J. Electrical Systems 13-3 (2017): Regular paper

Transcription

1 Mng-Yuan Cho 1, Hoang Th Thom 1,* J. Electrcal Systems 13-3 (2017): Regular paper Fault Dagnoss for Dstrbuton Networks Usng Enhanced Support Vector Machne Classfer wth Classcal Multdmensonal Scalng JES Journal of Electrcal Systems In ths paper, a new fault dagnoss technques based on tme doman reflectometry (TDR) method wth pseudo-random bnary sequence (PRBS) stmulus and support vector machne (SVM) classfer has been nvestgated to recognze the dfferent types of fault n the radal dstrbuton feeders. Ths novel technque has consdered the ampltude of reflected sgnals and the peaks of cross-correlaton (CCR) between the reflected and ncdent wave for generatng fault current dataset for SVM. Furthermore, ths mult-layer enhanced SVM classfer s combned wth classcal multdmensonal scalng (CMDS) feature extracton algorthm and kernel parameter optmzaton to ncrease tranng speed and mprove overall classfcaton accuracy. The proposed technque has been tested on a radal dstrbuton feeder to dentfy ten dfferent types of fault consderng 12 nput features generated by usng Smulnk software and MATLAB Toolbox. The success rate of SVM classfer s over 95% whch demonstrates the effectveness and the hgh accuracy of proposed method. Keywords: Classcal multdmensonal scalng, dstrbuton feeder, fault dagnoss, support vector machne. Artcle hstory: Receved 2 March 2017, Accepted 29 June Introducton Power dstrbuton system plays an mportant n power system because t provdes electrcal energy from transmsson system to users. Thus, t s essentcal to protect dstrbuton networks agast electrcal faults n order to guarantee the realblty of power system. However, fault dagnoss n dstrbuton networks s not easy due to mult-branch topology, unbalance operaton and wde varaton load [1-2]. As a result, varety of approaches have been proposed to dagnose fault n power dstrbuton systems. These approaches can be dvded three followng categores: mpedance-based method, travelng wave-based method and artfcal ntellgence-based method. In [3], an ntellgent electronc devce (IED) s used to measure voltage and current sgnals for the purpose of locatng fault. However, t s mprecse wth hgh fault resstance and only employs on 11kV networks. The wavelet transform (WT)-based fault dagnoss method calculates the wavelet coeffcent of dfferent branches based on cross-correlaton (CCR) of reflected and ncdent sgnals [4-5]. The man dsadvantage of ths method s unable to apply for dstrbuton networks wth sgnfcant topology and specal feeders. Besdes, t requres to use hgh samplng rate equpments whch s very dffcult for practcal mplementon. Wth the capacty of strongly robust and nonlnear mappng, the artfcal neuron network (ANN)-based method has developed to overcome the drawback of WT-based method n detectng electrcal faults [6-7]. A combnaton of them was descrbed n [8-9]. In a recent paper, a fault dagnoss technque has been mplemented by means of tranng of neural fuzzy nference system (NFIS) wth features extracted from recorded * Correspondng author: Hoang Th Thom, E-mal: thomht@ntu.edu.vn 1 Department of Electrcal Engneerng, Natonal Kaohsung Unversty of Appled Scences, Kaohsung, Tawan Copyrght JES 2017 on-lne : journal/esrgroups.org/jes

2 H. T. Thom et al: Fault classfcaton for dstrbuton networks usng enhanced SVM... sgnals [10]. Among these method, tme-doman reflectometry (TDR) s one of the most common technques for fault classfcaton and locaton n dstrbuton networks [11-13]. An expert system s proposed to detect fault n hgh voltage dstrbuton networks, but dd not concern mult-branch cables [14]. Whle an automatcally fault locatng technology s appled for dstrbuton systems that consst of three-phase tees, however, the sngle-phase tee cables are not mentoned [15]. An automatc fault locator s used for low votltage underground dstrbuton systems, n whch sngle phase faults and sngle phase tees are dstngushed by usng an adaptve flter [16]. However, the accuracy of ths method s not hgh because of sngle pulse stmulus attenuaton of along the lne. To overcome ths problem, a TDR method wth nput pseudo-random bnary sequence (PRBS) s developed for fndng fault n transmsson systems [17]. The reflectometry method s very dffcult to apply for mult-branch dstrbuton networks due to varous reflectons n the recorded reflectometry trace, thus requres ntellgent algorthms to support. Wth the ablty of hgh generalzaton and global optmzaton, support vector machne (SVM) has emerged as a powerful tool for analyzng such datasets [18-20]. A combnaton of TDR and SVM to determne fault locaton n mult-tee dstrbuton networks s presented n [21], but the complexty of buldng a state transton matrx model from the reflectometry curves s the man dsadvantage of ths method. In ths paper, a new scheme based on reflectometry algorthm and SVM classfer s nvestgated to dagnose the dfferent fault types n dstrbuton networks, ncludng sngle phase to ground fault (AG, BG, CG), lne to lne (AB, AC, BC), double lne to ground fault (ABG, ACG, BCG) and three phase short crcut fault (ABC). The SVM s traned and valdated wth a relable dataset obtaned from reflectometry trace. In addton, the CMDS technque s appled to select approprate nput features n order to mprove the tranng tme and the classfcaton accuracy. All the smulaton works n ths paper have been performed n MATLAB. Rest of the paper s organzed as follows. Secton 2 revews basc concepts of the proposed fault dagnoss method. In Secton 3, a CMDS-based SVM classfer has been developed. Expermental results and dscusson has been gven n Secton 4. Fnally, the conclusons are presented n Secton Concepts of the proposed fault dagnoss method The proposed fault dagnoss method consders the dataset recorded by usng TDR wth ncdent PRBS. Ths dataset are used for tranng SVM whose accuracy s enhanced by CMDS feature extracton algorthm. The basc concepts of the proposed fault dagnoss method are dscussed below TDR and PRBS testng The most popular fault dagnoss technque used for power dstrbuton networks s based on reflectometry method, n whch a sngle pulse s njected nto a cable and then a part of pulse energy s reflected by any mpedance msmatches. These mpedance msmatches can be faults, tee jonts or lne termnals, so the reflected sgnals are used for purpose of fault classfcaton and locaton. 416

3 J. Electrcal Systems 13-3 (2017): Assume a dstrbuton lne s modelled by a lumped-parameter equvalent crcut wth a dstrbuted seres nductance L, resstance R and capactance C per elemental dstance, as shown n Fgure 1. The voltage and current travellng along the lne can be expressed as: ( x, t) v( x + x, t) v( x, t) = L x t v( x, t) ( x + x, t) ( x, t) = C x t where v( x, t) and ( x, t) respectvely; are the ncdent travellng voltage and current waves (1) (2) (x+t) L( x) (x+ x,t) v(x+t) C x + v(x+ x,t) x x+ x Fgure 1. Equvalent model of an overhead lne. Takng the Laplace transform of eqns. (1) and (2) and then dfferentate them wth respect to x, ther soluton after takng the nverse Laplaec transform can be gven as: + x x v( x, t) = v ( t ) + v ( t + ) υ υ (3) + x x ( x, t) = ( t ) + ( t + ) υ υ (4) where v + ( t x / v) and + ( t x / v) sgnals respectvely; v ( t + x / v) and ( t x / v) are the ncdent travellng voltage and current + are the reflected travellng voltage and current sgnals. The result after ncorporatng eqns. (3) and (4) can be gven as: sx sx υ υ I( x, s) [V (s)e -V (s)e ] Z where Z = (5) C C L C = s called the characterstc mpedance. When any mpedance msmatches Z C occurs on the lne then: 417

4 H. T. Thom et al: Fault classfcaton for dstrbuton networks usng enhanced SVM... V( l, s) Z ( s) I( l, s) = (6) Solvng for V ( l, s) R 2s V ( l, s) ( s) V + ( s) e τ where Γ = from eqns. (5) and (6): = Γ (7) Z Z R R Z + Z C C s called the recevng end voltage reflecton coeffcent; τ l υ = s the transt tme. The TDR method usng a sngle pulse for fault dagnoss s mprecse due to stmulus attenuaton wth fault dstance and phase change dstorton wth frequency [22-23]. To overcome the dsadvantages of the tradtonal TDR method, nstead of usng sngle pulse, a PRBS perturbaton s nputted nto the lne under test for the purpose of fndng the fault as shown n Fgure 2. Then echo responses of ths pulse energy are cross-correlated wth the ncdent PRBS by the followng formula: L 1 C ( k) = x( ) y( + k) xy (8) L = 1 where C xy s cross-correlaton (CCR) functon between reflected wave and ncdent wave; x s the forward sgnal and y s the feedback sgnal. In ths paper, the CCR along wth the reflected sgnals obtaned from TDR trace are used for SVM tranng phase for the frst tme. R PRBS SS LOAD Fgure 2. Sngle-lne dagram of a radal dstrbuton system Support vector machne Support vector machne s one of the most optmal technques for data classfcaton, whch was frst mentoned by Vapnk n 1995 [24]. SVM works based on the structural rsk mnmzaton prncple combned wth statstcal machne learnng theory (SLR). The global optmzaton and hgh generalzaton ablty are the man advantages of SVM as comparng to artfcal neuron network (ANN). SVM s employed to map the nput data (x) nto a hgh-dmensonal feature space and buld an optmal hyperplane to separate samples from two classes. To buld the optmal hyperplane, the quadratc optmzaton equaton has to be solved: Mn: 1 w m + C ξ (9) = 1 418

5 J. Electrcal Systems 13-3 (2017): y w x + b 1 ξ, ξ 0, = 1,..., m Subjec to: ( ) where x R n are feature vectors, y (-1,+1) are label vectors, C s the regularzaton parameter and ξ s the penalzng relaxaton varables. Equaton (10) ensures that: w φ( x ) + b + 1 f y = + 1 (11) w φ( x ) + b 1 f y = 1 (12) The nonlnear classfer can be denoted n the nput space as: m * * ( ) = ( α (, ) + ) = 1 f x sgn y K x y b (10) (13) where f(x) s the decson functon, α the Lagrangan multplers, K( x, y ) s the kernel functon. * b s the bas and It can be clearly seen from eqn. (13) that the performance of SVM s dependent on tranng samples and kernel functon. Thus, t s necessary to select an approprate kernel functon. In ths paper, the followng radal bass functon (RBF) s used: 2 (, ) exp( γ ) K x y = x y (14) where γ s the kernel parameter. To obtan a good performance, some parameters n SVM must be chosen carefully. These parameters nclude the regularzaton parameter C and the kernel functon parameter γ, these two parameters are automatcally selected by means of 5-fold cross-valdaton method. Consequently, classfcaton problem plays a major role n varous felds of computer scence and engneerng. SVM s known as the most optmal technque to solve ths problem. It has a clear and sold theoretcal foundaton and smple structure to employ. Furthermore, SVM s a strongly regularzed method, whch s sutable for classfcaton problem. It unfolds a unque technque wth small tranng tme Classcal multdmensonal scalng For mentoned approach, varous TDR responses are recorded, n whch there are some rrelevant data that may be confusng to the SVM classfer and ncrease the tranng tme. Feature extracton s the most effectve method to select approprate nput features n order to mprove the speed of tranng and the success rate of classfcaton. Prncple component analyss (PCA) [25], sngular value decomposton (SVD) [26] and multdmensonal scalng (MDS) have been wdely appled to remove redundant varables n feature vectors [27]. In ths artcle, classcal multdmensonal scalng (CMDS) s employed to select optmal features n order to provde a relable dataset for the SVM classfer. It s a nonlnear optmzaton technque to yeld a lower dmensonal representaton of hgh dmensonal data. The detal of CMDS feature extracton method has been well studed n [28-29]. Suppose havng a collecton of n subjects, the par-wse dstance matrx s gven as: 419

6 H. T. Thom et al: Fault classfcaton for dstrbuton networks usng enhanced SVM... δ δ K δ = δ δ K δ δ δ K δ where n n n δ j s the dstance between x and x j. The am of CMDS s to fnd n vector 1 2 x, x,..., xn RL functon called STRAIN. The STRAIN s defned as follows; ( ) S X 2 ( bj ( x, x j ) ) < j = 2 b j < j where b j are the terms of the nner product B, 1/2 b b K b = = b31 b32 b K 3n n ' B X * X b21 b22k b2 n (15) to mnmze a loss (16) (17) 3. Development of Methodology Snce TDR technology alone s not able to dagnoss the fault n dstrbuton networks and hence requres pattern recognton technques to support t. In ths work, a CMDS-based SVM classfer s appled to mprove the performance of TDR method n dentfyng fault types n radal dstrbuton systems. Fgure 3 shows the overall structure of the proposed approach. SVM 1 AG Testng dataset SVM 2 BG CG AB AC Reflected data acquston or dataset Feature extracton by CMDS Tranng dataset SVM 8 BC ABG ACG BCG SVM 9 ABC Fgure 3. The overall structure of the proposed algorthm. 420

7 J. Electrcal Systems 13-3 (2017): The one to others SVM algorthm has developed for the mult-class fault dentfer. Nne layers SVM are employed to classfy all 10 types of short crcut faults. When the nput of SVM s an AG sample, the output of SVM1 s set to +1; otherwse -1. Wth samples of the reman faulty group, SVM2 s traned to separate BG fault from eght types of short crcut fault, the output of SVM2 s set to +1, otherwse -1, and so on. Therefore, t can be seen that the multlayer SVM classfer s obtaned wth all subclassfers Data descrptons Whenever a fault occurs n dstrbuton networks, the reflected responses wll be produced and travel between fault locaton and the substaton. Note that the magntude of reflected responses s proportonal to the fault dstance from the substaton. By ncreasng fault dstance, the ampltude attenuaton along the lne ncreases and so the magntude of reflected sgnals goes down. These fault responses are cross-correlated wth the ncdent mpulse by eqn. (8) as mentoned above. On the other hand, the magntude of feedback wave changes for the dfferent fault types, as a result, the peaks of CCR between reflected sgnal and ncdent sgnals are not the same for each of fault type. Based on the above analyss, the reflected voltage and current magntude along wth the peaks of CCR are chosen as the nput feature vectors of the SVM classfer, and the correspondng fault type s chosen as the output. Therefore, the total number of features s 12, n whch sx features are the reflected voltage and current values avalable at the substaton and the remanng sx features are the peaks of CCR functons between reflected and ncdent waves Feature selecton For classfcaton problems, feature extracton plays a major role n removng redundant one whch can ambgutes for classfcaton n order to ncrease the tranng speed and mprove the classfcaton accuracy. In ths paper, CMDS algorthm s ntroduced for selectng requred features as dscussed n Secton 2. The expermental results show that CMDS s used to fnd 6 best optmal features and lead to reduce the tranng tme and the classfcaton error wth the lower feature space dmenson Tranng phase The SVM classfer s traned usng eqns. (9) and (10). The RBF n equaton (14) s chosen as a kernel functon, where C s the penalty parameter of the error term and γ s kernel parameter. These two parameters are selected usng the 5-fold cross-valdaton method n whch the tranng set s classfed nto 5 subsets wth equal sze. After that, each subset s tested usng the classfer traned on the remanng 4 subsets. Therefore, each case of the tranng set s dentfed once, as a result, the classfcaton accuracy s the percentage of data that are correct classfed. The man advantage of cross-valdaton s the capacty of removng the overfttng problem. Furthermore, a grd-search on C and γ usng crossvaldaton are employed n ths artcle. As a result, the best cross-valdaton accuracy s selected from varous couple (C, γ) values are tred. 421

8 H. T. Thom et al: Fault classfcaton for dstrbuton networks usng enhanced SVM Testng phase As the performance of the valdaton dataset starts to separate from that of the tranng dataset, learnng procedure s stopped. After the tranng phase, new patterns of the testng dataset are nputted to the traned multlayer SVM classfer for purpose of dentfyng ten types of fault The output of SVM classfer The types of fault dvded nto the followng categores: sngle-phase-to-ground fault (AG, BG, CG), lne-to-lne fault (AB, AC, BC), double-lne-to-ground fault (ABG, ACG, BCG) and three-phase fault (ABC). 4. Results and dscusson The proposed fault dagnoss method s used to analyze varous faults classfcaton on a smple two-branched dstrbuton system shown n Fgure 4. It s constructed from major components such as conductors, dstrbuton transformers and loads. Fgure 4. Modelng of a typcal two-branched dstrbuton network. 422

9 J. Electrcal Systems 13-3 (2017): Fgure 5. The waveform of PRBS excaton on the lne. In ths paper, the fault types are consdered usng a 127 bt PRBS nput gven n Fgure 5 wth the frequency f = 1MHz propagatng along the lne wth the velocty of 198,000 km/s. When a fault occurs on the man feeder or on a lateral, an nput pattern can be obtaned at substaton by TDR analyss. After that, each type of fault can be dentfed by the SVM classfer whch has been traned earler. Fgure 6 shows TDR curves of voltage and current, generated by smulaton of some types of fault of AG, ACG, BC and ABC on the frst lateral, locate at dstance of 2 km from the substaton. (a) (b) 423

10 H. T. Thom et al: Fault classfcaton for dstrbuton networks usng enhanced SVM... (c) (d) Fgure 6. The forms of voltage and current reflected wave n fault cases: (a) AG, (b) ACG, (c) BC, and (d) ABC. Fgure 6 llustrates the magntude of the reflected voltage and current are dfferent for the dfferent fault types, as a result, the peaks of CCR between reflected sgnal and ncdent sgnal are not the same for each of fault type. Therefore, the ampltude of reflected sgnals along wth the peaks of CCR are chosen as the nput features of SVM classfer to dentfy the short crcut fault types. Table 1 Dataset of 10 types of fault located at dstances of 1km and 2km from the substaton va vb vc a b c cc-va cc-vb cc-vc cc-a cc-b cc-c AG BG CG BCG ACG ABG AB AC BC ABCG Legends: AG, BG and CG are sngle phase to ground faults; BCG, ACG and ABG are double lne to ground faults; AB, AC and BC are lne to lne faults; ABCG s three phase to ground. v a, v b, v c, a, b and c are the magntudes of reflected voltage and current, respectvely. cc-v a, cc-v b, cc-v c, cc- a, cc- b and cc- c are the CCR between reflected and ncdent sgnals. 424

11 J. Electrcal Systems 13-3 (2017): Through smulaton 5700 nput dataset have been generated by creatng varous faults at dfferent locatons on two laterals wth varyng fault mpedance value. Tranng and testng set are randomly separated from these datasets and 1200 datasets are used for tranng and testng set respectvely. Table 1 gves some samples of the dataset, generated by smulatng all 10 types of fault on the frst lateral, locate at dstances of 1km and 2km from the substaton for brevty. Table 2 gves the results of the classfcaton accuracy whereas Fgure 7 shows all the 10 clusters of the classfed fault types for SVM algorthm usng dataset wth and wthout CMDS feature extracton. Table 2 The results of SVM classfcaton wth and wthout consderng CMDS optmzaton technques SVM classfer No. of Classfcaton accuracy C γ features (%) Tranng tme (s) Wthout CMDS Wth CMDS From Table 2, t s observed that the optmum values of C and γ of SVM classfer are and wthout consderng CMDS and are and wth consderng CMDS. It s clearly seen from ths table that the classfcaton accuracy n the case of usng all the feature s 93% whereas ths percentage s 95.25% after usng CMDS feature extracton. It can be observed that the overall tranng tme taken by SVM classfer wthout CMDS s sec whereas wth CMDS s sec. Thus, t can be concluded that the proposed CMDS method s not only capable of mprovng classfcaton accuracy, but also ncreasng the tranng speed. (a) 425

12 H. T. Thom et al: Fault classfcaton for dstrbuton networks usng enhanced SVM... (b) Fgure 7. The clusterng results of 10 class SVM classfer (a) wthout CMDS and (b) wth CMDS. Furthermore, from Fgure 7(b), t s observed that the boundares between any two clusters are more straght than that n Fgure 7(a). Thus, overlappng among clusters n Fgure 7(b) s less than that n Fgure 7(a). Ths observatons demonstrates the superorty of SVM classfer wth CMDS than that wthout CMDS. 5. Conclusons In ths paper, a new electrcal fault classfcaton technque wth the help of support vector machne (SVM) by utlzng tme-doman reflectometry (TDR) method wth pseudorandom bnary sequence (PRBS) stmulus has been developed. Furthermore, to mprove classfcaton accuracy of SVM, a combnaton of classcal-multdmensonal scalng (CMDS) feature extracton algorthm and kernel parameter optmzaton method has been ntegrated to the SVM. In the proposed technque, TDR method usng PRBS exctaton not only overcomes the stmulus attenuaton but also surmounts the mpact of nose n order to provde a relable dataset for SVM classfer. The proposed approach has been successful appled to dentfy all 10 types of short crcut fault. The acheved hgh accuracy n classfyng fault types (over 95%) demonstrates the effectveness of the proposed approach than the other exstng fault dentfers. 426

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