and !< ...·it~, hes the al'L ual ne t lo.ur' k topology is determined . All nude and br'anches i mpedances are thrn a"sumcd knuIo.·n and retriev e d from computer memory . So a complete netlo.·o rk model is avallnblc fOl' state estimation pU t' pose . If changes in topl.]ngy arf' detected or a set of measurements has been deleted . a test uf obs~rvabi ­ li t y c"ndition must be performed , If there is sume t aek of 'Ibservabi I i ty, pseuciomea"u r e ments must be added . L'sually pseudo measure ments are taken from the data ca"e as the past estimated \'alues uf the required \"ariables .

At t his moment the state estimation algo r ith m can bc run , onc of the main goals of a good state estima t ion algorithm is the detection of erroneo u s da t a in order to assure a reliab le state estimation . So , bad data mus t be d etec ted and d eleted . The de l etion of a ny meas u rement must be f ol10...·ed b~ its replac emen t by altern a tivl'l measu reme nts . if possi b le and in a ny c a s e, so me o bservability comp utatio n s must be d one . Once t he state esti ma tio n is perfo rmed, branc h fl o ws and bus injectio n s a re c o mputed. Al so

I1I

.... here x ; n-di mensi.onal vecto r of state va riables (magnitude and phase of bus volt a g e s) m-dim!.'nsional measurement vector, main l y formed by i.njeetion and li ne flo,"" po,",ers and voltage magni tud es.. ze r o-mean vandom vecto r rep r esenting the measurement noise . The I<;eightea least - squares esti mato r computes the o p ti mal state x , the state estima ted vecto l', mini mizi n g the- cost functional h( x l]

(2)

...·he r e R is s ome positive d e f in i te mat r i x. us u~ lly a ss ume d to be th e noise covar i a nc e matrix. ( 1] . The mi n i mi zati o n o f (2) is pe r fo rmed numer ic al l y and an ite r a t ive appr o a c h is u sed . So , i n rea l t ime o pera tion, a li ne a r ized mo del o f equati o n (1) is ad opted. I f we a s sume

On-l ine Observability Determination in Electric Power Network

an opera tio na l initial point given by the st3 te vector xk ' the measur e men t func t ions may be e xpressed by x • v

H

131

I'here the state and measurement vectors are the increment "'ith respect to the ope ra tio nal point and H is the jacob ian matrix, obtai_ ned by H

I" obviously . the jacobian matrix is numerically dependent of the op~rational point. The mInImizat io n of the cOSt functional J . related tu the I inearized mudel (31 , l'equires the inversion uf the matrix

The ~,bse l'vabi I i ty problem in the estimation of the state of an electric po .... er system deals "'ith the determinati on of the sufficiency of the measurement set 't to provide enough information to allol' the computa tion of the state x . A power system is said to be observable "'ith respect to a measurement set 7, . if all Lhe components of the state vector can be computed from a measurement sample, Other.... ise t he po .... er system is said to be unobse r vable . In that case some subsets of the stale vector can be determined in an absolute or rdative value . It is said that thel'e arc obse r vable islands in the net,,·ork . The previons definitions are referred to an opcrating point . Numerical problems can arise if II-matri x inversion is performed at different states , If the re are not, the po"'er system is sai d to be numerically o bserva ble, This condition is more restrictive than the above o ne, that is named as algebraic o bservability . The o bservabil ity condition can be stated by the follo"'ing equivalent cxpresions , [ 21 rank

H = n

IHT HI;

0

I IIT R-IH I ~o

11 ' 11<"

( Sa) ( 5b ) ( 5c)

603

puted approximation to it . stales that all the elements of this ma t rix must be upper bounded. The check of these conditions needs Ih<' us" o f fioatiflg point calculati ons and su '>n; ~ off-li ne me asurement equipment design algl' rithms . are based on them . Ne\-er'theJe8~ . th.., last cond itivn (SdI , ,,'hen cnnsidel'ed ":lJy for a reduced number of mellsuremenl \'CI' tion . Topological obsel'\'abll i tc; c"ndl

t

iUll

Po,,-er fl o .... equations can bt" simplifl"U .,,,sumlng small phase angles (51 and d·,s<' tu [,,,minal " ul lage magn itudes (\'1 In till' bus e .. m_ plcx voltages uf the nC\"'nrk, t 3] ,'Ih is !'Oim plification, I'hen tlpplied tu thc mca su I'em,;!1t functions (I), all ol'5 the s),s\(."m "quati"ll d.-coup ling, groupi ng bllt h a<'\ i vc p"I'e,- and phase angles, P - 6 and !'ea<'\ ~\". 1'''''<':''' and vol tage magn; ludes . Q-\' . Th< I; !l(:o' I'; -,<'J mea surement equation 131 is great I," simp: ified and the lI - matrix beco mes b lock diag"n,d .... ith submatrices and 11, ,'elating ~h"",' groups "f variables .

11 ,

Let us assume aN-bus ne t "'''l'k, The d i m,'n ~i"n of the state va r iable vcctur' is 2N-\ and it can be split into an X" N-dimcn siolln] \('l'tUl' of bus vol tuge magni ludes :md a X ,,-I d imensional vector of bus q,}tasc angle" (t he slack bus is taken as a r.,ference f"r phase angles) The pO"'er system is said tll bc P - 6' "bscJ'\,lble if a sofficient number...,f llrtivc Jin.., flo'" and active bus injection po,,'e l' measu re me nts exists , That is , if the r'ank o f matr' i x li t is N-I, The po .... er system is s;lid trj be Q-v obse r vable if a sufficient number
( 5d)

The last inequa lity , ",here tbe A-ma tr ix is the inverse ma trix of HT R- i H or some co m-

The mea surement system decoupling allo"'s a ne,,' approach to the observability determination and more simple observability condi -

604

P. Albertas, C . Alvarez and J . A. de l a Puente

lions may be stated . For instance, some authur's [ 4 J have proposed atgori thms based on the chec k of the jacobian matrix connectivit,\', In this ",ay the observabili ty condition is transformed into a connect;\'ity one . A po_ ;.:cr nct "'ork is P - S observable i f all the nclKurk nodes a re r elated thruugh active poIo.:cr measur'emcnts in such a "ay that all the n"de \'Ililage anglcs .::ore computable ,,·hen a re ferenec node is fixed . In the above f r ame;.,:ork, the lngical observability cundition must be slated as foll",",s ; a po",cr system is l"gicall~· ubser";:l.ble if the jncubian m:nrix o f the mcasur'c mt:>nl [un('liun is c(.>nnected. l."gi"al algu!'ithms for m:uwrk <)bsen-abiiily d"tcrmlnat i"n aJ'C ba<;eu un thiS pruperty . Of ~"'Ul'SC, l "gi~·.)l "bser\'ab,l it..., cundition is a "·callel' l·"nditiun than numlTinll 'H' algebrac "bst'nubility c(>ndlli"n. But. un the ut her hand, un thc"c alg"rithms , only lugical " pe ral l.,ns arc perfo rmcd ~md \<0 , they Hre suita bl" for .111-1 ine applll·ation . The recent papCI' or Bongers, Ri ckc and Handschin l !'i ) is the best I'cfcrence for this kind ,)f algorithms.

,\o"the l' approal'hes arc bused (111 the cootept tupol,)gical o bservability. fill the abo,'e m('otioned methods and criteria are based 00 the relatinnshlp bet"'een nell
,.1'

In order t o define the tnpological observabi lity condition let u.<> introduce some prelimi nary concepts l 6 ) A net"'ork graph associa _ ted to a pn..'er system is defined as a graph I
1 ine . In this framework, topological ob se r va b ility

can be stated a s follol
PROPOSED ON-llNE OBSERVABIllTY ALGORITHNS Topologic a l approach The first algorit.hm to test observability [ 81 can be considered as a modification of the topological method ( 6 ) . incol'porating the concept of redundancy level and a different I
On-line Observability Determination in Electric Poyer Net york

measure of its relevance for state estimation purposes, and can be computed together "'ith observability determination, as it will be sho·..m. ~'easurement

redundancy is due to either:

-~'easuring

pO"'er fl ow at both ends of a

branch . -Measuring power flo ...· in all the branches of a loop. -Measuring power injeCtion at a bus and power fl ow in all the branches incident to it. or a combination o f these. The algol'i thm proc esses all types of redundancies In a systematic way and at the same time bu il ds up a spanning forest (i .e. a set of trees ( 9) ) for the net ...·ork by selecting one branch f or each flow measurement (letting as i de r edundant measurements). Branches are also added for injection measurements that can be individually assigned to them,in such a way that the number o f trees is reduced . If the process results in a single spanning tree, the system is observable. Other,,·i se each tree in the spanning forest defines an observable area (subsystem) . Let us briefly present the structul'e of the algori thms . In a fir st stage, flo ....· measurements are processed . First of a ll redundancies due to bo th end measurements are considered. Then a spanning forest is bu ild by means of a d~p first search algorithm ( 9] (only branches with flo . .· measurements are consi dered ) . At the same time loop branches are identified, so that loop redu ndancies can be processed . Mul tiple loops may produce further redundancies. Each ti me a redundancy is d~tected , the redundancy level of the related measurements is accordingly increased . Processing of injection measurements begins ....·ith injections in nodes included in a loop of flo ....· measuremen ts , whi ch form a mixed redundant configuration . Then nodes with flow measurements in all the i.ncident branches are processed. None of these pr ocess adds branches to the forest, so the number of t r ees is not changed. Each tree can be considered as an equivalent node with respect to all its components . If there is a set of I' injections measurements connecting r nodes or trees(w i th no 1'-1 dimension subsets fulfilling this pro-

605

perty), these measurements are redundant, and the connecting branches can be added to the fores t . This implies the fusing of all the involved nodes into a single tree (equivalent node). This process continues until all the injection measurements are processed. At the end of the algorithms, the sys tem is observable if there are s equivalent nodes connected by s-l injection measurements . A more detailed description can be found in

(s J

.

Numerical approach. A second way to accomplish the study of the network obse rvabili ty is more convenient i f an on-line state est i mat ion has bean pre\iol'!<' ly performed. This method is especially well suited if only one measurement failure is to be considered.

This method 2 can be classified with in the methods in wh ich the search of the observability condition is focused on the compu tation of rank of the A matrix. 1n that way, if the i measuremen t is deleted! the A matrix changes and the new ma t rix Al can be expressed by Ai

0

A

,

(

A fi

fiT A)

(6a)

Pi t1 i

,-

fiT

A

fi

<,

(6b)

where fi: row i ct H matrix j ~ i:weighting factor of measuremen 1':i ( usually the inverse of its variance) observability parameter attached to measuremen t zi . Then , being A a n-rank matrix, the necesary condition for Ai not to be a full rank matrix is P i'" 0 Then, the observability network monitoring is equivalent to the parameter monitoring. The parameter attached to a fundamental measurement, is close to zero In most of the current state estimation a l gorithms this computation is very easy to implement: a) Owing to fisparsity, the compu tation of the row vector fiA can be simplified. Only the A rows associated to the state variables correspondieng to the non-zero elements of fi must be computed.

606

?

Alberta!; , C. Alvare z a nd J. A. de la Puente

b) To solve the minimization problem (2) it is usual to ~roceed through the triangularizatlOn of A- . $0, in that process it

is easy to store the changing coe f icients (pivots! corresponding tu the

rows of A ...·c

need to compute . Then, the evaluation of each

\.. ould be required t o ma ke the entire net"'<.lrk observal:lle . Although only logical operations are performed, a lot of informati<.lll ill handled and stored for further processing,

A-row only requires onc bac k substitu-

tion process, the time required being much shorter than that used in the triangulariza-

lion process. Then, as a result of these considerations,

AS pointed out in the introduction . fig,l. on-line observability detet'minati on p,'{'sents di fferent requ I rements , T",,, kind s of abm,ll'malities can be conside,'ed: a1slight l'hanges in the rr,eaSu)'ement. system. bl d!'[\sti~'al \"llriations in the measurement system and n r' in the nel\o:ork topuh'gy ,

the following algorithm for the observabili-

ty coeficient dete r mination has been proposed ( 2 ) 11 Civen i determine the number and po si t ion uf the nun-?ero elements of fi ·

21 Triangularize

A-I

J)

Cumpute the rows (If A ;.;c need e, ,. 0. taking as independent terms cl " 'c n . (the change vectors corresponding to the non zero state variables coeficients of fi )

<\ )

Compute

F·

5)

Compute

fJ i

,

T

fi • A

This algorithm has the important drawback that it is not very efficient to deal with a great number of simultaneous meter devices failure (RTU loss\. It must be also noticed that due to numerical errors the 15 parameters never are equal to zero. Then, a measurement will be conside red as fundamental ,... hen its ~ parameter is valued close to zero .

ON-LINE OBSERVABILITY DETERm NATION .

At the design stage . an adequate set of measurements must be chosen in order to assure pOl«er system observability, as ... ell as good redundancy to avoi d loss o f the observa b i lity condition if a measurement or teleme t e ring device failure happens . The topological algorithm propose d in the last section fulfils all the requirements for meter- placement studies. It p rovides informatio n about the networ k obse r vability, relevance of any measu r ement in th e state estimation pr ocess and in particul a r the set of fundamental measurements , t he o b se r vab le isl a nds i n t he network if it is uno b servab le a s well a s possi b le me a suremen ts that

a I 51 ight changes in the me:lSUI'em~'nt system occur when a mcaSUl'emen t or a set "f n"n-I'elated measur'ements are IITung . L'su"lly, as a result of the stale estimati(lI'I "lg,,:'rlhm, bad-da t a are dcte~'ted, .\ mcasut'cmclll ddn'led as erroneous is n<>n - cr'iticai mId ma~' be dele t ed . Neve ,'theless o ther measu,'emcnts ~'fm become critical if they only ha\'e lc\'el-I redundancy, So , ufter' u bad-da lr. detection the ~-parameter attached tu t he measure ments grouped in the same r'edundant gr(,UP that the assumed err'oneons nne must bc ,'ecalculated , In this ,,'ay, ne'" critil'aJ measurements, if there are. ar'e pointed (J ut. unly a fe,,' ~ -parameters must be computed and a best information about the accuracy o f IIct,,'ork st .. le estimatIon is obtained, b J l i there is a chnnge in the net,,'nrk \()pology 01' a grnup of I'elated mensuremcnts fails , (for instance if a remote lransmisi"n unit becomes out of o r'derl . the appl'oximalive approach before descl'ibed is nu m'lI'e useful. A complete observabilIty lest must be run , Nevertheless, most of the infol'ma110n provided by the topolugical algorithm is already known because only a fe,,' measurcments or branches ha\'e been mod i fi ed.

If a group of related measurements fails , the redundancy level attached to these measurements may give us information about the loss of the observability property, If It is not the case, or if the change affects the net"'ork topology, a partial application of the topological algorithm allo"'s us the o bsen'a bility determination . In this ,,'ay I«e must loo k for the measurements , Let us consider , as an applicat ion , the s~'s _ te rn in fig . 2 , which represents a laborato ":' ry net wor k connected to a process computer , The application of the topological algorithm yields the r edundancy levels sho wn in table 1 , as well as the spanning t r ee shalom in fig . ;) a ,

On- line Observability Determinat i on in Electr ic Power Network

607

NZ

TABLE I. Hcdundancy levels f or samp le n~·l,,"ol·k.

meIlSUl'emen~

fl 0 '"

3-4

4

3-~

3

3-~

3-7 4-3 .1- 5 ti-~

j

In,i~.'t

-3

j"n ! 5

•

N4

level

N.

N5

., 4 4

3 3

., 0 0

Ni

N3

"

1 fundament a I) I fundamenta I I

3 3 3

example of slIght changes in the measu_ rement s .... ' I ... t us consider ... hat happens ~ith Ihe P,'''CI' fl(, .. meaSI..II'ement on branch 4-5 .. hen "the l' I'elated ReaSUI'cments a re deleted VIlC by \1I\e, lh~' applied stat e estimation al _ g,,,.ithm 'i.. 2) ful'nishes a ~aJue of the fo parameter attached t~\ this mellSUI'ement vf 0.23 .. hen po,,'e!' Inject\on measul'e:nent at node 5 is deleted. Then , if the flv,,' measurement at b r'anch 3-5 \5 discarded the ll-para me t er is l11ghly I'cduced IV 0.1\ . finally if the ill _ je ..·tion al node 6 fails , the I'" parameter \'alue dr'ops tu 0.i8 x 10- 3 , This re sult points out that the measurement has become fundamcnl a I .

• •

injection measurement po...e r flo,", measurement

Fig.2 , Sample net ... o rk


,\5 31\

N"" as a drastic change situation, let us .onsider in the initial measurement system a fat lul'(,' in a tclemeterlng station that turns vff all the measurcments in node 3, The ,.bse l\"ablly test und redundancy level l'cCl'mputali,m (;un be perfol"!l\ed by a partial appl ication uf the tupological algo r ithm to thc subnet"'o rk in the equivalent node 3 )\ Iflg . 41. AS sho .... n in the figu r e , a full rank spanning tree (:'an bt: still built for the subnet"'ork, so there are no internal un<)bservable Islands and th e equivalent nodes rcm81n connected as indicated in figure 3 . c . Therefvre the full system remains obser _ vable , even though the re dundancy levels have decreased as sho ... n in ta b le 2 . CONCLUSIO NS Real time operation o f electric po ...er net works under safe conditions needs not only a reliable state esti ma tio n but t he kn o ... ledge about the local reliability o f the measu-

3

•

4

,

,

4

7

a) Spann ing t r ee

/

0'

7

hi Net"'o rk scheme


J

3"

/'

cl Equivalent nodes tree branches 1flow measured I loop branches ( fio'" measured' unmeasured branches injection measurcments

"

fig . 3 . Spanning tree fo r samp le net"'ork

3

•

4

5

4

1/

5

7

.1 Initial system

~ ! . 7

b) After fai lure

fig. 4 , Subne t "'o rk at node J *

6

P. Albe rt os, C.

608

Alva r e ~

and J. A. de l a Puente

TABLE 2. Redundancy levels afte r failu r e at

measurement fl 0'"

injection

nod~

level

4 -3 4-5 6-7 7 -3

2 2

2

0 0 2

,

5 6 7

REFERE NCES

J.

2

2

2

(fundamental)

3

(fundamental) 4

2

2

remcnt equipment. In this way a revie'" of -

the existent on-line observability

algori~s

has been presented. In order to attac k diffe _ rent , si tuations generated by a single or

5

multiple bad-data detection and/or a change in the network topology, some new c:mcepts

related t o the obse r vability condition are introduced . A general approach to deal with these situations has been proposed , based on both numerical and topological techniques . Two COIl".piementary algori thms are used in or der to r educe the computation time, using

6

7

the best suited according to the abnormality presented. The method has been tested on a reduced order laboratory net wor k. 8

9

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