Localisation of partial discharges sources using acoustic transducers arrays

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1 Comput Applcatons n Elctcal Engnng Vol. 4 Localsaton of patal schags soucs usng acoustc tansucs aays Flp Polak, Wojcch Skosk, Kzysztof Soła Poznań Unsty of Tchnology Poznań, ul. Potowo a, -mal: Kzysztof.Sola@put.poznan.pl Ths pap concns th ssu of th patal schag (PD) soucs locaton usng acoustc msson tansuc aays tchnqu an th hgh soluton cton of aal stmaton tchnology. In aton to th thotcal assumptons of both tchnqus, th smulaton sult, n whch an unfom lna aay (ULA) was us fo gstaton of th acoustc msson sgnals gnat by fcts n pow tansfom nsulaton systm w shown. To stmat th cton of aal (DOA) of acoustc sgnals, that popagat fom th schag-gnatng fct to th tansuc aay nstall on tansfom tank, ultpl Sgnal Classfcaton (USIC) algothm was chosn. Wth th ablty to locat multsouc schags (n at y low sgnal-tonos ato SNR), th aopt soluton has aantags o conntonal tchnqus. KEYWORDS: Patal Dschag, Sgnal Souc Localsaton, Tansuc Aay, Dcton of Aal (DOA) Estmaton, USIC. Intoucton Dfcts n hgh-oltag nsulaton systm, bng a souc of patal schags (PD), a on of th majo causs of falu of lag pow tansfoms. Issus latng to th tcton, ntfcaton an localsaton of PD soucs a cuntly th subjct of xtns sach [-6]. Th am, among oths, s lopmnt an mpomnt of th lablty of cuntly us agnostc an montong tchnqus of pow tansfoms bas on th tcton of PD phnomna, of whch th man ons a: conntonal lctcal mtho (IEC 67), lctomagntc mthos (HF/VHF/UHF), acoustc msson mtho (AE) an ssol gass analyss mtho (DGA). Authos sach focuss on fnng nw thotcal an tchnologcal solutons that woul gatly mpo th accuacy of locaton of fcts n hgh-oltag nsulaton systm. On concpt nols th us of snso aays tchnqus to stmat th cton of aal (DOA) of th sgnal popagatng fom patal schags. Th ogn of tacklng ths ssu s th fact that th popula locaton tchnqus (stana an aanc auscultatoy tchnqu an tangulaton tchnqu), n a y ffcult fl contons,.. th psnc of multpl soucs of PD, o cong nosy sgnals, os not allow to tmn th xpct accuacy of th fct n XYZ coonats. Snso aay tchnology, 7

2 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags suppot by th nwst hgh soluton DOA stmaton algothms (USIC, Root-USIC, ESPRIT, VDR tc.) s, at last thotcally, f fom awbacks an lmtatons of th afomnton conntonal tchnqus [7]. Futh pat of ths atcl scusss th thotcal bass fo th us of a lna AE tansucs aay an USIC algothm fo locatng soucs of patal schags.. Lna tansucs aay ata mol Cons a Unfom Lna Aay (ULA) consstng of ntcal, nly spac an locat along a sngl ln, masung tansucs. Th stanc btwn ajacnt tansucs s Δ, an th stanc fom th fct (sgnal souc) to th fst c of tansucs aay (lookng fom th gh s. Th sgnal gnat by th souc s fn as [8]: s cos[f ct ], () wh: α ( sgnals ampltu, f c ca fquncy, β ( phass, numb of soucs. Lt assum that ths sgnals a naowban. Ths mans that th ampltu α ( an phas β ( changs slowly wth spct to τ, whch s th wa popagaton tm btwn succss lmnts of th aay (Fg. ). Thfo: ( t ), () ( t ). Slowly ayng ampltus α ( an phass β ( nsu that as a sult of th Fou tansfom of quaton (), th majoty of th fquncy componnts n clos poxmty to th omnant fquncy f c wll b obtan. Equaton () can also b psnt as a complx nlop, o n th fom of so-call n j ( t ) Phaso: s n j f c s R s t., such as Gaussan at wht nos Small popagaton tm Souc >> D Souc - Souc - Lna an sotopc mum Souc Elmnt Elmnt - Elmnt Elmnt 8 Fg.. Scnao un consaton n th atcl

3 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags Now lt assum that a plan wa gnat by th souc achs th aay wth locty an angl θ (Fg. ). -th souc m D >> (m-) -th lmnt m-th lmnt Scon lmnt Fst lmnt Fg.. Data mol fo DOA stmaton of soucs wth a lna aay of th lmnt Th sgnal comng though stanc as fst at th tansuc closst to th souc aft tm s s. It can b wttn as: ( t ) ( t )cos[f ( t ) ( t )] j[fc ( t ) ( t ) fc ] s R ( t ). R Bcaus all th cng tansucs of th aay a locat along a sngl ln, th sgnal c by th m-th tansmtt tals, as compa to th sgnal achng th xtm ght (fs cont, a futh lngth, whch can b tmn fom th followng latonshp: m ( m ) sn, m,,..., c (). (4) Lt assum that th sgnal achs th m-th tansmtt wth lay τ m : m sn m ( m ). (5) Thfo, th sgnal gst by th m-th snso can b fn as a lay son of th sgnal s ( (co by th fst tansuc ghtmos wth an atonal lay τ m : s s ( t ) s ( t ) ( t )cos[f ( t ( t )cos[f ( t ) ( t ) ( m ) ] m m c c m R[ s m m) ], m ) ( t )] m (6) 9

4 wh 4 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags f c sn sn spatal fquncy assocat wth -th sgnal souc, gnatng sgnal at ncnc angl θ ; walngth cosponng to th ca fquncy f c. In tmnng th quaton (6) th appoxmaton () was takn nto account. In th complx fom, th abo c sgnals cospon to: j[fc ( t ) ] m) m) sm ( t ) s. (7) Equaton (7) shows that th sgnal s m (, gst by th m-th tansmtt, whch was gnat by th -th souc, s ntcal to th sgnal s ( co by th fst (xtm gh tansuc, but wth an atonal phas shft facto m-)μ. Ths facto s pnnt only on spatal fquncy μ an th poston of th aay lmnt lat to th fst lmnt. Fo ach ncnc angl θ th s a cosponng spatal fquncy μ. Thfo, th pmay goal of stmaton of th cton of aal of th sgnal, s to xtact spatal fquncy μ fom th sgnals c by th tansucs aay. It s mpotant to fulfl th conton of mnmum stanc btwn th tansucs Δ, whch shoul b lss than o qual to half th walngth λ. Now cons th stuaton wh all th sgnals s (, gnat by - soucs, an th nos n m ( c by th m-th tansmtt at th tm t, can b psnt by th followng quaton: x m s n m s m) s n m) m. n m f c m,,..., In a matx fom quaton (8) can b wttn as: s( s x( a( ) a( )... a( ) n( As( n(, (9)... s wh: x x x... x T ata column cto c by th ( aay, s s s... s T ( sgnal column cto gnat by th soucs, n n n... n T zo-man Gaussan nos. Th aay stng column cto s fn as (spatal fquncs μ a unknown): a( ) wttn n th fom of a matx (of sz ): (8) j j j ( )... T, ()

5 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags... j j j... A. () j ( ) ) j ( ).... Dcton of aal stmaton usng multpl sgnal classfcaton (USIC) algothm USIC (ultpl Sgnal Classfcaton) algothm s on of th most wly us tchnqus of hgh soluton cton of aal stmaton. It blongs to th goup of th subspac mthos an th opaton of th algothm can b bfly psnt n th followng stps: Stp : Rgst nput sgnals x( t n ), n,,..., N an mak th stmaton of th coaanc matx: N ˆ H Rxx Rxx x( tn ) x ( tn ). () N n Stp : Pfom th composton of th coaanc matx lat of th gnalus Rˆ xx V VΛ, () wh ag,,...,,... a th gnalus an V contans all th gnctos Rˆ xx. Stp : Estmat th multplcty k of th smallst gnalu λ mn an thn th numb of sgnals fom as: k. (4) Stp 4: Dtmn th USIC fquncy spctum: P P a V V a, USIC (5) H H n n wh V n = [q +,, q ] wth q l, l = +, +,..., bng th gnctos cosponng th smallst gnalu λ mn. Stp 5: Fn pck alus n P USIC (θ) fquncy spctum, whch cospon th DOAs. 4. Localsaton of PD soucs n pow tansfom tank smulaton sults Patal schags, pnng on th typ of th fct an th nsulatng systm n whch thy occu, mt AE was n w ang of fquncs ( 4

6 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags khz 6 khz). In pfom smulatons, an AE sgnal was mol as a combnaton of sn an xponntal functons: 5 ( ( )) t t,5 sn(ft ) t t t,s f 4 wh: (6) ( ( tt )),5 sn(ft ) t t t t,4s wth th fquncy f= khz. Th alu of f was ctat by th fact, that t s th omnant fquncy of sufac schags pulss (gst wth PAC WD tansuc) whch pos th gatst that to th pap-ol nsulaton systm of th tansfom [6]. In o to flct, as pcsly as possbl, ffcult masung contons palng ung actual agnostc tsts (hgh lls of nos an boaban ntfnc), Gaussan wht nos was a to th clan hamonc sgnals. Such mol sgnals w chaactz by a y low Sgnal-to-Nos Rato (SNR) (Fg. ). 5 Ampltu [V] Tm [s] x - Fg.. Exampl fgus of mol AE tm sgnals (clan - black an nosy - gay) gnat by th sufac-typ patal schags Fo cng sgnals a mathmatcal mol of Unfom Lna Aay consstng of fou snsos, wth paamts cosponng to th popula boaban pzolctc tansucs typ of PAC WD (fquncy spons: - khz; th sonant fquncs: 5 khz, khz, 8 khz, 4 khz, 5 khz, ctty: ±.5 B) was us [6]. To fulfll th conton of mnmum stanc btwn th lmnts of th aay, whch shoul b lss than, o qual to half of th walngth λ, t s assum that thy a spac at ntals of Δ = 5 mm. It shoul b mphasz that wth th ULAs t s possbl to tmn only th azmuth angl (θ). In o to stmat th cton of aal n th mnsons, t s ncssay to ha knowlg of th laton angl. Ths s possbl only though th us of at last two-mnsonal aay (.g. ccula o ctangula). Thfo, th conuct smulatons assum smplfcaton that th souc of th acoustc msson sgnal gnat by th PD s on th sam ll as th tansucs aay. As a sult of ths assumpton th Z coonat, whch s th coonat of th th mnson, was omtt (Fg. 4).

7 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags As an objct of stuy, a pow tansfom tank was mol, wth lngth x = 6 m an wth y = m. It was assum, that th pont wth coonats [,] s locat n th low lft con of th tank mol. To tmn th XY coonats of th fct, snso aay must b plac n, at last, two ffnt placs on th tank (as a sult of that, two ffnt DOAs a obtan). Intscton pont of two lns, l at sgnat angls fom th cnt of th aays, wll tmn th souc locaton. In pfom smulatons, tansucs aays w plac on th x-axs (font wall of th tansfom tank) at a stanc of two an fou mts fom th ogn [,] (Fg. 4)., m 9 θ > θ -9 y x, m 4, m 6, m Fg. 4. Schmatc mol of pow tansfom tank (top w) wth mak locatons of th tansucs aays an th angl of sgnal aal tmnng mtho Scnao aopt n th smulaton consst of two cass. In fst cas (mak as A) th AE sgnal was gnat by th souc wth coonats x=5,5 m an y=,5 m, n th scon cas (B) th sgnal souc was locat n x=,5 m an y=m (Fg. 5). a) b) c) Wth [m] A X: 5.5 Y: Wth [m] X: 5.5 Y: Wth [m] X: Y: Wth [m] B X:.5 Y: 4 6 Wth [m] X:.5 Y: 4 6 Wth [m] X:.5 Y: Fg. 5. Smulaton o PD soucs localsaton usng lna AE tansucs aay: a) locaton of smulat fcts (cas A an B), b) xampl sult fo clan sgnal (SNR ), c) xampl sult fo hghly nosy sgnal (SNR = -4 B) 4

8 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags Th sults of th smulaton show that by usng a hgh-soluton fquncy spctum stmaton algothm (USIC), th o of th locals coonats of th patal schag souc s nglgbly small. Fo hghly nosy sgnals th aag o of th localsaton was 5.5 cm along th OX axs an 5. cm along th OY axs. Fg. 6. PD souc localsaton os (n [cm]) awn n th Catsan coonat systm (th [,] pont stans fo th al fct locaton) 5. Concluson Th atcl psnts th sults of sach concnng th tmnaton of th applcablty of th acoustc msson tansucs aay an hgh-soluton algothm (USIC) fo stmatng th cton of aal to th localsaton of patal schags soucs n pow tansfoms. Th sults of smulatons suggst that nw mtho popos by th authos may b a pf altnat to th conntonal tangulaton tchnqu (spcally whn th co sgnals a hghly nosy, o fo th multsouc schags). Th nxt stag of th plann sach wll nclu th sgn an constucton of a twomnsonal tansucs aay an futh laboatoy tsts on a al mol of th tansfom tank. Rfncs [] Snaga H.H., Phung B.T., Blackbun T.R., Rcognton of sngl an multpl patal schag soucs n tansfoms bas on ulta-hgh fquncy sgnals, IET Gnaton, Tansmsson & Dstbuton, ol. 8, pp. 6-69, 4. [] Youchn Wang, Chaoj Zhu, Qaohua Wang, Zhhao Wang, Y Yn, Pocssng of patal schag ulta-hgh fquncy sgnals fom a tu sz tansfom, IEEE Intnatonal Confnc on Sol Dlctcs (ICSD), pp. -5,. 44

9 F. Polak, W. Skosk, K. Soła / Localsaton of patal schags [] Ahm.R., Gll.A., Khall A., Pow tansfom fault agnoss usng fuzzy logc tchnqu bas on ssol gas analyss, st tanan Confnc on Contol & Automaton (ED), pp ,. [4] akalous S., Tnbohln S., Fs K., Dtcton an locaton of patal schags n pow tansfoms usng acoustc an lctomagntc sgnals, IEEE Tansactons on Dlctcs an Elctcal Insulaton, ol. 5, pp , 8. [5] Skosk W., Sola K., oana H., Zomk W., Locaton of patal schag soucs n pow tansfoms bas on aanc auscultatoy tchnqu, IEEE Tansactons on Dlctcs an Elctcal Insulaton, ol. 9, pp ,. [6] Skosk W., Zomk W., Dtcton, Rcognton an Locaton of Patal Dschag Soucs Usng Acoustc Emsson tho (Chapt ), Acoustc Emsson, InTECH Publsh, ISBN ,. [7] Yan-Qng L, Qng X, Nan Wang, Xn Xang, Fang-Chng Lu, Smulaton of PD locaton n pow tansfom bas on Root ultpl Sgnal Classfcaton mtho, IEEE 9th Intnatonal Confnc on th Popts an Applcatons of Dlctc atals ICPAD 9, pp , 9. [8] Zhzhang Chn, Gopal Goka, Yqang Yu, Intoucton to Dcton-of-Aal Estmaton, Atch Hous, ISBN ,. 45

Load Equations. So let s look at a single machine connected to an infinite bus, as illustrated in Fig. 1 below.

Load Equations. So let s look at a single machine connected to an infinite bus, as illustrated in Fig. 1 below. oa Euatons Thoughout all of chapt 4, ou focus s on th machn tslf, thfo w wll only pfom a y smpl tatmnt of th ntwok n o to s a complt mol. W o that h, but alz that w wll tun to ths ssu n Chapt 9. So lt