A fuzzy logic based relay for power transformer protection

Transcription

1 A fuzzy logic based relay for power ransformer proecion In accordance wih an &D agreemen beween ABB and he Universiy of Wroclaw, Poland, a muli-crieria proecive relay based on fuzzy ses and logic has been developed for use wih hree-phase power ransformers. welve crieria are used o sabilize he relay. he proecion scheme feaures inernal funcions and coefficiens which allow off-line self-adjusmen of he relay prior o insallaion. hree unique procedures for he seings make he relay self-organized. esuls of ess show significan gains in sensiiviy and seleciviy for he self-organized relay compared wih radiional approaches o he problems of proecive relaying. P roecion schemes employing he differenial relaying principle exhibi cerain limiaions in applicaions wih power ransformers. his is because he deecion of a differenial curren does no clearly disinquish beween inernal fauls and oher possible condiions. Among he phenomena mos likely o upse he curren balance and cause he relay o malfuncion are inrush magneizing currens, saionary overexciaion of a core, exernal fauls in he presence of curren ransformer (C) sauraion, and/or C and power ransformer raio mismach. o miigae hese problems, a number of more or less reliable proecion crieria have been developed which suppor he radiional biased differenial characerisic in combinaion wih 2nd and 5h harmonic resrains [1,2]. hey include he -differenial principle, direc waveshape idenificaion, proecive algorihms based on elecromagneic equaions of he proeced ransformer, and adapive approaches, o name jus some of he recogniion echniques inroduced in recen decades. he measuring unis of conemporary relays are also improved by he use of Fourier mehods, Kalman filering echniques and opimal sae observers. esearch work in he above areas naurally focuses on a muli-crieria approach o power ransformer relaying. One resul of his work has been he developmen of a general fuzzy logic based Dr. Murari M. aha Birger Hillsröm ABB Nework Parner AB Dr. Bogdan Kaszenny Dr. Eugeniusz osolowski echnical Universiy of Wroclaw plaform for a muli-crieria ransformer relay ha inroduces several new arificial inelligence (AI) relaed conceps [ 5]. A proecive device wih AI feaures offers enormous poenial for opimizaion. I has a number of inernal coefficiens, funcions and hresholds [, 4] ha can be adjused in order o une a relay o a proeced elemen and improve he qualiy of he proecion. However, no recommendaions exis for an approach of his kind; neiher is any pracical experience available ha could be used o se he inernal relay parameers menioned. esearch was herefore underaken o resolve his problem. In he following, a look is aken a a 12-crieria Fuzzy Logic proecive elay (FL) 1 for power ransformers and a he unique algorihms used for is auomaic, off-line self-adjusmen prior o insallaion. Proecion crieria for power ransformers he following modes of power ransformer operaion have been idenified from he poin of view of proecive relaying: a Inrush condiions b aionary overexciaion of a ransformer core c Exernal faul combined wih C sauraion d Exernal faul or high load curren wihou C sauraion, bu wih mismached raios of he ransformer and Cs e Inernal faul f Normal operaion Usually, i is assumed ha he proeced ransformer leaves he normal operaion mode (f) when is relay is acivaed. Here, as is normally he case, pick-up of he relay will be assumed o be based on he insananeous overcurren principle. ABB eview 1/

2 When acivaed, he relay issues he ripping command provided ha, based on he informaion carried by he relaying signals, i is capable of rejecing he noninernal faul hypoheses (a d). his approach is convergen wih common pracice in ransformer proecive relaying whereby, insead of confirming an inernal faul, he relay rules ou he remaining supposiions. welve proecion crieria welve proecion crieria, C 1 C 12, have been idenified for power ransformers []. In he following, each individual crierion is described and he iem of knowledge i covers formalized by he definiion of a signal for i. he shape of hese signals is high for inernal fauls and low for oher condiions, or vice versa (for crieria C 1, C 2, C 4, C 9, C 1, C 11, C 12 high values call for ripping, while for C, C 5, C 6, C 7, C 8 low values call for ripping). he processing of he signals o obain he ripping command is based on fuzzy logic laws. Case a Magneizing inrush may be ruled ou if: Crierion C 1 : he value of he differenial curren is higher han he highes expeced inrush curren level (insananeous overcurren principle). he quesion o be answered here is wheher he absolue value of a sample of he differenial curren, is fundamenal componen ampliude, or even a combinaion of he wo, should be used. For he purpose of his discussion, he ampliude will be used as he crieria signal : 1(n) = I 1(n) (1) I i Ampliude of he ih harmonic of he differenial curren (i = 1 is he fundamenal frequency componen) C C V CB CB ( v) ( i 1 ) ( i 2 ) M e a s u r i n g u n i k Crieria signal (k = 1 12) n Discree ime index 1 he proecive relay is assumed o be a complex of hree idenical sub-relays, one for each phase. hus, 1 has o be compued for all hree phases (he phase index is omied o simplify he noaion). For wo of he presened crieria (C 2 and C 11 ), however, all hree phases are checked simulaneously. Only he sample definiion of 1 is given here; deails of he res of he crieria signals may be found in []. Crierion C 2 : cerain fragmens of he waveshapes of he differenial currens in all hree phases are no shown (secions 2 Fuzzy seings Weighing facors µ 1 w 1 µ 2 µ w 2 w uling-ou of he hypohesis of saionary overexciaion of a ransformer core ( crieria 4-6 ) uling-ou of he hypohesis of an exernal shor-circui combined wih C sauraion ( crieria 7-9 ) uling-ou of he hypohesis of an exernal faul combined wih raio mismach ( crieria 1-12 ) implified block diagram of a fuzzy logic based relay for power ransformer proecion δ Fuzzy ripping suppor CB Circui-breaker µ 1 Coninuous logic signals C Curren ransformer ω 1 4 Inrush signals V Volage ransformer ripping hreshold Crieria signals 1 ω ω ω 1 Min lasing no less han 1 6 of a cycle) when he levels of boh he curren and is derivaive are close o zero (direc waveshape idenificaion). he differenial curren may also exhibi such periods during severe inernal fauls accompanied by curren ransformer sauraion. However, when observed in all hree phases hey are shifed in ime, while during inrush hey are perfecly synchronized ( 7a, 8a ). Crierion C : he second harmonic in he differenial curren is below abou 1 15 % of is fundamenal (2nd harmonic resrain). ω 4 2 δ δ & rip 1 42 ABB eview 1/1998

3 Case b aionary overexciaion of a ransformer core may be ruled ou if: Crierion C 4 : he level of he differenial curren is higher han in cases of ransformer overexciaion (overcurren principle). he overcurren crierion is repeaed here. I should be noed, hough, ha C 4 is dedicaed o saionary overexciaion, while C 1 recognizes inrush condiions. he seing for C 4 is usually much lower han for C 1. hus, for cerain inernal fauls C 4 is able o exclude overexciaion, while C 1 is no able o rule ou inrush. However, in he muli-crieria approach, he inrush hypohesis may be excluded because of some oher crieria, enabling he ripping command o be sen. I is in his way ha muli-sage analysis of he differenial curren improves he relay. Crierion C 5 : he inegral of he erminal volage ampliude for half a cycle, which reflecs he flux in a ransformer core, is below he sauraion level (simplified flux based resrain). Crierion C 6 : he level of he 5h harmonic in he differenial curren is below abou % of is fundamenal (5h harmonic resrain). Case c An exernal shor circui combined wih sauraion of Cs may be excluded if: Crierion C 7 : he high value of he hrough-curren does no exis during he cycle before he high differenial curren value was deeced (sequence of evens). his crierion is based on he observaion ha Cs usually ransform accuraely for a leas 1 4 of a cycle afer he faul incepion before becoming sauraed. Crierion C 8 : he level of he 2nd harmonic in he differenial curren is below abou 2 % of he fundamenal componen. Crierion C 9 : he differenial curren is greaer han he highes curren during an exernal shor-circui in he presence of C sauraion (overcurren principle). Case d An exernal faul or high load curren wihou C sauraion may be ruled ou if: Crierion C 1 : he differenial curren is much higher han he hrough-curren (biased differenial characerisic). o gain sensiiviy, he -differenial rule is applied []. By subracing he relevan pre-faul values, his approach considers only he fracions of he differenial and hrough-currens caused by a faul. Crierion C 11 : he relaionships beween he differenial and hrough-currens are differen in all hree phases of he relay (asymmery checking an inernal, hree-phase symmerical faul in a power ransformer is pracically impossible). Crierion C 12 : he differenial curren is greaer han he highes expeced curren value caused by a near, major Disribuion of he 2nd harmonic percenage in he differenial curren under inernal faul (a) and inrush (b) condiions. he sample probabiliy densiy funcions for blocking (f BL ) and ripping (f ) are given for = 5 ms. 2 ime Crieria signal (2nd harmonic resrain) f BL f f ms ms 1 a b ABB eview 1/1998 4

4 1. µ = ms µ µ = 2 ms µ = 4 ms Arbirary fuzzy seing µ for he 2nd harmonic resrain (crierion C ) µ Fuzzy seing Crieria signal (2nd harmonic resrain) µ = 1 ms Green ed Cerain non-inrush Cerain inrush µ = 1 ms Example of self-adjused fuzzy seing for he 2nd harmonic resrain (crierion C ). creenshos of he ime-varying seing, aken a =, 2, 4, 1 and 1 ms afer relay sar-up µ Fuzzy seing Crieria signal (2nd harmonic resrain) exernal faul and he larges possible mismach of he ransformer and C raios. Proecive relay based on fuzzy logic Measuring uni he measuring uni 1 of he considered FL for power ransformers measures he curren on boh sides of he proeced uni and also he erminal volage (if he laes signal is no available, C 5 is ignored and recogniion of overexciaion is based on C 4 and C 6 only). he uni forms he differenial and hrough-currens according o he ransformer winding connecions, acivaes he relay, measures he required relaying signals, and forms he crieria signals he measuremens are based on Finie Impulse esponse (FI) full-cycle orhogonal filers, designed using he leas square mehod, wih perfec separaion beween he 1s, 2nd and 5h harmonics. 1 khz is assumed as a sampling rae (2 samples per cycle). Fuzzy seings he crieria signals are nex fed ino he non-linear funcions, called fuzzy seings. 2 and explain he idea of a fuzzy seing: 2 shows ime disribuions of he raio of he 2nd and 1s harmonic ampliudes of he differenial curren ( ) for inrush condiions 2b and inernal fauls 2a. he figures are obained by ploing he signal I 2(n) / I 1(n) on he same plane for all he colleced cases (for inrush in 2b and for inernal fauls in 2a ). From comparison of he figures and observaion of he overlapping region beween he disribuions, i is concluded ha here is no perfec hreshold for he signal in erms of avoiding recogniion errors. Increasing he hreshold speeds up operaion of he relay under inernal faul condiions accompanied by C sauraion, bu i may cause false ripping under inrush condiions. On he oher hand, reducing he hreshold improves relay sabiliy, bu a he same ime delays operaion 44 ABB eview 1/1998

5 of he relay. he same uncerainy applies o all he crieria signals, especially when he decision has o be made fas [ 5]. o resolve he problem and model his uncerainy numerically, he idea of a fuzzy seing has been inroduced [4, 5]. shows an arbirary fuzzy seing µ for crierion C. If he percenage of he 2nd harmonic ( ) is below 1 %, he case is classified by he crierion C as cerain non-inrush and he coninuous logic signal µ akes he value 1.. If he signal is above 15 %, he inrush supposiion is confirmed wihou any doub, and he signal µ equals.. he doubful region exends over he 1 15 % range, where µ changes from 1. (inrush excluded) o. (inrush confirmed). he signal µ k may be undersood as he level of permission for ripping provided by he crierion C k. As a resul of his signal-seing comparison, he crieria signals 1 12 conver ino he coninuous logic signals µ 1 µ 12. Muli-crieria aggregaion If he siuaion is clear, he signals µ 1 µ 12 reduce o boolean logic variables and equal eiher or 1. Under unclear condiions, however, hey may ake values from he 1 inerval, and hus give parial suppor o cerain hypoheses. Moreover, he recogniion provided by he differen crieria may be conradicory. On op of his, he crieria differ in erms of he qualiy of heir recogniion; some are more, some less reliable. In order o resolve his and balance he decisions made by he crieria wih he crieria powers, muli-crieria decision-making mehods are recommended [4, 5]. For he cases under consideraion, he weighing facors mehod is used []. he crieria C 1, C 2 and C, on recognizing inrush condiions, are aggregaed by compuing he average level of ruling ou of he inrush hypohesis ω 1 : ω 1 = w 1 µ 1 + w 2 µ 2 + w µ, w 1 + w 2 + w = 1 w k (2) Weighing facor reflecing he recogniion power of crierion C k Analogous compuaions are performed for ω 2, ω and ω 4. Under ideal condiions i is observed ha inrush causes ω 1 =, overexciaion induces ω 2 =, ec. And when an inernal faul occurs: ω 1 = ω 2 = ω = ω 4 = 1. Decision-making he relay should rule ou all he non-inernal faul hypoheses (a d) prior o ripping. Consequenly, signals ω 1 ω 4 are aggregaed ino he overall ripping suppor (δ ) by means of a coninuous logic AND-operaor []: δ = min(ω 1, ω 2, ω, ω 4 ) () ripping is iniiaed if δ is greaer han he ime-varying, even adapable ripping hreshold : rip = (δ ) (4) hus, all he logical operaions are performed in he fuzzy logic sysem and he necessary conversion o he boolean logic akes place once only a he oupu of he proecion scheme. Algorihms for self-adjusmen of he relay he following componens of an FL may be self-adjusing and se prior o insallaion []: Fuzzy seings, µ 1 µ 12 Crieria weighing facors, w 1 w 12 ripping hreshold, All hree componens can be eiher saionary or non-saionary (ime-varying). he algorihms have been developed primarily for he non-saionary varians, bu he mehods can be easily re-consiued for he saionary versions. he algorihms are based on probabiliy densiy funcions of he crieria signals under he operaing condiions mos relevan for a proeced ransformer. uch probabilisic diagrams have been found by means of a large number of simulaions performed wih AP- EMP [8]. es cases A digial, AP-based model of a hreephase, wo-winding, Yd-conneced, five-leg core ype power ransformer raed a 5.86 MW and 14/1.52 kv, provided he inpu for he FL. he mos imporan facors aken ino accoun by he model [7] included: represenaion of boh he sauraion and hyseresis loop of a ransformer iron core, he feasibiliy of inpu of a residual flux, represenaion of he main Cs in erms of heir possible sauraion, represenaion of he relay inpu circuis wih relay Cs and ani-aliasing analog filers, and he feasibiliy of modelling urn-o-urn inernal fauls. During he simulaion, cerain random variables were disribued uniformly o ensure he diversiy of he sudied cases. hese variables included he residual magneism, volage angle a he beginning of he disurbance, faul locaion and resisance, number of shor-circuied urns, ype of faul, pre-faul ransformer burden, C sauraion levels, mismach of he ransformer and C raios, and he power sysem configuraion. elf-adjusmen of he fuzzy seings Comparison of 2a and 2b shows where he disribuion of he sample crieria sig- ABB eview 1/

6 depending on he hreshold esablished for his signal. his region also changes wih ime, and wih i he abiliy of he crierion C o disinguish beween inrush and inernal faul paerns. aking his w 1 w 7 w 2 w 8 w w 9 w 4 w 1 w 5 w 11 w 6 w 12 2 ms 4 2 ms 4 ino accoun by making he seing µ ime-varying as well as fuzzy furher improves he qualiy of recogniion of he crierion. As shown in [], he shape of a fuzzy seing may be found auomaically by analyzing he simulaion of a proeced elemen prior o insallaion of he relay. his makes he relay self-seing and o some exen capable of learning, eg as in arificial neural nework applicaions [6]. 4 shows, as an example, he self-organized fuzzy seing µ. I should be noed ha some ime afer he beginning of a disurbance (relay sar-up) he seing becomes less fuzzy o accommodae he fac ha Cs change from he sauraed sae o he non-sauraed sae in he even of cerain severe inernal fauls. elf-adjused weighing facors for he proecion crieria ime w 1 12 Weighing facors for crieria 1 12 nal ( ) overlaps, his region being likely o cause a delay in relay operaion or even failure of he relay o operae, elf-adjused ime-varying ripping hreshold ime ripping hreshold ms elf-adjusmen of he weighing facors By analyzing he behaviour of each crierion under boh inernal faul and oher condiions i is possible o judge he srengh (recogniion power) of he crieria. hese recogniion powers are direcly refleced by he values of he weighing facors 1. he proposed formal numerical algorihm can be found in []. From 5, which shows he self-adjused weighing facors for he FL, i can be concluded ha: All he considered crieria reach heir maximum level of recogniion capabiliy, as given by he weighing facors, in one cycle. he FL is herefore effecively non-saionary, wih respec o he weighing facors, only during he firs cycle of operaion. he overcurren crierion (C 1, C 4, C 9 and C 12 ) is iniially weak, bu gains some 1ms afer acivaion of he 46 ABB eview 1/1998

7 ±7.62 ±.681 ±1. I DIF I H IP a ms b ms c ms elay operaion under sample urn-o-urn faul condiions during energizaion of he ransformer 7 I DIF Differenial curren ime I H hrough-curren IP ripping command relay due o he dynamics of he measuring uni. he 2nd harmonic resrain wih respec o he inrush condiions (C ) gains afer one cycle. his change in recogniion power is induced by ransien overshoos of he raio I 2 /I 1 during inernal fauls 2a, being refleced by delayed ripping. he differen naure of he ransiens of he raio I 5 /I 1 makes he 5h harmonic resrain (C 6 ) much faser. he weighing facor w 7 of he sequence of evens crierion (C 7 ) does no change wih ime as i operaes very fas or no a all. A similar effec is observed for he crieria C 1 and C 11. elf-adjusmen of he ripping hreshold he ripping hreshold represens a boundary in he universe of he ripping suppor δ beween he ripping and blocking regions. o overcome seleciviy and sabiliy consrains, he seing algorihm opi- mizes he ripping hreshold as follows []: o improve he seleciviy of he relay, he hreshold is se as low as possible. o ensure relay sabiliy, he hreshold is se as high as necessary. he self-se ripping hreshold for he FL is shown in 6. he non-saionary ripping hreshold (n) adjused using he algorihm depends on he fuzzy ripping suppor δ, which in urn depends on crieria weighing facors and, consequenly, on he fuzzy seings. Bearing he above relaionship in mind, he sequence recommended for self-adjusing procedures is: 1 Fuzzy seings 2 Weighing facors ripping hreshold esing he relay he seleced examples demonsrae boh he sabiliy and he sensiiviy of he fuzzy logic proecive relay. 7 shows he differenial and hrough-cur- rens as well as he ripping signal for a urn-o-urn inernal faul occurring 5 ms afer he ransformer is energized and involving 16 % of he Y-side winding urns on column. he relay is acivaed when energizing begins, bu is blocked during inrush condiions. he ripping command is sen 16 ms afer he faul incepion. he operaion of he relay under inernal faul condiions (-o--o-ground faul a he erminals on he -side) accompanied by C sauraion is shown in 8. he relay is acivaed afer 2 ms and rips 5 ms laer. Conclusions he described muli-crieria, self-organizing fuzzy logic based proecive relay for hree-phase power ransformers demonsraes imporan gains in sensiiviy and seleciviy compared wih radiional approaches o proecive relaying. he novel algorihms for off-line self-seing of he relay prior o insallaion are based on saisical informaion obained by mass-simulaion ABB eview 1/

8 ± ±14.71 ±1. I DIF I H IP a ms b ms c ms elay operaion under sample inernal faul condiions accompanied by C sauraion 8 I DIF Differenial curren ime I H hrough-curren IP ripping command using an AP package and allow a learning phase similar o ha known from arificial neural nework applicaions in power sysem proecion schemes. he examples and resuls of relay esing demonsrae he high seleciviy and sensiiviy of he relay, which operaes wih an average ripping ime of less han half a cycle. he robusness of he relay has also been confirmed. eferences [1] M. A.ahman, B. Jeyasurya: A sae of he ar review of ransformer proecion algorihms. IEEE rans. on Power Delivery, Vol, No 2, April 1988, [2] M. Habib, M. A. Marin: A comparaive analysis of digial relaying algorihms for he differenial proecion of hree phase ransformers. IEEE rans. on Power ysems, Vol, No, Augus 1988, [] B. Kaszenny, E. osolowski, M. M. aha, B. Hillsrom: A self-organizing fuzzy logic based proecive relay an applicaion o power ransformer proecion. IEEE rans. on Power Delivery, Vol 12, No, July 1997, [4] A. Wiszniewski, B. Kaszenny: Fuzzy ses approach o ransformer differenial relay. Proceedings of he 199 Developmens in Power ysem Proecion Conference, York, UK, 199, [5] A. Wiszniewski, B. Kaszenny: A muli-crieria differenial ransformer relay based on fuzzy logic. IEEE rans. on Power Delivery, Vol 1, No 4, Ocober 1995, [6] P. Basard, M. Meunier, H. egal: A neural nework classifier for he analysis of a proecion ransformer differenial curren. Proc. of he Inernaional Conf. on Inelligen ysem Applicaion o Power ysems, Monpellier, France, ep. 5 9, 1994, [7] B. Kaszenny, E. osolowski, M. M. aha, B. Hillsrom: A power ransformer model for invesigaion of differenial proecion schemes. In. Conf. on Power ysem ransiens, Lisbon, ep. 7, 1995, [8] Alernaive ransien Program (AP). ule Book, K.U. Leuven EMP Cener, Leuven, Belgium, Auhors addresses Dr. Murari M. aha Birger Hillsröm ABB Nework Parner AB Väserås weden elefax: murari.saha@sene.mail.abb.com birger.hillsrom@sene.mail.abb.com Dr. Bogdan Kaszenny Dr. Eugeniusz osolowski echnical Universiy of Wroclaw Wroclaw, Poland elefax: ABB eview 1/1998