Radio Location of Partial Discharge Sources: A Support Vector Regression Approach

Transcription

1 Ioryase, E T ad Tachtatzs, C ad Lazards, P ad Glover, I A ad Atso, R C (07) Rado locato of partal dscharge sources : a support vector regresso approach IET Scece, Measuremet ad Techology ISSN 75-88, Ths verso s avalable at Strathprts s desged to allow users to access the research output of the Uversty of Strathclyde Uless otherwse explctly stated o the mauscrpt, Copyrght ad Moral Rghts for the papers o ths ste are retaed by the dvdual authors ad/or other copyrght owers Please chec the mauscrpt for detals of ay other lceces that may have bee appled You may ot egage further dstrbuto of the materal for ay proftmag actvtes or ay commercal ga You may freely dstrbute both the url ( ad the cotet of ths paper for research or prvate study, educatoal, or ot-for-proft purposes wthout pror permsso or charge Ay correspodece cocerg ths servce should be set to the Strathprts admstrator: strathprts@strathacu The Strathprts sttutoal repostory ( s a dgtal archve of Uversty of Strathclyde research outputs It has bee developed to dssemate ope access research outputs, expose data about those outputs, ad eable the maagemet ad persstet access to Strathclyde's tellectual output

2 Rado Locato of Partal Dscharge Sources: A Support Vector Regresso Approach E T Ioryase, C Tachtatzs, P Lazards, I A Glover, R C Atso Departmet of Electroc ad Electrcal Egeerg, Uversty of Strathclyde, Royal College Buldg, 04 George Street, Glasgow, G XW, UK Departmet of Egeerg ad Techology, Uversty of Huddersfeld, HD 3DH, Huddersfeld, UK ephramoryase@strathacu Abstract: Partal dscharge (PD) ca provde a useful forewarg of asset falure electrcty substatos A sgfcat proporto of assets are susceptble to PD due to cpet weaess ther delectrcs Ths paper exames a low cost approach for uterrupted motorg of PD usg a etwor of expesve rado sesors to sample the spatal patters of PD receved sgal stregth Mache learg techques are proposed for localsato of PD sources Specfcally, two models based o Support Vector Maches (SVMs) are developed: Support Vector Regresso (SVR) ad Least-Squares Support Vector Regresso (LSSVR) These models costruct a explct regresso surface a hgh dmesoal feature space for fucto estmato Ther performace s compared to that of artfcal eural etwor (ANN) models The results show that both SVR ad LSSVR methods are superor to ANNs accuracy LSSVR approach s partcularly recommeded as practcal alteratve for PD source localsato due to t low complexty Itroducto Electrcal substato assets such as trasformers are ow to be susceptble to partal dscharge (PD) PD occurs whe a electrcal dscharge partally brdges the delectrc betwee coductors; t teds to be hghly focused where electrc feld stregth s greater tha the breadow stregth of the sulator Example locatos of local defects clude ar pocets sold sulato, gas bubbles or partcles lqud sulato [] [] [3] Regardless of the uderlyg cause, PD s dcatve of degraded sulato The dscharges themselves further deterorate the qualty of the sulato thereby gvg rse to a vcous crcle of atrophy utl falure [4] Isttutg a motorg process permts PD actvty to be detected at a early stage ad proactve mateace ca be employed to avod catastrophc falure of assets Thus, uplaed outages ad expesve repar costs ca be sgfcatly amelorated The occurrece of partal dscharge ca be determed usg protecto equpmet that motors chages the electrc curret [5] The dscharges also produce acoustc emssos [6] [7]; cosequetly, ultrasoc detectors have bee used to determe ther locato Ths s partcularly useful small door stallatos Aother approach s to motor the rado spectrum for RF pulses emtted by the dscharges [8] [9]; the method s more suted to larger trasmsso substatos I recet past, effort towards accurate PD localzato has bee reported Hou proposed a PD locato method based o L-shaped array [], whch composed of four UHF omdrectoal ateas I [4] ad [0], remote radometrc techology was used to locate PD source twodmeso (-D) I [] ad [], tme delay method based o eergy accumulato was employed to estmate the locato of a PD source three dmeso (3-D) The setup composed of four omdrectoal mcro-strp ateas ad four omdrectoal dscrete ds-coe ateas [3] used four omdrectoal ateas to capture the UHF sgals radated by PD ad the prcple of sgal tme delay estmate based o hgh order statstcs to locate PD sources I [8], omdrectoal ad drectoal ateas were both used to locate PD source ar-sulated substato The tme-delay was computed usg the cross-correlato algorthm based o wave-frot A vehcle, such as a va, furshed wth the ecessary equpmet ca be tae perodcally to substatos to motor for the presece of dscharge [4] [5] I prevous wors, radolocato-based approaches for localsato of PD sources used Tme Dfferece of Arrval (TDoA)/Tme Delay Estmato (TDE) ad Drecto of Arrval (DoA) [6] [7] [8] [9] of the RF sgal as the basc prcples However, tme based methods requre accurate temporal sychrosato, mag t expesve ad complex, ad hece too costly to deploy for cotuous motorg of PD The DoA method s also complex, requrg drectoal atea array Cosequetly, alteratve soluto to etwor relatvely low-cost sesors for cotuous motorg a etre substato are of practcal terest ad are beg explored The cost/complexty of other approaches prompts a vestgato to methods based solely o the use of Receved Sgal Stregth (RSS) measuremets due to ther smplcty, low-power cosumpto ad cost effectveess Theoretcal RSS-based methods requre owledge of the uderlyg rado propagato evromet (eg path loss) such that a sutable propagato model that defes the relatoshp betwee RSS ad dstace to a atea ca be bult It s ot approprate to use a ready-made propagato model due to multpath problem that ofte characterse the real-lfe rado evromets whch PD s expereced Alteratve methods based o rado fgerprtg preset themselves [0] [] These cosst of detfyg rado sgatures (fger prts) from dscharges at ow locatos,

3 ad sophstcated mache learg algorthms ca be used to estmate the locato of true dscharge Fgerprtg ofte volve a resource tesve survey stage where a ew rado map (of sgatures) s eeded each tme a chage occur the propagato evromet order to mata the eeded accuracy I ths wor we suggest a low-cost Wreless Sesor Networ (WSN) approach where the etwor tself bulds the spatal RSS map of sgatures autoomously ad cotually Wth ths approach PD motorg system ca be permaetly deployed ad thus motor the substato real-tme at low cost wthout terrupto The ey challege of the above descrbed PD localsato procedure s how to effectvely ad effcetly model RSS/locato relato ad hece derve PD locato from RSS The complexty of ths verse problem motvates the use of flexble models based o mache learg Ths approach ot oly obvate the eed for a propagato model but ca also mprove localsato precso The rest of ths paper s orgazed as follows Secto presets the statemet of the problem I secto 3, a descrpto of the PD localsato learg algorthms s preseted The expermetal set up ad data preparato procedure are addressed secto 4 The expermetal results are dscussed secto 5 Fally, the cocludg remars are stated secto 6 Problem Statemet Ths low-cost approach s based o the deploymet of wreless sesors at arbtrary but ow locatos the substato compoud; these sesors ca record rado emsso from PD sources real-tme The locatos of these sources ca be ferred by sophstcated algorthms Due to the topography of assets a substato, PD localsato ths settg ca be regarded as a dmesoal problem The compoud s modelled as a fte locato space L = l,, l } of dscrete locatos where { x y l = ( l, l ) represets the D coordate of a PD source physcal space I ths paper we explot the mathematcal relatoshp betwee PD locato ad sgal atteuato to estmate a fucto whch provdes PD source locato l = ( l x, l y modelled as; ) l f ( r) + e( r) from measured sgal stregth Ths ca be = () where r Î R s the vector cotag the RSS from M ow locatos captured by Q ateas, f = Q R M L ad e accouts for the ose Each of the sesors tae a tur at emttg a rado pulse, whch s motored by the others Gve that they are at ow locatos, ths permts a database of to be bult whch mplctly characterses the rado evromet of the substato The database s defed as D = { D,, D M } wth D = r, l ) where r = r, r ] are the RSS m ( m m m [ Q m m measuremet from the Q ateas at locato m The trasmsso power of a true PD source s depedet o a l great may factors ad caot be ow a pror, furthermore, t creases severty over tme Therefore, the rato of RSS compoets betwee pars of sesor odes s preferred to absolute values of RSS our model It s assumed that for ay par of PD sources close the physcal locato space, ther RSS, hece RSS rato vectors should be smlar compare to sources far away Ths assumpto s based o the fact that these locatos may have relatvely smlar propagato chaels ad may exhbt comparable RF characterstcs Suppose r = r,, r ] ad r = r,, r ] are the sgal [ Q j [ j jq stregth vectors from locatos l ad j small, the r r - j should also be small l If l - l j s The ey challege s to develop a model that ca determe as accurate as possble the plaar locato of PD sources based o the locato data at low cost Both the recevg sesor odes ad the PD sources are made statoary durg measuremet 3 Modellg ANN ad SVM for PD Locato 3 Artfcal Neural Networ The artfcal eural etwor (ANN) [] approach for PD localsato s regarded as a fucto approxmato problem cosstg of a olear mappg of the PD sgal stregth put oto dual output varables represetg the locato coordates of the PD source I ths wor, two varats of ANN; the multlayer perceptro (MLP) [3] [4] ad the radal bass fucto eural etwor (RBFN) [5] [6] models are adopted for PD localzato 3 PD Localsato Based o Multlayer Perceptro The MLP etwor cossts of a put layer, hdde layer(s) ad a output layer A MLP wth a sgle hdde layer ca be represeted graphcally as show Fg A sgmodal actvato fucto s used the hdde layer to provde robustess agast outlers ad a lear actvato fucto the put ad output layers The MLP-type ANN s based o the bac propagato [4] trag of error estmate It s geerally a teratve o-lear optmsato techque I ths study, the MLP approach has bee processed two phases: a trag phase ad locato estmato phase Durg the trag phase, the MLP etwor s traed to form a set of fgerprts as a fucto of PD locato Iput vector Iput layer Hdde layer Fg MLP Archtecture Output layer Output

4 x, y Trag phase SSR, SSR SSR3, Database ANN Trag error ' SSR, SSR, SSR ' ' 3 Real-tme measuremets Traed ANN Estmato phase X, Y Estmated PD locato Fg MLP model for PD localsato A set of trag examples (fgerprt (RSS) ad ther correspodg locatos) s appled to the etwor to lear the relato betwee fgerprts ad ther locatos Ths volves tug the values of the weghts ad bases of the etwor to optmse etwor performace The batch mode trag s mplemeted ths wor All the puts the trag set are appled to the etwor before weghts are adjusted to mmse the error betwee the etwor output ad the desred output The MLP model developed for PD localsato s as show Fg Durg the estmato phase, the PD sgal stregth values from uow locatos are appled to the put of the traed etwor to gve output correspodg to the PD locato To develop a approprate MLP model for PD localsato, cross valdato s used to determe a sutable etwor structure terms of umber of hdde euros The avalable trag data s radomly parttoed to dsjoted sets The etwor s traed for each set of parameters, o all the subsets except for oe ad the valdato error s measured o the subset left out The procedure s repeated for a total of trals, each tme usg a dfferet subset for valdato The average of MSE uder valdato represet the performace of the etwor Ths process s repeated for dfferet etwor archtecture terms of umber of hdde euros The 3-4- etwor model wth 3 puts odes, 4 hdde euros ad outputs odes has the best performace ad s adopted ths wor I order to mprove the geeralsato of the model (that s model s ablty to do well o usee data rather tha just trag set) ad avod overfttg, Bayesa regularsato [3] s used to tra the etwor 3 Radal Bass Fucto Networ Method I geeral, Radal Bass Fucto (RBF) etwors are ANNs that have sgle hdde layer wth olear radal bass fucto I ths wor, the RBF etwor archtecture used for PD localsato cosst of three puts, correspodg to the RSS measuremet data from the three sesors, a hdde layer ad a output layer wth two euros, represetg PD locato coordates ( x, y) The structure of a fully coected PD localsato RBF etwor s as show Fg 3 A radal bass type actvato fucto (Gaussa fucto) s used for euros the hdde layer ad a lear actvato fucto for the output layer The fully coected RBF etwor s used to approxmate f = Q R M L, a mappg of PD RSS fgerprts oto PD locatos the physcal space Fg 3 RBFN PD localsato model The RBF etwor cosst of two phases: a learg phase ad a estmato phase I the learg phase, the RBF etwor s traed to form a set of RSS fgerprts as a fucto of PD locato Each fgerprt s appled to the put of the etwor ad correspods to the measured RSSlocato data The weghts betwee the hdde layer ad the output layer are teratvely adjusted to mmse locato error I the real-tme estmato phase, measured PD RSS s appled to the put of the RBF etwor (actg as a patter matchg algorthm) The output of the RBF etwor whch s the weghted sum of the radal bass fucto s the PD locato estmate Gve a PD fgerprt r (RSS), the estmated locato lˆ gve by the weghted sum of Gaussa bass fucto [5] s j l ( r ) = f ( r ) = H ˆ () = b w u( r - h Where ( r - h ) = exp( - r - ) s the Gaussa h radal bass fucto H s the umber of euros (bass fuctos) the hdde layer whch correspod to the umber of trag samples, h s the 3-dmesoal ceter for hdde layer euro, ad ) w are the -dmesoal weghts for the lear output layer b s the spread or wdth of the Gaussa fucto For mproved performace, the ormalzed bass fucto ca be used the model The weghts ca be determed order to optmze the model Each fgerprt defes the ceter of a euro ad the wdth b s obtaed va cross valdato Thus, formg the followg set of equatos; l = H = w u( r( l, m) - h ), =,, L, m =, M (3) Ths system of lear equatos ca be wrtte matrx form as Uw = d ad the weghts are easly obtaed by - w = U d U = { u( r - h ) ( j, ),, R} ad j = u ( ) s the ormalsed Gaussa bass fucto The computed weghts are the used durg the estmato phase to locate PD RBF etwors suffer from hgh memory requremets sce all referece fgerprts are used as ceters for the bass fuctos ad requred for localsato 3

5 3 Support Vector Mache Support Vector Maches (SVM) [3] [7] [8] are erelbased learg techques applcable to both classfcato ad regresso problems SVMs are based o the dea of mappg the orgal put data pot to a hgh dmesoal feature space where a separatg hyper-plae ca be easly detfed SVMs have show tremedous success applcatos such as data classfcato, tme seres predcto, detfcato systems ad data clusterg [8] [9] [30] [3] [3] I the cotext of PD localsato, SVM s formulated as a regresso tas, whch cosst of trag a model that defes the o-lear mappg fucto betwee the PD RSS ad ts geo-spatal locato hgh dmesoal feature space, leadg to Support Vector Regresso (SVR) [33] [34] [35] 3 Support Vector Regresso: 3! Basc theory of SVR Support vector regresso techque s a learg procedure based o statstcal learg theory whch employs structural rs mmsato prcples [33] SVR uses trag data to buld ts predcto model Ths method ca solve both lear ad olear regresso problems If the trag samples are olear, SVR maps the samples to a hghdmesoal feature space by a olear mappg fucto, where samples become learly separable ad the optmal regresso surface s costructed [36] Suppose we are gve trag dataset D = r, l )} wth r Î R ad l = L f R L {(, the goal of SVR s to fd the mappg = ad mae f ( r ) ~ l, where r s put feature vector For olear problem, the trag patters are pre-processed by a map to some feature space before SVR s appled SVR fds the best or optmal regresso surface f (r) wth a devato e as the predcto model, leadg to epslo-svr [37] The model ca be expressed as f ( r) = áw, rñ + b, wîâ, b ÎÂ (4) Where, deotes the dot-product ad w ad b are the support vector weght ad bas respectvely A small w s desred to get a optmal regresso surface Ths ca be acheved by solvg the followg optmsato problem wth the trag data D = [ R, L] : m w ìl - w, r - b e subject to í î w, r + b - l e Where w, w (5) w = The problem (5) mght be restrctve by boudg the rage of errors of the trag data wth e Thus, to deal wth otherwse feasble costrats, troduce slac varables x x for each pot, The slac varables allow errors to exst up to the value of x ad x wthout degradg performace Wth slac varables the problem becomes [38]: m subject to w ìl í î - w, r + C( x + x ) = w, r - b + b - l x, x e + x e + x ³ 0 Where C s the box costrat, a postve umerc value that cotrols the pealty mposed o data pots that le outsde the e marg ad helps to prevet overfttg (regularsato) To solve the problem (6), a stadard dualsato method wth Lagrage multplers a a ca I PD localsato problem, sesors are deployed at arbtrary but ow locatos a two-dmesoal substato compoud; these sesors record rado emsso from PD sources real-tme ad estmate the locato of the PD The compoud s dvded to a x squared grd Each grd pot represeted by x-y coordate s cosdered a PD locato (source) Therefore, to compute PD locato, two SVR models are requred; oe for each x-y coordates The PD features/patters used to develop the SVR models s the receved sgal stregth Frstly, RSS from ow locatos are gathered by the three sesors deployed the substato compoud These RSS ad ther locatos form a database for the compoud Suppose the true coordates of PD 4 N, be used [36] By solvg the dual problem, w ca be expaded as w = Where ³ 0 N = ( -a ) r a ad a ³ 0 (6) a (7) Substtutg (7) (4), ad replacg the dot-product, wth a erel fucto ( r, r) [38] to smplfy the olear mappg from the put space to the feature space SVR, the model ca be expressed as < N f ( r) = ( -a ) ( r, r) + b = a (8) a are the Lagrage multplers whch satsfy 0 a < C, r are the support vectors whose a s ot zero, ad N s the umber of support vectors Equato (8) shows that the decso fucto depeds o support vectors Ths meas optmal regresso surface s costructed by these support vectors The dea of support vectors form a sparse subset of the trag data that ca be used ad s partcularly useful for resource costrat applcatos such as the oe uder vestgato 3 PD Localsato based o SVR

6 locato l are ( x, y ) ad the correspodg values of 3 RSS for the PD from ths locato are ( r, r, r ) Fg 4 SVR PD Localsato model 3 The vector [ r, r, r ] R = s tae as the SVR put feature vector ad used to fer the locato l ( x, y ) All the feature vectors from ow locatos ad ther correspodg locato coordates costtute the SVR trag sample set Usg ths trag set, the SVR s traed to buld a PD localsato models that would subsequetly be used to predct or estmate PD locato gve RSS vector Durg trag, the put features (RSS) from each ow locato are trasformed to a ew feature space wth N features, oe for each support vector That s to say that, they are represeted oly terms of ther dot products wth support vectors (specal data pots chose by the SVR optmsato algorthm) Gaussa erel fucto s employed the trasformato to provde a olear mappg from the put space to the ew feature space I the locato estmato phase, for a gve RSS vector the erel fds the smlarty or a dstace measure betwee the vector ad the support vectors stored after trag The correspodg coordates of the support vectors closest to the RSS vector are used to compute the PD locato for the gve RSS vector The SVR PD locato model s as show Fg 4 However, whe the electromagetc evromet chages due to exteral flueces, for example chage the locato of a electrcal equpmet, the localsato model would be retraed by the latest collected data The retrag process ca be doe automatcally, trggered by the locato error aalyss If the locato error exceeds a predefed threshold, the retrag begs The optmal combato of the RBF erel based SVR hyper-parameters (erel parameter, sestve loss fucto ad regularsato parameter) s obtaed va cross valdato/grd search method 3 Least Squares Support Vector Regresso: Least squares support vector regresso (LSSVR) algorthm [3] [39] s a reformulato of the stadard SVR algorthm descrbed secto 3, whch leads to solvg a system of lear equatos The dea of lear equatos maes LSSVR more appealg ad computatoally more ecoomcal compare to solvg the covex quadratc programmg (QP) for stadard SVR LSSVR algorthm for PD localsato cosst of two phases: Trag ad Localsato Durg the trag phase, the parameters of LSSVR algorthm are estmated usg PD measuremets at ow locatos (trag pots) I the localsato phase, PD measuremets tae at uow locatos are aalysed, ad ther locatos obtaed usg the parameters estmated the trag phase Gve a trag data set {( r, l ), ( r, l ),,( r, l )} Ì Â PD put (RSS) data Î Â Â of pots, wth coordate) data r, ad output (PD locato l ( x, y ) Î Â -dmeso, the LSSVR based PD locato optmsato problem the prmal weght space s formulated as: m J ( w, e) = w + g e (9) w, b, e st = l = w, F( r ) + b + e, =,, h wth ( ) :Â Â j a fucto whch o-learly map the put space to the so-called hgher dmesoal feature h space, weght vector wî Â prmal weght space, bas term b ad error varable e = Â The error term here represets the true devato betwee actual PD locato ad estmated locato, rather tha a slac varable whch s eeded to esure feasblty (as SVR case) g ³ 0 s a regularsato costat To solve the optmsato problem the dual space, oe defes the Lagraga T L( w, b, e; a ) = J ( w, e) - a { w F( r ) + b + e - l } (0) = wth Lagrage multplers optmalty are gve by ì í î LLS -SVR w LLS -SVR b LLS -SVR e LLS -SVR a = 0 = 0 = 0 = 0 w = = a ÎÂ a = ge w, F( r ) = a = 0 a F( r ) The codtos for + b + e - l = 0 () After elmatg w ad e, the soluto yelds the followg lear equatos: where é 0 ê êë v W + ùébù é ù ú ú = I ê ê ú úû ë û ël û T v 0 g a () T T l = ( l,, l ), v = (,,) ad ) T a = ( a,, a the Lagrage multplers Applg 5

7 Mercer s codto [3], the -th elemet of W s gve T by W = F( r ) F( r ) = K( r, r ), =,,, where W s a postve defte matrx ad -th elemet of the matrx W = K r, r ) s a symmetrc, cotuous ( fucto The resultg LSSVR model for PD locato estmato becomes: f ( r ) = a K( r, r ) + b (3), b = where a are obtaed durg the trag phase by solvg (0) I LSSVR, there are oly two parameters to be tued: the erel settg ad the regularsato costat Cross-valdato/grd search s used to determe the optmal combato of the parameters 4 Expermetal Procedure 4 Expermetal Set Up I order to verfy the effectveess of the PD localsato system that s based o the deploymet of a etwor of sesor odes, a systematc test expermet was coducted a 90m x 840m laboratory at the Uversty of Strathclyde capturg the RF sgals were deployed at predefed locatos The arragemet of ths procedure s show Fg 5 A hgh-speed multchael osclloscope wth memory fucto was used as a sgal-acqusto system to capture ad store the PD traces The osclloscope has a badwdth of 9GHz The PD data acqured from measuremet were sampled at GS/s A sample waveform of the receved PD sgals s show Fg 6 The jected PD pulse waveform ad the sesor respose are show Fg 7 4 Data Preparato RF sgals collected durg the measuremet campag are corrupted by ose/terferece ad ths eeds to be removed before the PD sgals are aalysed I ths wor, the process of ose removal s accomplshed usg a wavelet multvarate de-osg techque [6] Ths deosg scheme combes the decomposto of formato gve by wavelet trasform ad the ablty of decorrelato amog varables gve by the Prcpal Compoet Aalyss (PCA) [40] The objectve s to obta better de-osed data so as to extract meagful formato from the raw data for PD locato The eergy (defed here as the sgal stregth) cotaed each PD trace s the calculated The average of the 0 dvdual measuremets tae at each trag ad test locatos s computed Fg 8 shows PD sgal stregth varato wth respect to locato for each of the ateas The uque sgatures created by PD sgal stregth at dfferet locatos facltate the applcato of mache learg algorthms for PD localsato I order to provde more robustess to our system, the rato of the averaged sgal stregth compoets betwee pars of recevg ateas s computed ad used as fgerprt put vectors to the developed models 3 x 0-3 Fg 5 Measuremet grd for measuremet campag The laboratory cotaed a great deal of clutter cludg metallc objects whch gves rse to a multpath rch rado evromet Wth the accessble area of the laboratory, 44 dstct trag locatos ad 3 testg locatos were uformly selected to form a grd such that the spacg betwee adjacet trag locatos s m ad the spacg betwee a trag locato ad ts earest testg locato s 07 m whch represet a array of sesor odes Pulse emulated PD sources were set up ad 0 RF PD measuremets collected at each trag ad testg locato, resultg 880 trag ad 640 testg cases I real lfe however, the electrcal equpmet whch PDs are most lely to appear are ot evely arraged substatos ad moreover some areas may be accessble Sgal stregth decays as the trasmsso dstace creases Ths sgal propagato characterstc cojucto wth a terpolato algorthm ca be explore to automatcally estmate PD sgal stregth at uobserved locatos based o the ow data values The durato ad the repetto frequecy of the dscharge pulses were 0ps ad 00 Hz respectvely Three omdrectoal ateas used for Ampltude (mv) Tme (s) Fg 6 Recorded PD sgal Fg 7 Respose of the recever sesor for the jected PD pulse 6

8 The localsato error s computed as the Eucldea dstace betwee the true locato ad the estmated locato of the PD source CDF descrbes the probablty of locatg PD wth a specfy rage of localsato error Ths shows how cosstet the models perform ad capture both the accuracy ad precso of the models Fg 9 ad Fg 0 show the errors each coordate (x ad y) of the test locatos for the three models Ths result shows that the locato errors x ad y vary from -35 m to 9 m ad -37 m to 37 m respectvely for the MLP model ad from -5 m to 3 m x ad -39 m to 36 m y for RBFN For SVR model, the errors x ad y vary from -34 m to 5 m ad -37 m to 9 m respectvely The result for LSSVR model s smlar to that for the other models wth errors x ad y varyg from -33 m to 5m ad -39 m to 33 m respectvely It s observed that the overall accuracy of each of the models wll be affected mostly by the y- coordate predctos Fg shows the localsato error Eucldea dstace for each test locato The maxmum localsato error for MLP, RBFN, SVR ad LSSVR models s foud to be 390 m, 60 m, 45 m ad 399 m respectvely wth LSSVR model producg locato estmate wth the lowest error of 0 m Fg shows CDFs of localsato error for the models The LSSVR model has a precso of 7 % wth 5 m compare to SVR, RBFN ad MLP models wth precso of 69 %, 54% ad 60 % wth 5 m respectvely I other words, the localsato error s less tha 5 m wth probablty of 7 %, 69 %, 54% ad 60 % for LSSVR, SVR, RBFN ad MLP respectvely Fg 8 Spatal varato of RSS for each atea 5 Results ad Dscussos The performace of SVM-based models (SVR ad LSSVR) o the PD data collected s preseted ad compared wth the ANN method The emprcal evaluato of the models s based o statstcal operators of locato error as well as ther cumulatve dstrbuto fuctos (CDFs) Fg 0 Model localsato error y-coordate Fg 9 Model localsato error x-coordate Fg Model localsato errors 7

9 Fg CDF of model localzato errors combato of RSS measuremet I ths study, sgal stregth rato s used as locato fgerprts rather tha absolute RSS The performace of the proposed methods have bee evaluated ad compared wth ANN terms of statstcal operators of localsato error The results dcate that SVM-based approaches are superor to ANN accuracy showg a reducto meda locato error ad represet practcal alteratves for PD source localsato It s beleved that the superor performace of SVM-based approaches s due to ther ablty to coverge to a global mmum whereas eural etwors are susceptble to covergg to local mma Gve the rch complexty of the uderlyg rado evromet covergece to a local mma s hghly lely; therefore, SVM-based approaches are more approprate ths evromet Ths PD localsato system ca motor ad locate dscharges from several tems of plat cocurretly mag t sutable for substato-wde PD localsato 7 Acowledgmets The authors acowledge the Egeerg ad Physcal Sceces Research Coucl for ther support of ths wor uder grat EP/J05873/ ad Tertary Educato Trust Fud (TETFud) Ngera 8 Refereces Fg 3 Model locato accuracy Table Cumulatve error probablty of model locato error MLP RBFN SVR LSSVR CEP= CEP= CEP= Comparso of the performace of the models based o localsato error correspodg to 05, 050, ad 075 overall cumulatve error probabltes (CEP) s preseted Table Ths clearly shows that half of the tme PD sources were located wth error less tha m whe LSSVR algorthm s used for localsato The results of localsato accuracy for the models are show Fg 3 It s clear that there s a steady mprovemet locato accuracy terms of meda error whe the SVM-based models are used compared to ANN models LSSVR model partcularly shows a 83 % ad 8 % reducto meda locato error whe compared wth MLP ad RBFN models respectvely 6 Cocluso Mache learg techque for locatg PD sources based o RSS measuremet have bee cosdered The prcple ad computatoal realsato of the methods based o support vector mache have bee descrbed Support vector regresso (SVR) as well as least squares support vector regresso (LSSVR) approach uses the spatal patter of receved sgal stregth to costruct a regresso surface a hgh dmesoal feature space where PD locato s determed Ths approach models PD locato as a lear [] H Hou, G Sheg, ad X Jag, Localzato algorthm for the PD source substato based o L-shaped atea array sgal processg, IEEE Trasactos o Power Delvery, vol 30, o, pp , 05 [] H A Illas, M A Tuo, A H A Baar, H Mohls, ad G Che, Partal dscharge pheomea wth a artfcal vod cable sulato geometry: expermetal valdato ad smulato, IEEE Trasactos o Delectrcs ad Electrcal Isulato, vol 3, o, pp , 06 [3] R Rostama, M Sae, M Vala, S S Mortazav ad V Parv, Accurate power trasformer PD patter recogto va ts model, IET Scece, Measuremet Techology, vol 0, o 7, pp , 06 [4] P J Moore, I E Portugues, ad I A Glover, Partal dscharge vestgato of a power trasformer usg wreless wdebad radofrequecy measuremets, IEEE Trasactos o Power Delvery, vol, o, pp , 006 [5] F P Mohamed, WH Sew ad JJ Soragha, Ole partal dscharge detecto medum voltage cables usg protecto ad strumet curret trasformers, Secod UHVNet Colloquum o hgh voltage measuremet ad sulato research, Glasgow, 009 [6] D Evagorou, A Kypraou, PL Lew, A Stavrou, V Efthymou, AC Metaxas, ad GE Georghou, Feature extracto of partal dscharge sgals usg the wavelet pacet trasform ad classfcato wth a probablstc eural etwor, IET Scece, Measuremet & Techology, vol 4, o 3, pp 77-9, 00 [7] Y Lu, X Ta ad X Hu, PD detecto ad localsato by acoustc measuremets a ol-flled trasformer, IEE Proceedgs - Scece, Measuremet ad Techology}, vol 47, o, pp 8-85, 000 [8] P L, W Zhou, S Yag, Y Lu, Y Ta ad Y Wag, Method for partal dscharge localsato ar-sulated substatos, IET Scece, Measuremet & Techology, 07 [9] F P Mohamed, W H Sew, J J Soragha, S M Stracha ad J Mcwllam, Remote motorg of partal dscharge data from sulated power cables, IET Scece, Measuremet Techology, vol 8, o 5, pp 39-36, 04 [0] I E Portugues, P J Moore, I A Glover, C Johstoe, R H McKosy, M B Goff, ad L Va Der Zel, RF-based partal dscharge early warg system for ar-sulated substatos, IEEE Trasactos o Power Delvery, vol 4, o, pp 0--9, 009 8

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