Indirect Symmetrical PST Protection Based on Phase Angle Shift and Optimal Radial Basis Function Neural Network

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1 Indrect Symmetrcal PST Protecton Based on Phase Angle Shft and Optmal Radal Bass Functon Neural Networ Shalendra Kumar Bhaser Department of Electrcal Engneerng Indan Insttute of Technology Rooree, Inda emal: Manoj Trpathy Department of Electrcal Engneerng Indan Insttute of Technology Rooree, Inda emal: Vshal Kumar Department of Electrcal Engneerng Indan Insttute of Technology Rooree, Inda emal: Abstract Ths paper proposes a new algorthm for blocng the operaton of Indrect Symmetrcal Phase Shft Transformer (ISPST) dfferental relay when subjected to dfferent operatng condtons except nternal fault condton. The proposed algorthm s amalgamaton of Phase angle shft (PAS) threshold and Optmal Radal Bass Functon Neural Networ (ORBFNN). PAS between source and load sde currents of fundamental frequency s used as threshold. PAS threshold dentfes whether the abnormal condton s n ISPST or out of ISPST. ORBFNN s used for the dscrmnaton of nternal fault from magnetzng nrush condton. The ORBFNN s desgned by usng Partcle swarm optmzaton (PSO) technque. The performance of proposed ORBFNN algorthm s compared wth more commonly reported Feed Forward Bac Propagaton Neural Networ (FFBPNN). The smulatons of dfferent operatng condtons of an ISPST are performed by usng PSCAD/EMTDC software. Keywords Dfferental protecton; phase shft transformer; artfcal neural networ; partcle swarm optmzaton; I. INTRODUCTION Phase Shft Transformer (PST) s an mportant electrcal component used for the power flow control through specfc lne n a complex power transmsson networ. The basc functon of the PST s to change the effectve phase dsplacement between nput and output voltage of a transmsson lne. Power flow control usng PST s gven by (1). There are dfferent types of PST accordng to ther constructon as dscussed n [1]. Indrect Symmetrcal PST (ISPST) s wdely used because of ts features and smple constructon as shown by lne dagram n fg. 1. It helps n the utlzaton of power transmsson lnes whch mprove the system operatng performance and effcency. where V and S phase angle between V S and to ISPST. VS VL P sn( ) XT (1) V are source and load sde voltage, s L V L, s phase angle shft due Consderng the mportance and cost of an ISPST, t requres fast and relable protecton. However, there are many protecton schemes such as dfferental protecton, overload protecton, over exctaton protecton, through current bacup Fg. 1. Crcut of Indrect Symmetrcal Phase Shft Transformer [3] protecton etc. [], but dfferental protecton s the man protecton scheme whch s appled for nternal faults n an ISPST. In dfferental protecton, an ISPST s protected for both seres and exctaton unt [3, 4]. Ths needs 18 CTs, 9 for each protecton, whch maes the protecton qute costly. Instead of ths, ISPST protecton can be done le power transformer by usng phase angle shft compensaton [5]. It taes tme for calculaton, whch maes delay n trppng of relay. Furthermore, dfferental relay s prone to mal-operaton n presence of magnetzng nrush current of an ISPST, whch s caused by transent n ISPST magnetc flux []. As dscussed about the power transformer, to enhance the relablty of dfferental protecton, voltage sgnal, current sgnals and dfferental power s utlzed n three methods such as Harmonc restrant (HR), waveform dentfcaton and other methods [6-7]. The HR prncple s based on the second harmonc component of the magnetzng nrush whch s consderably larger than n a typcal nternal fault current [8]. But the modern transformers are dfferent n desgn and materal, therefore run at hgh flux densty, and hence generate low harmoncs contents durng the nrush currents, whch affect HR scheme [9]. Smlar to the power transformer protecton, ISPSTs dfferental protecton also brngs challenge of non-standard phase shft between two ends [6, 10]. The ntroducton of Artfcal Neural Networ (ANN) n the protecton has been removed the drawbac of conventonal dfferental relayng. There are dfferent types of ANN such as Multlayer feed forward Neural Networ (MFFNN), Feed Forward Bac propagaton Neural Networ (FFBPNN) etc /14/$ IEEE

2 These have been used for dscrmnaton of dfferent operatng condton (Normal, nternal fault, magnetzng nrush etc.) by consderng dfferent parameter le power, voltage, dfferental current, flux etc. [11]. Radal bass Functon Neural Networ (RBFNN) has become a very popular algorthm due to several advantages over other tradtonal multlayer neural networ [1]. These advantages nclude: ndependent tunng of RBFNN parameters, one layer of nonlnear transformaton s suffcent for nput-output mappng and clusterng problem s ndependent of output layer weght. Ths paper proposes a smple decson mang threshold based on the phase angle shft (PAS) whch dscrmnate normal and external fault condtons from magnetzng nrush and nternal fault condtons. An Optmal Radal Bass Functon Neural Networ (ORBFNN) s used for the dscrmnaton of nternal fault from magnetzng nrush condton. The ORBFNN has been developed based on slope of the dfferental current just before frst pea after PAS decson under nternal fault and magnetzng nrush condton. Generally, ORBFNN tranng ncludes r-nearest neghbor heurstc for wdth or smoothng factor, K-mean clusterng for calculaton of centers and tranng of output layer weghts by least square technque [13]. However, n ths paper calculaton of centers and optmal wdth or smoothng factor s obtaned by usng Partcle Swarm Optmzaton (PSO) technque because these factors are very mportant for ORBFNN to ncrease the accuracy n classfcaton problem. A comparson between the performance of ORBFNN and FFBPNN s presented for the dscrmnaton of nternal fault from magnetzng nrush condton. II. OPTIMAL RADIAL BASIS FUNCTION NEURAL NETWOTK RBFNN has become a very powerful tool to many techncal problems because of ts unversal approxmaton capablty and fast learnng speed [1, 14]. The nputs to the hdden layer are the lnear combnatons of scalar weghts and nput vector x [ x1, x,... x ] T n, where the scalar weghts are usually assgned unty values and n s number of nputs. Thus the nput vector becomes the nput to each neuron n the hdden layer. The ncomng nput vectors are mapped by the radal bass functon n each hdden nodes. The output layer produces a vector y [ y1, y1,... y m ] for m outputs by lnear combnaton of the outputs of hdden nodes to produce the fnal output, whch s gven by (). y w ( x) 1 () where w denotes the hdden-to-output weght correspondng to the th hdden node and ' ' s the number of hdden nodes, ( x) s the hdden layer output of the th hdden node. Each hdden node represents a sngle RBF and computes a Gaussan ernel functon of ' x '. Gaussan ernel functon s consdered as actvaton functon, as suggested n [15]. The Gaussan actvaton functon s represented as follows (3): n 1 xj c ( x) exp j1 (3) where c and denotes the center and wdth of the th hdden node respectvely. The structure of sngle nput and sngle output, three layered radal bass functon neural networ s shown n fg.. Generally, the Gaussan RBFNN tranng s done n to two stages. Determne the optmal parameters of radal bass functons,.e., Gaussan center and wdth or smoothng factor. Determne the output weght w by supervsed learnng method. The frst stage s very crucal, snce the performances of RBFNN crtcally depend on the choce of the centers and wdths. In ths wor optmzed values of centers and wdths are calculated by PSO for each hdden neuron. III. PARTICLE SWARM OPTIMIZATION TECHNIQUE PSO technque s nspred by socal behavor of brds, nsects and fsh. It s a populaton based stochastc optmzaton technque developed by J. Kennedy and R. Eberhart n 1995 [16]. The man advantages of PSO algorthm are smple concept, robust to control parameters, easy to mplement and computatonally effcent as compare to other optmzaton technques. In PSO, populaton s called swarm and ndvduals are called partcles. All partcles move wth an adaptable velocty wthn search space and recollect the best poston t ever encounters n memory. The best poston of partcle s shared wth other partcles n the swarm after each teraton. In PSO algorthm, two varants were developed [17]. One s local varant and other s global varant. Accordng to local varant, each partcle moves towards ts best prevous poston and toward the best partcle n ts restrcted neghborhood, whereas accordng to global varant, each partcle moves towards ts best prevous poston and towards the best partcle n the swarm [17]. In general, the global varant exhbts faster convergence rates compare to local varant. The partcle expresses the ablty of fast convergence Fg.. Typcal Sngle nput, sngle output RBF networ

3 to local and/or global optmal poston(s) over a small number of generatons. Consder an n-dmensonal search space, there are three elements, current poston P ( p, p,... ) 1 p, current n velocty V ( v 1, v,... vn ) and the past best poston Pb ( pb 1, pb,... pbn ) for partcle n the search space to represent ther features. Each partcle n the swarm s teratvely updated accordng to the predefned attrbutes assumng that the ftness functon f s to be mnmzed so that new velocty of every partcle s updated by (4): 1 V w V c1r 1( Pb P ) cr ( Gb P ) (4) where s the number of teraton, V s the velocty of the th partcle for teraton, w s the nerta weght of velocty, c 1 and c denote the acceleraton coeffcent, r 1 and r are two unform random values n the range between (0, 1), Gb s global best poston untl teraton. The new best poston of the th partcle s calculated by (5): 1 1 P P V (5) The past best poston of each partcle s updated by: 1 1 Pb, f f ( P ) f ( Pb ) Pb 1 P, otherwse (6) Each partcle performance s calculated accordng to a predefned ftness functon f whch s problem dependent. The nerta weght w s usually a monotoncally decreasng functon to control the mpact of prevous hstory of veloctes on the current velocty. The nerta weght w can be set to the followng [18]: w w max mn w wmax ter termax where wmax mn number of teraton and (7) 0.9, w 0.4, ter s maxmum max th ter s teraton number. In ths wor, the ftness functon f to optmze the wdth and center of RBFNN s defned by the mean square errors (MSE) of ts outputs for all tranng samples. The optmal wdth and center c for the tranng set m X s gven 1 by ftness functon: External Fault Condton Over-exctaton Condton Out of these operatng condtons dfferental relay should operate only n nternal fault condton. But due to nonstandard phase shft between two ends of an ISPST, dfferental current s not equal to zero. It requres phase shft compensaton, whch ncreases the relay tme of operaton due to compensaton calculaton. The proposed algorthm s based on the PAS threshold between source and load sde current for each phase. Normal operatng condton n advance and retard phase shft mode of operaton wth maxmum PAS and PAS threshold s shown n fg. 3. The non-standard phase shft wll vary between these two boundares of an ISPST. In case of magnetzng nrush PAS becomes approxmately equal to 90 degree because t s prmarly nductve at no-load as revealed n fg. 4. But n case of on-load magnetzng nrush, PAS becomes less than 90 degree, because of loadng condton. In case of nternal fault n seres unt or exctaton unt, ether source current or load current would be reversed and hence PAS between them becomes greater than 90 degree as shown n fgs But n few cases (such as turn to turn), the PAS becomes less than 90 degree due to non-reversal of current ether source or load sde and advance phase angle shft. In case of external fault condton, there s no reversal of current ether source or load sde and hence PAS between them s almost equal to zero as shown on fg. 7. Fg. 8 shows case of over-exctaton wth PAS threshold. Hence a PAS based threshold can dscrmnate other operatng condton from magnetzng nrush and nternal fault condton. Fg. 3. Phase angle shft of phase a n normal operatng condton m X c f (, c) arg mnt exp 1 where t s the desred output for the nput sample X. (8) IV. PROPOSED ALGORITHM Durng ISPST operaton t encounters anyone of the followng condton: Normal Condton Magnetzng Inrush Condton Internal Fault Condton Fg. 4. Phase angle shft of phase a n case of magnetzng nrush at tme t=0.15sec.

4 A low slope characterstc of the waveform near to pea n case of nternal fault condton. Ths feature can easly dscrmnate nternal fault condton from magnetzng nrush condton. An Optmzed RBFNN s used for the dscrmnaton between nternal fault and magnetzng nrush condton usng ths feature. The flow chart for the proposed algorthm s shown n fg. 10. Fg. 5. Phase angle shft of phase a n case of nternal fault (A-G) n exctaton unt at tme t=0.15sec. Fg. 9. Behavor of (a) Magnetzng Inrush and (b) Internal Fault Fg. 6. Phase angle shft of phase a n case of nternal fault (A-G) n seres unt at tme t=0.15sec. Fg. 7. Phase angle shft of phase a n case of external fault (A-G) at tme t=0.15sec. Fg. 10. Flowchart for proposed algorthm V. SIMULATION AND TRAINING CASES The proposed algorthm has been evaluated for aforementoned operatng condtons of an ISPST. Dfferental currents are obtaned for each phase wth star connected current transformers (CTs) on both sdes of an ISPST usng PSCAD/EMTDC. The lne dagram s shown n fg. 11. Fg. 8. Phase angle shft of phase a n over-exctaton condton Dscrmnaton of nternal fault current from magnetzng nrush current s based on the followng characterstcs of the dfferental current as shown n fg. 9: A large slope characterstc of the waveform near to pea n case of magnetzng nrush condton. Fg. 11. Lne dagram of smulated model Three phase 300MVA, 138V/138V, 155A/155A, 60Hz ISPST wth max phase shft of ±30 degree and maxmum loadng of 40MW and 180MVAR s consdered to

5 test the performance of the proposed algorthm [3]. Relevant CTs wth the rato 000/5 are connected n star on both sdes of an ISPST whose parameter s reported n [19]. Snce the wave shape and magntude of the magnetzng nrush current depends on the swtchng-n angle, loadng condton and remanent flux n the core, the magnetzng nrush condton s smulated wth varyng swtchng-n angle, dfferent loadng condton and remanent flux varyng from 0% to 80% of the pea flux generated at rated voltage n advance and retard mode of operaton. The tranng and testng sgnals are obtaned by varyng swtchng-n angle n step of 30 degree from 0 to 360 degree. Along the varous faults n ISPST seres and exctaton unt, phase to ground faults and turn-to-turn faults occurs more frequently. For protecton devce pont of vew, phase-to-ground fault can further be classfed as heavy level fault, medum level fault and low level fault. In all the cases, abnormalty nature s almost same but magntude of dfferental current changes. So the tranng and testng data s obtaned by smulatng phase-to-ground fault from 1% to 50% of seres and exctaton unt wndng turns wth the help of transformer fault model presented n PSCAD. Phase-to-phase and three-phase-to-ground fault s also smulated wth dfferent fault ncepton angles for advance and retard mode of operaton of an ISPST. External fault s also smulated for phase-to-ground, two-phase-to-ground and three-phase-toground fault. Some typcal sgnals for varous operatng condton of an ISPST are shown n fgs The dgtal relay decdes ther operaton on the bass of slope of dfferental current just before frst pea after dsturbance detected by PAS threshold. The data wndow sze s chosen dependng on the algorthm beng used. Snce ORBFNN s based on slope dentfcaton method, a calculated slope s gven as an nput to ORBFNN, therefore data wndow sze s one. Fg. 1. Typcal dfferental current waveform under normal operatng condton of retard phase angle shft Fg. 13. Typcal dfferental current waveform under magnetzng nrush condton Fg. 14. Typcal dfferental current waveform under nternal fault condton Fg. 15. Typcal dfferental current waveform under external fault condton Fg. 16. Typcal dfferental current waveform under over-exctaton condton VI. IMPLEMENTATION OF PROPOSED ALGORITHM The dfferental current and PAS s taen as an nput to the proposed algorthm. A threshold s decded on the bass of PAS whch have been dscussed n secton IV. For the used ISPST ratng, PAS threshold s 60 degree by analyzng all the smulated operatng condton wth varyng dfferent parameter. Ths PAS threshold decdes whether t s normal, over-exctaton and external fault condton or magnetzng nrush and nternal fault condton. If PAS s greater than threshold, the dfferental current s taen as nput to calculate the slope. Ths slope s consdered as nput to neural networ. A sldng data wndow of one sample s consdered that s called pattern. The proposed ORBFNN of three layer archtecture s used. In frst layer one neuron as an nput, n the hdden layer four neurons and n output layer one neuron s taen. Tral and error method s used to fnd out the optmal number of neuron n the hdden layer. Fg. 17 shows the percentage mean square error (MSE) correspondng to number of neuron n the hdden layer. It s clear that mnmum MSE s found correspondng to four number of neuron n the hdden layer. At the output layer, only bnary decson (to trp or to not trp) s requred, therefore only sngle neuron s suffcent n output layer. In present wor, optmal wdth and center s crucal for the classfcaton accuracy of RBFNN. It s obtaned by PSO. The parameters settngs of the PSO algorthm are ntalzed

6 randomly wth 0 swarm partcles. Typcally the number of swarm partcles ranges between The value of acceleraton coeffcents s chosen. for both c 1 and c. The maxmum number of teraton s set to The nerta weght s monotoncally decreasng functon whch s gven by (7).In tranng, the output of nternal fault s ndcated by one and for magnetzng nrush t s ndcated by zero. Out of 1869 sets of data, 140 (75% of total) sets are used to tran the ORBFNN wth optmzed wdths and centers whch s obtaned by PSO technque. Remanng 467 (5% of total) sets are used for the testng to chec the generalzaton ablty of traned networ. The FFBPNN model s used for the comparatve study. It has one nput neuron n the frst layer, four neurons n hdden layer and one neuron n output layer. The unpolar sgmodal actvaton functon s used n the hdden layer and output layer. Smlar type of FFBPNN structure s selected to perform the comparatve study wth ORBFNN. The performance results of FFBPNN and ORBFNN s shown n Table-I. The classfcaton accuracy s calculated by (9). From the Table-I, t s clear that ORBFNN gves better classfcaton accuracy as compare to FFBPNN. Fg.17. Effect of number of hdden layer neuron on MSE Number of False sets Classfcaton A ccuracy(%) Total number of sets (9) TABLE I. Neural Networ Topology FFBPNN (1-4-1) ORBFNN (1-4-1) COMPARISON OF CLASSIFICATION ACCURACY (%) OF ORBFNN AND FFBPNN Operatng Condton Number of Sets Tranng Accuracy (%) Testng Accuracy (%) Magnetzng Inrush Internal Fault Magnetzng Inrush Internal Fault VII. CONCLUSION Ths paper presents a novel algorthm based on PAS threshold and ORBFNN technque. The proposed algorthm s amalgamaton of PAS threshold and ORBFNN. PAS threshold s used to dscrmnate the normal and external fault condton from nternal fault and magnetzng nrush condton. ORBFNN s used to classfy nternal fault from magnetzng nrush based on the slope characterstc. The optmal centers and wdths are obtaned by Partcle Swarm Optmzaton (PSO) technque for ORBFNN. The performance of proposed ORBFNN s compared wth FFBPNN. From the results, t s revealed that the ORBFNN has better slope classfcaton and generalzaton ablty compare to FFBPNN. The advantage of proposed algorthm s that t does not requre any phase shft compensaton. REFERENCES [1] J. Verboomen, D. Van Hertem, P. Schavemaer, W. Klng, and R. Belmans, Phase Shftng Transformers: Prncples and Applcatons, IEEE Conference on Dgtal Object Identfer, pp. 1-6, 18 Nov 005. [] J. Blade and A. Montoya, Experences wth parallel EHV phase shftng transformers, IEEE Trans. Power Del., vol. 6, no. 3, pp , Jul [3] M.A. Ibrahm and F. P. Stacom, Phase angle regulatng transformer protecton, IEEE Trans. Power Del., vol.9, no.1, pp , Jan [4] IEEE Power System Relayng Commttee: Worng Group K1, Protecton of Phase Angle Regulatng Transformers, IEEE Power System Relayng Commttee: Worng Group K1, [5] Z. Gajc, Use of Standard 87T Dfferental protecton for specal threephase power transformers-part I: Theory, IEEE Transacton on Power Delvery, vol. 7, no. 3, pp , July 01. [6] J. Faz, and S. Lotf-Fard, "A novel wavelet-based algorthm for dscrmnaton of nternal faults from magnetzng nrush currents n power transformers," IEEE Trans. on Power Delvery, vol. 1, no.4, pp , October 006. [7] M. Trpathy, Applcaton of Neuro-Fuzzy technques for power transformer protecton, Ph.D. Thess, Indan Insttute of Technology Rooree, Inda, 008. [8] M. Trpathy, R. P. Maheshwar, and H. K. Verma, Advances n transform protecton: A revew, Elect. Power Compon. Syst., vol. 33, no. 11, pp , Nov [9] U.N. Khan, T.S.sdhu, "Protecton of standard-delta phase shft transformer usng termnal currents and voltages," Electrc power systems research, vol. 110, pp , May 014. [10] T. Hayder, U. Schaerl, K. Feser, L. Schel, Unversal adaptve dfferental protecton for regulatng transformers IEEE Transactons on Power Delvery, vol. 3, no., pp , Aprl 008. [11] S. A. Khaparde, N. Ware, and S. H. Agarwal, "Adaptve relayng usng artfcal neural networ," IEEE , pp , [1] M.J.D. Powell, "The theory of radal bass functons approxmaton," Advances of Numercal Analyss, pp , Oxford: Clarendon Press, 199. [13] F. Bellor, A. Fache, and A. Bllat, "A general approach to construct RBF net-based classfer," ESANN'1999 proc.-european Symposum on Artfcal Neural Networs Bruges (Belgum), D-Facto publc., ISBN X, pp , Aprl [14] Z.Z. Que, W.X. Dong, L.C. Y, G. Herve, G. Jun, Optmzng wdths wth PSO for center selecton of gaussan radal bass functon networs, Sc. Chna Inf. Sc., 013, 56, do: /s [15] D. Smon, "Tranng radal bass neural networ wth the extended Kalman flter," Neurocomputng, vol.48, pp , 00. [16] J. Kennedy, and R. C. Eberhart, "Partcle swarm ntellgence," n Proc. Int. Conf. on Neural Networ, IEEE Servce Center, Pscataway, NJ, vol.4 no , [17] K.E. Parsopoulos, M.N. Vrahats, "Recent approaches to global optmzaton problems through partcle swarm optmzaton," Natural Computng, vol.1, pp , 00. [18] M.S. Sachdev, "Mcroprocessor relays and protecton systems," IEEE Tutoral Course Text, Publcaton No.88EH PWR, [19] Power System Relayng Commttee, EMTP reference models for transmsson lne relay testng, IEEE PES/PSRC, 005.