Analysis of Potential Use of the SVM Technique for Transformer Protection

Transcription

1 Analyss of Potental Use of the SVM Technque for Transformer Protecton Danel Bejmert, Waldemar Rebzant Wroclaw Unversty of Technology, Poland Ludwg Schel Semens AG, Germany Abstract Relable and fast dscrmnaton between nternal faults and nrush condtons s stll a challengng ssue. In ths paper an applcaton of Support Vector Machne (SVM for the transformer dfferental protecton s dscussed. To acheve the satsfactory classfcaton strength varous nput vectors and tranng parameters were consdered. Fnally, 6 dfferent versons of SVM classfers are proposed. The developed SVM based power transformer protecton unts have been traned and tested wth EMTP-ATP generated sgnals. The operaton performance of desgned SVM classfers s compared to standard dfferental protecton wth tradtonal second harmonc stablzaton approach. Moreover, potental hardware mplementaton of the presented SVM classfers s analyzed. Keywords protectve relayng, transformer dfferental protecton, SVM I. ITRODUCTIO Dfferental current prncple belongs to the oldest and wdely used crtera n power system protecton. Ths protecton s usually employed to protect hgh voltage power transformer whch are very mportant for proper system operaton. It means that false trppng of the dfferental protecton usually leads to outages to large number of customers and may sgnfcantly affect power system stablty. Thus, hgh securty requrements (under eternal dsturbances and transformer energzaton are mposed on the power transformer dfferental protecton. Obvously the very hgh securty cannot deterorate dependablty and operaton speed. In order to satsfy abovementoned requrements dfferental protecton relays usually employ based dfferental prncple and second harmonc blockng logc. These solutons usually ensure good stablzaton durng eternal faults and at the same tme satsfactory level of senstvty under nternal faults. evertheless, undesrable operatons may take place when durng transformer energzaton second harmonc content n dfferental currents s low. Hence, there s stll the need to mprove the performance of transformer dfferental protecton. In the past few decades, varous tools of artfcal ntellgence (neural networks, fuzzy logc epert systems have been used to mprove selectvty, sensblty and operaton speed of the power transformer protecton [,,3,]. Recently, n order to acheve effectve dscrmnaton between magnetzng nrush and nternal fault, a new approaches based on Support Vector Machne (SVM have been proposed [5,6,7,,]. In ths paper varous versons of the SVM based power transformer protecton are proposed and tested under varety of dsturbances. In comparson to the solutons presented n [5,6,7,,] dfferent nput data vectors have been consdered and more attenton has been devoted to the potental hardware mplementaton of the SVM classfers desgned. The frst part of the paper contans short descrpton of the bascs of SVMs wth specal consderaton to the general features, tranng parameters selecton and hardware mplementaton. In the other part of the paper operaton relablty and potental hardware mplementaton of proposed versons of SVM based transformer protecton s analyzed and dscussed. In the paper 6 varous versons of SVM classfers (acheved for dfferent nput vectors and tranng parameters are presented. Each verson s characterzed n detals and process of the tranng/testng data preparaton s eplaned. The EMTP model of power transformer have been used to generate varous cases of faults as well as transformer energzaton. Vast base of sgnals was employed to tran and verfy performance of all desgned SVM classfers. Furthermore, hardware mplementaton of the best classfers s analysed from the vew pont of computatonal complety. The last secton closes the paper wth some conclusons and prospect of further nvestgaton. II. SUPPORT VECTOR MACHIE BASICS The Support Vector Machne s a wdely used classfer employed to solve ether lnear and nonlnear classfcaton problems. The basc understandng of the theory behnd SVMs s presented below. A. Lnearly Separable Data Let us consder a lnear classfcaton problem amng to fnd optmal separatng hyperplane wth mamum margn. Assumng that for the set of n tranng data [8,9,,3]: d {(, y ; R, y {, } T ( where:,,..., n; d-dmensonal nput vector; y ndcates a class ( or - of a gven nput vector; t s possble to fnd lnear hyperplane that dvdes the eamples characterzed by approprate class, as shown n Fg.. 8 th Power Systems Computaton Conference Wroclaw, Poland August 8-,

2 In such case the hyperplane w + b ( where: w weght vector, b bas, dvdes the hyperspace nto two regons classfed as postve (Class and negatve (Class. Addtonally t s possble to fnd two hyperplanes wth no ponts between them: w + b (3 w + b ( Then a dstance between these two functons s Margn (5 w Accordng to above equatons lnearly separable data for whch there ests a lnear decson boundary that separates postve from negatve eamples may be depcted as n Fg.. Snce the dstance between these two functons s equal to / w, then to ncrease ths dstance w has to be mnmzed. Ths optmzaton problem s solved by ntroducng Lagrange multplers and then class of the unknown data may be determned as follows: where: SV T Class ( sgn α y + b (6 SV w α y (7 T s tranng vector (support vector, y s class of a gven tranng vector, s nput data of SVM classfer, α s Lagrange multpler (calculated n tranng process, b s a bas (calculated n tranng process, SV s the number of support vectors. The tranng data whch are the closest to the class boundary (crcled ponts n Fg. determne the margn separatng these two classes and they are called as Support Vectors. ξ w + b w + b w + b w B. Lnearly onseparable Data When tranng data cannot be lnearly separated, then nput data must be mapped from the nput space to a new feature space. For ths purpose nonlnear functon φ s used. Then the class of unknown data may be epressed as follows [8,9,]: SV T Class( sgn α y φ( φ( + b (8 When the term φ( T φ( s replaced wth kernel functon defned as [8,9,] T K (, φ ( φ ( (9 the decson functon of nonlnear SVM s [8,9,]: SV Class( sgn α y K + b (, ( The most common kernel functons are [8,9,]: Polynomal Hyperbolc tangent K(, Gaussan radal bass functon ( d ( c K(, tanh κ + K(, ep σ d ( ( (3 C. Soft Margn It may happen that even n new feature space t s mpossble to splt ths space nto two classes. Then, soft margn method may be employed to moderate optmzaton constrants. Soft margn method allows the classfer to msclassfy some eamples, what s llustrated n Fg.. Ths method ntroduces two parameters (used n tranng process [8,9,]: ξ slack varables that allow patterns to be n the margn (< ξ <, margn errors or to be msclassfed (ξ >, C constant whch s used to penalze msclassfed and margn error eamples. Hgher values of C brng lower number of msclassfcatons but at the same tme decreased margn. When the soft margn method s employed the optmzaton problem s also solved by ntroducng Lagrange multplers. The class of unknown data may be estmated wth the same formulas: (6 for lnear and ( for nonlnear classfer. Fg.. Illustraton of hyperplane wth mamum margn and slack varable ξ. for msclassfed data. D. General Features Support vector machne s consdered as a promsng method for classfcaton due to [8,]: - sold mathematcal foundatons, 8 th Power Systems Computaton Conference Wroclaw, Poland August 8-,

3 - fast optmzaton algorthms, - no local optma, unlke n neural networks, - SVMs mamze the margn, whch corresponds to mamzng the generalzaton performance, - SVMs deal wth nonlnear classfcaton effcently (employng the kernel trck, - good generalzaton performance even n case of hghdmensonal nput vector and a small set of tranng data. Snce SVM belongs to the famly of artfcal ntellgence technques and ts dea s smlar to ths behnd the artfcal neural network (A, below a comparson of ths two approaches s presented. The most mportant dfferences between SVM and A are [6,8]: - the soluton to an SVM s global whle As can suffer from multple local mnma, - SVMs have a smple geometrc nterpretaton, - computatonal complety of SVMs does not depend (drectly on the dmensonalty of the nput space, - SVMs are less prone to overfttng than As. The performance effcency of SVM based classfer depends on properly conducted tranng process. The basc am of SVM supervsed learnng s to mamze the generalzaton by mamzng the margn (boundary to the closest data n the feature space and to avod over- and underfttng. Learnng process s supported by kernel trck and the effectveness of SVM depends on: - approprate selecton of features creatng nput vector (these features should characterzed the classfed problem well, - good tranng model (large number of varous data from each class, - chosen kernel functon, - kernel functon parameters, - trade-off parameter (C between mamal margn and mnmal error. E. Hardware mplementaton To asses computatonal complety of SVM based classfer hardware mplementaton of SVM s consdered n ths subsecton. If one assumes that the class of unknown data w s estmated accordng to the followng formula: SV Class( w sgn α y K(, w + b ( the general block scheme of such classfer s presented n Fg.. It s well seen n Fg. that there are three man factors whch affect computatonal complety, namely: - dmenson of nput vector, - number of support vectors, - chosen kernel functon. III. PROPOSED SCHEME OF SVM BASED TRASFORMER PROTECTIO In ths secton four varous versons of SVM based transformer protecton schemes are proposed. Each verson s characterzed n detals and process of the tranng/testng data preparaton s eplaned. SV,,, [ w w ] w,..., w d,, SV, [ y y ] y,..., y SV..., d..., d... SV, d [ α α α ] T α,..., Fg.. Block dagram of SVM operaton prncple. SV SVM based transformer protecton Verson I In ths verson, an nput vector of SVM classfer conssts of consecutve samples (full cycle of dfferental current (nstantaneous values, separately for each phase LX ( n [ dff dff ( n,..., dff ( n + ] (5 where: n number of actual (the most recent sample, number of samples n one cycle of fundamental component, LX phase nde. Transformer protecton scheme based on Verson I s actvated when dfferental current of partcular phase eceeds.5i. SVM based transformer protecton Verson II Input vector of Verson II of SVM classfer s calculated accordng to the same equaton as Verson I (5. Transformer protecton scheme based on Verson II s actvated 5 ms after detecton of sudden change of termnal currents (dsturbance dentfcaton and when dfferental current of partcular phase eceeds.5i. SVM based transformer protecton Verson III Input vector conssts of consecutve samples (full cycle of dfferental current (nstantaneous values, separately for each phase normalzed as follows: [ dff dff ( n,..., dff ( n + ] LX ( n ma( ( n,..., ( n + (6 dff dff dff Transformer protecton scheme based on Verson III s actvated 5 ms after detecton of sudden change of termnal currents (dsturbance dentfcaton and when dfferental current of partcular phase eceeds.5i. SVM based transformer protecton Verson IV In ths verson nput vector conssts of frst 7 ampltudes of spectral lnes of the dfferental current. The spectrum s calculated wth full cycle dscrete Fourer transform (separately for each phase. LX ( n [ Adff ma( A _ dff _ Adff A _ dff _..., Adff..., A _ 6 dff _ 6 ( n] ( n (7 8 th Power Systems Computaton Conference Wroclaw, Poland August 8-,

4 where: A dff_lx_ ampltude of spectral lne calculated wth DFT ( DC component, 6 sth harmonc. To prepare tranng data, approprate vectors were etracted from each case from the sgnal base (see Secton IV. Features related to steady state were taken from two data wndows captured rght before the begnnng of dsturbance. To collect date at the begnnng and after the dsturbance, tme span of 6 ms was taken nto consderaton. Wthn ths tme span feature vectors were captured (wth 5 samples step. Procedure descrbed above s presented here wth reference to Verson I of proposed algorthm: Data captured before the dsturbance casex pre dff dff ( n + 3 ( n + ( n + dff 3 dff ( n + dff dff ( n ( n / Data captured at the begnnng and after the dsturbance casex post dff dff ( n dff ( n + ( n + 9 ( n 9 dff ( n 9 + dff ( n dff dff ( n + dff ( n + + ( n dff (8 (9 where n ndcates the begnnng of dsturbance. Fnally, above vectors etracted from each case were aggregated nto one tranng/testng data matr. IV. PERFORMACE AALYSIS In ths subsecton operaton relablty and potental hardware mplementaton of proposed versons of SVM based transformer protecton s analyzed and dscussed. In order to obtan the data for tranng and valdaton of proposed algorthms the EMTP model of the power system shown n Fg. 3 was used. It comprses the protected transformer (Trafo as well as equvalent feedng systems from both sdes that are represented by electromotve sources behnd approprate mpedances (postve and zero sequence values. The protected transformer could be fed from the HV sde, MV sde and from both sdes. Addtonal load was connected on ether of the transformer sdes. The HV/MV transformer consdered was a 3MVA 5/kV Yd unt wth fve-leg core. The transformer consdered was a saturable unt, whch s reflected n the EMTP-ATP model n form of saturable nductances (wth hysteress ntroduced at the Delta sde. E SA 5 kv Z SA D D D3 Z O D Z Trafo Fg. 3. Power system model under study. Z O Load kv Z SB D8 To consder vast range of dsturbances followng stuatons were smulated n abovementoned model: eternal faults at HV/MV sde, nternal faults at HV/MV sde, nter-turn faults D5 F D6 D7 D9 E SB at HV sde and transformer energzaton. Addtonally, varaton of the followng system parameters have been taken nto account: faults type, HV/MV source mpedances, CTs load, fault ncepton tme, energzaton sde, swtchng tme, remanent flu. A total number of 86 cases were generated under mentoned above operatng condtons: eternal dsturbances, nternal faults. All these cases were used to perform both tranng and testng of desgned SVM based transformer protecton. Under tranng process varous kernel functons (KF, kernel functon parameters and tranng parameters were used. As a result of such approach many dfferent classfers were obtaned, but n the paper only 6 chosen ones are presented. In Tab. overall error rate (whch epresses number of ncorrect dsturbance dentfcaton and number of support vectors of each classfer are presented. It may be notced that all consdered solutons dd not acheve suffcent level of relablty. evertheless, snce hgh relablty of transformer protecton s requred t seems that Verson I (Gaussan KF, γ, C provdes the best performance. But t may be also notced that ths classfer comprses of 7 support vectors what may pose hard to overcome hardware mplementaton dffcultes. The hardware mplementaton s understood as a mplementaton on a currently used dgtal protecton relay platform (e.g. Intellgent Electronc Devces (IED. Snce t s mpossble to get precse data (nstructon per second, cycles per mathematcal operaton of mcroprocessors embedded n IED, here only the total number of requred mathematcal operatons s dscussed. Overall number of mathematcal operatons requred to calculate sngle decson sgnal may be assessed wth use of Fg.. In a case of SVM Verson I one may fnd: - *7 summatons, - *7*7+*7 multplcatons, - 7 operatons of KF. It s well seen that so hgh number of support vectors results n enormous number of math operatons. Ths wll obvously brng hgh computatonal burden (especally when kernel functon s comple for hardware platform. On the other hand one may fnd that for classfers wth lower number of support vectors operaton effcency s much below the epectatons, at least ths acheved from statstcal analyss. In the further part of ths secton testng results of SVM based power transformer protecton are presented. The SVM classfer characterzed by the hghest effcency (Verson I, Gaussan KF, γ, C was selected to be eamned under varous dsturbances. The operaton results wll be compared wth performance of classc dfferental protecton wth second harmonc restrant and cross-block functon. Case Two-phase-to-ground eternal fault at HV sde In ths case transent CT saturaton under eternal fault takes place at both sdes of the protected transformer. Due to the dfferences n saturaton level of CTs nstalled at both sdes substantal and strongly dstorted dfferental currents arse, as shown n Fg.. In Fg. 5 one may observe that under such condtons classc dfferental protecton remans stable thanks to hgh level of second harmonc content as well as 8 th Power Systems Computaton Conference Wroclaw, Poland August 8-,

5 employment of cross-block functon (reacton of classc protecton only n phase L3. At the same tme SVM soluton turned out unrelable undesrable trppng decson was ssued, see Fgs. 6. TABLE I. Input Vector Verson I Verson II Verson III Verson IV I dff [pu], ph. L I dff [pu], ph. L I dff - PERFORMACE RESULTS OF PROPOSED SVM CLASSIFIER Kernel Functon KF Parameters Gaussan γ Polynomal Gaussan γ Polynomal Gaussan γ Polynomal Gaussan γ Polynomal C Dfferental currents SV Overall Error Rate [%] Fg.. Dfferental currents under Case., ph.l, ph.l, ph.l3.5 sgnals Pckup Pckup Pckup Fg. 5. sgnals of classc dfferental protecton wth nd harmonc blockng under Case., ph.l, ph.l, ph.l3.5 sgnals SVM - Verson I Fg. 6. sgnals of SVM classfer Verson I under Case. Case Three-phase eternal fault at MV sde Under consdered here condtons, hgh value short-crcut currents flowng n all three phase on both sdes of protected transformer evoke substantal and sgnfcantly dstorted dfferental currents, as shown n Fg. 7. In Fg. 8 one may observe that under such condtons classc dfferental protecton remans stable thanks to hgh level of second harmonc content as well as employment of cross-block functon (trppng sgnal s ssued only n phase L. As far as SVM soluton s concerned, undesrable reacton s observed n phases L and L3 what would lead to maloperaton of proposed protecton scheme, see Fgs. 9. I dff [pu], ph. L I dff [pu], ph. L I dff - - Dfferental currents Fg. 7. Dfferental currents under Case. 8 th Power Systems Computaton Conference Wroclaw, Poland August 8-,

6 , ph.l, ph.l, ph.l3.5 sgnals Pckup Pckup Pckup Fg. 8. sgnals of classc dfferental protecton wth nd harmonc blockng under Case., ph.l, ph.l, ph.l3.5 sgnals SVM - Verson I Fg. 9. sgnals of SVM classfer Verson I under Case. Case 3 Two-phase nternal fault at MV sde Under nternal faults fast and relable operaton of the power transformer protecton s requred. In presented case of nternal fault deep and permanent CT saturaton occurs at both sdes of the transformer rght after fault ncepton. Obvously, n such condtons hgh level heavly dstorted dfferental currents are observed, as shown n Fg.. It may be notced that n ths case all tested algorthms provde approprate reacton after fault ncepton, see Fgs. and. evertheless, t should be emphaszed that operaton speed of SVM based algorthm s slghtly hgher as compared to classc dfferental protecton under such dsturbance. I dff [pu], ph. L I dff [pu], ph. L I dff Dfferental currents Fg.. Dfferental currents under Case 3., ph.l, ph.l, ph.l3.5 sgnals Pckup Pckup Pckup Fg.. sgnals of classc dfferental protecton wth nd harmonc blockng under Case 3., ph.l, ph.l, ph.l3.5 sgnals SVM - Verson I Fg.. sgnals of SVM classfer Verson I under Case 3. Case Transformer energzaton from HV sde The last analyzed case s transformer energzaton wth smultaneous deep CT saturaton. It creates substantal and hghly dstorted dfferental currents, what s shown n Fg. 3. Snce the content of second harmonc n dfferental currents drops for a short perod below the blockng threshold classc approach s not able to provde stablzaton under such condton, see Fg.. On the contrary, SVM based approach Verson I provdes suffcent stablzaton level and does not ssue trppng sgnal, see Fg. 5. I dff [pu], ph. L I dff I dff [pu], ph. L Dfferental currents Fg. 3. Dfferental currents under Case. 8 th Power Systems Computaton Conference Wroclaw, Poland August 8-,

7 , ph.l, ph.l, ph.l3.5 sgnals Pckup Pckup Pckup Fg.. sgnals of classc dfferental protecton wth nd harmonc blockng under Case., ph.l, ph.l, ph.l3.5 sgnals SVM - Verson I Fg. 5. sgnals of SVM classfer Verson I under Case. V. COCLUSIOS In the paper applcaton restrctons, prerequstes, performance requrements and general features of Support Vector Machne (SVM based transformer dfferental protecton are dscussed. The paper starts wth presentaton of SVMs theoretcal bascs. Then four varous versons of SVM classfers (characterzed by dfferent nput vectors and tranng parameters are proposed. Presented results of performance analyss show that Verson I ensures better dscrmnaton between eternal and nternal dsturbances and hgher operaton speed as compared to classc dfferental protecton wth second harmonc restrant and cross-block functon. But t must be emphaszed that overall error rate of all desgned SVM based transformer dfferental protecton versons s at too hgh level. It turned out that the most challengng cases for the proposed SVM protecton scheme were: eternal fault wth deep CTs saturaton and transformer energzaton characterzed by low level of second harmonc content n dfferental currents. Moreover, due to large number of support vectors of SVM based classfer, ts hardware mplementaton currently used dgtal platforms (e.g. on Intellgent Electronc Devces would be dffcult. In the future some further nvestgatons may be done to reduce number of support vectors and to fnd more effectve SVM classfers. REFERECES [] M.M. Saha, B. Kasztenny, AI methods n power system protecton, Eng. Int. Systems, Vol. 5, o., Dec. 997, pp [] B. Kasztenny, E. Rosołowsk, M.M. Saha, B. Hllstrom, A selforganzng fuzzy logc based protectve relay an applcaton to power transformer protecton, IEEE Transactons on Power Delvery, Vol., o. 3, July 997. [3] D. Bejmert, W. Rebzant, L. Schel, L. Staszewsk: ew Mult-Crtera Fuzzy Logc Transformer Inrush Restrant Algorthm, Proceedngs of the DPSP Conference, 3-6.., Brmngham, UK, paper O.. [] D. Bejmert, W. Rebzant, L. Schel: Transformer Dfferental Protecton wth eural etwork Based Inrush Stablzaton, Proceedngs of the 7 IEEE Lausanne PowerTech Conference, Ecole Polytechnque Federale de Lausanne, Swtzerland, -5 July 7, CD- ROM, paper 67. [5] A. M. Shah, B. R. Bhalja,: Applcaton of Support Vector Machne for Dgtal Protecton of Power Transformer, Inda Conference (IDICO, Annual IEEE. [6] D. Vkramadty, S. Avdhesh: Operaton of Dfferental Relay for Power Transformer Usng Support Vector Machne, Transmsson and Dstrbuton Conference and Eposton, IEEE, Chcago - Aprl 8. [7] S. Subramanan, B. Mathur, J. Henry: Wavelet Packet Transform and Support Vector Machne Based Dscrmnaton of Power Transformer Inrush Current from Internal Fault Currents, Modern Appled Scence, Vol, o 5 (. [8] A. Ben-Hur, J. Weston: A User's Gude to Support Vector Machnes, Methods n Molecular Bology, vol. 69, pp. 3-39, Humana Press. [9] How to use the DK Support Vector Machne (SVM MATLAB toolbo, [] D. Mahmood, A. Soleman, H. Khosrav, M. Taghzadeh: FPGA Smulaton of Lnear and onlnear Support Vector Machne, Journal of Software Engneerng and Applcatons,,, pp [] B. R. Bhalja, A. M Shah: A new approach to dgtal protecton of power transformer usng support vector machne, th Canadan Conference on Electrcal and Computer Engneerng, 8- May, agara Falls, O, pp. -. [] M. Hajan, A. Akbar Foroud: Protecton scheme of power transformer based on tme frequency analyss and KSIR-SSVM, Journal of AI and Data Mnng Vol., o., 3, pp [3] C. Cortes, V. Vapnk: Support-Vector etworks, Machne Learnng,, 995, pp th Power Systems Computaton Conference Wroclaw, Poland August 8-,