Observer-based fault detection and identification scheme for power systems

Transcription

1 Oserver-se fult etetion n ientifition sheme for power systems M. Aleen n F. Crus Astrt: A sheme suitle for the etetion n ientifition of fults in power systems is presente. Two notle ontriutions re me: re-moelling of fulty omponents of power systems tht is pplile to oth norml n fulty onitions, n fult etetion sheme for power systems. The fults re moelle s unknown inputs, eouple from the stte n output mesurements through oorinte trnsformtions, n then estimte through the use of oserver theory. The propose sheme is pplie to power system onsisting of synhronous genertor, n exiter, turine n spee-governing system, n network of lines n los. The se where fults our on the trnsmission network is onsiere. It is shown tht the propose fult etetion proeure llows for the rel-time ientifition of the ourrene of the fults n etermines their ext lotions. Results of etile simultion stuies involving isturnes n fults ourring in liner n nonliner moels of the power system re presente. List of symols flux linkge x stte vetor y output vetor f fult prmeters A, B, C, D, E, G, W onstnt prmeter mtries rotor shft ngle o rotor shft spee o B spee se quntity v, V mhine n network voltge i, I mhine n network urrent 7 7 mgnitue of vetor E FD fiel wining exittion voltge H synhronous mhine inerti onstnt k rotor mping oeffiient T m, P m mehnil torque n power M mhine-network oorinte trnsformtion onstnts Supersript n susripts. supersript refers to nominl vlue. q susript refers to the qurture xis. G.Q susript refers to mper winings on the qurture xis. susript refers to the iret xis. D susript refers to mper wining on the iret xis. F susript refers to fiel wining r IEE, 6 IEE Proeeings online no. 4 oi:.49/ip-gt:4 Pper first reeive th July 4 n in finl revise form n Septemer M. Aleen is with Deprtment of Eletril & Eletroni Engineering, University of Melourne, Vitori, Austrli F. Crus is with Deprtment of Eletril n Computer Systems Engineering, Monsh University, Vitori, Austrli E-mil: frneso.rus@eng.monsh.eu.u. q susript refers to vetor; ½: q : Š T. SE susript refers to swing eqution. ex susript refers to exiter. N susript refers to network. G susript refers to governor. REF susript refers to terminl voltge estimte of ^ Introution Power systems re no ifferent to ny other lrge-sle interonnete system in tht they re suseptile to vrious forms of fults whih oul our in ny of the omponents tht mke up the system. For exmple, fults n our in generting units, trnsformers, the trnsmission network n/or los. Fults tht tke ple in ny of these omponents n use signifint isruption of supply n in some ses my hve the unesirle effet of estilising the entire system, n in extreme ses leing to rownouts n lkouts. It is therefore importnt to e le to etet n isolte suh fults s quikly s possile, in orer tht remeil tion n e tken. In this work the fous is shifte from stuying the effet of externl isturnes on the power system in terms of lo ngle swings n effets on voltge profiles n tie-line power flows, to the etetion n ientifition of the fult itself. Although this pproh offers onsierle enefits per se, espeilly when inorporte with protetion systems, its full potentil n e relise when it is inorporte into wier tive fult tolernt ontrol sheme, whih is urrently the sujet of ongoing reserh. Over the pst ee onsierle vnes hve een me in the re of fult etetion n isoltion [, ] prtiulrly in the res of erospe, nuler retors, n proess ontrol systems. However, literture survey revels tht the pplition of nlytil moel-se fult etetion tehniques to power systems is presently t its infny, lthough few pplitions of neurl networks to fult etetion in power systems hve een reporte [3, 4]. The ft tht onventionl ynmi moels of power IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6 7

2 systems s reporte in the literture [, 6] re not iretly menle to existing fult etetion tehniques my e the min reson ehin the lk of ny mjor ontriutions in this re. A prerequisite for fult etetion in power systems is the erivtion of n pproprite moel. The pproh to the moelling of power systems for fult etetion purposes is onsierly ifferent from tht opte in onventionl stility stuies. The ifferene stems from the nee for the stisftion of itionl requirements onerning the ourrene n etetion of fults s outline elow: () eh omponent of the system shoul e moelle with fult onitions effete internlly suh tht oth norml n fult onitions n e simulte uniformly n systemtilly; () the ility to isolte n remove the fult from the network; () the ility to ifferentite etween fult signls n norml signls. These requirements must e stisfie without etrting from the integrity n omplexity of the power system moel, n in this work they re met s follows. Requirements () n () n e hieve y introuing ifferent swithing mehnisms in the pproprite ples of the omponent eing moelle, where s requirement () is hieve y treting fult onitions s externl unknown signls. The nee for the re-moelling of the power system s outline ove stems prtilly from the ft tht existing fult etetion tehniques [7 ] re se on the priniple of the fult eing moelle s n externl unknown input tht enters ffinely into the system, n prtilly from the requirement tht the moel shoul e ple of exhiiting the power system ehviour uner oth norml n norml operting onitions. Conventionl fult etetion lgorithms re typilly se on oserver theory in whih ynmi moel of the plnt is generte, n from this n oserver is onstrute. The resiul error etween the oserver n plnt sttes then serves s n initor for fult etetion. For exmple, unknown input oserver theory is use in [8, 3, 4], n H-infinity is use in [, 6]. The resiul genertion lgorithms generlly require for these pprohes, re not require in more reent pprohes suh s [7], in whih unknown input oserver theory is iretly employe, n [9], in whih sliing moe oserver theory is use. In this stuy we introue n lterntive pproh to fult etetion n ientifition in power systems. Firstly, we present moels for those omponents of power systems tht my experiene fults. The moels re evelope so s to provie urte representtions of the omponents uner norml n fult onitions without the nee to mke ny hnges. Seonly, we present sheme for the etetion n isoltion of fults. Unlike existing theory, the sheme is ple of eteting multiple fults n ientifying their ext lotions in rel-time n on-line, s emonstrte in the esign n simultion exmple of Setion 4. Therefore, the pproh to fult etetion presente in this work is twofol, n involves firstly the re-moelling of the power system to eouple the fult from the system s outline ove, n seonly, the pplition of suitle oserver theory for fult etetion in power systems. The ovementione tehnique n e use to ientify fults in ll of the omponents of the power system. However, for the ske of revity n ue to spe limittions, the emphsis in this stuy is restrite to the speifi se of fults ourring in the trnsmission network. For this purpose, n pplition exmple of power system omprising generting unit onnete to n infinite usr vi oule-iruit trnsmission line n lol lo is presente. Power system moel The stuie power system is generting unit onnete to n infinite us-r through trnsmission lines. The generting unit omprises synhronous genertor, n exiter [], n stem-turine spee governor [8]. A etile nlysis of the moelling of eh these omponents is given in [9]. Although stnr moels of power systems omponents re ville in the literture, (see [] n [6], for exmple), moels of power system omponents inorporting fult senrios re not urrently ville. Our fous is therefore shifte to the moelling n inorportion of fults in power system. For this purpose we opt the eigth-orer genertor moel, thir-orer IEEE ST exiter moel, n thir-orer IEEE governor moel erive in [7] n re-moel the trnsmission system inorporting fult onitions. In the erivtion of the trnsmission system, we llow for fults to tke ple nywhere in the system. We lim tht this is the first time suh n pproh to moelling, simultion, n esign of fult etetion shemes, whih tkes into ount vrious fult senrios, hs een reporte.. Moel of generting unit A set of linerise equtions for n eigth-orer synhronous mhine moel with one mper wining on the -xis n two mper winings on the q-xis, n IEEE ST exiter n n IEEE spee governing system re erive in [7]. For ese of referene, the stte spe moels for eh of these omponents is provie elow... Synhronous mhine moel: D _x M ¼ A M Dx M þ B v Dv q þ B FD DE FD þ B m DP m ðþ where x M ¼½ q G Q F D _ Š T n v q ¼½v q v Š T... Exiter moel: D _x ex ¼ A ex Dx ex þ B ex Du ex DE FD ¼ C EFD Dx ex ðþ ð3þ where x ex ¼½V V 3 E FD Š T re the exiter sttes (s efine in Fig..4 of []), n u ex ¼ V REF...3 Spee governor moel: D _x G ¼ A G Dx G þ B G Du G DP m ¼ C G Dx G where x G ¼½P m P GV P SR Š T,nu G ¼ P r. ð4þ ðþ. Stte spe moel of generting unit Comining the synhronous genertor, exiter n governing moels, les to omplete stte spe moel for the generting unit. This moel n e expresse s: D _x gu ¼ A gu Dx gu þ B gu Du gu þ B gu;v Dv q ð6þ 7 IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6

3 where x gu ¼½x M x ex x G Š T, u gu ¼½V REF P r Š T, n 3 3 A M B FD C EFD B m C G A gu ¼ 4 A ex, B gu ¼ 4 B ex, A G B G 3 B v B gu;v ¼ 4..3 Mhine-network referene frme trnsformtion In orer to interfe the generting unit with the trnsmission system, the following linerise networkmhine trnsformtions for oth the voltge n urrent, se on Prk s oorinte trnsformtion [], re require: Dv q ¼ C N DV N þ C Dx SE ð7þ DI N ¼ U q Di q þ U Dx SE ð8þ where x SE ¼½ _ Š T, C N ¼ M v Tð Þ, C ¼½ M v T ð ÞV N Š, U q ¼ M i ðtð ÞÞ T, U ¼½ M i ðt ð ÞÞ T i q Š. The prmeters M v n M i re se-hnge onstnts for voltge n urrent, respetively. The terminl voltges n urrents re efine in terms of their q- n -xis omponents s V N ¼½V Nq V N Š T, v q9 ½ v q v Š T, I N9 ½ I Nq I N Š T, i q9 ½ i q i Š T. The Prk s trnsformtion mtrix n its erivtive re efine s: Tð Þ9 os sin sin os ; T ð Þ9 sin os os sin Using these efinitions, n fter some mnipultion, eqns. (7) n (8) my e expresse in terms of the generting unit stte vetor s: Dv q ¼ C N DV N þ C C Dx gu ð9þ DI N ¼ U q Di q þ U C Dx gu ðþ Tking into ount tht i q ¼ SL Qx gu, where S is 8 seletion mtrix with ll elements zero exept Sð; Þ ¼nSð; 4Þ ¼, L ¼ðL qgq ; L FD Þ with: 3 3 L q L AQ L AQ L L AD L AD L qgq ¼ 4 L AQ L G L AQ ; L FD ¼ 4 L AD L F L AD L AQ L AQ L Q L AD L AD L D n Q9½ 6 8 Š, the generting unit moel of eqution (6) together with the output eqution () eomes: D _x gu ¼ðA gu þ B gu;v C C ÞDx gu þ B gu Du gu þ B gu;v C N DV N DI N ¼ C N;gu Dx gu where C N;gu9 U q SL Q þ U C. ðþ ðþ.4 Network moel Here we onsier trnsmission network omprising two prllel lines onnete to n infinite us n lol line supplying lol lo, s shown in Fig.. We stuy the se where the power system is initilly operting uner norml onitions n then either or oth of lines n my unergo three-phse line-to-groun fults t lotions g i, i ¼f; g from the genertor terminls. The lol line is ssume to e fult-free. Lines G Fig. n my therefore e moelle s follows: I N ¼ð ÞY ðv N V B Þþr Y V N ð3þ I N ¼ð f ÞY ðv N V B Þþr Y V N ð4þ where Y ¼ Z, Y ¼ Z, enote the mittne of lines n.here,f i, i ¼f; g represent the fult signls, where f i ¼ signifies no fult onition n f i ¼ signifies fult onition on line i. The vriles g i, i ¼ f; g represent the lotion of the fults long the lines, mesure from the genertor terminls. For exmple, g i ¼ represents fult t the mhine terminls, wheres g i ¼ represents fult t the infinite us-r. For nottionl onveniene, we further efine r 9 =g.thelollo (ssume to e fult-free) is moelle s: I N3 ¼ Y L V N ðþ Using these efinitions, (3), (4) n () re linerise s follows: DI N ¼ð f þ r ÞY DV N þðv B V N ÞY D þ Y V N Dr DI N ¼ð f þ r ÞY DV N þðv B V N ÞY Df þ Y V N Dr DI N3 ¼ Y L DV N Thus, the totl terminl urrent is: DI N ¼ DI N þ DI N þ DI N3 DI N ¼fð f þ r ÞY þð f þ r ÞY þ Y L gdv N ð6þ ð7þ ð8þ þðv B V N ÞY D þðv B V N ÞY Df þ Y V N Dr þ Y V N Dr ð9þ Let f ¼½ r f r Š T, then (9) my e rewritten s: DI N ¼ K V DI N þ K f r Df ðþ where K V ¼ð f þ r ÞY þð f þ r ÞY þ Y L, K f r ¼½ r f r Š T, K ¼ðV B V N ÞY, K f ¼ðV B V N ÞY, K r ¼ Y V N n K r ¼ Y V N. Eqution (9) my e rerrnge s follows: DV N ¼ Z N DI N þ Z f Df ðþ where Z N ¼ K V V N II network moel Z 3 γ Z n Z ¼ K V K f r. ( γ )Z γ Z ( γ )Z f line-to-groun fult. Stte spe moel of power system Comining the equtions for the generting unit moel, () n () with the network moel of (), n sustituting x for x gu,nu for u gu les to the following V B IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6 73

4 stte-eqution moel for the power system: D _x ¼ ADx þ BDu þ EDf ðþ where A ¼ A gu þ B gu;v C C þ B gu;v C N Z N C N;gu, B ¼ B gu, n E ¼ B gu;v C N Z f. Next we erive linerise equtions for the outputs of interest. These re efine ove s the lo ngle, elertion, output power n mgnitues of the terminl voltge n urrent. As the lo ngle itself is stte vrile, it n e esily inorporte into the output eqution. In the following we erive expressions for the remining output vriles... Terminl voltge: The mgnitue of the genertor terminl voltge V N is require s feek signl to the exittion system n lso s n input to the network moel n mhine-network trnsformtion, n s n output for the oserver. A linerise expression for the mgnitue of the terminl voltge is reily erive s: DjV N j¼k VN DV N ð3þ where K VN9ðV N ÞT =jv Nj. Sustituting () into (3) les to: DjV N j¼k VN Z N DI N þ K VN Z f Df ð4þ However, from (8) n, fter some strightforwr mnipultion, DjV N j n e represente s: DjV N j¼k VN Z N C N;gu Dx þ K VN Z f Df ðþ.. Terminl power: An expression for the mhine output tive power is erive from lineristion of P N ¼ V T N I N s: DP N ¼ðI N ÞT DV N þðv N ÞT DI N whih together with () n () les to: DP N ¼ C P;gu Dx þði N ÞT Z f Df where C P;gu9 ððv N ÞT þði N ÞT Z N ÞC N;gu. ð6þ ð7þ..3 Aelertion: The elertion output is otine from the swing eqution: ¼ o B H T m T e k _ ð8þ o B where T e ¼ M T M v M i T eg, n T eg ¼ i q q i. From the urrent-flux reltions for the q-n-xes, we otin: i q ¼ L q q þ L AQ G þ L AQ Q ð9þ i ¼ L þ L AD F þ L AD D ð3þ where 3 3 L q L AQ L AQ L q L AQ L AQ L AQ L G L AQ 94 L AQ L G L AQ ; L AQ L AQ L Q L AQ L AQ L Q 3 3 L L AD L AD L L AD L AD L AD L F L AD 94 L AD L F L AD L AD L AD L D L AD L AD L D Linerising, we otin: DT eg ¼ðL q i ÞD q þ L AQ D G þ L AQ D Q ðl q i q ÞD L AD q D F L AD q D D D ¼ o B H DT m k H D_ o B H M T M v M i n o ðl q i ÞD q þ L AQ D G þ L AQ D Q þ o B H M T M v M i n o ðl q i q ÞD þ L AD q D F þ L AD q D D D ¼ C Dx M þ o B H DT m ð3þ where C 9 M½i L q L AQ L AQ L q i q L AD q L AD q k =H MŠ n M9 o B H M T M v M i. The mehnil power n torque re relte y: P m ¼ o B þ _! T m o B Sine, for smll hnges in spee, ðo B þ _ Þ=o B ffi, for the linerise system it follows tht DT m ¼ DP m.from()it follows tht DT m ¼ C G Dx G, n therefore (3) eomes: D ¼ C Dx ð3þ where C h o i B ¼ C 3 H C G. We efine the output mesurements s: y9 ½ jv N j P N ji N j Š T. The output eqution my therefore e otine from (), (), (7), n (3) s follows: Dy ¼ CDx þ WDf ð33þ where C ¼ 6 4 C C K VN Z N C P;gu C N;gu 3 7,nW ¼ K VN Z f ði N ÞT Z f For simpliity, we rop the elt nottion to rrive t the overll power system moel, whih is otine from () n (33) s: _x ¼ Ax þ Bu þ Ef e ð34þ y ¼ Cx þ Wf w where f e ¼ f w ¼ f. ð3þ 3 Development of unknown input oserver-se fult sheme In this Setion we evelop n unknown input-oserverse fult etetion sheme suitle for multivrile systems, suh s power systems. The sheme is se on the ie of eoupling the stte n output equtions into fultfree n fult-epenent prts. The fult-free prt is then use to esign n oserver tht woul gurntee estimtion of the entire stte vetor irrespetive of the mgnitue n nture of ny fult signls. One this tsk is hieve, then the oserver is use to provie estimtes of the stte vetor to fult etetion filter, whih is esigne speifilly to provie estimtes of ll fult signls. This evelopment is outline in the following Setions. 3. Deoupling the output eqution Using singulr vlue eomposition, mtrix W n e expresse s: W ¼ UR W V T S ¼½U U Š V T ¼ U R V T ð36þ 74 IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6

5 where U < mm, R W < mq w, V T < q wq w, U < mq w, U < mðm q wþ n R < q wq w. Eqution (3) my then e written s: y ¼ Cx þ UR W V T f w ð37þ Define f w ¼ V T f w ; f w < q w n pre-multiply (37) y U T to otin: " U T y ¼ UT y # " # y U T y 9 ð38þ y Then (37) eomes: " y ¼ U # T Cx þ R y U T From (39) we hve: y ¼ U T Cx þ R f w f w ð39þ ð4þ y ¼ U T Cx ¼ UT y ð4þ Thus, the output eqution hs now een eouple, s shown in (4) n (4). Note tht ompring (38) with (4) revels tht y is not ffete y the output fult signl, f w. 3. Deoupling the stte eqution Singulr vlue eomposition of mtrix E < nq e gives: E ¼ QR E R T R ¼½Q Q Š R T ¼ Q R R T ð4þ where Q < nn, R < nq e, R < q eq e, Q < nq e, Q < nðn qeþ n R < q eq e. Define: f e ¼ R T f e ; f e < q e n x ¼ x9q T x ð43þ x so tht A9Q T A AQ ¼ A A A ; Q T B ¼ B9 B ð44þ B then (34) eomes: _x ¼ A x þ A x þ B u þ R f e ð4þ _x ¼ A x þ A x þ B u ð46þ Use this oorinte trnsformtion x ¼ Qx ¼ Q x x in (4) to otin: y ¼ Cx ð47þ where C < ðm qwþn is efine s: C9U T CQ ¼½ C C Š ð48þ with C < ðm q wþq e,nc < ðm q wþðn q e Þ. Then (47) eomes: y ¼ C x þ C x ð49þ Sine rnk C ¼ q e,nðm q w Þðm q w Þ nonsingulr mtrix my e onstrute from: C N ¼ þ ðþ M where C þ <q eðm q w Þ is the pseuo-inverse of C, efine s C þ ¼ð C T C Þ C T,nM <ðm q w q e Þðm q w Þ is n ritrrily selete mtrix so tht N < ðm q Þðm q Þ is nonsingulr. Premultiplying (47) y () gives: C þ C y M ¼ þ C M C x x Sine C þ C ¼ I qe,()yiels: x ¼ C þ ðy C x Þ ðþ ðþ My ¼ MC x þ MC x ð3þ Sustituting () into (46) yiels: _x ¼ðA A C þ C Þx þ B u þ A C þ y ð4þ Using y ¼ U T y in (4) gives: _x ¼ A ~ x þ B ~ u þ G ~ y ðþ where A ~ ¼ðA A C þ C Þ, B ~ ¼ B n ~G ¼ A C þ UT. Sustituting () into (3) gives: MðI m q C C þ Þy ¼ MðI m q C C þ Þ C x ð6þ Define: ~C9MðI m q C C þ Þ C ; ~H9MðI m q C ð7þ C þ ÞUT Using the efinitions in (6) gives: ~Hy ¼ Cx ~ ð8þ Define: ~y ¼ Hy ~ ¼ Cx ~ ð9þ Thus, we now hve fult-free system esrie y the stte eqution, (), n the output eqution, (9), i.e.: _x ¼ A ~ x þ B ~ u þ G ~ y ð6þ ~y ¼ Cx ~ ð6þ where the imension of the stte vetor, x,isn q e. 3.3 Oserver esign If the pir f A ~ ; Cg ~ is oservle, then the following system n t s n oserver for the system esrie y (6)n (6): _^x ¼ A ~ ^x þ B ~ u þ G ~ y þ Lð~y C^x ~ Þ ð6þ where L is the oserver gin mtrix n must e foun so tht the oserver mtrix A ~ L C ~ is stle. One n estimte of x is otine from the oserver esrie in (6), the estimte of x n e foun from () s: ^x ¼ C þ ðut y C ^x Þ ð6þ Finlly, the estimte, ^x, of the originl overll stte vetor, x, is now onstrute from (43) s: ^x ¼ Q^x ¼ Q ^x ð63þ ^x 3.4 Estimtion of fult signls In this Setion, we erive two fult estimtion shemes, one for fult signls tht pper in the stte eqution n the other for the fult signls tht pper in the output eqution Estimtion of output fult signls: Sustituting (6) into (63) gives the following: ^x ¼ Q x^x þ Q y y ð64þ IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6 7

6 where Q C þ C x9q, Qy9Q C þ UT. From (37), I n fter repling x y its estimte, ^x, we hve: ^f w ¼ VR UT ðy C^xÞ ð6þ δ δ 3.4. Estimtion of input fult signls: From (64) we hve: _^x ¼ Q x _^x þ Q y _y ð66þ Sustituting (6) into (66) gives: _^x ¼ Q x ½ð A ~ L CÞ^x ~ þ B ~ u þð G ~ þ L HÞyŠþ ~ Q y _y ð67þ From (34) n (67), the estimte of the fult signl f e my e otine, fter repling x y its estimte, ^x, s: ^f e ¼ RR QT W ^x þ W y þ W 3 _y þ W 4 u ð68þ where W ¼ Q x ð A ~ L CÞ A ~ Q x, W ¼ Q x ð G ~ þ L HÞ ~ AQ y, W 3 ¼ Q y,nw 4 ¼ Q ~ x B B... V N V N P N P N 4 Design n simultion results In this Setion we esign the unknown input oserver esrie y (6) n proee to esign the fult reonstrution filters esrie y (6) n (68). Then the resulting fult etetion sheme is teste through omputer simultion involving five istint se stuies involving liner n nonliner moels of the power system. It will e shown tht the esigne oserver-se fult etetion sheme is ple of eling with ll possile fult senrios n provie ext informtion out the fult onitions. 4. Oserver esign The proeure outline in Setion 3 is rrie out on the power system moel outline in Setion. This silly involves the erivtion of the fult-free system esrie y (6) n(6) n then the esign of the unknown input oserver esrie y (6). The oserver esign involves the etermintion of the oserver gin mtrix L to stilise ~A L ~ C. The tul esign prmeters re not liste here ue to spe onstrints, ut my e otine, together with the power system moel n t, y ontting the uthors iretly. The reson for not proviing these esign prmeters is tht they my only mke sense if ompnie y etile moels of eh of the power system omponents n their respetive t. To o so woul require llotion of isproportionte spe, whih the uthors eem not to e neessry. 4. Cse stuies n simultion results In this Setion we report on the performne of the oserver-se fult etetion sheme outline in Setion 3 n esigne in Setion 4. The performne of the sheme is teste through the Simulinkt progrm for the following five se stuies re onsiere. 4.. Cse stuy : This initil stuy tests the performne of the esigne oserver. In oing so, we ritrrily set ll initil stte vlues for the power system to the vlue., while mintining ll oserver initil sttes t zero vlue. Then t time t ¼ s, we pply % step inrese in V REF. The response of smple of the output vriles, inluing responses of the lo ngle, elertion n output power, re shown in Fig.. Figure emonstrtes the onvergene property of the oserver, s the oserver outputs onverge to the true outputs fter 4 Fig. Oserver onvergene properties for se ginst t 7V N 7 ginst t P N ginst t roun 4 s. One the onvergene tkes ple the oserver emultes extly the ehviour of the power system, s expete. Figure lso shows tht fter the pplition of the step hnge in V REF t time t ¼ s, the lo ngle slips k, llowing for the exittion system to inrese the resultnt irgp flux, whih in turn oosts the terminl voltge up to the require level. One this is hieve, the lo ngle settles to new stey stte, s expete. Finlly, Fig. shows tht s the net hnge in the power is zero, the output power, fter experiening smll initil trnsient response, remins unhnge. This is gin in line with the physil ehviour of power system uner stuy. 4.. Cse stuy : In this stuy, we ssume tht the power system is in equilirium operting uner norml ( fult-free) onition. We lso ssume tht the oserver ws swithe on for long enough for it to trk the sttes of the power system. Then the exittion system referene ommn, V REF,issteppe%ttimet ¼ s. This is followe y soli three-phse line-to-groun fult ourring hlf-wy long line t time t ¼ s. This fult is simulte y setting the fult prmeters s: ¼ n g ¼ : (whih orrespons to r ¼ ). The purpose of this stuy is first to etet the ourrene of the fult, seon to ientify the fulty line, n thir to etermine the ext lotion of the fult. This simultion stuy hs een performe using the Simulinkt moel. The simultion results re shown in Fig. 3. Figure 3 shows the ommn signl V REF eing pplie t time t ¼ s. Figures 3 3e show the estimtes of the two fult signls n their lotions. From Figs. 3 3e it n onlue tht the fult etetion sheme is insensitive to externl isturnes suh s V REF n P r. This is emonstrte y the ft tht wheres the system itself unergoes trnsient perio fter the pplition of the step hnge in V REF, s shown in Fig. 4, the fult etetion filter oes not respon. Figures 3 n 4 lso emonstrte the ft tht the fult etetion filter is le to instntneously etet 76 IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6

7 γ f γ V REF Fig. 3 Cse stuy : step hnge in Dv REF t t ¼ s, fult on line tt¼ s V REF ginst t ginst t g ginst t f ginst t e g ginst t voltge mgnitue, V N, pu Fig. 4 Voltge response of se stuy fult when it ours n provie its ext lotion. In this prtiulr stuy, s there is no fult on line, no response is inite, ut when fult ours on line, it is immeitely reognise n its lotion is evlute on-line ninrel-time Cse stuy 3: In this stuy, we run the power system in equilirium onition, i.e. isturne free n fult free, for s. Then the referene ommn, V REF,is steppe % t time t ¼ s. This is followe y soli threephse line-to-groun fults on oth lines. The fults on lines n our t lotions g ¼ : ng ¼ :8 wy from the genertor terminl, respetively. The fult on line e tkes ple t time t ¼ 6 s, wheres the fult on line tkes ple t time t ¼ s. The purpose of this stuy is first to etet the ourrene of the two fults, n then to etermine their ext lotions. Therefore, for this se stuy four prmeters nee to e estimte on line n in rel-time. They re, g, f,ng. The simultion results re shown in Fig.. Figure shows the ommn signl V REF eing pplie t time t ¼ s. Figures e show the estimtes of the two fult signls n their lotions. From Figs. e it n e esily seen tht the fult etetion sheme propose in this stuy is insensitive to known externl isturnes suh s V REF n P r. This is orne out y the ft tht wheres the system itself experienes some trnsient ehviour fter the introution of the hnge in V REF,sshowninFig.6, the fult etetion filter remins unffete. Figures n 6 lso emonstrte the suessful etetion of the two fults, t the preise moment of their ourrene, n the suessful etetion of their ext lotions. V REF γ f γ e Fig. Cse stuy 3: step hnge in Dv REF t t ¼ s, fult on line tt¼6s, fult on line t t ¼ s V REF ginst t ginst t g ginst t f ginst t e g ginst t 4..4 Cse stuy 4: In this stuy, we repet the sme senrio of se stuy 3, ut with the following ltertion: the fult on line is lere fter. s n the line is restore. The simultion results re shown in Fig. 7. Figures 7 n 7 show tht the filter ws le to instntneously etet the fult on line t the time it ourre n lso etermine its ext lotion. They lso show tht when the IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6 77

8 voltge mgnitue, V N, pu Fig. 6 Voltge response of se stuy 3 V REF γ f γ e Fig. 7 Cse stuy 4: step hnge in Dv REF t t ¼ s, fult on line tt¼6slere fter. s, fult on line t t ¼ s V REF ginst t ginst t g ginst t f ginst t e g ginst t fult ws lere the filter etete this gin n swithe k to no-fult moe. The sme is emonstrte y Figs. 7 n 7f shown in Fig. 8, where the sheme ws le to etet the ourrene of fult on line n its ext lotion. The voltge response of this stuy is here gin, s for the se stuies 3, Figs. 7 n 8 emonstrte the ility of the fult etetion sheme to el with ll possile senrios n provie ext results. 4.. Cse stuy : In this stuy the sme fult etetion filter is teste on the originl nonliner system using the nonliner simultor reporte in []. The test involves the pplition of series of isturnes to the nonliner power system moel, followe y fult. The voltge mgnitue, V N, pu Fig. 8 Voltge response of se stuy 4 V REF P r est f f est performne of the fult etetion filter is then exmine. The speifi isturnes re pulses to the exittion system n turine governor system setpoints, v REF n P REF,of mplitue. pu. The urtion of theses isturnes is s, pplie t t ¼ s n t ¼ s, respetively, s shown in Figs. 9 n 9. Thentt ¼ 8 s, soli three-phse shortiruit is pplie, t lotion miwy long line (i.e. g ¼ :), s shown in Figs. 9 n 9e. The proesse estimte fult signls, ^f e n ^f e ¼ ^g ^fe re shown in the Figs. 9 n 9f. From whih it n e seen tht the fult etetion filter is: (i) insensitive to the isturnes; (ii) le to lerly etet the onset of the fult t t ¼ 8 s; n (iii) le e f Fig. 9 Cse stuy : isturne in v REF t t ¼ s, followe y isturne in P r t t ¼ 4 s, followe y fult on line t t ¼ 8s V REF ginst t P r ginst t ginst t estimte ginst t ef ginst t ff estimte ginst t 78 IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6

9 f e est.. senrios hve een stuie. Simultion results on liner n nonliner moels of the power system hve shown tht in ll of the stuie ses, the fult etetion sheme ws not only le to urtely etet the ourrene of fults, ut lso their ext lotions. f e est to estimte the lotion of the fult s, ^g ¼ ^f e =^f e ¼ :786=:338 ¼ :87 (whih is lose to the tul vlue of.). It is to e note tht, in generl, fult etetion filters esigne for linerise moels of power systems re not expete to perform optimlly when use on the originl nonliner moels. This is silly euse the presene of the severe fults (lrge isturnes) n shift the operting onition rstilly to point where the lineristion is not vli. In suh ses some simple signl proessing my nee to e employe. In generting the responses of Figs. 9 n 9f, simple proessing of the originl signls, shown in Fig., ws neessry euse of the severe nture of the pplie fult (line-to-groun fult). The proessing of the fult signl involves pturing the fult signl immeitely fter its ourrene. In hrwre this n e implemente y using rely where the threshol n e juste ppropritely. Conlusions Fig. The estimte fult signls uner nonliner simultion for se f e estimte ginst t f e estimte ginst t A fult etetion sheme for power systems hs een propose. The sheme hs een shown to e le to provie ext informtion out ny fult or omintion of fults when n where they our. One of the min vntges of the propose pproh is tht only one oserver esign is require to etet ny numer of fults, provie tht the output mesurement ontins enough informtion out the stte of the system. The propose sheme hs een teste on power system onsisting of generting unit onnete to n infinite usr through oule-iruit trnsmission line. Vrious fult 6 Referenes Ptton, R., Clrk, R., n Frnk, P.M.: Fult ignosis in ynmi systems: theory n pplitions. Prentie-Hll interntionl series in systems n ontrol engineering (Prentie Hll, Englewoo Cliffs, NJ,, 989), Vol. xv, p. 6 De Persis, C., n Isiori, A.: A geometri pproh to nonliner fult etetion n isoltion, IEEE Trns. Autom. Control,, 46, (6), pp Swrup, K., n Chnrsekhrih, H.: Fult etetion n ignosis of power systems using rtifiil neurl networks. Presente t the st Int. Forum on Applitions of Neurl Networks to Power Systems, 99 4 Mori, H. et l.: A hyri intelligent system for fult etetion in power systems. Presente t the Joint Int. Conf. on Neurl Networks, (IJCNN ), Anerson, P.M., Fou, A.A., n Institute of Eletril n Eletronis Engineers (U.S.): Power system ontrol n stility (IEEE Press, Pistwy, NJ, 993), Vol. xiii, p Kunur, P., Blu, N.J., n Luy, M.G.: Power system stility n ontrol. EPRI Power System Engineering Series (MGrw-Hill, New York, 994), Vol. xxiii, p Hou, M., n Muller, P.C.: Fult etetion n isoltion oservers, Int. J. Control, 994, 6, (), pp Hou, M., n Muller, P.C.: Design of oservers for liner systems with unknown inputs, IEEE Trns. Autom. Control, 99, 37, (6), pp Tn, C.P., n Ewrs, C.: Sliing moe oservers for etetion n reonstrution of sensor fults, Automti,, 38, (), pp. 8 8 Hmmouri, H., Kinnert, M., n El Ygoui, E.H.: Oserverse pproh to fult etetion n isoltion for nonliner systems, IEEE Trns. Autom. Control, 999, 44, (), pp Koenig, D.M.S.: Design of lss of reue orer unknown inputs nonliner oserver for fult ignosis. Presente t the Amerin Control Conf., Xiong, Y., n Sif, M.: Sliing moe oserver for nonliner unertin systems, IEEE Trns. Autom. Control,, 46, (), pp. 7 3 Wng, S.H., Dvison, E.J., n Dorto, P.: Oserving the sttes of systems with unmesurle isturnes, IEEE Trns. Autom. Control, 97,, pp Drouh, M., Zszinski, M., n Xu, S.J.: Full-orer oservers for liner systems with unknown inputs, IEEE Trns. Autom. Control, 994, 39, (3), pp Hou, M., n Ptton, R.J.: An LMI pproh to H_infinity fult etetion oservers. Pro. UK/ACC Int. onf. on Control, 996, pp Irki, S., Surynrynn, S., n Tomizuk, M.: H-infinity optimiztion of Luenerger stte oservers n its pplition to fult etetion filter esign. Presente t the 4th IEEE Conf. on Deision n Control, 7 Crus, F., n Aleen, M.: Fult etetion n ientifition of power systems. Pro. IASTED Conf. on Intelligent Systems n Control, 3, pp IEEE Working Group on Power Plnt Response to lo hnges: MW response of fossil fuelle units, IEEE Trns. Power Appr. Syst., 9, (), pp Aleen, M., n Crus, F.: Moulr moelling of nonliner omplex systems. in Presente t the 4th IEEE Int. Conf. on Control n Automtion, ICCA 3, Montrel, Cn, 3 Anerson, P.M. et l.: Susynhronous resonne in power systems (IEEE Press, New York, 99), vol. xiii, p. 68 Prk, R.H.: Two-retion theory of synhronous mhines: generlise metho of nlysis - Prt I, AIEE Trns., 99, 33, pp Crus, F., n Aleen, M.: Moelling n simultion of nonliner interonnete lrge-sle systems, Int. J. Moel. Simul.,,,(), pp IEE Pro.-Gener. Trnsm. Distri., Vol. 3, No., Jnury 6 79