MultCraft Internatonal Journal of Engneerng, Scence and Technology Vol. 2, No. 3, 200, pp. 29-44 INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY www.jest-ng.com 200 MultCraft Lmted. All rghts reserved Improved transformer protecton usng probablstc neural network and power dfferental method Manoj Trpathy *, R. P. Maheshwar 2, H. K. Verma 3 * Department of Electrcal Engneerng, Motlal Natonal Insttute of Technology Allahabad, INDIA 2,3 Department of Electrcal Engneerng, Indan Insttute of Technology Roorkee, INDIA * Correspondng Author: e-mal: manoj_trpathy@redffmal.com, Tel +9-94205058, Fax. +9-532-24450 Abstract Ths artcle presents a novel technque to dstngush between magnetzng nrush current and nternal fault current of power transformer. An algorthm has been developed around the theme of the conventonal dfferental protecton method n whch parallel combnaton of Probablstc Neural Network (PNN) and Power Dfferental Protecton (PDP) methods have been used. Both PNN and PDP method are ndependent of harmonc contents of dfferental current. The proposed algorthm s capable of detectng fault and ts type n the eventualty of fault n the transformer. Moreover, the combnaton of PDP method wth the PNN makes t capable to detect lght nternal faults for all ratngs of transformers whch mprove the overall performance of dgtal dfferental protecton scheme. For evaluaton of presented algorthm, relayng sgnals of varous operatng condtons of power transformer, ncludng nternal faults, external faults, over-exctaton and nrush condtons were obtaned through modelng of transformer n PSCAD/EMTDC. The performance of proposed amalgamated technque (.e. combned PNN and PDP method) s compared wth the PNN, Feed Forward Back Propagaton (FFBP) neural network and the conventonal harmonc restrant methods. The results amply demonstrate the capablty of the proposed algorthm n terms of accuracy and speed. The algorthm has been mplemented n MATLAB. Keywords: Dgtal dfferental protecton, Protectve relayng, Probablstc neural network, Actve power relays, Power dfferental method.. Introducton Protecton of large and medum power transformers by means of dfferental relayng has been a common practce. Dfferental relayng technque s based on comparson of the transformer s two wndng currents. When these currents devate from a predefned relatonshp an nternal fault s assumed and relay operates. However, durng magnetzng nrush condton, very hgh current of the order of 0-5 tmes of full load current of transformer may pass through the prmary sde of power transformer (Sdhu et al, 992). Ths hgh current causes mal-operaton of the relay. Therefore, man challenge s to precsely dstngush between magnetzng nrush and fault current to avod any mal-operaton of relay. Lterature revew suggests that broadly two approaches are appled to dscrmnate between magnetzng nrush and fault currents; these are Harmonc Restrant (HR) based method and Waveform Identfcaton (WI) based method (Trpathy et al, 2005). The HR method s based on the fact that the second/ffth harmonc component of the magnetzng nrush current s consderably larger than that n a typcal fault current. It has been extensvely used n comparson of WI method (Trpathy et al, 2005, Wang et al, 2009). However, ths method sometmes fal to dscrmnate between magnetzng nrush and nternal fault currents because hgh second harmonc components are generated durng nternal faults and low second harmonc component are generated durng magnetzng nrush havng modern core materal of power transformer and due to the presence of shunt capactance or dstrbutve capactance n long Extra Hgh-Voltage (EHV) transmsson lne to whch power transformers are connected (Shn et al, 2003). Therefore, the detecton of second/ffth harmonc s not a suffcent ndex to dscrmnate between the nrush and fault currents of a power transformer. The second method dstngushes magnetzng nrush current from nternal fault current on the bass of WI method. In 986, Verma and Basha reported mcroprocessor based waveform dfferental relayng scheme (Verma et al, 986). The magnetzng
30 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 nrush current exhbts a characterstc peaked wave, whch s caused by asymmetrc saturaton of the transformer core. In 2006, B. He et al. presented an algorthm to dentfy nrush current and nternal fault current n transformer by usng the characterstc of nrush current.e. peaked wave and dead angle (He et al, 2006). Another group of researchers have nvestgated the use of wavelet analyss for the classfcaton between fault and healthy state of power transformer. Wavelet transform based methods have better ablty of tme-frequency locaton. Ther dsadvantages are that they need long data wndow and are also senstve to nose and unpredcted dsturbances, whch lmt ther applcaton n relayng (Arboleya et al, 2006, Trpathy et al, 2009). It has been demonstrated that the advanced Dgtal Sgnal Processng (DSP) technques and Artfcal Intellgence (AI) approaches to power system protecton can mprove dscrmnaton between normal and fault condtons and facltate faster, more secure and dependable protecton for power transformers. Owng to ts superor learnng and generalzaton capabltes Artfcal Neural Network (ANN) can consderably enhance the scope of WI method. ANN approach s faster, robust and easer to mplement than the conventonal waveform approach. The use of neural network can provde an ntellgent dgtal dfferental protecton scheme. Snce 994, many researchers have proposed ANNs based transformer dfferental protecton wth varous topologes. Most of them used Multlayer Feed Forward Neural Network (MFFNN) wth back-propagaton learnng technque (Bastard et al, 995, Tan et al, 2004). Another ANN model called Radal Bass Functon Neural Network (RBFNN) has also been reported n the lterature for power transformer protecton (Moravej et al,2003, Borghett et al, 2008). However, they have so far left some unsolved problems, ncludng those of local mnma and slow convergence n tranng and the need of emprcal determnaton of structure and neural network parameters. In (Trpathy et al,2007), Probablstc Neural Network (PNN) has been used to dscrmnate between nrush current and nternal fault current of power transformer but t fals to detect turn-turn fault current (.e. lght nternal fault current). Ths paper presents an algorthm n whch PNN s appled n conjuncton wth Power Dfferental Protecton (PDP) method (Yabe, 997). The PNN and PDP methods together are used to dscrmnate between magnetzng nrush current and nternal fault current, and also used to determne the type of fault n a power transformer. They are able to detect nternal fault current even f the fault current contans a large second harmonc component, as PNN method and combned PNN and PDP method are ndependent of harmonc components present n operatng sgnal to the relay. PNN method s based on pattern recognzaton whle PDP method s based on the average nstantaneous power flowng nto the transformer. The proposed amalgamated technque s used to mprove the relablty and accuracy as compare to PNN based method and conventonal HR method. In ths paper, the results of the proposed algorthm are compared wth the conventonal Dscrete Fourer Transform (DFT) based method, Feed Forward Back Propagaton (FFBP) based method and optmal PNN based transformer dfferental protecton method. 2. Probablstc Neural Network (PNN) PNN s a knd of feed forward neural network. The orgnal PNN structure s a drect neural network mplementaton of Parzen nonparametrc Probablty Densty Functon (PDF) estmaton and Bayes classfcaton rule (Specht, 990). The standard tranng procedure of PNN requres a sngle pass-over all the patterns of tranng set (Specht, 990). Ths characterstc renders PNN faster to tran as compared to FFBP neural network and RBFNN (Specht et al, 99). The only drawback of PNN s the requrement of larger storage for exemplar patterns. As the computer memory has become very cheap and effectve, the cost and sze of large storage are no longer of concern these days. PNN s wdely used n the area of pattern recognzaton, nonlnear mappng, fault detecton and classfcaton, estmaton of probablty of class membershp and lkelhood ratos (Tan et al, 200). x out put x xd Input Layer Pattern Layer Summaton Layer Fgure. Probablstc neural network structure Output Layer The PNN structure s shown n Fgure. It s a four layer feed forward neural network that s capable of realzng or approxmatng the optmal classfer. Generally, Gaussan actvaton functon s used n PNN because f the pattern falls wthn certan regon then the functon output s otherwse functon output s 0. It s not related to any assumpton about normal
3 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 dstrbuton. The actvaton functon for PNN s derved from estmates of PDF based on the tranng patterns as followng (Bose et al, 996): d Let X R be a d-dmensonal pattern vectors and ts assocated class be ( S, S2, S3,..., Sk ). Where, k s the number of possble class. If a posteror probablty, P r ( S / x) that s from class S, s by Bayes rule, Pr ( S x ) ( x / S ) Pr ( S ) P ( x ) Pr / = () where, Pr ( x / S), =, 2, 3,..., k s a pror PDF of the pattern n classes to be separated. P ( S ), =,2,3,..., k are the pror probabltes of the classes. r P ( x ) s assumed to be constant. The decson rule s to select class P ( x S ) P ( S ) P( x / S ) P ( S ) S for whch P ( S x) r / s maxmum. Ths wll happen f for all j / r > j r j (2) It s assumed that a pror probabltes ( ) r S P of the classes are known and the a pror PDF, ( x ) P / S s Gaussan then the estmator for a pror PDF s T ^ n ( x x j) ( x x ) j P ( x / S ) = exp d (3) 2 2 d ( 2 π ) σ j 2 S = σ Where, x j s j th exemplar pattern from class S S = n the cardnalty of the set patterns n class S σ = Smoothng factor d The nput layer has d unts, to whch the d-dmensonal nput vector X R s appled. The frst hdden layer has one pattern unt for each pattern exemplar. Therefore, each such pattern unt may be assocated wth a generc term depcted n the summaton of equaton (3) for the th class. The second hdden layer contans one summaton unt for each class. The output layer s decson layer used for mplementng the decson rule by selectng maxmum posteror probablty, pr ( S x) from outputs precedng summaton layer for each. The network s constructed by settng weght vector to one of the pattern unt equal to each dstnct pattern vector n the tranng set from a certan class and then connectng the outputs of the pattern unts to the approprate summaton unts for that class. For PNN, many algorthms are avalable n the lterature to acheve optmzed exemplar pattern set that means removng redundant data or duplcate nformaton. It ncreases the speed of classfcaton wth reduced sze of exemplar pattern set whle stll provdng suffcent data to fll the data space (Berthold et al, 998). The optmal selecton of smoothng parameter n PNN classfer s very mportant factor. The PNN decson boundary vares from a hyper plane to a very nonlnear boundary when the smoothng parameter vares from 0 (Zero) to (nfnte). In lterature many methodology are reported for the selecton of approprate wdths or smoothng factor (Hammond et al, 2004, Musav et al, 992). In the present paper a very smple method s used for the calculaton of smoothng factor to avod complex calculaton (Bose et al, 996): σ g = d javg (4) Where, d j = Dstance between the j th exemplar pattern and nearest exemplar pattern n class. g = Constant that has been by found tral and error. 3. Power Dfferental Protecton (PDP) Method The nflow and outflow of nstantaneous power through transformer s accordng to the magnetc energy stored n transformer wndng. Under normal operatng condton, about of the transformer power flows n the magnetzng crcut. In normal operatng condton, total power flowng nto transformer s about of the transformer capacty because the copper losses and core losses are of the same order. The PDP method s based on average nstantaneous power flow nto transformer wndng durng
32 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 one cycle perod T (20 ms for 50 Hz system). The PDP algorthm calculates the products of nstantaneous current and voltage and then calculates the average nstantaneous power as gven by t 2 2 w() t = ( u + u22 - r - r 22) dt T (5) T t To mplement the PDP method by dgtal relay the followng mathematcal expressons are gven as (Yabe, 997): p( t) = u + u - r - r (6) 2 2 2 2 2 2 w ( t) = N n p t T T n = N n =, 2, 3,..., N (7) Where, u, u2,, 2 are nstantaneous voltage and current at prmary and secondary wndng termnals respectvely. r, r 2 = Prmary and secondary wndng resstances respectvely p ( t ) = Instantaneous power w ( t ) = Average power of one perod tme N = Number of samples per cycle PDP method s not affected by the harmonc components present n ether nternal fault current or nrush current because t uses average nstantaneous power (Yabe, 997). In magnetzng nrush condton, average nstantaneous power from second perod after energzaton s almost equal to core losses plus stray losses. On the other hand, under an nternal fault condton large amount of power s consumed proportonal to fault degree (as a porton of wndng s short crcuted). Therefore, by settng a sutable threshold of average power flowng nto the transformer, magnetzng nrush and fault condton can be dscrmnated. In the proposed algorthm, the PDP method s utlzed to dstngush lght nternal fault current only as t needs at least one cycle to dscrmnate dfferent operatng condton of power transformer and ths s affordable n case of lght nternal fault only. Ths technque s capable of detectng fault and ts type n the eventualty of fault n transformer. It s operated n conjuncton wth PNN method. The trp decson of the relay s based on ORng of the two decsons obtaned. 4. Smulaton and Tranng Cases Durng power transformer operaton, t encounters any one of the followng condtons: Normal condton Over-exctaton condton Magnetzng / sympathetc nrush condton Internal fault condton External fault condton In normal condton, rated or less current flows through the transformer. In ths condton normalzed dfferental current s almost zero (only no load component of current). Whenever, there s large and sudden change n nput termnal voltage of transformer, ether due to swtchng-n or due to recovery from external fault, a large current s drawn by transformer from the supply. As a result, the core of transformer gets saturated. Ths phenomenon s known as magnetzng nrush. Magnetzng nrush can also occur n an already energzed transformer when a nearby transformer s energzed. A common stuaton of sympathetc nrush s encountered when a transformer s energzed n parallel wth another transformer already n servce. The phenomenon whch causes nrush current to flow n a prevously energzed transformer s known as the sympathetc nrush. As the paralleled transformer s beng energzed by closng the breaker, an nrush current s establshed n the prmary of ths transformer and ths nrush current has DC component. The DC component of the nrush current can also saturate the already energzed transformer, resultng n an apparent nrush current. Ths transent current, when added to the current of already energzed transformer, results n an asymmetrcal current that s very low n harmoncs. Ths would be the current flowng n the supply crcut to both transformers. Sympathetc nrush current may not have suffcent amount of the second harmonc n t to prevent the relay from trppng. Sympathetc nrush current depends on same factors on whch swtchng-n and recovery from fault magnetzng nrush current depends.
33 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 PSCAD/EMTDC smulaton s used to generate tranng as well as testng sgnals under dfferent operatng condtons of transformer as mentoned above. The smulaton set up s gven n Fgures 2-4. Whle smulatng magnetzng nrush condton, energzaton angle, remanent flux n the core and load condton are consdered because the magntude and the wave-shape of magnetzng nrush current depends on these factors. Fgure 2. Smulaton dagram of magnetzng / sympathetc nrush condton of transformer Fgure 3. Smulaton dagram of phase-to-ground fault under full-load condton of transformer Fgure 4. Smulaton dagram of magnetzng nrush under no-load consderng remanence flux n transformer Energzaton angle s vared from 0 to 360 degrees n steps of 30 degrees, and remanent flux s vared from 0 to 80 of the peak flux lnkages generated at rated voltage wth no load and full load condtons to generate tranng sgnals, whereas, the testng
34 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 sgnals are generated by varyng energzaton angle n step of 5 degrees. The desred remanence can be set n un-energzed transformer wth controlled DC current sources n PSCAD/EMTDC smulaton model (Woodford, 200). For nternal fault, tranng and testng s formed by smulatng fault from to 99 of power transformer wndng turns. Phaseto-ground fault at dfferent locatons as 5, 5, 25, 40 and 50 of the wndng as well as termnal fault are smulated. The detaled nformaton of power transformer PSCAD/EMTDC smulaton model to smulate nternal fault (Fgure 8) s gven n the Appendx-. Three-phase transformer of 35 MVA at 400/220 kv, 200 MVA at 220/0 kv and 60 MVA at 32/220 kv are modeled usng PSCAD/EMTDC. For the smulaton of these transformers through PSCAD/EMTDC, the parameters are used that are obtaned from M. P. State Electrcty Board, Jabalpur Inda. The test sgnals so acqured by smulatng varous operatng condtons of a transformer are shown n Fgures.5-. The smulaton was done at the rate of 2 samples per cycle of 50 Hz A.C. supply n vew of reported experence on dfferent dgtal relay desgns (Sachdev, 998). The developed fault detecton algorthm was mplemented n MATLAB. Operatng Sgnal (pu) 0.08 0.06 0.04 0.02 0-0.02-0.04-0.06-0.08 0 0. 0.2 0.3 0.4 0.5 Tme (s) Fgure 5. Typcal dfferental current waveform under normal operaton Operatng Sgnal (pu) 0 8 6 4 2 0-2 -4-6 Fault occurred here 0 0. 0.2 0.3 0.4 0.5 Tme (s) Fgure 6. Typcal dfferental current waveform for ground fault Operatng Sgnal (pu) 7.0 6.0 5.0 4.0 3.0 2.0.0 0.0 -.0 Swtchng-n occurred here 0 0. 0.2 0.3 0.4 0.5 Tme (s) Fgure 7. Typcal dfferental current waveform for magnetzng nrush
35 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 Operatng Sgnal (pu) 4 3 2 0 - -2-3 -4 0 0. 0.2 0.3 0.4 0.5 Tme (s) Fgure 8. Typcal dfferental current waveform for over-exctaton Power (pu).5 0.5 0-0.5 - -.5 0 0.05 0. 0.5 0.2 Tme (s) Fgure 9. Typcal nstantaneous power waveform for ground fault Power (pu).2 0.8 0.6 0.4 0.2 0 0 0.02 0.04 0.06 0.08 0. 0.2 0.4 0.6 0.8 Tme (s) Fgure 0. Typcal average power waveform for magnetzng nrush Power (pu).05 0.95 0.9 0.85 0.8 0 0.02 0.04 0.06 0.08 0. 0.2 0.4 0.6 0.8 Tme (s) Fgure. Typcal average power waveform for ground fault
36 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 5. Implementaton and Relay Logc 5.. Implementaton of PNN Based Algorthm and Comparson wth FFBP Neural Network Four layered PNN structure s used as shown n Fgure. Input layer of PNN model has 2 neurons. The number of neuron of nput layer are decded based on the dmenson of feature space.e. 2 samples per cycle. The frst hdden layer conssts of 777 neurons and t s decded based on total number of exemplar pattern set used to construct the PNN model. In tranng exemplar pattern set, 444 patterns of magnetzng nrush (ncludng sympathetc nrush patterns), and 333 patterns of faults are used. Second hdden layer has two neurons, as there are only two classes to be classfed. In output layer, sngle neuron s used, as t s the decson layer and t s used for selectng the maxmum posteror probablty, from the outputs of the summaton layer. The PNN requres one node or neuron for each exemplar pattern. Varous clusterng technques have been used to reduce ths requrement to one node per cluster center. Clustered data s requred to construct the PNN because the output of frst hdden layer s added and ths belongs to one specfc cluster that s clear from the PNN archtecture. To construct an optmzed and effcent PNN, the tranng data are clustered by usng K-means clusterng (Specht, 992), and the smoothng factor for each class s calculated by equaton (4). The optmal value of multplcaton factor (g) s obtaned by tral and error method and thus optmal smoothng factor s acheved (see Appendx-2). Out of 925 sets of data (patterns), 777 patterns sets are used to construct PNN wth optmal smoothng factor whch s already obtaned by the conventonal method and remanng 48 sets are used to test the network s generalzaton ablty that are dfferent from those used to tran the network. These 48 test exemplar pattern sets contan nternal fault and magnetzng nrush condton only as these two condtons are very dffcult to dscrmnate as compared to other operatng condtons lke external fault condton, over-exctaton and normal operaton from protecton pont of vew. Out of these 48 cases 74 are that of magnetzng nrush and rest are for nternal faults. As other condtons have been taken care before ths stage, hence there s no chance of gettng exemplar patterns of other operatng condtons at ths stage. Start Input data (Operatng Sgnal ) Over exctaton/ Normal Operaton? Yes NO Check for Inrush or Fault by PNN? Inrush Fault Issue Trp Sgnal Fgure 2. Flow chart of PNN based algorthm External fault and normal operatng condton are ruled-out by comparng two consecutve peaks of operatng sgnal whereas the over-exctaton condton s determned by comparng actual value of voltage-to-frequency rato wth ts rated value (shown n Fgure 2). If these condtons do not exst then the processng s contnued to detect the magnetzng nrush and nternal fault condtons by PNN. The posteror probabltes are calculated by the summaton layer of PNN and the decson layer selects maxmum posteror probablty from the precedng summaton layer and on the bass of maxmum posteror probablty, the patterns are classfed. Accordngly, the PNN gves trppng sgnal f an nternal fault condton s detected.
37 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 Many experments have been made to evaluate the performance of the PNN model. The fault and magnetzng nrush condtons are tested wth all possble patterns. The results are gven n Table- whch presents the natural logarthm of probablty of the test pattern to be nternal fault or nrush condton. By comparng the magntude of these probabltes, the test data belongngness s decded. The values gven n the Table- are the condtonal probablty estmated by PNN. On the bass of these condtonal probablty PNN based classfer takes decson.e. the test data represents ether nternal fault current or nrush current. To obtan data for the testng of relayng algorthm fault current magntude, remanent flux, load condton and swtchng-n angle are vared to nvestgate ther effects on the performance of the PNN model. Snce the profle of magnetzng nrush current wave changes wth varaton of swtchng-n nstant of transformer hence, t s vared between 0 to 360 degrees. Smlarly, due to remanence flux, the magntude of magnetzng nrush current may be as hgh as 2 to 6 tmes to that of the magnetzng nrush wthout that, although the wave-shape remans same. It s found that the PNN classfer based relay s stable even wth such hgh magntude of magnetzng nrush current caused by remanence flux whereas the conventonal harmonc based relay may maloperate due to such hgh magntude of magnetzng nrush current. Table-. Condtonal probablty estmated by PNN Type of test data Probablty of fault Probablty of nrush Inrush data 8.90 26.004 Fault data 3.742 22.99 The PNN s faster than FFBP neural network. The tranng requred for PNN s very dfferent and much faster than that requred for FFBP neural network (Specht et al, 99). The tranng process of PNN s one pass wthout any teraton for the weght adaptaton, as aganst a large number of teraton (epochs) necessary n case of FFBP neural network. As an example, 000 teratons are requred for convergence n case of FFBP neural network mplemented by the authors, thereby gvng a rato of about 000: n terms of the tranng tme. Therefore, the PNN s free from the demerts lke local mnma and slow convergence n tranng and emprcal determnaton of network structure and parameters. Furthermore, n PNN, sngle parameter namely smoothng factor s to be tuned whereas n the FFBP neural network at least four parameters lke learnng rate, momentum coeffcent, weghts etc. are to be tuned durng tranng of neural network. Ths makes PNN easy to desgn and smple n use than the classcal ANN. Fgure 3. Varaton of accuracy versus multplyng factor (g) on 35MVA power transformer usng PNN classfer Table-2 demonstrates that the optmal PNN fals to dscrmnate some lght nternal fault.e. false negatve error. Ths optmal PNN s desgned wth optmal value of smoothng factor that s obtaned by classcal method gven n Table-3. Fgure 3 shows the effect of the multplyng factor on the classfcaton accuracy of a PNN classfer n case of 35MVA power transformer. From the expermental results, t s found that when PNN s traned wth one transformer and tested on dfferent ratng of transformer, t fals n case of lght nternal fault condton only. Fgure4 llustrates the typcal waveform of lght nternal fault case. The nature of waveform s smlar to the typcal nrush waveform, and because of smlarty n wave-shapes of typcal nrush waveform and lght nternal fault waveform, the boundary of classfcaton becomes narrow and therefore, t s dffcult to dscrmnate the lght nternal fault cases. Therefore, for such cases PDP technque s appled, whch s also ndependent of harmonc component present n fault current and nrush current.
38 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 Operatng Sgnal (pu).5 0.5 0-0.5 0 0.02 0.04 0.06 0.08 0. 0.2 0.4 0.6 Tme (s) Fgure 4. Typcal waveform of phase-to-ground fault at 2 of the wndng from the neutral end Start Input data (Operatng sgnals) Over-exctaton / Normal operaton? Yes No Inrush Check for nrush or fault by P D P method? Check for nrush or fault by PNN? Inrush Fault Fault OR Logc Issue trp sgnal Fgure 5. Flow chart of PNN and PDP algorthm 5.2. Implementaton of Hybrd PNN & PDP method and Result Dscusson The PNN and PDP methods are parallely operated. The flow chart (Fgure 5) llustrates all the steps of the hybrd PNN and PDP method to dscrmnate between nrush and nternal fault condtons. In PDP method nstantaneous power (shown n Fgure 9) and average power (shown n Fgure ) are calculated by usng equaton (6) and (7) respectvely. From Fgure 0 and Fgure, t s clear that there s large dfference n average power after one cycle of tme. Therefore, wth proper settng of threshold value, operatng condton of transformer can be montored. The threshold value depends on transformer ratng and ts other parameters. By ths method, the type of fault n transformer can also found due to large dfference among the threshold values and that for lght nternal fault, external fault and phase-to-phase fault condtons. Ths technque s used for the detecton of low level nternal faults only as there s one cycle delay n decson makng whch s affordable n ths case only, whereas n other cases PNN wll
39 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 recognze the dfferent operatng condtons of power transformer wthn half cycle of ts occurrence. Therefore, by combnng these two methods, fault can be detected wth certanty whch mprove the relablty and stablty of dfferental relayng algorthm. The relay utlze OR logc that means, any nput sgnal ether OA or OP s hgh the relay wll ssue the trp sgnal. Where, OA and OP are the output of PNN method and PDP method respectvely. O s output of the relay and the hgh state of output mples the trp sgnal to be generated. No.of False Postve + No.of False Negatve Classfcaton Error (n ) = 00 Total Number of Test Cases Classfcaton Accuracy (n ) = 00 Classfcaton Error (n ) (8) Table-4 presents the classfcaton n accuraces (n percentage) wth FFBP neural network, PNN and combned PNN and PDP method. The classfcaton n accuracy s calculated by usng (8). From the results of Table-4, t s clear that the classfcaton ablty of PNN s better than the FFBP neural network n ths applcaton. However, from Table-4, t s observed that the proposed combned method has ablty to dscrmnate between the lght nternal fault (turn-to-turn fault) as well as magnetzng nrush condton and classfcaton n accuracy of the combned (PNN and PDP) method has mproved as compare to the FFBP neural network and PNN method. Dscrete Fourer Transform (DFT) based harmonc restrant method s mplemented, to compare performance of the proposed optmal PNN based algorthm n power transformer dfferental protecton. Fgures 6-7 show the rato of second harmonc to fundamental of the dfferental current under typcal magnetzng nrush and nternal fault condton respectvely. Durng one cycle under nternal fault condton, the rato of the second harmonc s qute hgh and n the same range as n case of magnetzng nrush condton. Therefore, t s dffcult to dscrmnate between nternal fault and nrush condtons merely settng a preset threshold. From Fgures 6-7, t s also clear that the rato values are fluctuatng, whch create problem to decde a preset threshold. Moreover, due to the presence of second harmonc durng nternal fault condton dgtal relay wll take longer tme to make trp decson (one cycle or more than one cycle). In contrast, the optmal PNN based method s able to detect such a fault n 6 ms (half cycle or wth n half cycle) except lght nternal fault (turn-to-turn fault) cases. However, the harmonc restrant method s capable to dscrmnate between these two condtons but does not seems to be ntellgent to take decson n case of fluctuatng rato of second harmonc to fundamental of the dfferental current due to dfferent loadng condtons, severty of nternal faults, swtchng-n angles etc. and hence mal-operaton of relay wll occur. Whle the proposed amalgamated technque (.e. combned PNN and PDP method) s ntellgent and more relable than the conventonal harmonc restrant method, FFBP based method and PNN based method. rato of second to fundamental component 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 0 0.04 0.06 0.08 0. 0.2 0.4 Tme(s) Fgure 6. Rato of second harmonc to fundamental of the dfferental current under typcal nrush condton (nrush occurs at 0.04 sec.)
40 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 rato of second to fundamental component.2. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 0 0.04 0.06 0.08 0. 0.2 0.4 Tme(s) Fgure7. Rato of second harmonc to fundamental of the dfferental current under typcal nternal fault condton (nternal fault occurs at 0.04 sec.) Table-5 shows the number of post abnormalty samples requred for decson by FFBP neural network, PNN and PNN conjuncton wth PDP method based relays. From Table-5, t s clear that the PNN s faster than the FFBP neural network and PNN conjuncton wth PDP method. However, t fals to recognze some typcal lght nternal fault (turn-to-turn fault) cases whereas the PNN conjuncton wth PDP method has 00 classfcaton capablty wth a reasonable speed as compared among these three methods. In ths table actual value ndcates the number of post abnormalty sample requred for detecton of a test pattern by concerned algorthm whle logcal value provdes nformaton regardng the of maxmum number of post abnormalty samples avalable n a pattern. Tremendous capablty of PNN for classfcaton problems shows sutablty for dfferental transformer protecton. It s also mmune from the dfferent harmoncs contaned n operatng sgnals whch makes t smpler and robust than the conventonal dgtal flterng algorthms. Table 2. Number of false detectons n optmal PNN Tested transformer ratngs Tranng transform er ratngs 35 MVA 200 MVA 60 MVA False postves False negatves False postves False negatves False postves False negatves Inrush Faults Inrush Faults Inrush Phase-to- Phase-tophase Phase-to- Phase-to- Phase-to- Phase-tophase Swtchng -n Swtchng -n Swtchng -n ground ground phase ground angles angles angles fault fault fault fault fault fault Degrees * * Degrees * * Degrees * * 35 MVA 0-0 - 0-0 - 2 0-0 - 0-0 - 200 MVA 0-0 - 0-0 - 0-0 - 0-2 2,5 0-60 MVA 0-2 0-0 - 2 2, 5 0-0 - 0-0 - * Represents locaton of wndng from the neutral end at whch fault occurs Represents number of recurrence
4 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 Table -4. Traned transformer ratngs Table-3. Optmal multplcaton factor (g) Tested transformer ratngs Traned transformer ratngs 35 MVA 200 MVA 60 MVA 35 MVA..4. 200 MVA 0.5 0.3 0.5 60 MVA 0.3 0.3. Classfcaton accuraces (n ) wth FFBP, PNN and combned PNN and PDP method Tested transformer ratngs 35 MVA 200 MVA 60 MVA FFBP () PNN () PNN & PDP () FFBP () PNN () PNN & PDP () FFBP () 35 MVA 99.32 00 00 94.59 98.65 00 98.64 00 00 200 MVA 96.62 00 00 99.32 00 00 98.64 96.93 00 60 MVA 98.64 98.65 00 96.62 97.3 00 00 00 00 PNN () PNN & PDP () Table 5. Cases Number of post abnormalty samples requred for decson by FFBP, PNN and PNN & PDP method based relays FFBP neural PNN and PDP PNN network method Number of samples requred Number of samples requred Number of samples requred Actual Logcal Actual Logcal Actual Logcal Magnetzng nrush (0 0 ) Internal fault (Lght phaseto-ground fault at 2) 2 05 2 05 2 0 2 06 2 8 24 6. Conclusons Ths paper presents a novel approach, by amalgamaton of PNN and PDP methods, to enhance dscrmnaton between transformer nternal fault and magnetzng nrush and to classfy the type of fault n power transformer. The PNN s faster than the classcal ANNs and easy to desgn. The reported PNN algorthm s based on wave-shape dentfcaton technque whch s ndependent of amount of harmonc contents of operatng sgnal of relay, and sutable for modern power transformers that use hgh-permeablty low coercon core materals. Wth these core materals hgh second harmonc components may be generated durng nternal faults whle these components may reman low durng magnetzng nrush, and hence the conventonal harmonc restrant technque that uses second harmonc component as the ndcator of magnetzng nrush may fal. As the PDP method montors the power flow nto transformer rrespectve of the harmonc contents of fault currents, and hence s sutable for protecton of modern power transformers. In the proposed hybrd method, stablty of dfferental relay s ensured durng the magnetzng nrush, sympathetc nrush, over-exctaton and external fault condtons. The combnaton of PDP method wth PNN makes t capable to detect lght nternal faults (turn-to-turn faults) for all ratngs of transformers whch mprove the overall performance of dgtal dfferental protecton scheme. In addton to that the hybrd method s ntellgent, relable and capable to take decson even n case of fluctuatng rato of second harmonc to fundamental of dfferental current unlke the conventonal harmonc method. Real tme mplementaton of dfferental relayng usng the proposed algorthm applyng PNN as the core classfer would essentally requre a PNN processor and t s matter of further research.
42 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 Nomenclature x Input of neural network y Output of neural network S Cardnalty of the set patterns n class S PxS / Class condtonal probablty densty functon of x ( ) ( ) r Pr S Probablty that a vector belongs to class d j g σ S regardless of the dentty of that vector Dstance between the j th exemplar pattern and nearest exemplar pattern n class Multplcaton factor (Constant) Smoothng factor x j j th exemplar pattern from class S u, u 2 Instantaneous voltage at prmary and secondary wndng termnals respectvely, 2 Instantaneous current at prmary and secondary wndng termnals respectvely r, r 2 Prmary and secondary wndng resstances respectvely p ( t ) Instantaneous power wt () Average power of one perod tme N Number of samples per cycle Appendx- Fgure 8 shows a typcal PSCAD/EMTDC transformer model to smulate nternal faults (turn-to-turn, phase-to-ground, and phase-to-phase) at dfferent locaton of transformer wndng from the neutral end of the wndngs. In ths model MVA ratng, voltage ratng, base frequency, leakage reactance, magnetzng current, and fault locaton (n ) etc. can be defned. Fgure8(a). Typcal PSCAD/EMTDC transformer model to smulate nternal fault
43 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 Fgure 8(b). Typcal PSCAD/EMTDC transformer model to smulate nternal faults at dfferent locatons Appendx-2. Calculate smoothng factor (σ ) by usng Eucldean dstance between the ponts representng the tranng k k k patterns n feature space for each class.e. d j Eucldean dstance between x and x j n class k.. Take average of Eucldean dstances. Select a constant g by tral and error method Fnd optmal value of g based on the applcaton. References Arboleya, P., Daz, G., Alexandre, J. G., and Moran, C. G. 2006. A soluton to the dlemma nrush/fault n transformer dfferental relayng usng MRA and wavelets. Electrc Power Systems and Research, Vol. 34, No. 3, pp. 285-30. Bastard, P., Meuner, M., and Regal, H. 995. Neural network based algorthm for power transformer dfferental relays. IEE Proc. Generaton Transmsson & Dstrbuton, Vol. 42, No. 4, pp.386-392. Berthold, M. R., and Damond, J. 998. Constructve tranng of probablstc neural networks. Elsever Scence, Neurocomputng, Vol. 9, No. -3, pp.67-83. Borghett, A., Bosett, M., Slvestro, D. M. and Nucc, A. C. 2008. Contnuous-wavelet transform for fault locaton n dstrbuton power networks: defnton of mother wavelets nferred from fault orgnated transents. IEEE Trans. on Power Delvery, Vol. 2, No. 23, pp.380-388. Bose, N. K., and Lang, P. 996. Neural Network Fundamentals wth Graphs, Algorthms, and Applcatons. McGraw-Hll Book Co. Internatonal Edtons. Hammond, M. H., Redel, C. J., Rose-Pehrsson, S. L., and Wllams, F. W. 2004. Tranng set optmzaton methods for a probablstc neural network. Elsever Scence, Chemometrcs and Intellgent Laboratory System, Vol.7, No., pp.73-78. He, B., Zhang, X., and Bo, Z. Q. 2006. A new method to dentfy nrush current based on error estmaton. IEEE Trans. on Power Delvery, Vol. 2, No. 3, pp.63-68. Moravej, Z., Vshwakarma, D. N. and Sngh, S. P.: 2003. Applcaton of radal bass functon neural network for dfferental relayng of a power transformer. Computer and Electrcal Engneerng, Vol. 29, No. 3, pp.42-434. Musav, M. T., Kalantr, K., and Ahmed, W. 992. Improvng the performance of probablstc neural networks. Proc. IEEE Int. Conf. Neural Networks, Vol., pp.595-600. Sachdev, M. S. (coordnator). 988. Mcroprocessor relays and protecton systems. IEEE Tutoral Course Text, (Publ. No.88EH0269--PWR). Shn, M. C., Park, C. W., and Km, J. H. 2003. Fuzzy logc based relayng for large power transformer protecton. IEEE Trans. on Power Delvery, Vol. 8, No. 3, pp.78-724. Sdhu, T. S., and Sachdev, M. S. 992. On lne dentfcaton of magnetzng nrush and nternal faults n three phase transformers. IEEE Trans. on Power Delvery, Vol.7, No.4, pp.885-89.
44 Trpathy et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 3, 200, pp. 29-44 Specht, D. F. 990. Probablstc neural network. Neural Networks, Vol. 3, No., pp.90-8. Specht, D. F., and Shapro, P. D. 99. Generalzaton accuracy of probablstc neural networks compared wth back-propagaton networks. Proc. IEEE Int. Jont Conf. Neural Networks, Seattle, pp. 887-892. Specht, D. F.992. Enhancements to probablstc neural networks. Proc. IEEE Int. Conf. on Neural Networks, Vol., pp.76-767. Tan, K. C., and Tang, H. J. 2004. New dynamcal optmal learnng for lnear multlayer FNN. IEEE Trans. on Neural Networks, Vol. 5, No.6, pp.562-568. Tan, B., Azm-Sadjad, M. R. 200. Comparson of two dfferent PNN tranng approaches for satellte cloud data classfcaton. IEEE Trans. on Neural Networks, Vol. 2, No., pp.64-68. Trpathy, M., and Ala, S. 2009. Optmal radal bass functon neural network transformer dfferental protecton. Proc. IEEE Int. Conf. on Innovatve Ideas towards the Electrcal Grds of the Futures, 28 June-2 July 2009, Bucharest, Romana, pp.-8. Trpathy, M., Maheshwar, R. P., and Verma, H. K. 2005. Advances n transform protecton: a revew. Electrc Power Components and Systems, Vol. 33, No., pp.203-209. Trpathy, M., Maheshwar, R. P., and Verma, H. K. 2007. Probablstc neural network based protecton of power transformer. IET Electrcal Power Applcaton, Vol., No. 5, pp.793-798. Verma, H. K., and Basha, A. M. 986. A mcroprocessor-based nrush restraned dfferental relay for transformer protecton. Journal of Mcrocomputer Applcaton, Vol. 9, No.4, pp.33 38. Wang, H., and Ln, X. 2009. Studes on the unusual mal-operaton of transformer dfferental protecton durng the nonlnear load swtch-n. IEEE Trans. on Power Delvery, Vol. 4, No. 24, pp.824-83. Woodford, D. 200. Introducton to PSCAD V3. Mantoba HVDC Research Centre Inc., 400-69 Pembna Hghway, Wnnpeg, Mantoba, R3T 3Y6, Canada. Yabe, K. 997. Power dfferental method for dscrmnaton between fault and magnetzng nrush current n transformers. IEEE Trans. on Power Delvery, Vol.2, No.3, pp.09-8. Bographcal notes Manoj Trpathy was born n Gorakhapur, Inda, n 976. He receved the B.E. degree n electrcal engneerng from Nagpur Unversty,Nagpur, Inda, n 999, the M. Tech. degree n nstrumentaton and control from Algarh Muslm Unversty, Algarh, Inda, n 2002, and the Ph.D. degree from the Indan Insttute of Technology Roorkee, Roorkee, Inda, n 2008. He was an Academc Staff Member wth Shobht Unversty, Meerut, Inda. He s presently Assstant Professor wth the Department of Electrcal Engneerng, Motlal Nehru Natonal Insttute of Technology Allahabad, Allahabad, Inda. Hs research nterests nclude power system protecton, developments n dgtal protectve relay, and power system montorng. Dr. Trpathy s a Revewer for varous nternatonal journals n the area of power systems. He s a member of IE (Inda), and member of IEEE. Rudra Prakash Maheshwar was born n Algarh, Inda, n 960. He receved the B.E. and M.Sc. (Engg.) degrees n electrcal engneerng from Algarh Muslm Unversty (AMU), Algarh, Inda, n 982 and 985, respectvely, and the Ph.D. degree from Unversty of Roorkee, Roorkee, Inda, n 996. He was an Academc Staff Member wth AMU. He s presently a Professor wth the Department of Electrcal Engneerng, Indan Insttute of Technology Roorkee, and a Consultant n the area of small hydro power plants. He has publshed more than 75 research papers n varous nternatonal/natonal journals and conferences. Hs research nterests nclude power system protecton, developments n dgtal protectve relay, and protectve relay testng. Dr. Maheshwar s a member of edtoral boards and a revewer for varous nternatonal journals n the area of power system protecton. H. K. Verma was born n Gojra, Inda. He receved the B.E. degree n electrcal engneerng from the Unversty of Jodhpur, Jodhpur, Inda, n 967, and the M.E. degree n power systems engneerng and the Ph.D. degree n electrcal engneerng from the Unversty of Roorkee, Roorkee, Inda, n 969 and 977, respectvely. Currently, he s a Professor and Deputy Drector of the Indan Insttute of Technology, Roorkee. From 980 to 982, he was a Manager (R&D) of Unversal Electrcs Ltd., Fardabad (a Brla Group Publc Ltd. Co.). Hs research nterests are n the areas of Intellgent nstrumentaton, dgtal/ numercal relays, and power system protecton, montorng, and control. He s assocated wth many Government projects of natonal mportance. He has publshed a large number of research papers n varous nternatonal/natonal journals and conferences. Receved November 2009 Accepted March 200 Fnal acceptance n revsed form March 200