Adaptive Control of Shunt Active Power Filter Using Interval Type-2 Fuzzy Logic Controller

Transcription

1 Proeengs of the 4 th Interntonl Mle Est Power Systems onferene (MEPO ), ro Unersty, Egypt, Deemer 9-2, 2, Pper ID 59. Apte ontrol of Shnt Ate Power Flter Usng Interl Type-2 Fzzy og ontroller G. M. Srhn A. A. Elkosy A. A. Hgrs n Sh. M. S Deprtment of Eletrl Engneerng tehnology Deprtment of Eletrl Power Engneerng Deprtment of Physs ylotron Proet Hgh Insttte of Tehnology Flty of Engneerng ler Reserh entre Unersty of enh Unersty of ro Egyptn Atom Energy Athorty (EAEA) enh 52, Egypt ro 26, Egypt Ao Zl, ro 759, Egypt elkosy@yhoo.om {shrf97&shokryms}@yhoo.om Astrt Ths pper proposes new pte ontrol tehne for three phse shnt te power flter (SAPF) sng nterl type-2 fzzy log ontroller. The synhronos referene frme (SRF) s hosen to ompre the performne of the te flter sng PI ontroller, type- fzzy n Interl type-2 fzzy ontrollers (IT2F). Desgn proere of the IT2F s explore n etl. An effent type reton metho lle s e-tn metho s se nste of the most ommonly se methos whh ges lose form expresson n rees the omptng power neee to mplement tme reton. We pply the nterl type-2 fzzy ontroller to ontrol the lne rrents, otpt D oltge n lso to ree the nflene of prmeter nertnty. Smlton reslts lerly show tht the propose ontroller hs goo performne n rost to the prmeter nertntes ompre wth other nonlner strteges. Inex Terms Shnt te power flter, Apte ontrol, Interl type -2 fzzy ontrol. I. ITRODUTIO The nrese se of nonlner los sh s retfer ees n TV, oens n teleommntons power systems n ommerl lghtng systems se exesse netrl rrents, hrmon neton n rete power ren n the power system. They reslt n poor power ftor n lower effeny of power system. onentonlly, psse flters were the hoe for the elmnton of hrmons n the mproement of power ftor. These psse flters he the sntges of lrge sze, resonne n fxe ompenston. In the lst oples of ees the onept of te power flters hs een ntroe n mny pltons he ppere on ths set. A omprehense reew of te power flters onfgrtons, ontrol strteges, seleton of omponents n other relte sses re gen n [-4]. Most APF s re se on oltge sore nerters e to ts hgher effeny. Aorng to PWM ontrol lws, the D lnk oltge of nerter mst e kept onstnt n orer tht APF n ompenste hrmons n rete power effetely. ese of smple rthmet n hgh rellty n stey stte, PI ontroller gns extense pplton n the D-lnk oltge ontrol system. t PI ontroller epens on ext mthemtl moel of system n hs poor rostness n trnsent stte. It tens to se D oltge oershoot n nrsh sore rrent, whh wll le to proteton or een mge when APF s plnge nto. The oltge oershoot n nrsh rrent he een the ottlenek whh restrts the eelopment of APF [6]. Howeer onentonl PI ontrollers were se to generte referene rrent templte. The PI ontroller reres prese lner mthemtl moels, whh re fflt to otn n fls to perform stsftorly ner prmeter rtons, nonlnerty, lo strne, et. Reently, Fzzy log ontrollers (Fs) he generte goo el of nterest n ertn ppltons. The ntges of Fs oer onentonl ontrollers re tht they o not nee n rte mthemtl moel, they n work wth mprese npts, n hnle non-lnerty, n they re more rost thn onentonl nonlner ontrollers [5-8]. The onept of type-2 fzzy sets (T2FSs) ws frst ntroe y Zeh [9] s n extenson of the onept of well known ornry fzzy sets, type- fzzy sets. Typlly, T2FSs he the hrtersts of gres of memershp fzzy themseles []. Very smlr to TIF strtrlly, T2F lso ontns the omponents s: fzzfer, rle se, fzzy nferene engne, n otpt proessor whh omprses type reer n efzzfer s shown n fg.. Fg. The rhtetre of nterl type-2 (IT2) fzzy logl system (FS) Smlr to TF, the fzzfer n T2F mps npts nto type-2 fzzy sets. The otpt proessor nles the typereer n the efzzfer; whle the former otpts Tl FS n the ltter otpts rsp nmer. T2Fs n e se t the nertn rmstnes when the memershp gres n not e etermne extly. As type-2 fzzy set s hrterze y fzzy memershp fnton,.e., the memershp gre for eh element lso s fzzy set n [,], nlke type-l fzzy set, where the memershp gre s rsp nmer n [,] []. 25

2 The memershp fntons of type-2 fzzy sets re three mensonl n nle footprnt of nertnty (FOU), whh s the new thr menson of type-2 fzzy sets n the footprnt of nertnty proes n tonl egree of freeom to mke t possle to retly moel n hnle nertntes []. ormlly, T2Fs he hrtersts of ntense omptton e to hey ompttonl lo t the step of type reng proess. To smplfy the omptton the seonry memershp fntons n e set to ether zero or one n lle nterl type-2 FSs [2]. The type reton metho tht s most ommonly se n onnton wth IT2 FSs s the Krnk-Menel (K-M) terte lgorthm. Reently seerl moftons to the K-M type reer he een propose []. The enhnements reslte n 9% reton n the omptton tme. Another type reton strtegy s the nertnty ons metho [4]. Inner n oter on sets re ntroe to estmte the nertnty n n IT2 FS, resltng n n pproxmte type ree set. In spte of the reent reserh reslts there s stll room for reng the omptng power neee to mplement tme reton. Frthermore theoretl nlyss of IT2 FS s hllengng ese the exstng type reton lgorthm n t e expresse n lose form. In ths pper new type reton metho lle e-tn metho ws se to ree the orer of the type of IT2 fzzy sets whh ges lose form expresson for the otpt of n IT2 FS. The mn e of ths metho s to ree the orer of n IT2 FS y sng the ertl sle, nste of the wy representton [5]. Ths pper s orgnze s follows. In seton II the shnt te flter ws moele n smlte n omprson ws me etween PI n fzzy ontrollers. In seton III n IT2F ws esgne step y step n etl. In seton IV the smlton reslts of IT2F n type- fzzy ontrollers ws presente. The onlsons re rwn n seton V. II. OTRO OF SAPF USIG PI AD FUZZY OTROERS The ompenston hrtersts of shnt te power flter re se on netng rrent of the sme mgnte wth reerse phse of the lo hrmons n/or the rete omponents t the pont of onneton to nel them. The ompenston pltes of shnt te power flter nle: -rrent hrmons neton. -Rete power proton. -Resonne mpng. -Unlne lo rrent ompenston. The synhronos referene frme (SRF) s hosen to ompre the performne of the PI n fzzy ontrollers e to ts hgher effeny ese the SRF se ontroller s lmost nsenste to spply oltge stortons, sne ny non omponents n the SRF n e ttrte to hrmons n stey stte. Fg. 2 Shnt te power flter wth oltge sore nerter A. Moelng of SAPF sng PI ontroller The shnt te flter shown n fg. 2 s moele n the sttonry frme s esre n [6-8]: R t 2n Where:, R n n () n n R, : Two of the three phse nerter rrents. : D lnk oltge. n n : The resstne n ntne of the flter.,, : The three phse swthng stte fntons. n,, : Three phse spply oltges. : The ptne of the D lnk. In orer to onert nttes from the sttonry frme to the rottng frme the trnsformton mtrx s neessry: 2π 4π os( wt) os( wt ) os( wt ) 2 2π 4 T sn( ) sn( ) sn( π wt wt wt ) (2) o A phse loke loop (P) sheme s se to etermne the ngle for the referee frme orentton sh tht n Vˆ ssmng the spply oltge s gen 2 y (). Vˆ os( wt) Vˆ os( wt 2π / ) Vˆ os( wt 4π / ) n () 254

3 In stey stte ontons the fnmentl omponents of nttes s onstnt. To mpose the hrmons on the nerter of fg. 2 t s neessry to seprte the onstnt rrent omponent from the oslltng omponent. Ths oslltng omponent wth reerse phse s the referene of the ontroller. The AF n e moele n the referene frme from () wth the m of reng ontrol omplexty f ompre wth moelng n the sttonry referene frme. The ynm moel whh s esre n [6-9] s otne from etons () n (2) resltng n: R n w R (4) n w t n n Where n n n re the swthng stte fntons of the system n the referene frme n w s the spply nglr freeny. The frst n seon lnes n e wrtten s: R w n t (5) R w n t (6) et n e the rght se terms of etons (5) n (6): w (7) n w n (8) The terms n re the respete otpts of the two rrent PI ontrollers: ~ ~ k k t (9) p ~ ~ k k t p () Where ~ n ~ re the rrent errors. Wth etons (7) n (8) the swthng stte fntons () n (2) n e fon. n n w w w () (2) The terms n w n () n (2) re lle ompenston prts n n e e or not to the otpt of the PI ontrollers. The thr eton of the moel (4) s gen y: n n () t Ths eton n e wrtten s: n n (4) In orer to ontrol the D oltge, PI ontroller s se: k ~ k ~ p t (5) Where ~ s the oltge error. The ontrol effort s otne from eton (6). n n o (6) n n Assmng tht the rrent loop s el, the followng propertes hol: n (7) n Assmng the spply oltge s gen y eton () the trnsformton of n to oorntes yels / 2Vˆ n. As reslt: n, n Vˆ. 2 The ontrol effort n e pproxmte y: 2 o (8) Vˆ The nstntneos te power s: p. In orer to mntn the D lnk oltge, the -xs rrent n (8) mst e e to ese the rrent oesn t ontrte for the te power to mntn the D lnk oltge.. Moelng of SAPF sng Fzzy ontroller The PI ontrollers re reple y fzzy ontrollers s shown n fg. 4. The nternl strtre of the fzzy ontroller s shown n fg.. The fzzy ontroller s hrterze s follows: ) Seen fzzy sets for npt n otpt. 2) Trnglr memershp fntons for smplty. ) Fzzfton sng ontnos nerse of sorse. 4) Defzzfton sng the heght metho. Fg. The rhtetre of type- (T) fzzy logl system (FS) 255

4 Fg. 4 Shemt grm of SAPF wth SRF se PI ontroller The memershp fntons re hosen to e trnglr ese the prmetr fntonl esrpton of trnglr MF s most eonom one. Trnglr MF re preferre ese of ther strkng smplty, sol theoretl ss n ese of omptton, sne they re symmetrl n he zero le t some pont wy from ther entre. For ths work seen nel spe trnglr memershp fntons he een hosen for representng eh lngst rle, M, S, Z, PS, PM, P. The nmer of lngst rles s retly relte to the ry of pproxmtng fntons n plys n mportnt role for pproxmtng the nonlner npt otpt mppng. As the nmer of lngst rles nreses the otpt of the fzzy ontroller eomes lner fnton of the npt. To tre off etween ry n omplexty, throgh rgoros smlton stes t hs een fon tht seen memershp fntons re sffent to proe esre reslts n rere n. Reng the nmer of MFs wll proe mproper reslts t some n, whle nresng the nmer of MFs wll proe ely e to more ompttonl steps rere [2].. Smlton of SAPF Usng PI n fzzy ontroller The system of fg. 4 ws smlte wth MATA n SmPower systems enronment. The smlton moel s shown n fg. 5. Fgs. 6-7 show the smlton reslts of the propose SAPF sng the PI n fzzy ontrollers. The prmeters selete for smlton stes re: V s 2 V (rms), R.2 ohm, 2 mh, R ohm n 2 mh. It s ler from smlton reslts tht the trnsent response of the D oltge s etter for the fzzy ontroller ompre to the PI ontroller n tkes shorter tme to reh the stey stte. The THD of sore rrent efore ompenston s 25.8% n fter ompenston s 4.7% n 4.% respetely whh omply wth the IEEE-59 stnrs. Dsrete, Ts 5e-6 s pow erg Is (A) If (A) V () I (A) A sn_os _to_ sn_os _to_ sn_os _to_. Fre Sn_os wt Dsrete Vrtl P 5 Hz A V Three-Phse V. Mes. Termntor Termntor5 I A Termntor Termntor2 Termntor Fo2Hz Hgh pss flter Termntor4 - R A I g A - Votge sore nerter -K- -K- A R lo - Unontrolle retfer t e-6 s On/Off Dely 27 onstnt PI PI Ulph Plses Uet Dsrete SV PWM - V 6 V ref. De De2 PI /z Unt Dely /z lph sn_os et - to lph-et Fg. 5 The smlton moel n SmPower systems enronment Fg. 6 The response of shnt te power flter sng PI ontroller 256

5 Is (A) If (A) V () Fg. 7 The response of shnt te power flter sng fzzy ontroller III. DESIG OF IT2 FUZZY OGI OTROER The rhtetre of nterl type-2 (IT2) fzzy logl system (FS) s shown n fg. : A. Fzzfer In ths pper we opt two npt one otpt F to ntroe the esgn proere of IT2 F tht s we onser error n rte of error sle to the sme rnge s the npts of the propose gonl type F. The trnglr memershp fntons for error n rte of error re shown n fg. 8. The fzzy lels re negte g (), negte mem (M), negte smll (S), zero (Z), poste smll (PS), poste mem (PM), poste g (P). A sngleton fzzfton wth mnmm t-norm s se n ths work. (). Rle se The rles for IT2 FS re stll remne the sme s tht of T FS. t ther nteeents n onseents wll e represente y IT2 fzzy sets. The gonl rle tle s smmrze n tle I whh s onstrte for the senro n whh error n hnge of error pproh zero wth fst rse tme n wthot oershoot. TAE OTRO RUE TAE ė e M S Z PS PM P Z S M M PS Z S M M S PM PS Z S S M Z PM PM PS Z S M M PS P PM PS PS Z S M PM P P PM PM PS Z S P P P P P PM PS Z. Fzzy nferene engne The nferene engne omnes ll fre rles n ges nonlner mppng from npt IT2 FS to otpt IT2 FS. In the nferene engne mltple nteeents re omne sng the meet operton. D. Type reton n Defzzfton The e-tn metho s formlte sng the ertl sle representton of n IT2 fzzy set (FS). For n IT2 FS, eh ertl sle s n emee type- fzzy set tht n e esly type ree. Ths hrterst motte the proposton tht omptton oerhe n e ree y frst type reng eh ertl sle, efore efzzfng the resltng type- fzzy set to otn the entro of the IT2 FS. The e-tn metho sppose tht the ontnos ertl sle s esretze nto n ponts, n then the entro of eh ertl sle n e ompte s follows: n n n / (9) n For n IT2 FSs, the erge of ertl sle tht omprses n srete ponts s the men of the pper n lower MF, Hene, n ( ) (2) n 2 Where n re the pper n lower gres of the type ree set. The entro (or the efzzfe le) of the nterl type-2 fzzy set n e expresse s: () Fg. 8 The memershp fntons for () error n hnge of error n () otpt () 257

6 x x / x [.5 ( ) /.5 ( ) x x Eton (2) shows tht the e-tn formlton of the rsp otpt of n IT2 FS epens only on the lower n pper ons of ts foot prnt of nertnty. As tertons re no longer neee to llte the efzzfe le of n IT2 FS, the omptton ost of type reton my e gretly ree. Another ntge s (2) s lose form eton. After tht the efzzfton s one y the heght metho whh s mnly se on mltplton, ton n strton. IV. SIMUATIO RESUTS The smlton of shnt te power flter s rre n MATA/SmPower Systems enronment. The smlton moel s s shown n fg. 5 t replng the PI ontroller wth the IT2 fzzy ontroller. Fgs. 9- show the trnsent response of the D oltge sng IT2 fzzy ontroller n T fzzy ontroller when the nertnty R n re ntroe wth 5 % of the nomnl le. The smlton reslts lerly show tht no hnge n the trnsent response sng IT2 fzzy ontroller n spte of the nertnty whle the T fzzy ontroller hs smll stey stte error. V () V () () () (2) V () () Fg. 9 The trnsent response of D oltge sng IT2 fzzy ontroller wth () nertn () nertn R () nertn R n nertn 5 V () V () V () () () () Fg. The trnsent response of D oltge sng T fzzy ontroller wth () nertn () nertn R () nertn R n nertn 258

7 V. OUSIO A shnt te power flter ws moele n smlte n the synhronos referene frme. The smlton reslts ssre tht the reglton performne for the fzzy ontroller s etter ompre to the PI ontroller. The THD of sore rrent efore ompenston s 25.8% n fter ompenston s well elow 5%, the hrmons lmt mpose y the IEEE-59 stnrs. A new pte ontrol tehne sng IT2 Fzzy ontroller s propose. Smlton reslts show tht IT2F s etter thn the T fzzy ontroller n s rost gnst prmeter rton n rle nertnty. Reently, T2FSM (type-2 fzzy slng moe ontrol) n T2F (type-2 fzzy nerl network) he propose to mnmze the nmer of rles n ree the omplexty of nlyss whh wll e reporte lter. AKOWEDGMET The thors wol lke to thnk ylotron Proet (EAEA-Egypt) n Trk PET entre (Ao Aemy Unersty- Fnln) for fnng ths reserh proet n for prong the fltes for ong the reserh. Thnks lso re e to Dr. Hesels (Dretor of Ao Aemy Unersty) n Prof. Dr. Usm Sek (Dretor of ylotron Proet) for spportng ths work. REFEREES [] Akg, ew trens n te flters for power ontonng, IEEE Trns. Ins. Appl., ol. 2, no. 6, pp. 2-22, o./de [2]. Sngh, K. Al-H n A. hnr, A reew of te flters for power lty mproement, IEEE Trns. In. Ele., ol. 46, no. 5, pp.96-97, Ot [] M. El-Hrok, M. K. Drwsh n P. Meht, Ate power flters: reew, IEE Pro. Ele. Power Appl., ol. 47, no. 5, pp. 4-4, Sept 22. [4] F. Z. Peng n D.J. Ams, Hrmon sores n flterng pprohesseres/prllel, te/psse n ther omne power flters, IEEE IAS, pp , 999. [5] T.-S. ee, K.-S. Tee n M.-S. hong, Fzzy terte lernng ontrol for three phse shnt te power flter, IEEE Inter. Symp. on In. Ele., pp , ISIE 26, n. [6] X. Dngo, H., W. We, Sty on fzzy ontroller wth selfstle ftor of te power flter, 2n Annl onf. of the IEEE Instrl Ele. Soety, pp , IEO 26 [7]. Shrmeel, M. R. Mohn, G. Um n J. skrn, Fzzy log se ontrolle three phse shnt te flter for lne hrmons reton, Jornl of ompter Sene, ol., no.2, pp. 76-8, 27. [8] S. K. Jn, P. Agrwl n H. O. Gpt, Fzzy log ontrolle shnt te power flter for power lty mproement, IEE Pro. Ele. Power Appl., ol. 49, no. 5, pp. 7-28, Sept. 22. [9]. A. Zeh, The onept of lngst rle n ts pplton to pproxmte resonng I, Inforn. S., ol. 8, pp , 975. [].. Krnk, J. M. Menel, n Q. ng, Type-2 fzzy log systems, IEEE Trns. Fzzy Systems, ol. 7, pp , De [] J. Menel n R. John, "Type-2 fzzy sets me smple, IEEE Trns. Fzzy Systems, ol., pp. 7-27, Apr. 22. [2] Q. ng n J. Menel, Interl type-2 fzzy log systems: theory n esgn, IEEE Trns. Fzzy Systems, ol. 8, pp , Ot. 2. [] D. W. n J. M. Menel, Enhne Krnk-Menel lgorthms For nterl type-2 fzzy sets n systems, Pro. In Pro. AFIPS, Sn Dego, A, pp , 27. [4] D. W. n J. M. Menel, Unertnty ons n ther ses n the esgn of nterl type-2 fzzy log systems, IEEE Trns. Fzzy Systems, ol., no. 5, pp , 22 [5] M. e, W. Wn Tn, Towrs n effent type reton metho for nterl type -2 fzzy log systems, IEEE Inter. onf. Fzzy Systems, pp , 28 [6]. Menlek, K. Al-H, F. Fneh n. A. Dessnt, onlner ontrol strtegy pple to shnt te power flter, Pro. IEEE Power Eletrons Spelst onf., pp , PES2, Jne 2. [7]. Menlek, K. Al-H, Moellng n nonlner ontrol of shnt te power flter n the synhronos referene frme, IEEE IHQP 2, pp. -5, 2. [8]. Menlek, K. Al-H, F. Fneh n. A. Dessnt, onlner ontrol tehne to enhne ynm performne of shnt te power flter, Pro. IEE Ele. Power App., ol. 4, pp. 7-79, Jly 2. [9]. R. mong, M.. lnt, F. A. S. ees n G. M. S. Azeeo, Implementton of gtl sgnl proessor ontrolle shnt te flter, Eletrl power lty n Utlzton Jornl, ol. XII, no.2, pp. 5-4, 26. [2] G. K. Sngh, A. K. Sngh n R. Mtr, A smple fzzy log se rost te power flter for hrmons mnmzton ner rnom lo rton, Eletr Power System Reserh, ol. 77, pp. -, 27. [2] P.-Z. n,.-m. n,.-f. Hs n T.-T. ee, Type-2 fzzy ontroller esgn sng slng-moe pproh for pplton to D-D onerters, IEE Pro. Ele. Power Appl., ol. 52, no. 6, pp , o. 25 [22] M.-Y. Hso n T.-H. S., Desgn of nterl type-2 fzzy log ontroller, IEEE Interntonl onferene on Systems, Mn n yernets, pp , Ot. 26, Tpe, Twn. 259