Wavelet Transform Based Relay Algorithm for the Detection of Stochastic High Impedance Faults

Transcription

1 International Conference on Power Systems Transients IPST 3 in New Orleans, USA Wavelet Transm Base Relay Algorithm the Detection of Stochastic High Impeance Faults T. M. ai,.a. Snier an E. o () Dept. of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, ( tmlai.ee@polyu.eu.h, eesnier@polyu.eu.h, eewclo@polyu.eu.h) Abstract High impeance faults (HIF) are faults which are ifficult to etect by overcurrent protection relays. This paper presents a practical pattern recognition base algorithm electric istribution high impeance fault etection. The scheme recognizes the istortion of the voltage an current wavefo cause by the arcs usually associate with HIF. The analysis using Discrete Wavelet Transm (DWT) yiels three phase voltage an current in the low uency range which fe to a classifier pattern recognition. The classifier is base on the algorithm using nearest neighbour rule approach. A HIF moel was also evelope, where the ranom nature of the arc was simulate using MATAB. Keywors High Impeance Faults, Wavelet Transm, Pattern Recognition I. INTRODUCTION High impeance faults (HIF) are ifficult to etect. When a conuctor such as a istribution line maes contact with a poor conuctive surface or substance the resulting level of fault current is usually lower than the nominal current of the system at the fault location. Theree, conventional protection relay system will not be able to etect the HIFs an trip the protection relay. The failure of HIF etection may lea to potential hazars to human beings an potential fire []. HIFs on electrical transmission an istribution networs involve arcing an/or nonlinear characteristics of fault impeance which cause cyclical pattern an istortion. Theree, the objective of most etection schemes is to evaluate the special features in patterns of the voltages an currents in HIFs. Some researchers propose various etection schemes base on fractal techniques [], igital signal processing [3], expect systems [4]-[5], neural networs [6]-[8], crest factor [9], wavelet transm in high uency noise patterns [] an ominant harmonic vectors [] []. They offer potential solutions to these problems currently associate with conventional schemes. While irect calculation of fractal imensions is not effective ue to relatively short ata sets available estimation, the use of high uency harmonics is not feasible in practical relay because of the filtering by substation current transmers. The scheme propose in this paper, which uses the nearest neighbour rule approach, offers a simpler pattern recognition alternative to recognise the istortion ue to HIFs. Moreover, these schemes can also potentially be applie on on-line training an customization using actual fiel HIF ata. This propose etection scheme nees evaluation on merely low orer harmonics of voltage an current. In this paper a stochastic metho applie towars the etection of HIFs is presente. The metho incorporates the statistical nature of the high impeance faults an fault locations in orer to preict the istortions on voltage an current wavem in the electrical supply networ. The immunity of the propose relay to confouning from contingencies such as loa an capacitor switching in electrical networs is evaluate through simulation. After capturing the voltage an current wavefo from the power system simulations, they are analyse by iscrete wavelet transm (DWT) to prouce various wavefo uner ifferent uency ranges. The values of these voltage an current wavefo in their various uency ranges are fe into the pattern classifier to etermine the fault or non-fault situations. II. DISCRETE WAVEET TRANSFORM (DWT) MODE AND MUTI-RESOUTION ANAYSIS (MRA) The wavelet transm is a tool that ivies up ata, functions or operators into ifferent uency components, an then stuies each component with a resolution matche to its scale [3]. The multi-resolution analysis (MRA) using iscrete wavelet transm (DWT) in wavelet is use in this propose metho. The objective of multiresolution analysis is to evelop representations of a sophisticate signal f(t) in te of wavelet an scaling function. Multi-resolution analysis was mulate base on the stuy of orthonormal, compactly supporte wavelet bases. Wavelets theory an its applications are rapily eveloping fiels in applie mathematics an signal analysis. The scaling coefficients (approximation) can be compute by taing the inner proucts of the function f(t) with the scaling basis: c f t), φ ( t) f ( t) ( t t () j, ( φ ) The wavelet coefficients (etails) can be compute by taing the inner proucts of the function f(t) with the wavelet basis: j, ( ψ ) f t), ψ ( t) f ( t) ( t t () where scale function φ (t) an wavelet function ψ (t) is etermine by the selection of a particular mother wavelet ψ(t) an the following equations. j / j φ ( t) φ( t ) j / j ( t) ψ ( t ) ψ (3)

2 International Conference on Power Systems Transients IPST 3 in New Orleans, USA c,, h h Analysis Filter Decimator c,,, c, ( f c ), ( f ), ( f ) f (t) Input h h Analysis Filter Decimator c,, h h Analysis Filter Decimator c,,,, -, ( f ) -, ( f ) j - - Multi-resolution Analysis of Discrete Wavelet Transm Fig. Schematic Diagram of Discrete Wavelet Transm (DWT) The schematic iagram of DWT is shown in Fig. Discrete Wavelet Transm (DWT) resolves the input signal to time, scales an scale coefficients an wavelet coefficients. The scales, scale coefficients an wavelet coefficients are not commonly use because they cannot reflect the physical properties in the uency analysis. Theree, these following sections woul introuce some mappings from scale an scale coefficients an wavelet coefficients to uency ranges an values of scale coefficients an wavelet coefficients in each DWT resolution levels, respectively. A. Mapping from Scales to Frequency Ranges In iscrete wavelet transm, resolution scale is commonly use to represent the egree of resolution. The structure of DWT is shown in Fig. Two efinitions of resolution level are commonly use: ascening orer from the finest resolution level () to the coarsest resolution level () an escening orer j from the finest resolution level (-) to the coarsest resolution level () where is total resolution level. The relationship between an j is efine as follows: j (4) an the resolution levels in te of an j are liste at the bottom of Fig. The resolution scale scale in each resolution level is efine as: scale (5) In each resolution level, the input signal j+ in the upper resolution level is split into the approximation c j by a lowpass filter h an the etail j by the highpass filter h in the lower resolution level. Both of output approximation an etail signal are then ecimate by. Base on the Nyquist theorem (which states that the highest uency which can be accurately represente is less than one-half of the sampling rate), the maximum uency of original signal f(t) sample at f(t) Hz is f(t) / Hz. The first approximation c - an first etail - in resolution level are sample at half of f(t). Theree, the maximum uencies of signals c j an j in each resolution level are given in Equation 6: s (6) Since the bounary of lowpass an highpass filter is half of nyquist uency, the upper bounary uency of lowpass filter h an the lower bounary uency of highpass filter h is the same as half of. Theree, the lower bounary uency ower an upper bounary uency Upper of both lowpass filter h an highpass filter h in each resolution level are efine as: ower Upper ower Upper f f f ( t) + ( t) + ( t) lowpass filter (7) highpass filter. (8) B. Calculation of values from Scale/Wavelet Coefficients Scale coefficients an wavelet coefficients coeff signal representing the istorte signal f(t) at ifferent resolution levels in multi-resolution analysis (MRA) are efine as: ow Frequency Range High Frequency Range signal [ c... ] coeff (9) where is maximum level in this multi-resolution analysis an c an j are the approximation in level an the etail in level j respectively. For the perioic moe of iscrete wavelet transm, the

3 International Conference on Power Systems Transients IPST 3 in New Orleans, USA values of their scale coefficients an wavelet coefficients can be calculate irectly from their scale coefficients an wavelet coefficients in their own resolution levels. The values the etails or approximation in each wavelet level can be represente in the perioic-paing (perioic extension at the eges) moe of iscrete wavelet transm. For the scale coefficient in level (j ), the value f c in level (j ) is: c ( ) f ( t) c f c () f(t) co f(t) co where f(t) is no. of points in f(t) an c o is no. of points in scale coefficient c. For the wavelet coefficients in each level, the values f j in level j are: f ( t) j ( ) j ( ) j f j j f(t) j j j () f(t) j j where j is no. of points in wavelet coefficients j Theree, the vector signal representing to scale coefficients an wavelet coefficients of the istorte signal f(t) at ifferent resolution levels is as follows: signal [ fc f f... f f ] signal ( )... c ( ) c o ( ) ( ) ( ) () In accorance with the above equations, the values calculate from scale coefficients an wavelet coefficients in multi-resolution levels can convert irectly from their scale coefficients an wavelet coefficients coeff signal. III. MODEING AND THEIR THEORIES A. Simulation Moel Proceures The system moel of this simulation was ivie into three parts: power system moel, filter moel an pattern recognition moel. Fig shows the flowchart of the simulation. Matlab was use to generate all the system parameters in the fault cases an non-fault cases the power system simulation accoring to ranom fault location an fault situations. The system parameters in fault an nonfault cases were then importe into the power system simulation an the power system toolbox etermine the targete voltage an current wavefo of the circuit breaer in the faulte istribution line. These wavefo of voltages an currents in the relay on the istribution sie of the transmer in the power system stuie were then transferre to iscrete wavelet transm progress to analyse the uency characteristics in various uency ranges. The values of that voltages an currents were calculate using the voltage an current wavefo from the iscrete wavelet transm. A classifier was use to recognize the fault cases an non-fault cases using values of voltage an current in various uency bans. Simulation of Power Systems Wavelet Transm (Frequency Analysis) Nearest Neighbors Rule - NNR (Classification) Classification Results Voltage, Current wavefo of targete circuit breaer from the power system values of Voltage an Current from the power system Fig. Simulation Moel Proceures Matlab Application B. Power System Moel - High Impeance Faults (HIFs) an ow Impeance Faults (IFs) Moel A simplifie -ioe moel [4] of HIF is use in the simulation. The circuit of the HIFs moel is shown in Fig 3. This HIF moel is base on arcing in sany soil. The moel inclues two DC sources, Vp an Vn, which represent the inception voltage of air in soil an/or between trees an the istribution line. The two resistances, Rp an Rn, represent the fault resistance: unequal values allow asymmetric fault currents to be simulate. When the phase voltage is greater than the positive DC voltage Vp, the fault current flows towars the groun. The fault current reverses when the line voltage is less than the negative DC voltage Vn. For values of the phase voltage between Vn an Vp no fault current flows. The typical fault current an voltage are shown in Fig 4. The low impeance fault (IF) moel comprises the appropriate fault resistance switche at the fault location in the istribution line. Dn Vn Rn Fig 3. Simplifie -ioe Fault Moel of HIF Rp Dp Vp 3

4 International Conference on Power Systems Transients IPST 3 in New Orleans, USA x 4 Typical Voltage an Current of High Impeance Fault Volatge Current 5 The root-mean-square values of voltages an currents in various uency ranges from the DWT are classifie into a training set an a test set respectively. 95% of the values are use as a training set to train the ecision bounaries using NNR an the rest of the ata acts as a test set to valiate their ecision bounaries. Voltage (V) Time (s) Fig 4. Typical Voltage an Current of HIF Current (A) IV. SYSTEM DESCRIPTION Three systems stuie in this paper are parts of 5V power istribution networs. A istribution networ with a single branch of a nonlinear loa, a raial istribution networ with three branches of nonlinear loas an one meshe networ with two sources an various nonlinear loas are escribe an their schematic iagrams are shown in Fig 5, 6 an 7, respectively. oa 5MVA 5MVA Delta / Star C. Implementation of Discrete Wavelet Transm (DWT) Moel an Multi-resolution Analysis (MRA) In this application, b4 in Daubechies family wavelets is selecte the mother wavelet an the uency banwiths were etermine in Table after ownsampling the input signal f(t) to the sampling uency of 96Hz in orer to reuce the computational time. 5V Measurement Point of Voltage an Current 5V Fault Moels ar oa 6-pulse rectifier Fig 5. Schematic Diagram of the Simulate 5V Single Branch Power System Networ Table : Scale to Frequency Range base on 5Hz Power Frequency 5 V Parameter Frequency Ban (Hz) Harmonics Inclue 6 c, 75 st 6, 75 5 n 3 r 5, r 6 th 4, th th 3 3, 6 - th - 4 th 4, th 48 th 5, th 96 th oa 5 MVA 5 V 5MVA Delta/Star Measurement Point of Voltage an Current 5 V 5 V I F Fault Moels ar 6-pulse oa rectifier ar -pulse oa rectifier ar 6-pulse oa rectifier D. Pattern Recognition Since the normal operation an fault situations o not have a specific pattern the istributions, a nonparametric approach in supervise learning is use in this fault classification problem. The nearest neighbour rule (NNR) metho [5] [6] is a typical recognition metho in the nonparametric approach. The NNR metho is initially use to select some samples ranomly from the ata to be classifie as a training set of labelle samples x r train. Since samples which are close in feature space liely belong to the same class, a new sample x r in the training gri is selecte an labelle to be the same class as the nearest labelle samples x r i in the training set of x r train. NNR can emonstrate the classification results an their ecision bounaries between two sorts of ata by plotting twoimensional contour graphs. Fig 6. Schematic Diagram of the Simulate 5V Raial Power System Networ oa 5 MVA 5 V 5MVA Delta/Star Measurement Point of Voltage an Current ar oa 5 V -pulse rectifier I F Fault Moels Fig 7. Schematic Diagram of the Simulate 5V Meshe Power System Networ 5MVA Delta/Star ar oa 6-pulse rectifier 5 V oa 5 MVA 4

5 International Conference on Power Systems Transients IPST 3 in New Orleans, USA In the single branch istribution networ, power is supplie at 5 V through a m istribution line from a 5 MVA transmer. The networ then istributes power to a 4 MVA linear loa with power factor.8 an a MVA nonlinear loa, where a 6 pulse converter is use to represent the nonlinear loa. In the raial istribution networ with three branches of nonlinear loas, two aitional branches of one MVA 6 pulse converter loa an one 4.6 MVA pulse converter loa are parallel to the istribution branch in the single branch istribution networ. In the meshe networ, a ring connection is constructe by two separate 3 phase voltage sources feeing two iniviual nonlinear loas with one MVA 6 pulse converter loa an one 4.6 MVA pulse converter loa. The resistance, inuctance an capacitance of positive an zero sequence of transmission lines are R.73 ohm/m; X.334 mh/m; C.833 µf/m an R.3864 ohm/m; X.496 mh/m; C.64 µf/m, respectively. The total impeance percentage of the transmers is an the uency of the system is 5Hz. In this paper, two sorts of cases are consiere in the simulation: non-fault cases an fault cases in each system. In fault cases, both high impeance fault moel an low impeance fault moel are applie separately to the istribution line ifferent fault cases. The arcing an nonlinear characteristics of HIFs may be similar to those of nonlinear loas an switching operations, especially capacitor switching. It must be ensure that these normal events o not confoun the HIF relay. In the simulations, the significant parameters are stochastically selecte base on those in real operations. The fault currents are assume to range from.5 to p.u. of overcurrent evice settings in full loa situation. A. Case I Non-fault Cases (Normal Operation) In all istribution networs, shunt capacitors bans ranging up to MVAr, linear loas up to their own maximum powers an nonlinear loas up to their own maximum ratings are switche at the sening en an receiving en of the istribution lines. The nonlinear loas comprise three phase 6 pulse converters an pulse converters an the three phase linear loas have their own power factor in accorance with their system configurations. The closing times of the breaers are stochastically selecte. B. Case II Fault Cases The moelle phase-to-groun HIFs an IFs with various fault inception angles are simulate at the ifferent positions along the faulte istribution lines from the circuit breaer at the source sie to istribution loas. Fault location, fault impeance an fault inception angles of both HIFs an IFs are stochastically selecte in the simulation which represents the variation of soil properties an other stochastic characteristics of the HIFs. The capacities of the linear loas an the nonlinear loas, operation scheule in the capacitors at the sening en an receiving en in the istribution lines of the simulate istribution networs are chosen ranomly. V. SIMUATION Table are total errors error total in the NNR metho. In the pattern recognition, the fault cases an non-fault cases are classifie into the training set, test set in the simulation. The probability errors in pattern recognitions were foun that lower probability errors mean higher successful rates to classify the two above cases. The total errors show average errors on each combination of wavelet coefficients. The errors of corresponing to values of voltage wavelet coefficients (, ) in level 6 are still approximately between.5% an 6.8% which is the lowest value in all combinations of various uency ranges in voltage an current. Moreover, the range of total errors is from.5% an 45.4%. It note that the major characteristic in recognizing of normal operation an fault cases is the combinations on voltages range from to 3 Hz an currents range from to 6 Hz. Theree, voltages an currents with low uency ranges are major factors to classify the high impeance faults an the common faults. Although the ecision bounaries coul verify all cases of the simulate systems, some occurrences of these high impeance faults beyon the simulate cases may still occur. Since high impeance faults constitute a fault perio in te of secons, tripping criteria are require. Positive ientifications in ten consecutive cycles of HIFs triggere by the traine pattern classifier coul classify an event as a high impeance fault. VI. CONCUSIONS This paper presente a stuy of the fault classification in 5V electrical istribution systems base on iscrete wavelet transm. The stuy involve computer simulation of power systems, iscrete wavelet transm an classification. The electrical faults incluing HIFs an common faults are stochastic in nature, an epen on factors such as fault location, fault impeance, fault inception angle, other electrical loas, etc. A statistical analysis was perme, an this etermine the error probability of classification between the fault cases an normal operation. The statistical ata was incorporate into the computer simulation, an the classification results ientifie both the fault cases an normal operation. The ifference of uency characteristics between high impeance faults an normal capacitor ban switching operation simulate by MATAB can be recognize by the classifier using nearest neighbor rule metho. Computer simulations the propose metho in three example power systems inicate that the metho provie a satisfactory results in the etection of HIF. The metho presente in this paper overcomes the ifficulty of using iscrete wavelet transm that the output scale coefficients an wavelet coefficients o not represent any physical properties. Using the relationship among scale coefficients an wavelet coefficients, signal energies an values, scale coefficients an wavelet coefficients can be converte to values irectly or through the calculation of signal energies. Theree, the clear istribu- 5

6 International Conference on Power Systems Transients IPST 3 in New Orleans, USA tion patterns among various characteristic voltage an current values calculate from scale coefficients an wavelet coefficients are emonstrate. VII ACKNOWEDGEMENT The authors gratefully acnowlege the financial support of the Research Grant Council of Hong Kong the project (PolyU 59/E). VIII. REFERENCES [] IEEE Tutorial Course Text, Detection of Downe Conuctors on Utility Distribution Systems, No. 9EH3-3-PWR, 989 [] A.V. Mamishev, B.D. Russell, C.. Benner, Analysis of High Impeance Faults using Fractal Techniques, IEEE Power Inustry Computer Application Conference, 995, pp 4-46 [3] A.A. Girgas, W.Chang, E.B. Maram, Analysis of High- Impeance Fault Generate Signals using a Kalman Filtering Approach, IEEE Transactions on Power Delivery, Volume 5 Issue: 4, Oct. 99, pp [4] C.. Kim, B.D. Russell, Classification of Faults an Switching Events by Inuctive Reasoning an Expert System Methoology, IEEE Transactions on Power Delivery, Volume 4, Issue 3, uly 989, pp [5] B.D. Russell, C.. Benner, Arcing Fault Detection Distribution Feeers: Security Assessment in ong Term Fiel Trials, IEEE Transactions on Power Delivery, Volume, Issue, April 995, pp [6] S. Ebron, D.. ubeman, M. White, A Neural Networ Approach to the Detection of Incipient Faults on Power Distribution Feeers IEEE Transactions on Power Delivery, Volume 5, Issue, April 99, pp [7].A. Snier, Y.S. Yuen, The Artificial Neural Networs Base Relay the Detection of Stochastic High Impeance Faults, Neurocomputing, Volume 3, 998, pp [8] A.M. Sharaf,.A. Snier, K. Debnath, A Neural Networ Base Relaying Scheme Distribution System High Impeance Fault Detection, Proceeings of First New Zealan International Two-Stream Conference on Artificial Neural Networs an Expert Systems, 993, pp 3-34 [9] C.. Kim, B.D. Russell, Analysis of Distribution Disturbances an Arcing Faults Using the Crest Factor, Electric Power Systems Research, Volume 35, 995, pp4-48 [] Davi T.W. Chan, Xia Yibin, A Novel Technique For High Impeance Fault Ientification, IEEE Transactions on Power Delivery, Volume 3, Issue 3, uly 998 pp [] B.M. Aucoin, B. D. Russell, Detection of Distribution High Impeance Faults Using Burst Noise Signals Near 6 Hz, IEEE Transactions on Power Delivery, Volume, Issue, April 987, pp [] D.I. eerings,.r. iners, A Practical Protective Relay Down-conuctor Faults, IEEE Transactions on Power Delivery, Volume 6, Issue, April 99, pp [3] I. Daubechies, Ten lectures on wavelets, Philaelphia, Pa. : Society Inustrial an Applie Mathematics, 99 [4] A.E. Emanuel, D. Cygansi,.A. Orr, S. Shiller, E.M. Gulachensi, High Impeance Fault Arcing on Sany Soil in 5 V Distribution Feeers: Contributions to the Evaluation of the ow Frequency Spectrum, IEEE Transactions on Power Delivery, Volume 5, Issue, April 99 pp [5] M. Naler, E.P. Smith, Pattern Recognition Engineering, Wiley, 993 [6] Dua, O. Richar, Pattern Classification, Wiley, Table. Total Error Percentages in Various Wavelet Scales V scale c, V wavelet V wavelet V wavelet V wavelet3 V wavelet4 V wavelet5 I scale I wavelet I wavelet I wavelet I wavelet3 I wavelet4 I wavelet5,,, 3, 4, 5, c,,,, 3, 4, 5, V scale c, V wavelet, V wavelet, V wavelet, V wavelet3 3, V wavelet4 4, V wavelet5 5, I scale c, I wavelet, I wavelet, I wavelet, I wavelet3 3, I wavelet4 4, I wavelet5 5,