Radiometric location of partial discharge sources on energised high voltage plant

Transcription

1 Radiometric location of partial dichare ource on eneried hih voltae plant P. J. Moore, Senior Member, IEEE, I. E. Portuue, Member, IEEE, and I. A. Glover Abtract Partial dichare (PD) enerate wideband radio freuency interference and coneuently can be detected uin radio receivin euipment. Due to the advance in ultra-hihpeed amplin euipment, it i poible to accurately meaure the propaation of the PD wavefront a it pae throuh a element antenna array. From thee meaurement the 3- dimenional poition of the PD ource can be calculated uin an iterative alorithm. The locatin euipment i uitable for ue within the vicinity of eneried hih voltae plant and can locate ource up to 5 m from the array. Reult are preented howin the location ability under laboratory and field condition. The inificant advantae of thi euipment lie in it ability to detect PD ource in eneried plant without the need for outae or electrical connection. Index Term partial dichare, diital monitorin, radiometric monitorin, impulive noie, condition monitorin. T I. INTRODUCTION HE ue of partial dichare monitorin a a mean of nondetructive condition monitorin of power ytem plant i widely etablihed. Partial dichare (PD) can be detected by a variety of mean includin ultraound, electrical contact method and radio freuency enin. Thee method can alo be applied to the location of PD which i of coniderable interet to utilitie ince it allow accurate prediction of plant aet life. A variety of location techniue have been propoed for power tranformer includin electrical contact method baed on the aumption that the tranformer behave a a linear time-invariant ytem [,]. Uin computer mo delin, the tranfer function at different location can be obtained, thu allowin the PD location to be calculated from difference in the waveform. The ue of neural network to claify the inal ditortion inherent in the location of dichare in power tranformer ha alo been invetiated [3]. The ue of ultraound enor on the outide of the tank wall [] and radiative meaurement uin UHF coupler [5] have alo been explored. The location of PD in enerator i principally undertaken uin two techniue, the delay time and top-top method [6,7]. The latter aume the inal diminihe with ditance to the oriin of the PD. The delay method ue the cro- Thi work wa upported in part by the UK Enineerin and Phyical Science Reearch Council under Grant GR/R7799. All the author are with the Department of Electronic and Electrical Enineerin, Univerity of Bath, BA 7AY, UK. correlation function between inal to etimate the time of fliht of the PD waveform and hence it location; thi method i hown to be more accurate than the top-top method [6]. The location of PD in olid dielectric cable uin meaurement of travelin electromanetic phenomena wa decribed over year ao [8]. Subeuently, many tudie have improved PD location accuracy and enitivity [e. 9-]. Depite thee advance, there ha been relatively little prore on a locatin ytem that can be enerally applied in a ubtation environment, rather than pecifically applied to an item of plant. In thi context the ue of radio freuency (rf) remote enin hold the biet promie ince it can be eaily deployed in a ubtation, doe not reuire any phyical contact, and can be applied to any enerized plant item. The development of rf remote enin techniue for ubtation ue include field probe [], and interferometric method [3,]. Both of thee approache uffer from the diadvantae of enin the entirety of the radiated PD waveform. It will be hown later in thi paper that only the initial portion of the waveform can be ued for location purpoe due to the preence of multipath propaation. The location accuracy of thee method will therefore be deraded. Thi paper decribe a eneral purpoe PD locatin ytem uitable for ue in the ubtation environment. The ability to locate PD relie on the hih peed diitization of the antenna inal which ha only recently become commercially practicable. The ytem ha been extenively teted on ite, and reult are preented for everal cae tudie in addition to conventional laboratory tudie. II. IMPULSIVE RADIATION FROM POWER SYSTEM PLANT The initial rie-time of the current waveform produced by a PD i ufficiently hih to caue the freuency pectrum to extend into the radio freuency reion. A a coneuence, a proportion of the PD enery i radiated into the free-pace adjoinin the ite of the dichare, ivin rie to the well known fact that PD can be detected uin radiometry. The majority of radiometric meaurement have been made uin narrowband, down-convertin radio receivin euipment. With recent development in diital amplin technoloy, it i now poible to record radiative PD waveform uin a reolution that ha not hitherto been poible [5]. Thee meaurement have the followin characteritic:. Directly-ampled: the antenna inal i not downconverted before amplin, thu improvin the fidelity of the inal.

2 . Wideband: typical analoue bandwidth are in the reion of GHz, with amplin freuencie in the Gia-Sample per econd (GSp) rane. Meaurement made uin thi hih-peed diital technoloy will be referred to a wideband, radiative partial dichare (WRPD) waveform. Compared to conventional meaurement, the extra reolution of WRPD waveform provide a ubtantial increae in information content - typically everal order of manitude. However, the majority of thi extra information relate to the ubtation environment, rather than the nature of the PD. Thi i explained in the followin ection: A. Nature of Dielectric The initial rie-time of the current impule created by a PD electron avalanche differ between dielectric, bein hiher for troner dielectric, uch a oil, than for weaker dielectric, uch a air. Due to the tochatic nature of PD, it i difficult to model the exact hape of the initial current waveform. Aumin thi to be exponential, however, then the reultin pectrum i hown in Fiure. The effect of troner and weaker dielectric can be een in thi fiure, with the troner dielectric bein better repreented at hiher freuencie; thi concluion i upported by experimental evidence [6,7]. Thi fiure alo illutrate that the majority of the enery radiated by a PD occur below GHz. Thi imple model of PD radiation i in many repect inadeuate and under practical condition the pectra of WRPD waveform may bear little reemblance to Fiure. The followin ection decribe why WRPD waveform are different when meaured within a ubtation. Normalied freuency pectra Fi.. Freuency pectra for differin dielectric. B. Backround Noie Stroner dielectric Weaker dielectric 6 8 Freuency (MHz) WRPD meaurement in electrical ubtation are made in the preence of broadcat tranmiion. Fiure how the pectrum of backround noie in a typical ubtation. The level of broadcat tranmiion vary coniderably, enerally bein hiher for ubtation cloe to metropolitan area. Additionally, the preence of everal PD ource can alo make the noie environment appear to be cluttered. For the locator decribed in the followin ection thi i not a problem ince multiple ource can be ditinuihed eometrically. Due to the hort duration of a WRPD impule (< µ), the probability of impule from differin ource appearin coincidently i extremely mall. Thu, the major ource of backround noie i therefore broadcat tranmiion. C. Nature of radiatin tructure The conductin metalwork attached to the PD ource typically bubar and connectin link - influence the radiation of rf enery. Due to reonance, the pecific hape and confiuration of thee conductor lead to preferential radiation of certain freuencie, whilt reducin that of other. Thi effect lead to the ditortion of the ideal PD pectrum decribed in ection A.. FM radio TV Antenna inal (V) Fi.. Backround radio pectrum recorded by locatin euipment.. Antenna Sinal (V) Time (n) Fi. 3. Line defect WRPD waveform recorded with antenna. Antenna Sinal (V).5 CB Freuency (MHz) Aeronautical -. 6 Time (n) Fi.. The ame WRPD a Fi. 3 recorded from adjacent antenna (). Antenna and were approximately m apart; the inal were recorded ynchronouly from each antenna. D. Nature of Subtation Environment Mobile phone -. 6 In addition to the effect of the radiatin tructure decribed in C, other metallic tructure in the vicinity of the ource and the receivin antenna will influence the nature of the WRPD

3 3 inal due to catterin and reflection. Reflection caue multipath propaation of the WRPD impule and reult in the inal meaured at the antenna bein the um of the direct path inal between the PD ource and the antenna, and multiple reflected inal. Due to the lare number of reflectin urface within the ubtation environment, the combined effect of C and D caue the detailed nature of the WRPD waveform to be influenced more by the local environment and the poition of meaurement, than by the inherent propertie of the dielectric cauin the PD. Thi i illutrated in Fiure 3 and which how PD inal caued by a defective overhead line conductor meaured imultaneouly from two different poition paced m apart. The dichare ource wa approximately m ditant from each antenna. It i apparent that the waveform are remarkably diimilar, iven the mall chane in antenna poition. hown a t, t, t 3 and t. By meaurin the time difference a the direct wave propaate throuh the antenna array, e.. t = t - t, the ource poition can be calculated. The calculation to perform thi are decribed in followin ection. # # t t 3 t t PD dichare ource Antenna Sinal (V)..5 Direct wave propaation Multipath propaation Antenna Start of -.5 impule Antenna Time (n) Fi. 5. Impule wavefront from Fi 3 and. Arbitrary timecale, waveform corrected for ditance to ource. III. LOCATION OF PD IMPULSES The previou ection aert that the propaation environment, rather than the PD, ha the reatet impact on WRPD waveform. Depite thi, the phyical location of the dichare ource can be found by analyin the initial part of the WRPD wavefront that repreent the direct path of inal from the ource before any reflection occur. The ditinction between the direct path and multiple reflected path component can be een in Fiure 5 which how the initial wavefront of the inal of Fiure 3 and. In thi fiure the inal have been corrected for the time delay and amplitude difference caued by uneual path lenth. It can be een that the initial 3 n of the inal are the ame at both antenna; thi i the direct wave. Followin the direct wave, the effect of reflection lead to difference in the received inal; thi i the multi-path reion. The time between the direct wave and the firt reflection i variable, bein a function of the poition of reflectin object in the vicinity of the ource and antenna. The 3-dimenional location of the dichare ource can be determined uin a paive -antenna array with direct amplin capable of meaurin the arrival time of the direct wave to ub-n accuracy. A conceptual view of the proce i hown in Fiure 6. Four antenna at known 3-dimenional poition are ituated cloe to the dichare ource. The time of fliht of the direct wave from the ource to the antenna are #3 # antenna array Fi. 6. Conceptual view of PD dichare location proce. A. Arrival Time Difference Calculation The arrival time difference calculation i achieved in two tep:. The direct wave arrival time at the array i found approximately uin a imple threholdin techniue on the diital record of each antenna inal. Thi ive an anwer to within one or two ample.. From a knowlede of the approximate poition of the direct wave in each channel, the arrival time difference are more accurately evaluated uin a cro-correlation techniue. The antenna inal are imultaneouly ampled to ive a diital euence for each channel: x (k), where =,,3 or, and =k=n. In practice, a value of N = 5 ha been ued which correpond to a euence lenth of µ at a amplin freuency of.5 GSp. ) Threholdin Threholdin find the approximate poition of the direct wave by comparin the diital euence for each channel aaint a threhold: the poition of the direct wave i identified where the euence value exceed the threhold. It i aumed that the firt m ample of each euence will not contain the WRPD impule waveform, and hence can be ued to characterie the backround noie. Thu, the peak backround noie value, ŝ, i found from: En

4 ( n) for n m ˆ = max x =, The threhold value, T, i et to a multiple of ŝ in practice a multiple of ha iven atifactory reult. The poition of the direct wave, d, i found a the firt value of n that atifie ( ) x n > T a n i varied from m to N. Note that abolute value of the inal and threhold are ued to avoid problem of polarity, ince the initial direction of the impule i dependent on the voltae polarity. Althouh crude, the threhold techniue ha the advantae of bein inenitive to the multi-path reion, actin only on the direct wave. The arrival time difference i found by ubtractin the value between antenna, e.. d = d - d. ) Cro-Correlation The arrival time difference i improved by cro-correlatin the direct wave reion of the inal from the two antenna. Cro-correlation find the imilarity of the two inal and, with the ue of interpolation, allow reolution of the timedelay to fraction of a amplin interval. Analyi baed on the direct-wave reion of the impule i enured by windowin the inal around the impule poition found from the previou threholdin approximation. Aumin the inal i windowed p ample either ide of the poition identified by threholdin, the windowed value for each channel y (n) can be expreed a: y n = x d p + + n for n =, p + En ( ) ( ) ( ) The extent of thi window mut be critically choen to enure that it doe not extend into the multipath reion: typically p = 5 ample. Cro-correlation of the windowed inal i achieved a follow: R p j + n= ( j) = y ( n j) y ( n) for j = p, p En 3 where R i the cro correlation product for channel and. An example i hown in Fiure 7; the delay between the windowed inal,?, i found from the offet of the peak of the cro-correlation product from the oriin. From the inet in Fiure 7, which how the peak in reater detail, thi delay can be een to be +.8 n (note that the calculation i performed in term of ample interval, rather than time). The accuracy of thi reult can be improved by interpolatin the crocorrelation product euence to a hiher amplin rate ince, it i clear from Fiure 7, that the true peak lie between ample. Althouh the true peak may be found to very hih accuracy by hih interpolation factor (i.e. ratio of pot to pre-interpolated data), experience of thi approach uet that interpolation to reater than time the oriinal amplin freuency doe not lead to any reater reolution of the time delay due to the preence of broadcat noie. Further, in the preence of PD inal-to-noie voltae ratio (decribed later) of le than, it i unlikely that interpolation will improve the arrival time difference accuracy. Application of a, lowpa interpolation alorithm to the data of Fiure 7 improve the reolution of the delay to +.68 n, compared to +.8 n without interpolation. Cro-correlation product Time (n) Fi. 7. Cro-correlation of wavefront from fi 3 and. Inet how detail around peak. The total arrival time difference i found from the um of the threholded arrival time difference and the cro-correlation delay, e.. t = d + En Thi procedure i normally conducted by takin one channel - uually channel - a a reference, to yield t, t 3 and t. Thee value are reuired for the location alorithm which i decribed in the next ection. However, it i alo poible to find all additional time delay between the channel, i.e. t 3, t 3 and t, which are needed under certain condition decribed later. B. Location Alorithm Location of the PD ource involve imultaneou olution of a et of non-linear eometric euation. Let a 3-dimenional poition be repreented in rectanular coordinate a (x,y,z), with a ubcript denotin the PD ource, and ubcript to (or more enerally ) denotin the antenna poition. The PD impule i aumed to be launched from the ource poition at unknown time τ, and to arrive at the four antenna at time t to t. Aumin that the WRPD wavefront expand pherically from the ource poition at the velocity of liht, c, the propaation can be decribed by the followin eneric euation: c ( t τ ) = ( x x ) + ( y y ) + ( z z Since τ i unknown, and the arrival time are only known a difference, the propaation euation can be more uefully written a: where = ct ct ct = 3 = 3 = ( x x ) + ( y y ) + ( z z and t = t - t, etc. Euation 6-8 contain three unknown (x, y, z ) and can be olved by iteration; Appendix I decribe a Newton-Raphon olution approach that ha worked ) ) En 5 En 6 En 7 En 8 En 9

5 5 atifactorily. Execution of thi alorithm can reult in three poible outcome:. The alorithm convere on the ource location.. The alorithm cannot convere, but enter into a limit cycle where the poition of ubeuent iteration lie on a line pain throuh the antenna array and the ource. 3. The alorithm divere aymptotically. Outcome and correpond to the PD ource bein located cloe to or far from the antenna array a decribed in the next ection. Outcome 3 i a function of the ratio of WRPD inal to backround noie. In the preence of noie, the time of arrival of the WRPD inal can be ditorted. Since backround noie varie patially, it i poible for a et of arrival time to be calculated that do not correpond to a phyical ource poition: in thi cae the alorithm can fail to convere. Thi i a particular problem where the antenna pacin i mall. It i poible to recover thi ituation by makin mall adjutment to the time delay to find the nearet poition of converence. A techniue for thi - the noiy inal alorithm - i decribed in Appendix II. C. Location Accuracy The location accuracy depend on the confiuration of the -antenna array and the ditance to the ource. In eneral the accuracy i difficult to uantify due to the non-linear nature of the location euation and the arbitrary array confiuration afforded by ite condition. Fiure 8 ive an appreciation of the accuracy that can be expected for a uare array of ide lenth 3 m. In thi plan view the antenna are hown a circle cloe to the oriin and the remainin point repreent ource location in 3-dimenional pace (up to 3 m vertically) where the time delay on the antenna correpond to exact inteer multiple of the amplin interval (. n, f =.5 GSp). Source location not coincidin with the point hown in Fiure 8 will be located to the nearet point. It can be een, therefore, that ource within 5 m of the array will be located to a hih accuracy typically a few ten of cm wherea ource at m can uffer a location error in exce of m. The maximum rane of the array occur alon the array diaonal, and the maximum reolution occur parallel to the array ide. Source location oriinatin beyond the limit of the point hown in Fiure 8 will not be located, but the 3-D bearin to the ource can be found with hih preciion, typically to within º. Fiure 9 how the location ability of a Y-haped array, where the larer antenna pacin i m. Thi confiuration i een to be inferior to the uare array in term of location accuracy, althouh the antenna pacin i lihtly maller. Note that thee fiure are conervative etimate of the locatin accuracy ince they do not take into account the interpolation of the cro-correlation product that allow time delay to be etimated to fraction of a amplin interval. Fi. 8. Location performance of uare array with antenna pacin 3 m. Fi. 9. Location performance of Y-haped array with antenna pacin m. IV. RECORDING HARDWARE The recordin euipment conit of dikcone antenna, amplin cope and peronal computer. The dikcone antenna, Fiure, conit of a dual cone element and an earth plane, and i both broadband and omnidirectional. Thi dein ha been extenively ued for locatin impulive noie and provide a relatively flat freuency repone to the vertical electric field in the rane.- GHz, with a contant impedance of 5 Ω. The antenna inal are diitized with a Tektronix TDS 7 Diital Phophor Scope that can ample four channel ynchronouly at a amplin rate of.5 Gia ample per econd (GSp) and ha an analoue bandwidth of GHz. An important feature of thi cope, iven the repetitive nature of PD, i the emented memory architecture that allow the main amplin memory of M-ample per channel to be emented

6 6 into eparately triered buffer of 5 ample each. Each time a buffer i triered, the cope record the tart time a a timetamp with a reolution of -9. The -channel memory data and accompanyin timetamp are downloaded to a peronal computer (PC) via a GPIB connection. Conventional amplitude trierin of the cope i ued. 5 mm Fi.. Dikcone antenna. The cone ection wa machined from olid aluminium. The bae plate wa fabricated from mm thick aluminium heet. V. SITE APPLICATION a) Settin-up The euipment i deployed on ite in the vicinity of upect euipment, or in poition where inificant radio freuency interference (RFI) ha been oberved, e.. with the ue of a RFI meter. The four antenna are ituated cloe to the round. Due to the limitation of ubtation pace, and the need to ituate the antenna away from metalwork to avoid reflection, it i rarely poible to form an exact uare and o a uadrilateral form i ued. The antenna are connected to the cope uin hihly creened coaxial lead. It i neceary to enure that the propaation delay of all four lead are identical, otherwie the PD ource location will be in error. Thi i achieved by contructin the lead with eual lenth of coaxial cable and ubeuently checkin their impule propaation delay uin a network analyzer. Lead lenth of 5 m have been uccefully ued on ite, but, with a hih-uality, hihly creened coaxial cable, lenth of up to everal hundred of metre hould be poible. b) Mappin conideration Followin itin of the antenna, their poition are meaured to the nearet cm (uin a meaurin tape), in relation to a convenient datum e.. relative to ome nearby euipment. From thee meaurement, the 3-dimenional rectanular coordinate of the antenna are calculated for incluion in the olution of location euation 6-8. Inherent in thi proce i the etablihment of an oriin and x and y direction. It i ometime poible to ue exitin ubtation mappin data to help in relatin the PD ource location to the ubtation euipment. c) Meaurement All data i recorded on ite and analyed for PD location offline. The trier level and enitivity of the ocillocope are et accordin to ite condition. In eneral, WRPD waveform do not exceed mv in amplitude. Data uitable for identifyin the location of a continuou PD ource can be recorded within a few minute. In view of the fact that many PD are intermittent, however, it i poible (with uitable weatherproofin) to leave the euipment for loner-term 7 33 mm. meaurement, e.. monitorin period of day or week. VI. RESULTS The locator ha been extenively teted in a variety of ite trial. Thi ection decribe the reult of a laboratory tet and two ite cae tudie. A. Laboratory Tet Locatin accuracy wa teted under laboratory condition. Fiure how a plan view of the arranement conitin of a inle phae tet tranformer, PD cell containin a point-plane ap with varyin dielectric, capacitive divider, connectin bubar and the locator -antenna array arraned in a Y- confiuration. The tranformer voltae wa raied until PD inception ( 6 kv dependin on the dielectric). The PD cell and bubar were located at a heiht of. m Tranformer antenna array PD tet cell Divider Bubar PD locator reult -7 - Fi.. Laboratory tet arranement (axe in metre). The arrival time difference from the locator were calculated a decribed in the previou ection. When applied to the location alorithm, diverent behaviour wa oberved and o the noiy inal alorithm decribed in Appendix II wa applied. Three dielectric were ued in thee tet: air, oil and SF 6. From the locator reult hown in Fiure, it can be een that there i little difference in the location amont thee dielectric. Typical location reult are hown in Table toether with PD inal-to-noie voltae ratio (SNVR). The PD SNVR i a ueful metric for decribin the ize of the PD in relation to the backround noie, it i defined a the ratio of the direct wave peak voltae to pre-impule noie peak voltae. It can be een from table that the inception level PD of differin dielectric yield varyin SNVR value, althouh thi did not affect the location. The error in the location (< m) i related to everal factor. Firtly the low PD inal to noie ratio would not allow interpolation of the cro-correlation

7 7 product to improve the arrival time difference accuracy. Secondly, iven thi fact, it can be een by reference to Fiure 9 that the PD ource i at the extremitie of the ueful Y-array area. three orthoraphic view of the antenna, overhead line, houe and locator output. 5 Antenna array ituated in arden Dielectric X (m) Y (m) Z (m) PD SNR Air Oil SF Table : Typical location reult for laboratory tet. B. Cae Study : Capacitor Bank Invetiatiot. Thi reult wa recorded at a 3 kv ubtation followin obervation of increaed level of RFI when a capacitor bank wa eneried. The location reult i hown in Fiure, which i uperimpoed on a ite plan. The vertical heiht of the location are in the reion of 3.5 m, which correpond the top row of capacitor. The PD SNR for thee reult wa approximately 5. Preence of the PD wa confirmed uin a directional ultraound un. Thi ituation i bein monitored by the utility. z axi (m) z axi (m) y axi (m) metre metre metre metre metre 5 5 Cct Cct x axi (m) x axi (m) Earth wire Phae conductor Overhead line conductor metre y axi (m) m Fi.. Capacitor bank invetiation. Antenna and PD location hown uperimpoed on ite plan. C. Cae Study : Overhead line defect Thi tudy wa conducted a the reult of a complaint brouht by reident whoe houe i ituated underneath a ditribution company 3 kv double circuit overhead line. The complaint concerned ditortion of televiion and FM radio reception which wa oberved to increae durin dry condition. The antenna array wa et up in the arden of the complainant. The meaured PD SNR wa 5. Fiure 3 how Fi. 3. Overhead line invetiation. Three orthoraphic view howin the PD bearin from the locator in relation to buildin and the overhead line. Application of the conventional locator alorithm revealed that the PD ource wa too far removed from the array (in exce of m) for converence on an exact location. In thi ituation the alorithm will iterate continuouly, each iteration producin a location output that lie on the line joinin the array centre and the ource. By howin the reult of over 3 eparately recorded WRPD impule, and haltin the alorithm after 5 iteration, thi line can be clearly een. (Note that alorithm reult occurrin cloe to the array have been uppreed.) In thi cae tudy, the lack of a definitive location

8 8 i not a diadvantae ince the location of the PD ource i clearly identified, bein the lowet phae on circuit, ituated approximately 5 m horizontally to the left of the complainant houe. Obervation of the reion of the line identified by the locator throuh binocular howed damae to the outer conductor trand. VII. CONCLUSIONS A radiometric partial dichare locator ha been developed that i uitable for application in the vicinity of enerized hihvoltae plant. The locator i baed on ultra-hih-peed, directly-ampled antenna meaurement that allow the direct wave component of the radiated inal to be reolved. The reult of the locator how that it can locate PD ource to within a few metre if the ditance to the antenna array i le than 5 m. PD ource ituated at reater than thi ditance cannot be located, but can be identified throuh the 3- dimenional bearin of the ource from the antenna array. The inificant advantae of thi euipment are:. No electrical connection are made to the plant,. No plant outae i reuired, 3. Meaurement are made whil t the plant i enerized,. The euipment i portable and eaily ite-deployable, 5. The euipment can be left to monitor unattended in ituation where the PD ource i intermittent. VIII. FURTHER WORK Further development of the locator i currently bein purued:. Vehicle baed olution: to improve the application of the locator a verion i currently bein fitted to a van. Thi verion ha a fixed array mounted to the roof, with the amplin euipment bein located within, and powered from, the van.. Subtation monitorin: a ytem intalled in a ubtation with a fixed array on the roof of the ubtation buildin i currently under trial. Both of thee project are in prore and i hoped to report on development in due coure. Additionally, the followin invetiation are bein planned: 3. Undertandin of the emiion of radiative PD inal: more reearch i reuired to explain thi effect, particularly where the PD ource i located within a teel tank, uch a defect in tranformer.. Correlation between PD manitude (pc) and radiated field meaurement. IX. ACKNOWLEDGEMENTS Thi project wa upported by the UK Enineerin and Phyical Science Reearch Council (rant GR/R7799), the National Grid Company (NGC) and the UK Radiocommunication Aency (RA). The enthuiam and kindne of many people have contributed to the ucce of thi project it i not poible to mention everyone. The author are particularly rateful to Tim Adam, Colin Wellenkamp, Jack Blakett and Geoff Lewi from NGC. Sean OConnell and Bob Taylor from the RA are epecially thanked for their expertie in the dein of the antenna. X. APPENDIX I: SOLUTION OF LOCATION EQUATIONS Euation 6 8 can be olved by application of the Newton Raphon techniue. Etimate of the variable x, y, and z will be denoted a x, y, and z repectively. To correct the etimate, a corrective term mut be added to ive the correct olution, e.. x + x = x and imilarly for the other variable where x, y, and z are the corrective term. Euation 6 8 can be re-expreed a: f etc, where function f, f 3 and f will be zero a tated, but enerally non-zero if etimated value are ued, i.e. x replaced with x, etc. Thee function can be expreed in a matrix formulation: x, y, z = f f f En A ( ) [ ] T F 3 Subtitutin euation A with the etimated variable and df( x,, z ) F( x, y, z ) = F ( x,, z ) + d( x, y, z ) En A3 expandin with the firt two term of a Taylor erie yield: T where = [ x z ] i a matrix of corrective term. The final derivative term in euation A3 i a Jacobean matrix of partial derivative, J. Thi matrix i pecifically evaluated a: x x x x J = x x ct = En A x x x x 3 x x 3 y y y y y 3 y z z z z z z z z z z 3 z z Finally, the corrective term of the etimated variable can be evaluated from: = J F ( x,, z ) from which improved etimate of the unknown variable may be found. Application of thi procedure will find the 3- dimenional PD ource poition to an accuracy of.5 m in, typically, iteration. Initially, the unknown variable are et to zero. XI. APPENDIX II: SOLUTION FOR NOISY SIGNALS In the preence of hih level of backround noie, the error in the time delay can lead to diverent behaviour of the location alorithm. Thi can be overcome by the followin procedure:. The time delay t, t 3 and t are calculated a previouly decribed, but additionally t 3, t 3 and t are 3 En A En A5 3

9 9 al o evaluated note that thee latter time delay are not ued in the location olution.. A mall adjutment i made to the time delay: t +?, t 3 +? 3 and t +?. 3. An error function, e, i calculated decribin the difference between the adjuted time delay and the additional time delay unued in the olution: h 3 + h3 h ε = h + where ( t + ( t + ) ) = etc. En A6. The olution alorithm i applied uin the adjuted time delay. 5. The above procedure i repeated for all combination of time delay adjutment?,? 3 and? in the rane -.5 to +.5 amplin interval at tep of.. 6. The PD ource poition i found from the convered alorithm olution that minimize e. 3 t3 XII. REFERENCES [] Z. D. Wan, P. A. Croley, and K. J. Cornick, Partial dichare location in power tranformer uin the pectra of the terminal current inal, Eleventh International Sympoium on Hih Voltae Enineerin (IEE Conf. Publ. No. 67),999, vol. 5, pp [] P. Werle, H. Bori, and E. Gockenbach, A new method for partial dichare location on power tranformer baed on a ytem theoretical approach, 6th International Conference on Propertie and Application of Dielectric Material,, vol., pp [3] P. Werle, A. Akbari, H. Bori, and E. Gockenbach, Partial dichare localiation on power tranformer uin neural network combined with ectional windin tranfer function a knowlede bae, International Sympoium on Electrical Inulatin Material,, pp [] K. Raja and T. Floribert, Comparative invetiation on UHF and acoutic PD detection enitivity in tranformer, IEEE International Sympoium on Electrical Inulation,, pp [5] M. D. Judd, G. F. Cleary and C. J. Bennoch, Applyin UHF partial dichare detection to power tranformer, IEEE Power Enineerin Review, Auut 3, pp [6] H. J. van Breen, E. Gulki and J. J. Smit, Localizin the Source of Partial Dichare in Lare Generator, 6th International Conference on Propertie and Application of Dielectric Material,, vol., pp [7] Y. Tian, P. L. Lewin, A. E. Davie, S. J. Sutton and S. G. Swinler, Partial dichare detection in cable uin VHF capacitive coupler, IEEE Tranaction on Dielectric and Electrical Inulation, vol., iue, April 3, pp [8] F. H. Kreuer, Dichare detection in hih voltae euipment, Temple Pre, London, 96. [9] J. P. Steiner, P. H. Reynold and W. L. Week, Etimatin the Location of Partial Dichare in Cable, IEEE Tranaction on Electrical Inulation, vol. 7, no., February 99. [] B. Quak, E. Gulki, F. J. Weter and P. N. Seitz, Advanced PD ite location in ditribution power cable, Seventh International Conference on Propertie and Application of Dielectric Material, Vol., 3, pp [] M. S. Mahikian, Preventive maintenance tetin of hielded power cable ytem, IEEE Tranaction on Indutry Application, Vol. 38, Iue 3, May/Jun, pp [] E. Lemke, A new procedure for partial dichare meaurement on the bai of an electromanetical enor, Fifth International Sympoium on Hih Voltae Enineerin, 988, Paper.. [3] A. Tunkanawanich, Z. I. Kawaaki, J. Abe and K. Matuura, Location of partial dichare ource on ditribution line by meaurin emitted pule-train electromanetic wave, IEEE Power Enineerin Society Winter Meetin,, Vol., pp [] M. Kawada, Ultra Wide Band VHF/UHF Radio Interferometer Sytem for Detectin Partial Dichare Source, IEEE Power Enineerin Society Winter Meetin,, Vol., pp [5] A. Cavallini et al, A new approach to the dianoi of olid inulation ytem baed on PD inal inference, IEEE Electrical Inulation Maazine, March/April 3, Vol. 9, No., pp [6] A. J. M. Pemen et al, On-line partial dichare monitorin of HV component, Eleventh International Sympoium on Hih Voltae Enineerin (IEE Conf. Publ. No. 67),999, vol. 5, pp [7] P. J. Moore, I. E. Portuue and I. A. Glover, Pollution of the radio pectrum from the eneration of impulive noie by hihvoltae euipment, IEE Conference on Gettin the mot out of the radio pectrum, London, October, IEE Publication /, pp 37/-37/5. XIII. BIOGRAPHY Philip Moore (M and SM 996) wa born in Liverpool, Enland in 96. He received hi BEn in Electrical Enineerin from Imperial Collee London in 98 and hi PhD in Power Sytem Protection from City Univerity London in 989. From 98 to 987, he wa a Development Enineer at Altom Protection and Control, formerly GEC Meaurement. From 987 to 99 he wa a lecturer in Electrical Enineerin at City Univerity. He joined the Univerity of Bath in 99 where he i preently a Senior Lecturer. Dr Moore' reearch interet include radio freuency emiion from power ytem plant, harmonic, numeric protection, hih voltae dichare, power ytem imulation and fault location. Dr Moore i a Chartered Enineer in the UK. Iliana Portuué wa born in Madrid, Spain in 979. She raduated with a MEn deree in Electronic and Communication Enineerin from the Univerity of Bath in. She wa awarded a Univerity Departmental prize for her work on harmonic meaurement. She i currently employed at the Univerity of Bath a a Reearch Officer in the Department of Electronic and Electrical Enineerin, invetiatin the characteritic radio freuency emiion from defective ubtation inulation.

10 Ian Glover trained, between 975 and 98, a a power enineer with the Yorkhire Electricity Board (UK) raduatin from the Univerity of Bradford (UK) in 98 with a BEn deree in Electrical and Electronic Enineerin. Between 98 and 98 he worked a a reearch tudent at the Univerity of Bradford. Between 98 and 999 he wa employed at the Univerity of Bradford, firt a a lecturer in Electronic and Electrical Enineerin and ubeuently a a enior lecturer. In 987 he wa awarded a PhD for a thei on microwave cro-polariation by the Univerity of Bradford. In 999 he moved to the Univerity of Bath (UK) where he i currently a enior lecturer in telecommunication. Ian Glover i, with Peter Grant, the author of Diital Communication publihed by Prentice-Hall. Hi principal reearch interet are in the area of radio cience and radio ytem, includin channel modelin, channel meaurement and the impulive noie environment.