A New Power System Oscillation Type Identification Method Based on Empirical Mode Decomposition and Hilbert Transform

Transcription

1 Proceedigs of he World Cogress o Egieerig ad Compuer Sciece 4 Vol I WCECS 4, -4 Ocober, 4, Sa Fracisco, USA A New Power Sysem Oscillaio Type Ideificaio Mehod Based o Empirical Mode Decomposiio ad Hilber Trasform Xiazhog Dai, Che She Absrac A ew mehod based o empirical mode decomposiio ad Hilber rasform o ideify power oscillaio ypes is proposed. The mehod uilizes ad amplifies he discrimiaive differece of he isaaeous ampliude chagig rules of he oscillaio. By repeaig EMD ad square calculaio aleraely imes we ca fid he damp facor has bee amplified by a facor of h power of. So he disicio degree of differe oscillaio ypes becomes more obviously. We obai he isaaeous ampliude by Hilber rasform, approximae i by wo differe expressios ad aalyze he correlaio bewee he approximae resuls ad he iiial daa. Fially, we deermie he oscillaio ypes accordig o he goodess of fi ad correlaio coefficies. The mehod is validaed i acual oscillaio icides i Chia Souher Power Grid. Idex Terms Empirical mode decomposiio, Hilber rasform, forced oscillaio, weak dampig oscillaio, oscillaio ype ideificaio P I. INTRODUCTION OWER oscillaio has become a major problem hreaeig he securiy of large-scale iercoeced power sysems []. Power oscillaio is divided io wo differe ypes accordig o differe irisic iducemes: free oscillaio (FRO) ad forced oscillaio (FOO). Free oscillaio is furher divided io posiive, zero ad egaive damp free oscillaio. Zero ad ear-zero egaive damp free oscillaio are called weak dampig oscillaio (WDO) i his paper. Forced oscillaio is furher divided io posiive, zero ad egaive damp forced oscillaio. Pracically, posiive dampig forced oscillaio is ypical forced oscillaio, so he forced oscillaio i his paper specifically refers o posiive dampig forced oscillaio. Weak dampig oscillaio is iduced by some poorly or egaively dampig geeraors []-[4]. Forced oscillaio is excied by exeral periodic disurbaces [5]-[7]. A mehod based o hybrid dyamic simulaio for disurbace source locaio is proposed i [8]. Eergy-based mehods have bee proposed o locae he sources of weak dampig oscillaio ad forced oscillaio usig wide area measureme sysem (WAMS) daa whe oscillaio occurs [9]-[]. Afer he oscillaio sources beig locaed, he key problem is o ake effecive Mauscrip received Jue 8, 4; revised July, 4. This work is suppored by he Naioal Naural Sciece Foudaio of Chia (57779, 535). The auhors are wih he Sae Key Lab of Power Sysems, Deparme of Elecrical Egieerig, Tsighua Uiversiy, Beijig 84, Chia ( daixz@mails.sighua.edu.c; sheche@sighua.edu.c). ISBN: ISSN: (Pri); ISSN: (Olie) emergecy corol acios o suppress he oscillaio. For he weak dampig oscillaio he commo corol acio is reducig he locaed geeraors oupu powers ad for he forced oscillaio ha is rippig he locaed geeraors. Obviously, he corol acios are differe for he differe oscillaio ypes. However wha he oscillaio ype is should be ideified firsly. Lieraure [] preses a secod order differeial mehod o ideify he power oscillaio properies based o he iiial period of wave. Takig he differeces i respose compoes ad heir oscillaory characerisics as crieria, a mehod for discrimiaio of free oscillaio ad forced oscillaio is proposed i [3]. The mehods proposed i [] ad [3] boh adop he damp facor of oscillaio mode as he key discrimiaive iformaio o ideify he oscillaio ypes. However i some cases he dampig facors of he oscillaio are so ear o zero ha i is hard o ideify he oscillaio ypes accuraely or righ. The mehods proposed i [] ad [3] ideifies he power oscillaio ypes based o he iiial period of wave, bu someimes iiial period of wave may be uavailable due o some reasos ad hus he mehods are ufeasible. Because oe weak (ear zero) dampig oscillaio mode ad oe posiive dampig oscillaio mode are ofe excied ad exis i he iiial period of wave a he same ime, he hypohesis i [3] ha free oscillaio have sigle oscillaio mode ad forced oscillaio have oe posiive dampig oscillaio mode ad oe weak (ear zero) dampig oscillaio mode i he iiial period of wave is o reasoable, ad hus he mehod i [3] would misakely ideify oscillaio ypes i codiios ha weak ad posiive dampig oscillaio mode are excied. Because of he dampig raio ideificaio error ad ureasoable hreshold selecig i [3], he mehod i [3] may be ivalid oo. To deal wih hese problems, his paper proposes a mehod which adops may imes of he damp facors as key discrimiaive iformaio o improve discrimiaio ad does o use he iiial period of wave ad ay hreshold o ideify he oscillaio ypes. The paper is orgaized as follows. Secio II iroduces he mahemaical ools used i he proposed mehod o ideify power oscillaio ypes i his paper. These ools icludes Empirical Mode Decomposiio (EMD), Hilber Trasform (HT) ad Correlaio Aalysis (CA). Secio III proposes a mehod o ideify power oscillaio ype i power sysems usig WAMS daa. The mehod is furher developed o a sysemic implemeaio process for pracical applicabiliy. Secio V preses es resuls i a simple es o WCECS 4

2 Proceedigs of he World Cogress o Egieerig ad Compuer Sciece 4 Vol I WCECS 4, -4 Ocober, 4, Sa Fracisco, USA illusrae he disribuio of he mehod ad es resuls i acual oscillaio icides o demosrae he validiy of he mehod. Secio VI is he coclusios. II. MATHEMATICAL TOOLS A. Empirical Mode Decomposiio The empirical mode decomposiio assumes ha ay daa cosiss of differe simple irisic modes of oscillaio. Adopig he sifig process i [4], EMD decomposes he sample daa io -irisic mode fucios (IMF) ad a residue which ca be eiher he mea red or a cosa. The decomposiio fially obais x() ci () r() () i Where x() is he sample daa, ci () is ih irisic mode fucio ad r () is he residue. If he sample daa icludes several oscillaio modes, he IMF resuls are physically meaigful: ih IMF is correspodig o he ih oscillaio mode. Thus we ca use EMD elimiaes he red ad decompose he modes apar. Fially, we ge a sigle mode i x ()= Ae si( ) () i i i I he mehod illusraed i secio III, we use EMD o ge oscillaio modes. EMD is repeaedly used o ge he oscillaio compoe of he daa processed by he mehod i secio III. B. Hilber Trasform Hilber rasform (HT) of x() is defied as [4] x( ) xˆ( ) x d (3) Wih he Hilber rasform, he aalyic sigal is defied as z () x () jx ˆ() Ae () i () (4) The isaaeous ampliude of x() is calculaed by A () x () x ˆ() (5) The Hilber rasform is used o ge he isaaeous ampliude of he oscillaio modes ad he isaaeous ampliude of he oscillaio compoe of he daa processed by he mehod i secio III. C. Correlaio Aalysis Correlaio aalysis of wo daa series ca describe heir similariy. Correlaio coefficie of daa series x ad y is defied as [5] Where R ( x x)( y y) i i i ( xi x) ( yi y) i i xi i (6) x (7) yi i y (8) Where xi is he ih sample poi of daa series x ad y i is he ih sample poi of daa series y. The value rage of R is bewee - ad +. The more R is close o, he correlaio is more srog bewee x ad y. Plus sig ad mius sig before R idicae posiive ad egaive correlaio respecively. Zero value of R meas x ad y are idepede. We uilize correlaio coefficie o deermie he similariy bewee isaaeous ampliude ad is fiig equaio i he proposed mehod o ideify power sysem oscillaio ypes i secio III. III. PRACTICAL METHOD FOR OSCILLATION TYPE IDENTIFICATION A. Theory of he Mehod If he sysem have weak dampig mode, some small disurbace will excie he oscillaio mode easily, ad he sysem operaors should ake measures o improve he dampig. So before he forced oscillaio happes he dampig is ofe good. So oly he weak dampig oscillaio ad posiive dampig forced oscillaio are cosidered i oscillaio ype ideificaio i his paper. Power sysem oscillaio is always icludig muli-modes as i (9). Bu usually oly oe mai mode whose dampig is weakes amog he modes excied domiaes he oscillaio. Afer he aeuaio of posiive dampig oscillaio modes, oly he weak dampig mode or he forced respose called mai oscillaio mode remais. For free oscillaio he mai mode has form as () ad for forced oscillaio ha has form as (). The ampliude of () chages expoeially wih cerai direcioal red. The ampliude of () keeps cosa i ideal codiio or flucuaio ear a cosa i ideal codiio cosiderig oises, ayway i chages wihou ay direcioal red. i x () Ae i si( i i) (9) i x () Ae si( ) () ISBN: ISSN: (Pri); ISSN: (Olie) WCECS 4

3 Proceedigs of he World Cogress o Egieerig ad Compuer Sciece 4 Vol I WCECS 4, -4 Ocober, 4, Sa Fracisco, USA x () Asi( ) () We ied o choose he iformaio wheher he ampliude chages wih cerai direcioal red as key discrimiaive differece o ideify he oscillaio ypes. Bu he differece exisig i he raw oscillaio daa for he wo ype oscillaio is so small ha i cao be used direcly o ideify he oscillaio ypes accuraely. So we propose a ew mehod illusraed as followig o amplify he differece by aleraely usig EMD ad square calculaio o process he raw oscillaio daa. We ca decompose oscillaio daa io -irisic mode fucios (IMF) ad a residue ad he exrac he isaaeous ampliude of every IMF by Hilber rasform. Choose he IMF whose isaaeous ampliude is he bigges as he mai oscillaio mode ad he ormalize i by dividig i by is isaaeous ampliude a =. For weak dampig oscillaio, he mai oscillaio mode c () m has form Square obai c () m c () e si( ) () m ad muliply he resul by wo, he we ( c ( )) m e ( cos( )) (3) Absrac oscillaio compoe from (3) by MED ad he we obai x (,) e cos( ) (4) Repeaig square calculaio i (3) ad EMD i (4) aleraely imes, fially we obai (, ) ( ) cos( ) x e (5) The isaaeous ampliude of oscillaio daa processed i (5) is A() e (6) The dampig facor ad oscillaio frequecy of oscillaio have bee amplified by a facor of h power of. The expoeially direcioal chagig red of he isaaeous ampliude of oscillaio has also bee amplified ad has become eve seeper. For forced oscillaio, he mai oscillaio mode c m() has form c () si( ) (7) m Repeaig square calculaio ad EMD aleraely imes, fially we obai x (, ) ( ) cos( ) (8) The isaaeous ampliude of oscillaio daa processed i (8) is A () (9) The oscillaio frequecy of oscillaio has also bee amplified by a facor of h power of. Bu isaaeous ampliude of oscillaio keeps cosa o havig ay cerai direcioal chagig red because he dampig facor is zero i (7). The above aalysis resuls are obaied i he ideal codiios. Facually, he pracical oscillaio daa coais disurbaces or oises. Thakfully, he disurbaces or oises are geerally irregular ad odirecive, herefor hey will o impac he direcioal chagig characerisic of he isaaeous ampliude of he oscillaio. So i he acual codiios, (6) ad (9) have he geeral forms respecively as () ad () b A() ae c () A() asib c () We ca use he differece i he geeral form of isaaeous ampliude of he oscillaio processed o deermie he oscillaio ype. Firs, exrac he isaaeous ampliude of (5) for weak dampig oscillaio or (8) for forced oscillaio ad fi i by expressio () ad () respecively, fially we ge he curve fiig resul A () ad he goodess of fi: sum of squares due o error (SSE), roo mea squared error (RMSE) ad coefficie of deermiaio (CD). Secod, calculae he correlaio coefficie R bewee isaaeous ampliude ad is fiig expressios () ad (). Third, if SSE ad RMSE for fiig expressio () are smaller ha ha for fiig expressio () ad meawhile CD ad R for fiig expressio () is bigger ha ha for fiig expressio (), we kow ha fiig expressio () is more similar o isaaeous ampliude ad ca coclude ha he oscillaio ype is weak dampig oscillaio. If SSE ad RMSE for fiig expressio () are bigger ha ha for fiig expressio () ad meawhile CD ad R for fiig expressio () is smaller ha ha for fiig expressio (), we kow ha fiig expressio () is more similar o isaaeous ampliude ad ca coclude ha he oscillaio ype is forced oscillaio. Whe he pracical oscillaio icides occur, sysem operaors would ake acios o resrai he oscillaio which may chage he oscillaio modes or forced disurbaces, ad hus he oscillaig curve would o have he geeral form as () havig a fixed mode or () havig coiuous forced disurbace. Before he oscillaig curve decayig obviously, hese chages abou oscillaio modes or forced disurbaces are so lile ha he exisig oscillaio did chage is propery ad we ca use he oscillaig curve o ideify he oscillaio ypes. ISBN: ISSN: (Pri); ISSN: (Olie) WCECS 4

4 Proceedigs of he World Cogress o Egieerig ad Compuer Sciece 4 Vol I WCECS 4, -4 Ocober, 4, Sa Fracisco, USA B. Deermiaio of Repeaig Times Afer repeaig EMD ad square calculaio aleraely imes, accordig Shao heorem we have f o fs () Where f o is he oscillaio frequecy, ad f s is he sample frequecy. Ad he he maximum of saisfies log f log f (3) max s The PMU daa samplig frequecy is Hz ad he oscillaio frequecy i power sysem is.~.5hz. So i pracical applicaio we choose =5 i secio IV. C. Sysemic Implemeaio Process of he Mehod Acive power has high measureme accuracy ad good observabiliy for elecromechaical oscillaio. We choose acive power of geeraors o ideify oscillaio ypes. The sample daa coais oises herefor we eed filerig processig. The oscillaio has muli-modes herefor we eed separae mai oscillaio mode from sample daa by EMD. The aim of ideifyig he oscillaio ype is o ake righ acio o elimiae he oscillaio, so we also eed locae he oscillaio source i advace. The sysemic implemeaio process of he mehod proposed above is as followig. ) Locae he oscillaio sources usig he mehod i [] ad choose hese geeraors acive power as ipu daa for oscillaio ype ideificaio. The ipu daa are wrie as x(). ) Filer x() by bad-pass filer o elimiae he oises ad he compoes beyod he frequecy rage of he elecromechaical oscillaio. The we obai x (). 3) Absrac all IMFs from x () by EMD. Exrac he isaaeous ampliude Ai () of ci () by Hilber rasformaio for i from o m. Choose ci () whose Ai () is he bigges as he mai oscillaio mode c () m whose isaaeous ampliude is Am (). Normalize cm() o c (, ) m j by dividig cm() by A m(), j, 4) Calculae ( cm(, j )) ad absrac is oscillaio compoe cm (, j +), j j 5) Repea 4) imes, he we ge (, ) cm. Here c (, ) m deoes simply as y(, ). 6) Exrac he isaaeous ampliude A() of y (, ) by Hilber rasformaio. Fi A () usig expressio as () ad () ad he we ge fiig resuls Ae () ad Al () respecively. A he same ime we obai he o goodess of fi: SSE, RMSE ad CD. Calculae he correlaio coefficie R bewee A () ad he fiig resuls. 7) Ideify he oscillaio ype usig he goodess of fi ad he correlaio coefficies. IV. TEST RESULTS A. Simple es The free oscillaio i (4) has oe posiive dampig oscillaio mode ad oe weak dampig oscillaio mode. x Ae si( ) Ae si( ) (4) free The forced oscillaio i (5) is posiive dampig forced oscillaio. x Ae si( ) A si( ) (5) forced Where A = A =,.8,.4, fs. Hz, rad/s. The iiial oscillaio curves are showed i Fig.. Afer sysemic implemeaio process of he mehod he isaaeous ampliude of processed free ad forced oscillaio are showed i Fig.. x forced x free ime/s Fig. Oscillaig curves of free oscillaio ad forced oscillaio Ampliude Forced oscillaio Weak damp oscillaio ime/s Fig. Isaaeous ampliude of processed free ad forced oscillaio The free oscillaio i (4) would be misakely ideified as forced oscillaio by he mehod i [3] which assume ha free oscillaio has oe weak dampig oscillaio mode ad forced oscillaio has oe posiive dampig oscillaio mode ad oe weak (ear zero) damp oscillaio mode i he iiial period of wave. The isaaeous ampliude of processed ISBN: ISSN: (Pri); ISSN: (Olie) WCECS 4

5 Proceedigs of he World Cogress o Egieerig ad Compuer Sciece 4 Vol I WCECS 4, -4 Ocober, 4, Sa Fracisco, USA free oscillaio has direcioal chagig red, bu he isaaeous ampliude of processed forced oscillaio does have direcioal chagig red. So he oscillaio ypes of oscillaio i (4) ad (5) ca be ideified exacly by he mehod proposed i his paper. So he mehod i his paper ca overcome he shorcomig of he mehod i [3]. B. Acual icides Cosider wo pracical oscillaio icides i Chia Souher Power Grid. Oscillaio i Pig Ba ad Fa Er is showed i Fig.3 ad Fig.5 respecively. Daa bewee wo verical lies i Fig. ad Fig.3 is chose as he ipu daa. Employig he sysemic implemeaio process i secio III, we ge fiig coefficies ad goodess, correlaio coefficies ad oscillaio ype ideificaio resuls showed i Table I. The curves of isaaeous ampliude ad is fiig resuls are showed i Fig.4 ad Fig.6. I Pig Ba oscillaio, SSE ad RMSE uder () are smaller ha ha uder (), ad meawhile CD ad R uder () are bigger ha ha uder (), herefor we cosider he oscillaio as.6.4 weak dampig oscillaio. I Fa Er oscillaio, SSE ad RMSE uder () are bigger ha ha uder (), ad meawhile CD ad R uder () are smaller ha ha uder (), herefor we cosider he oscillaio as forced oscillaio. I order o improve he ideificaio accuracy, we choose daa i differe ime rages as ipu daa ad employ he sysemic implemeaio process i secio III. The ideificaio resuls for every sigle daa rage are showed i Table II. Ad we coduc saisical aalysis for he ideificaio resuls. The oscillaio ype whose umber is more ha 5% of he oal ime rage umber for every oscillaio icide is he ype ideified a las. Oscillaio ypes ideified by he proposed mehod are cosise wih he pos-faul offlie aalysis resuls [6]-[7]. I Fa Er pla oscillaio, he iiial period of wave is uavailable, so he mehod i []-[3] cao be used o ideify he oscillaio ype. Bu he mehod proposed i his paper ideified he oscillaio ype accuraely P/p.u P/p.u Uavailable Fig. 3 Acive power oscillaio of G i Pig Ba Fig. 5 Acive power oscillaio of G4 i Fa Er Ampliude/p.u A A e A l Aampliude/p.u A A e A l Fig. 4 Isaaeous ampliude of processed acive power of G i Pig Ba Fig. 6 Isaaeous ampliude of processed acive power of G4 i Fa Er TABLE I FITTING COEFFICIENTS AND GOODNESS, CORRELATION COEFFICIENTS AND OSCILLATION TYPE IDENTIFICATION RESULTS Pla Expressio a b c SSE RMSE CD R Oscillaio Type Ideified Pig Ba Fa Er b ae c asib c b ae c asib c.73e Weak dampig Oscillaio Forced Oscillaio ISBN: ISSN: (Pri); ISSN: (Olie) WCECS 4

6 Proceedigs of he World Cogress o Egieerig ad Compuer Sciece 4 Vol I WCECS 4, -4 Ocober, 4, Sa Fracisco, USA TABLE II OSCILLATION TYPE IDENTIFICATION RESULTS IN DIFFERENT TIME RANGES Pla Sar Time (s) Ed Time (s) Oscillaio Type Ideified Saisics Oscillaio Type Ideified a Las 7 8 Weak dampig Oscillaio 8 9 Forced Oscillaio 9 Weak dampig Oscillaio Pig Ba Fa Er Weak dampig Oscillaio Weak dampig Oscillaio 3 Weak dampig Oscillaio 3 4 Weak dampig Oscillaio 4 5 Weak dampig Oscillaio Forced Oscillaio 38 4 Forced Oscillaio 4 4 Forced Oscillaio 4 44 Forced Oscillaio Forced Oscillaio Weak dampig Oscillaio 48 5 Forced Oscillaio 5 5 Forced Oscillaio 88% WDO Weak dampig Oscillaio 88% FOO Forced Oscillaio V. CONCLUSION The isaaeous ampliude of weak dampig oscillaio has cerai direcioal red bu ha of forced oscillaio does o have. We grasp ad amplify his discrimiaive differece o ideify oscillaio ypes by a mehod based o EMD ad HT. I his mehod, repeaig EMD ad square calculaio aleraely imes, he damp facor has bee amplified by a facor of h power of. Ad he here come wo differe resuls: direcioal chagig red of he ampliude of weak dampig oscillaio becomes more obviously bu he ampliude i forced oscillaio keeps cosa or flucuaes aroud a cosa o havig ay direcioal chagig red. We acquire he isaaeous ampliude of oscillaio ad use wo differe expressios o approximae i ad aalyze he correlaio bewee he fiig resuls ad i. Fially, we deermie he oscillaio ypes accordig o he goodess of fi ad correlaio coefficies. We use a simple es o illusrae he advaage of he mehod. The mehod is validaed i acual oscillaio icides. The mehod uilizes WAMS daa ad has he poeial for olie applicaio. REFERENCES [] E. Grebe, J. Kabouris, S. Lopez Barba, ad W. Saiger e al., Low frequecy oscillaios i he iercoeced sysem of coieal Europe, IEEE PES GM, Mieapolis,. [] F.P. Demello ad C. Cocordia, Coceps of sychroous machie sabiliy as affeced by exciaio corol, IEEE Tras. Power App. Sys., vol. PAS-88, o. 4, pp , Apr [3] R. T. H. Alde ad A. A. Shalou, Aalysis of dampig ad sychroous orques: Par I a geeral calculaio mehod, IEEE Tras. Power App. Sys., vol. PAS-98, o. 5, pp , Sep./Oc [4] R. T. H. Alde ad A. A. Shalou, Aalysis of dampig ad sychroous orques: Par II effec of operaio codiios ad machie parameers, IEEE Tras. Power App. Sys., vol. PAS-98, o. 5, pp.7 77, Sep. /Oc [5] M. A. Magdy, ad F. Coowar, Frequecy domai aalysis of power sysem forced oscillaios, Proc. Is. Elec. Eg., Ge., Trasm., Disrib, vo.37, pp. 6-68, 99. [6] C. D. Vouras, N. Krassas, ad B. C. Papadias, Aalysis of forced oscillaios i a muli-machie power sysem, i Proc. 4h I. Cof. Corol, 99, pp [7] N. Rosamkolai, R. J. Piwko, ad A. S. Mausik, Evaluaio of he impac of a large cyclic load o he LILCO power sysem usig ime simulaio ad frequecy domai echiques, IEEE Tras. Power Sys., vol. 9, o. 3, pp. 4-46, 994 [8] J. Ma, P. Zhag, ad H. J. Fu, e al., Applicaio of phasor measureme ui o locaig disurbace source for low-frequecy oscillaio, IEEE Tras. Smar Grid, vol., o. 3, pp , Dec.. [9] L. Che, Y. Mi, ad W. Hu, A eergy-based mehod for locaio of power sysem oscillaio source, IEEE Tras. Power Sys., vol. 8, o., pp , May. 3. [] Y. Li, C. She ad F. Liu, A eergy-based mehodology for locaig he source of forced oscillaios i power sysems, i Proc. 8h Powerco, Aucklad, New Zealad, Oc,, pp. 6. [] Y. Li, C. She ad F. Liu, A mehodology for power sysem oscillaio aalysis based o eergy srucure, Auomaio of Elecrical Power, vol. 37, o. 3, pp , 3, i Chiese. [] Y. Li, W.S. Jia ad W.F. Li, Olie ideificaio of power oscillaio properies based o he iiial period of wave, Proc. CSEE, vol.33, o.5, pp.54-6, 3, i Chiese. [3] H. Ye, Y.B. Sog ad Y.T. Liu, Forced power oscillaio respose aalysis ad oscillaio ype discrimiaio, Proc. CSEE, vol.33, o.34, pp.97-4, 3, i Chiese. [4] N.E. Huag ad S.S. She, Hilber-Huag rasform ad is applicaios. Sigapore: World Scieific Press, 5. [5] W.J. Coover, Pracical oparameric saisics. US: Joh Wiley & Sos, 98. [6] L. Che, Y. Mi ad W. Hu, Low frequecy oscillaio aalysis ad oscillaio source locaio based o oscillaio eergy par wo mehod for oscillaio source locaio ad case sudies, Auomaio of Elecric Power, vol. 36, o. 4, pp. -5,7,, i Chiese. [7] Y. Yua, Y.Z. Su ad L. Cheg, Power sysem low frequecy oscillaio moiorig ad aalysis based o muli-sigal olie ideificaio, Sci. Chia Tech. Sci., vol. 4, o., pp ,, i Chiese. ISBN: ISSN: (Pri); ISSN: (Olie) WCECS 4