A vestgatve stud o the fluece of correlato of PD statstcal features o PD patter recogto Abdullah Abubakar Mas ud Departmet of Electroc ad Electrcal Egeerg Jubal Idustral College, Jubal Idustral Ct, KA *Emal: masud_a@c.edu.sa Bra G. tewart Departmet of Electroc ad Electrcal Egeerg, Uverst of trathclde, Roal College Buldg, 204 George treet, Glasgow G1 1XW. Emal: bra.stewart.100@strath.ac.uk Abstract Ths paper vestgates the fluece of correlato coeffcets of partal dscharge (PD statstcal fgerprts o the classfcato performace of the esemble eural etwork (ENN. PD measuremets were carred out accordg to the IEC 60270 stadard. Idepedet statstcal parameters of skewess, kurtoss, cross-correlato, dscharge factor ad modfed crosscorrelato were aalzed ad utlzed as puts to the ENN. The ENN was appled to classf 2 PD datasets. Oe wth PD statstcal features ad the other a combato of PD statstcal features ad ther correlato coeffcets. The results dcate that the ENN appears to show a statstcall better performace usg the statstcal features med wth ther correlato coeffcets as compared to the other dataset. Ths clearl shows that the correlato coeffcets of statstcal features ca provde a mproved classfcato ad dscrmato of PD patters. Kewords partal dscharge, esemble eural etwork, correlato coeffcets I. INTRODUCTION Hgh voltage (HV equpmet such as trasformers ad udergroud cables pla a vtal role the operato of a power sstem etwork. A sudde sulato falure of a HV apparatus results a complete power sstem outage wth serous facal cosequeces. For codto motorg egeers, t s mportat to detect such faults at a earl stage order to arrve at the correct decso regardg the state of the sulato [1]. Oe maor source of sulato falure s partal dscharge (PD [2]. PD refers to a cofed electrcal dscharge that occurs wth the sulato sstem subected to HV stress [3]. Therefore, PD testg or classfcato s vtal to determe the qualt of the HV sulato sstem. Recet studes show that a esemble eural etwork (ENN s a effectve techque for classfg PD statstcal fgerprts [2]. A ENN s a eural etwork (NN model whch tras several costtuet eural etwork models ad combes ther output predctos. Therefore, ths paper proposes a mproved ENN model for classfg PD patters comprsg coroa ar, vod, surface dscharge ar ad surface dscharge ol. Idepedet statstcal fgerprts obtaed from the PD φ-q- (phase-ampltude-umber patters were aalzed ad appled as a put to the ENN. The φ-q- patters were obtaed from artfcall created PD models the HV laborator. The overall am of the work s to vestgate whether the ENN ca be able to recogze PD patter statstcal features ad ther correlato coeffcet ad to vestgate whether cludg correlato coeffcets mproves further the ENN capablt of recogto. II. PD MEAUREMENT YTEM I ths paper, the PD measuremets were coducted accordace wth the IEC 60270 stadard as show Fgure 1. The PD detecto sstem produces φ-q- patters real tme, wth a umber of cotrols for varg the umber of power ccle captures ad phase or ampltude resolutos. It ca measure specfc parameters assocated wth the PD smultaeousl, such as traset curret, apparet charge, umber of dscharges ad phase agle. To determe the apparet charge assocated wth the PD, calbrato was carred out throughout the epermetal process. Fg. 1: PD measuremet sstem. U s the hgh voltage source, C 1 s the AC measuremet capactor, C 2 s the PD measuremet capactor I ths work, four PD models were artfcall created the HV lab. These clude coroa ar, vod, surface dscharge ar ad surface dscharge ol.
The coroa PD model s a pot-plae arragemet as show Fgure 2a. The eedle has a tp radus of 10µm ad legth of 3cm. Vod measuremets were performed wth a vod of 0.6mm at the ceter of 9 laers of polethlee terephthalate (PET as show Fg 2b. To vestgate the surface dscharge ar, a small brass ball of appromatel 50mm dameter was placed o Perspe sulato as show Fgure 2c. Ol surface dscharge was vestgated b a eedle-pot placed o pressboard wholl mmersed Castrol sulatg ol as show Fg 1d. The eedle was placed at a agle of 10 oto the surface of pressboard ad 25mm from a earth coductor. The predcto of the ENN s computed as follows: f = k m= 1 w f ( a where the weghts (w are: w = k c m= 1 ( f ( a c( f ( a (b (c (d Fg. 3: A ENN model Fg. 2: Artfcall created PD faults a coroa ar b vods c surface dscharge ar d surface dscharge ol. III. THE ENEMBLE NEURAL NETWORK A ENN s a learg techque that tras a umber of compoet NNs ad combes ther output predcto [4]. It has bee broadl vestgated ad establshed that the ENN ca mprove the geeralzato performace of the sgle NN b smpl trag dverse NN models ad combg ther output predctos [5]. Fgure 3 shows the ENN model. There are 4 ma tpes of ENN such as the smplest ENN, the aïve classfer, the geeralzed ENN ad damcall weghted ENN. Amog them, the damcall weghted ENN provdes the optmum result at a gve tme the weght NN weghts are evaluated. It was assumed that the compoet NN the esemble has output predctos as the probablt of occurrece. For stace, f the b = f s the predcto of the etwork ad a s the put parameter. As b approaches a value of 1, t refers to a partcular class. O the other had, whe b approaches a value of 0, t s optmstc that t does ot refer to that specfc class. The certat of the NN s computed accordg to the lterature [6]. Assumg the c represets the certat of the NN. IV. THE TATICAL FINGERPRINT 3D φ-q- patters were obtaed from the PD measuremets. The, PD statstcal features comprsg skewess, kurtoss, dscharge factor, cross correlato ad modfed cross correlato were obtaed from the dstrbutos assocated wth pulse cout H (φ, mea pulse heght H q((φ ad umber-ampltude H (q plots. These dstrbutos were represeted both the postve ( ad egatve half power ccles (-. mlar to the lterature [6], ths paper apples 15 statstcal fgerprts as puts for trag ad testg the ENN. These comprses the skewess (sk ad Kurtoss (ku of the H q(φ, H q(φ-, H (q, H (q-, H (φ ad H (φ- dstrbutos, the cross-correlato (cc, dscharge factor (Q ad modfed cross-correlato (mcc. The mcc s the product of Q ad cc. The sk, ku, Q ad cc are obtaed as follows: ( 3 μ = P 3 σ 4 ( μ = P 4 σ sk (1 ku (2
Q N Q = Q (3 N (c cc = 2 2 2 ( 2 ( (4 where µ: represet the mea value σ: represet the stadard devato ad P s the probablt of the dscrete value ad as the case ma be. Q ad Q - : represet the sum of dscharge ampltudes both the ve ad egatve half power ccles N ad N - : represet the umber of dscharges both the ve ad ve half power ccle. (d Fg 4: statstcal cofdece tervals for statstcal fgerprts for a coroa ar b coroa ar ad ther correlato coeffcets c vod d vod ad ther correlato coeffcets. (b Fg 4 shows the 95% cofdece terval coverg mea values of statstcal fgerprts of coroa ad vod dscharges. For each of coroa ad vod, two datasets are cosdered, oe wth the statstcal features ad the other wth the same statstcal features med wth ther correlato coeffcets. Geerall, error bars are wder for vod as compared to coroa due to the low repetto rate ad hgher ampltude assocated wth the postve coroa [7] ad ths leads to the hgh peakedess of the H (q- dstrbuto. Geerall, for both coroa ad vod, as epected the cofdece tervals for statstcal features med wth ther correlato coeffcets are lower tha the umed scearo. These results were foud to be cosstet wth all the PD defects cosdered. The cluso of correlato coeffcets across the measured statstcal parameters as addtoal puts to the ENN s ow cosdered the fowlg secto.
V. PEARON PRODUCT-MOMENT CORRELATION COEFFICIENT The Pearso product-momet correlato coeffcet, or wdel kow as the correlato coeffcet (r, for a set of parameters refers to a techque of summarzg the degree of relatoshp betwee two parameters. The value of r usuall summarzes the relatoshp betwee two varables havg a lear relatoshp wth each other. If the two varables have a lear relatoshp the postve drecto, the r s regarded as postve. If the lear relatoshp s the egatve drecto, such that a crease oe varable leads to the decrease the other, the r s regarded as egatve. Thus the values of r fall betwee -1 to 1. A value of r close to 0 sgfes a weak relatoshp betwee the 2 varables. The mathematcal defto of r s as follows: where: X ad Y are the two varables to be aalzed. X s the mea of X. Y s the mea value of Y. VI. REULT AND DICUION I ths secto, atteto wll be draw to the performace of the ENN classfg ad dstgushg PD fgerprts of 4 defects.e. coroa ar, teral PD vods, surface PDs ar ad ol wth the cluso of correlato coeffcets measured over the durato of the tests. For each defect a seres of PD measuremets were coducted ad statstcal parameters computed. Two PD statstcal dataset were created for each defect. Oe wth ol the statstcal parameters obtaed from the φ-q- patters as before ad aother comprsg a combato of statstcal parameters ad ther correlato coeffcets. The overall am s to be able to observe the robustess of the ENN classfg the aforemetoed dataset. 30 samples are used as put to the ENN whle the remag 13 samples appled as the output parameters. The put values for the ENN, are the sk ad ku of the (H (φ, H (φ-, H q(φ ad H q(φ-, Q, cc ad mcc, whle the output values are [0 0], [0 1], [1 0] ad [1 1] for coroa ar, teral vod, surface dscharge ol ad surface dscharges ar respectvel. Owg to the stablt assocated wth the costtuet NNs the esemble, up to 100 teratos of the PD recogto rate were obtaed for each PD defect, uder dfferet tal states of weghts ad bases. Itall, the put data s ormalzed order to mmze the varace. 10 hdde laers wth mometum rate of 0.6 ad learg rate 0.05 are chose for each costtuet NN. Fgs 5a-d shows the average values, varaces of the classfcato result of the ENN for the 4 PD fault scearos cosdered, whe the ENN s traed wth a of the PD φ-q- fgerprts ad the cosequetl testg carred out wth all the defects. The ENN performace was vestgated ad the results compared for the 2 categores of dataset.e. oe wth ol the PD φ-q- statstcal parameters ad the other comprsg the PD φ-q- statstcal parameters plus ther correlato coeffcets. It s terestg to ote that whe the ENN s traed ad tested wth the same PD defects, as epected, the mea recogto rates ad ther varaces are as hgh as 97% for the 2 datasets. However, the PD statstcal dataset combed wth the correlato coeffcets appears to show lower varace ad hgher recogto rate most of the PD fault cases, showg a mproved accurac of the ENN result. As also epected, the varaces are hgher for the ENN result whe traed wth oe PD defect ad the tested wth aother dfferet defect. These results appear to be cosstet across all the varous trag ad testg schemes. Ths dcates that correlato coeffcets of statstcal features are addtoal good measures for the evaluato of PD patters wth ENN applcatos. To evaluate ad classf the PD patters, two approaches are adopted. Frst, the ENN was traed wth ether of the 4 PD defects (coroa ar, teral vod, surface dscharge ar ad surface PDs ol ad the testg carred out wth the others. A smlar strateg s the emploed for the other 3 PD faults. For the PD dataset wth ol statstcal parameters, 20 samples are radoml selected as put fgerprts for the ENN whle remag 8 automatcall becomes the testg parameters. Furthermore, for the PD dataset comprsg of both statstcal parameters ad ther correlato coeffcets,
(b (c defects d Trag wth surface dscharge ol ad testg wth all the PD defects VII. CONCLUION I ths paper, the statstcal features of PD defects were etracted ad appled as put varables to a ENN. Frstl, the ENN was appled to classf PD fgerprts of 4 categores recorded as coroa ar, teral vod, surface dscharge ar ad surface PDs ol. ecodl, the same ENN was aga appled to classf aother 4 categores of the aforemetoed statstcal features of the PD defects but wth the cluso of the correlato coeffcets betwee the statstcal parameters. The results clearl dcate that, addto to the PD statstcal parameters, cluso of correlato coeffcets mprove the recogto rate of the ENN ad ca thus ca be cosdered as addtoal good dcators for PD evaluato ad classfcato. ACKNOWLEDGMENT Ths s to ackowledge the support of the Hgh voltage lab of the Glasgow Caledoa Uverst for provdg the facltes to coduct ths research. (d REFERENCE [1] H. C. Che, "Fractal features-based patter recogto of partal dscharge XLPE power cables usg eteso method, "IET Geerato, Trasmsso & Dstrbuto", Vol. 6, pp. 1096-1103, 2012. [2] A. Abubakar Mas ud, B. G. tewart, ad. G. McMeek, "Applcato of a esemble eural etwork for classfg partal dscharge patters," Electrc Power stems Research, Vol. 110, pp. 154-162, 2014. [3] E. Gulsk ad A. Krvda, "Neural etworks as a tool for recogto of partal dscharges", IEEE Tras. Electr. Isul., Vol. 28, pp. 984-1001, 1993. [4] H. Navoe, P. Grato, P. Verdes, H. Ceccato, "A learg algorthm for NN Esembles", Artfcal Itellgece, vol. 12, 70 74, 2001. [5] D. Jmez, "Damcall weghted esemble of eural etwork for classfcato", : World Cogress o Computatoal Itellgece, Achorage, UA, 753 756, 1998. [6] A. Abubakar Mas ud, B. G. tewart, ad. G. McMeek."A vestgatve stud to the sestvt of dfferet partal dscharge φ-q- patter resoluto szes o statstcal eural etwork patter classfcato", Measuremet, vol. 92, 497-507, 2016. [7] N. Trh,."Partal dscharge XIX: dscharges ar Part I: Phscal mechasms", IEEE Isul. Magaz. vol. 11, o. 2, 23-29,1999. Fg 5: The ENN recogto rates a Trag wth coroa ar ad testg wth all the PD defects b Trag wth sgle vod ad testg wth all the PD defects c Trag wth surface dscharge ar ad testg wth all the PD