Parameter Estimation of Three-Phase Induction Motor by Using Genetic Algorithm

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1 360 Journal of Elecrcal Engneerng & Technology Vol. 4, o. 3, pp. 360~364, 009 Parameer Esmaon of Three-Phase Inducon Moor by Usng Genec Algorhm Seesa Jangj and Panhep Laohacha* Absrac Ths paper suggess he echnques n deermnng he values of he seady-sae equvalen crcu parameers of a hree-phase nducon machne usng genec algorhm. The parameer esmaon procedure s based on he seady-sae phase curren versus slp and npu power versus slp characerscs. The propose esmaon algorhm s of non-lnear nd based on selecon n genec algorhm. The machne parameers are obaned as he soluon of a mnmzaon of objecve funcon by genec algorhm. Smulaon shows good performance of he propose procedures. Keywords: parameer esmaon, nducon moor, genec algorhm. Inroducon In ac nducon moor drves, he elecrcal parameers are, generally, deermned va he classcal analyss no-load and loced-roor es may be obaned from acual machne es or from daa suppled by he manufacurer []. Esmaon of he performance, done by plong he seady-sae slp curve. Generally o oban he parameer, one mus use he equvalen crcu relaons and expermenal resuls obaned from he above-menoned classcal analyss. Therefore, he parameer values obaned by drec classcal approaches or expermenal can reveal sgnfcan dfference n he enre range of slp varyng from 0 o. To descrbe he performance of he nducon machne more precsely and o reduce he dfferences beween he esmaed and real performance, one mus modfy he parameers obaned from he classcal analyss []. To acheve hs purpose n moor, he use of denfcaon algorhms base on he arfcal algorhm appears o be promsng approach. In hs sudy s gnored ha he effec of measuremen errors, dsurbances, random sgnals, and core losses on he esmaed parameers. Snce he equaon relang he phase curren o slp and he crcu parameers nvolve many varables and are nonlnear, parameers can have dfference values n case of he change of load. Ths fac does no enable o one drecly use he many parameer esmaon procedures exsng n he leraure [3]-[6]. The esmaon mehod descrbed n hs paper dffers from oher approaches n hs followng ways. Ansuj and Shoooh [] presened a parameer esmaon procedure ha requred nowledge of full load power facor and effcency. Oher mehod of parameer esmaon employ leas Correspondng Auhor : Dep. of Elecrcal and Compuer Engneerng, Kasesar Unversy, Saon ahon,thaland. (fsessj@csc.u.ac.h) * Dep. of Elecrcal Engneerng, Kasesar Unversy, Bango, Thaland.(fengpl@u.ac.h) Receved 5 February 008; Acceped 9 July 009 square analyss of daa generaed durng acual ransen condons. In hs paper, obanng opmal parameer of he equvalen crcu of hree-phase nducon machne s suggesed by genec algorhm. Durng he execuon of he esmaon algorhm, we use he hree pons of seadysae daa of boh he npu power he saor curren.. Inducon Moor Model A hree-phase nducon machne suppled wh a hreephase symmercal volage source can be descrbed usng he equvalen crcu shown n Fg.. A lsng of he parameers n hs equvalen crcu and her dependences on he machne speed as reaed n hs paper follows. All crcu parameers are n ohm referred o saor wndng. Fg.. Equvalen crcu represenng seady-sae of polyphase nducon moor Vh Z h A I X R s B Fg.. Equvalen crcu smplfed by Thevenn s heorem

2 Seesa Jangj and Panhep Laohacha 36 R saor wndng ressance X saor leaage reacance R roor wndng ressance referred o saor sde X roor leaage reacance referred o saor sde X m magnezng reacance referred o saor sde s slp speed V ermnal volage saor curren I I roor curren referred o saor sde In case he saor curren and he npu power, he equaon for nducon moor can be deermned from he crcu of Fg. and are expressed as followng: V ( jx ) m V = h R + j( X + X ) m () jx ( R + jx ) m Z = h R + j( X + X ) m () From Fg., he roor curren can be deermned by he followng equaon. Vh I = (3) R Z + jx + h s For deermned he saor curren we can reduce he par of roor equvalen crcu as he below. Where Z deermned from he followng procedures. eq A = + jx ( R s+ jx ) (4) Z eq m = A (5) V I = ( R + jx ) + Zeq (6) I = I θ (7) pf = cosθ (8) P = 3 V I pf (9) n 3. Esmaon Framewor In order o deermne model parameers for he slp curve of equvalen crcu, reference [] uses he nonlnear curve fng problem saed as he soluon of he followng mnmzaon problem: mn J( Φ ) = [ y y( s, Φ)] (0) Φ Ω = where J ( Φ) s objecve funcon obaned by he sum of he square of he dfferences beween he expermenal and calculaed slp curve, Ω s he parameer space dependng on he number of parameers o esmaed, y s he expermenal daa value colleced from machne, ys (, Φ) s non-lnear funcon relang he measuremen daa, he crcu parameers, and he slp, and Φ s parameer vecor peranng o Ω. Therefore, n case of dmenson of parameer vecor Φ s defned as: Φ= [ R R X X X ] m () The above menon specfc equaon s for depend on he nd of avalable expermenal daa and for obanng a parameer vecor ha mnmze he quadrac performance ndex defned by (0). In hs case, snce one mus deal wh a non-lnear algorhm o acqure he desred soluon, some numercal problems may arse or drec approach would requre wrng down he normal equaons for he solvng hem. The mehod for numercal mnmzaon of performance ndex (0) mgh be modfed o updae he esmaed parameer vecor accordng load change. 4. Genec Algorhm 4. Fundamenal of Generc Algorhm Ths opmzaon mehod descrbed n [7] and [8] by George K. Sefopoulos, e al. n he followng. Genec Algorhms are opmzaon mehods nspred by naural genecs and bologcal evoluon. They manpulae srngs of daa, each of whch represens a possble problem soluon. These srngs can be bnary srngs, floang-pon srng, or neger srngs, dependng on he way he problem parameers are code no chromosomes. The srengh of each chromosome s measured usng fness values, whch depend only on he value of he problem objecve funcon for he possble soluon represened by he chromosome. The sronger srngs are reaned n he populaon and recombned wh oher srong srngs o produce offsprng. Weaer ones are gradually dscarded from he populaon. The processng of srngs and he evoluon of he populaon of canddae soluons are performed based on probablsc rules. Reference [7] provdes a comprehensve descrpon of genec algorhms. 4. Chromosome Represenaon Two ypes of represenaons have been nvesgaed, bnary and real. 4.3 Creaon of Inal Populaon The nal populaon of canddae soluon s creaed randomly. 4.4 Evaluaon of Canddae Soluons Each canddae soluon represens a parameer vecor Φ ; he evaluaon of each canddae soluon s based on he objecve funcon value J ( Φ ). oe ha he objecve funcon value s obaned afer sysem smulaon. The purpose of he process s o solve a mnmzaon problem; he objecve funcon o be mnmzed s defned as

3 36 Parameer Esmaon of Three-Phase Inducon Moor by Usng Genec Algorhm F( Φ ) = J( Φ ) + K () where K s small posve real number used as scalng coeffcen, n order o avod problems ha may arse as J ( Φ) approaches zero, and o conrol problem le premaure convergence. 4.5 Reproducon Reproducon refers o he process of selecng he bes ndvduals of he populaon and copyng hem no a mang pool. These ndvduals from an nermedae populaon. Three ypes of reproducon process are mplemened n hs wor: ) Roulee-wheel selecon, ) Tournamen selecon wh user-defned wndow, 3) Deermnsc samplng based on he fness proporonae selecon scheme. 4.6 Crossover Operaon In bnary represenaon he followng four ypes of crossover are used: ) -pon crossover ) -pon crossover 3) Unform crossover, whch s a crossover operaor ha swaps only sngle bs beween he wo paren bnary srngs. 4) Mul-pon crossover, n whch one crossover pon s seleced, randomly, for each parameer represened n he chromosome, and hereafer, -pon crossover s performed n each parameer. In floang-pon represenaon he crossover ypes used are: ) -pon crossover, ) -pon crossover, 3) Unform crossover, 4) Arhmecal crossover. 4.7 Muaon Operaon When bnary codng s used, he genec algorhm muaon smply changes a b from 0 o or vce versa. The bs ha undergo muaon are chosen based on a probably es. The probably of muaon s generally se o a small value, abou 0.00 o 0.0. In real represenaon, wo muaon operaors are mplemened: unform and non-unform muaon. ) Unform muaon: Ths operaor s analogous o he bnary operaor, bu apples o real values nsead of bnary bs; randomly replaces he parameer value wh anoher one from he approprae nerval: ) on-unform muaon: Ths muaon ype s descrbed n [8] and s responsble for he fne-unng capables of he real-codes. If a parameer of value u of a canddae soluon s seleced for muaon, s value s changed o u ; u +, UB u u = (3) u, u LB where u dependng on wheher a random bnary dg s 0 or. LB and UB are he lower and upper bounds of he ndvdual parameer belong o. The funcon (, y) reurn a value n he range [0, y] such ha he probably of (, y) beng close o 0 ncreases as he curren generaon number,, ncreases. Ths propery causes hs operaor o unformly search he space a nal sages, when s small, and very locally a laer sages. The funcon used s ( ) b (, y) y γ T = (4) where γ s a random number n [0,],T s he maxmal generaon number, and b s a parameer deermnng he degree of non-unformy [8]. In real represenaon, snce parameers do no change durng crossover, bu are jus recombned dfferenly (excep for he arhmecal crossover), he only way of affecng her values s by he muaon operaor. Moreover, he muaon probables used are greaer han he ones n bnary represenaon and may reach up o 5% [7]. 4.8 Creaon of he ex Generaon Afer muaon s compleed, he chldren populaon s creaed and he prevous populaon s replaced by he new generaon. Chldren are evaluaed and he fness funcon for each ndvdual s calculaed. The procedure s repeaed unl he ermnaon creron s me, defned by a maxmum number of generaon. 5. Smulaon The llusrae he applcaon of he propose mehod a 3 hp, 380V, 50 Hz hree-phase nducon moor was seleced. The performance of machne beween 0 of slp dffcul o deermne n pracce. Therefore, a compuer program was developed for PC o calculae he seady-sae performance from he real parameer. The npu daa of he propose mehod are he saor curren, he npu power, and he power facor, ha corresponded wh he 0 0. of slp. The genec algorhm suggesed n hs paper s smulaed and compared wh rue values. Objecve funcon J ( Φ) s used bu objec funcon J ( Φ) s nroduced for more opmal parameer selecon as follow: = [ ] J ( Φ ) = ( ) (, ) I s I s Φ c = + P ( s ) P ( s, Φ) n n c (5)

4 Seesa Jangj and Panhep Laohacha 363 J ( Φ ) = [ ] I ( s ) I ( s, Φ) c = + P ( s ) P ( s, Φ) n n c = + [ pf ( s ) pf ( s, Φ) ] c = (6) where I, P, and pf are he amplude of saor curren, power npu, and power facor, respecvely. Also, n and c are he quany of smulaed by rue value and genec algorhm selecon, respecvely. 6. Concluson Ths paper nvesgaes he applcaon of genec algorhm for he esmaon of seady-sae models of nducon moor. The man advanages of he proposed mehodology are usng only 3-5 of npu daa pons requred, flexbly, he smplcy of s mechansm, and he good resul even for bad nal of parameers. The propose mehod has been successfully appled o he dynamc esmaon of he oher machne models. The obaned resuls demonsrae he feasbly and praccaly of he proposed genec algorhm approach. Saor Curren (A) Slp Fg. 3. Varaon of I (s) by genec algorhm selecon and rue values Inpu Power (W) x Slp Fg. 4. Varaon of P n (s) by genec algorhm selecon and rue values Power Facor Slp Fg. 5. Varaon of pf(s) by genec algorhm selecon and rue values Table. The capon mus be followed by he able gen R R X X X m Inal J ( Φ ) J ( Φ ) Acnowledgemens Ths wor was suppored by Kasesar Unversy Chalermphraa Saon ahon Provnce Campus. References [] S. Ansuj and, F. Shoooh, and R. Schnzngger, Parameer Esmaon for Inducon Machnes Based on Sensvy Analyss, IEEE Transl, on ndusry applcaon,.vol. 5, no 6, pp [] Dong Hwa Km, and Jea Hoon Cho, Parameer Esmaon of a squrrel-double Cage Inducon Moor Usng Clonal Selecon of Immune Algorhm, IEEE Indusral Elecroncs Socey, Busan, Korea, p [3] P.Vaclave and P. Blaha, Lypunov-Funcon-Based Flux and Speed Observer for AC Inducon Moor Sensorless Conrol and Parameers Esmaon, IEEE Transl, on ndusry Elecroncs,.vol. 53, no, pp [4] M. Calvo and O.P. Mal, Synchronous Machne Seady-Sae Parameer Esmaon Usng eural ewors, IEEE Transl, on Energy Converson,.vol. 9, no, pp [5] D. J. Anson, P. P. Acarnley, and J.W. Fnch, Observers for Inducon Moor Sae and Parameer Esmaon, IEEE Transl, on ndusry Applcaons, vol. 7, no 6, pp [6] K. Wang, J Chasson, M. Bodson, and L.M. Tolber,

5 364 Parameer Esmaon of Three-Phase Inducon Moor by Usng Genec Algorhm A onlnear Leas-Squares Approach for Idenfcaon of he Inducon Moor Parameers, Proc. 43h IEEE Conference on Decson and Conrol, December 4-7, 004, Alans, Paradse Island, Bahamas, pp [7] G. K. Sefopoulos, P.S. Georglas,.D.Hazargyrou, and A.P. Sas Melopoulos, A Genec Algorhm Soluon o he Governor-Turbne Dynamc Model Idenfcaon n Mul-Machne Power Sysem, Proc. 44 h IEEE Conference on Decson and Conrol, and he European Conrol Conference 005, December -5, 005, pp [8] Z.Mchalewcz, Genec Algorhms + Daa Srucures = Evoluon Programs. ew Yor: Sprnger- Verlag, 996. Seesa Jangj He receved B.Eng and M.Eng degrees n elecrcal engneerng from Kasesar Unversy, Thaland. Currenly, he s lecurer a Kasesar Unversy, Saon ahon Campus. Hs research neress are elecrcal machnes, power sysem dynamc and conrol, and power sysem saably. Panhep Laohacha He receved B.Eng and M.Eng degrees n elecrcal engneerng from Chulalongorn Unversy, Bango, Thaland and Ph.D. n elecrcal engneerng from Olahoma Sae Unversy, USA. Currenly, He s an Asssan Professor a Kasesar Unversy, Bang Kean Campus, Thaland. Hs research neress are elecrcal machnes dynamcs, power sysem dynamc and power sysem saably.

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