A Compaatie Pefomance Analyi fo lo Minimization of Induction Moto Die Baed on Soft Computing Technique Keeti Rai Reeach Schola, Depatment of Electical and Electonic Engineeing National Intitute of Technology Jamhedpu, Jhahand, India. Ocid: --89-7 S B L Seena Pofeo, Depatment of Electical and Electonic Engineeing National Intitute of Technology Jamhedpu, Jhahand, India. A N Thau Pofeo, Depatment of Electical and Electonic Engineeing National Intitute of Technology Jamhedpu, Jhahand, India. Abtact Thi pape peent a compaatie pefomance aement fo lo minimization of ecto contolled induction moto (IM) die baed on thee diffeent efficient optimization algoithm, namely Paticle Swam (PSO), Genetic Algoithm (GA) and Golden Seach (GS). The peent wo deal with the ecalculation of optimized flux component of cuent baed on the mentioned technique, fo a bette optimal efficiency opeation of the IM die. All the thee algoithm baed IM die opeation how impoement in efficiency by eduction in the coe lo of the die ytem. Howee, it i PSO baed IM die opeation that ha the adantage of fat epone and high accuacy compaed to othe two cheme. The PSO baed enegy optimization cheme adaptiely adjut the flux component of cuent to minimize the ytem lo Moeoe, the thee appoache hae no effect on paamete aiation and alo need no additional hadwae fo hadwae implementation. The imulation eult fo aiou peed patten and opeating condition ae peented hee. Stability tudy of the whole die ytem i alo caied out utilizing the thee optimizing cheme. Keywod: Golden Seach Algoithm, Genetic Algoithm, Paticle Swam, Sytem Stability Analyi INTRODUCTION In pactical application, the enegy optimization of induction moto (IM) die in dynamic enionment i ital, that inole the enegy optimization algoithm to be capable of finding and tacing of changing optimum efficiency oe a peiod of time []. IM die hae been widely ued in indutie, both in fixed and aiable peed application, due to the deelopment of powe emiconducto deice, micoelectonic, and contol technique [, ]. Thee moto peent a adantage the ize, cot, weight, eliability, and eay maintenance [4, 5]. It i etimated that the induction moto conume two-thid of the electicity poduced in the United State, and in aeage, they opeate at 6 pecent of the ated load, becaue of oeized intallation o unde loaded condition, and theefoe hae low efficiencie [6]. Since, a lage numbe of IM die ae opeational woldwide and eey yea thee i definite poitie inceae in thei numbe, theeby an impoement in efficiency by minimizing the loe will ignificantly hae a good impact on enegy aing [4]. Minimization of lo in the induction moto i diectly elated to choice of the flux leel. But the exteme minimization caue a high coppe lo [5]. Fo contant peed opeation, poided toque i aiable the flux ha to ay, o a to impoe the die efficiency. A numbe of enegy optimization tategie uch a imple tate contol [6], each contol [7], and lo model baed contol [8] fo IM die hae been epoted in the liteatue. The lo model baed contol conit of computing loe by uing the machine model and electing a flux leel that can be ued to minimize the loe. The econd categoy i the powemeaue-baed appoach, alo nown a each contolle (SC), in which the flux i deceaed until the electical input powe ettle down to the lowet alue fo a gien toque and peed [9], [], & []. Thee ae numbe of each optimization technique uch a GA, PSO, Ant Colony, Bee Colony etc. But, the PSO i found moe popula due to it implicity and accuacy. Thi algoithm i deeloped by Kennedy and Ebehat in 99. The baic concept egading thi ae aailable in [7]. The application of thi algoithm tat inceaing in almot all the aea of engineeing. The paticle wam optimization (PSO) i chaacteized a imple in concept, eay to implement, and computationally efficient unlie the othe heuitic technique. PSO ha a flexible and well balanced mechanim to enhance and adapt the global and local exploitation abilitie [].
The genetic algoithm (GA) baed method mainly wo on pinciple of optimization of a ignificant paamete (e.g., DC lin powe o DC-lin cuent o tato cuent o die loe) by tial and eo method [], []. Unlie othe contol tategie, the method doe not depend upon the moto o conete paamete. They belong to the cla of EA, which ae ued to find olution optimizing complex poblem uch a the optimization of cloed-loop die-fed moto. Indeed thei ue to ole complex poblem epond to the neceity to geneate appoximate olution when the exact olution cannot be find with a claic optimization method (e.g. Newton-Raphon). Howee, the method uffe fom the toque ipple and low conegence ate. Neethele, the poblem may be oecome uing econd ode low-pa filte. The golden each algoithm i geneally ued to minimize the IM die lo. Thi alo ha a cloe elation to the Fibonacci each method [4]. Howee, the golden each technique ha a definite edge oe the Fibonacci each algoithm a the late need to now a pioi the numbe of ealuation in the minimum eaching poce, which i totally eliminated in the fome one [5]. To achiee a minimal machine coe lo, the golden each technique eache the optimal alue of oto flux efeence uing ey fat conegence algoithm. In the peent wo, the poblem i fomulated fo efficiency optimization by minimizing loe uing PSO, GA and GS baed algoithm ae ued to minimize the lo in the IM die. A compaatie pefomance analyi of the. W IM die ytem i caied out fo thee (PSO, GA and GS) algoithm in diffeent opeating condition togethe with conentional FOC method. The die ytem conit of an enegy optimization algoithm baed on the powe lo of die and peed eo ignal to geneate optimal alue of and hence optimal oto flux. LOSS MINIMIZATION MECHANISM The lo minimization algoithm i baed on eaching optimal alue of the flux component of tato cuent, fo which the input powe of the ytem can be minimal. The input powe i calculated a the poduct of the meaued DC oltage and DC cuent a follow: Pin Vdc Idc () The efficiency of machine i defined a the atio of the mechanical output powe to the electical input powe. Theefoe, fo inceaing the efficiency of a machine, the electical input powe can be optimized to educed alue by minimizing the total loe. Thu, the lo minimization i accomplihed by adjuting the flux leel though the efeence flux component cuent. The lo-model baed appoach [6], [7], [8], & [9] i utilized in thi wo fo the geneation of efeence flux cuent. In thi method, the lo i computed by uing the machine model and electing the flux leel that minimize the loe. GOLDEN SEARCH ALGORITHM In golden each baed algoithm, the maximum alue of the fluxcuentequaltoitatedalue idmax i d i defined andtheminimal alue equal to id, whee ~.5 depending on load leel. Thealgoithmcalculate the flux cuent in the inteal between i d min, id max, which i fed to the contol ytem to educe the total input powe of the die. The input owe i calculated in eqn.. The new alue of the efeence flux cuent id ae calculated uing two golden each ection; F and F a below; 5 5 F. 68 and F. 8 () The algoithm calculate two alue of the efeence flux cuent i d, i d in inteal i d min, id max uing the golden ection. The input powe coeponding to thee two cuent leel i calculated a a depicted in eqn.. The efeence flux cuent i d, i d conequently ae ecalculated and thei coeponding alue of input powe ae e-meaued and e-ealuated. The each pocedue epeat itelf until the deied accuacy i achieed. i d i d i () whee i i the flux cuent toleance. The final alue of efeence flux cuent i calculated by aeaging the alue of i d, i d d i d i d i (4) The golden each algoithm i fat and immune fo the moto paamete. The technique compie of all the loe including the lo in inete, ince the powe enteing to the ytem i meaued and ued in the optimization algoithm. GENETIC ALGORITHM Genetic algoithm (GA) [Goldbeg DE. Genetic Algoithm in Seach], i inpied by Dawin theoy about eolution the Suial of the fittet. In GA, the optimization poblem i eoled by imitating the pactice though natual ue i.e. election, cooe, mutation and accepting [4]. In the mot geneal ene, GA-baed optimization i a tochatic each method that inole the andom geneation of potential deign olution and then ytematically ealuate and efine the olution until a topping citeion i met. Set of non-
linea equation ae oled which ae epeented by objectie function baed on ome citeion GA i paallel, global each technique which tae the concept fom eolution theoy and natual genetic. They emulate biological eolution by mean of genetic opeato uch a epoduction, cooe and mutation etc. GA wo with a et of atificial ceatue (ting) called population. In eey geneation, GA geneate a et of offping fom old population accoding to a ue-defined fitne function. The fitne function epeent the pefomance of a poblem. The highe the fitne alue, the bette the pefomance of a ytem. By exchanging the infomation between eey indiidual, GA eep the bette cheme, which may yield highe fitne, fom geneation to geneation uch that the pefomance can be impoed [5], [6], [7], [8]. The GA i an adaptie heuitic each baed on the eolutionay idea of natual election and genetic. It i intelligent exploitation of andom each and exploit hitoical infomation to diect the each into the egion of bette pefomance within the each pace [9], [4]. In GA method applied fo optimization, the chomoome ae the olution fo poblem inoled in optimization. Each chomoome in the poce i aeed by blending it into the chedule with an objectie function. In GA poce, in the beginning tage, the chomome ae poduced andomly [4]. The mechanim of election, cooe and mutation lead to bith of upeio quantity offping fom the peiou geneation (paent). Howee, thoughout the genetic eolution, only the tonge chomoome uie. At the end tage of the eolutionay poce, nea-optimal o optimal olution can be achieed. Step inoled in GA optimization poce ae illutated below: Step : Geneation of andom population of popize chomoome (i.e. uitable olution fo the poblem). The initial andom population compiing of indiidual whoe chaacteitic i coded by the equence of zeo and one i achieed by the initialization geneation. Thee indiidual ae gene in a chomoome. The ize of the population i detemined accoding to the complexity of the contol poblem. Step : Ealuation of the fitne function f( i d ) of each chomoome i d in the population (f( i d ). Minimize (f( i d ), whee i d = id,id,id,..., idn. The fitne function i the indication of GA pefomance in eoling the pacticality of each chomoome. A fitne function i deigned baed on a uitable pefomance citeion. The fitne alue fo each chomoome inide the population i aeed then caled. Step : Ceation of a new population by iteating the election, cooe, mutation and accepting poce until the new population i complete. a. Selection: Selection i the poce to elect mot of the bette chomoome in each geneation to cooe and the et o ome of the et to mutate. The tounament method i adopted in ou GA. The eaon i that in the tounament method the objectie alue of a chomoome can be ued a the election citeion. b. Cooe: Cooe i the poce duing which two paent geneate two offping, uch that the offping inheit a et of building bloc fom each paent. Aume the numbe of the chomoome to be elected fo cooe i xize. Coing the paent with cooe pobability C = xize/popize to fom new offping and if no cooe i pefomed, offping i the exact copy of the paent. often C ϵ [.5,.9]. c. Mutation: Mutation i the poce duing which ome gene of a chomoome ae changed and a new chomoome i geneated. the numbe of the chomoome to be elected fo mutation i mize, and the atio M=mize/popize i temed mutation ate, often M ϵ [.,.]. d. Accepting: poitioning new offping in the new population. Step 4: Ue of new geneated population fo futhe un of the algoithm. Repoduction i the opeato caying old ting though into a new population, depending on the fitne alue. Indiidual with highe fitne alue will be moe liely to be elected than thoe with lowe fitne alue. Moeoe, the oulette wheel election [4] method i adopted in thi tudy fo epoduction. Step 5: If the end condition i atified, top and etun the bet olution in exiting population. The GA i teminated when the each goal i completed o the equied geneation i attained. If thi doe happen, etun to tep and epeat the tep again. PARTICLE SWARM OPTIMIZATION PSO, cited in efeence [4], equie only pimitie mathematical opeato and computation equie mall amount of memoy PSO i tochatic, population-baed, global optimization algoithm mainly dedicated to continuou poblem (continuity of the each pace). It wa intoduced in 995 (Kennedy and Ebehat, 995) [] and i baed on the obeation of the ocial behaio of a population of animal (bid, fihe). Thi method ha poen it efficiency in oling engineeing poblem and ha eceied inteet fom optimization and engineeing communitie. In addition, it depend on few paamete to be et. PSO i initially popoed to ole uncontained poblem. It i initialized with a et of paticle, each one coepond to a
candidate olution. PSO find the global optimum by moing each paticle with andomly weighted elocitie. Paticle wam optimization (PSO) i an eolutionay computation technique deeloped by Kenney and Ebehat in 995 []. The method ha been deeloped though a imulation of implified ocial model. PSO i baed on wam uch a fih chooling and bidflocing. Accoding to the eeach eult fo bid flocing, bid ae finding food by flocing (not by each indiidual). Lie GA [], []], PSO mut alo hae a fitne ealuation function that tae the paticle poition and aign to it a fitne alue. The poition with the highet fitne alue in the entie un i called the global bet (P,). Each paticle alo eep tac of it highet fitne alue. The location of thi alue i called it peonal bet ( e ). The baic algoithm inole cating a population of paticle oe the each pace, emembeing the bet (mot fit) olution encounteed. At each iteation, eey paticle adjut it elocity ecto, baed on it momentum and the influence of both it bet olution and the bet olution of it neighbo, then compute a new point to examine. The tudie how that the PSO ha moe chance to fly into the bette olution aea moe quicly, o it can dicoe eaonable quality olution much fate than othe eolutionay algoithm. Inpied by the flocing and chooling patten of bid and fih, Paticle Swam (PSO) wa inented by Ruell Ebehat and Jame Kennedy in 995. PSO might ound complicated, but it' eally a ey imple algoithm. Oe a numbe of iteation, a goup of aiable hae thei alue adjuted cloe to the membe whoe alue i cloet to the taget at any gien moment. Imagine a floc of bid cicling oe an aea whee they can mell a hidden ouce of food. The one who i cloet to the food chip the loudet and the othe bid wing aound in hi diection. If any of the othe cicling bid come cloe to the taget than the fit, it chip loude and the othe ee oe towad him. Thi tightening patten continue until one of the bid happen upon the food. It' an algoithm that' imple and eay to implement. The algoithm eep tac of thee global aiable: Taget alue o condition Global bet (gbet) alue indicating which paticle' data i cuently cloet to the Taget Stopping alue indicating when the algoithm hould top if the Taget in't found. Taget alue o conditio Global bet (gbet) alue indicating which paticle' data i cuently cloet to the Tag Stopping alue indicating when the algoithm hould top if the Taget in't found Each paticle conit of: Data epeenting a poible olution A elocity alue indicating how much the data can be changed A peonal bet (pbet) alue indicating the cloet the paticle' data ha ee come to the taget. Data epeenting a poible olutio A elocity alue indicating how much the data can be changed A peonal bet (pbet) alue indicating the cloet the paticle' data ha ee come to the taget. The paticle' data could be anything. In the flocing bid example aboe, the data would be the X, Y, Z coodinate of each bid. The indiidual coodinate of each bid would ty to moe cloe to the coodinate of the bid which i cloe to the food' coodinate (gbet). If the data i a patten o equence, then indiidual piece of the data would be manipulated until the patten matche the taget patten. The elocity alue i calculated accoding to how fa an indiidual' data i fom the taget. The futhe it i, the lage the elocity alue. In the bid example, the indiidual futhet fom the food would mae an effot to eep up with the othe by flying fate towad the gbet bid. If the data i a patten o equence, the elocity would decibe how diffeent the patten i fom the taget, and thu, how much it need to be changed to match the taget. Each paticle' pbet alue only indicate the cloet the data ha ee come to the taget ince the algoithm tated. The gbet alue only change when any paticle' pbet alue come cloe to the taget than gbet. Though each iteation of the algoithm, gbet gadually moe cloe and cloe to the taget until one of the paticle eache the taget. It' alo common to ee PSO algoithm uing population topologie, o "neighbohood", which can be malle, localized ubet of the global bet alue. Thee neighbohood can inole two o moe paticle which ae pedetemined to act togethe, o ubet of the each pace that paticle happen into duing teting. The ue of neighbohood often help the algoithm to aoid getting tuc in local minima. Algoithm fo implement PSO.. Initialize a population aay of paticle with andom poition and elocitie on D dimenion in the each pace.. Loop. Fo each paticle, ealuate the deied optimization fitne function in D aiable. 4. Compae paticle fitne ealuation with it pbeti. If cuent alue i bette than pbeti, then et pbeti equal to the cuent alue, and pi equal to the cuent location xi in D-dimenional pace. 5. Identify the paticle in the neighbohood with the bet ucce o fa, and aign it index to the aiable g. 6. Change the elocity and poition of the paticle accoding to the following equation (ee note below):
7. If a citeion i met (uually a ufficiently good fitne o a maximum numbe of iteation), exit loop. 8. end loop Note: epeent a ecto of andom numbe unifomly ditibuted in [ ] which i andomly geneated at each iteation and fo each paticle. i component-wie multiplication. In the oiginal eion of PSO, each component of i ept within the ange [-Vmax,+Vmax]. The popoed technique i applied to a -hp induction machine [] to identify fluxcomponent of cuent []. LOSS MODEL OF INDUCTION MOTOR The IM die model with ion lo (Figue ) i gien by following equation a [4], [44]: d q d R R R R id iq id i L pid Lm pidm e Liq Lmiqm (5) L piq Lm pidm e Lid Lmidm (6) d m dm e Li Lmiqm L i L i L pi L pi (7) m qm L pi L pi (8) e d m dm The d-axi and q-axi component of magnetic flux ae gien a; d Lid Lmidm (9) q Liq Lmiqm () d L id Lmidm () L i Lmiqm () The induced oltage on the magnetizing banch i gien a; di Lm pidm elmidm () qi Lm piqm elmiqm (4) The inteaction between tato cuent and magnetic flux component gie electomagnetic toque in d-q coodinate fame a; T em L P L m Lm i i i i d dfe d q qfe (5) The total lo i gien by; P o, lo P Whee, Pfe R i i R i i d q d q R f di qi (6) lo Pj Pj Pfe (7) P tato coppe lo; P j j oto coppe lo; coe lo including eddy cuent and hyteei lo. i R j L i L i fe R fe i L i m L m jl i R j Li Lmim j L m i m Figue : Equialent cicuit model of induction moto in T- fom with ion lo. INPUT POWER MEASUREMENT The die i equipped with DC oltage and cuent eno to ealuate Pin accuately. The moto i un in cloed loop peed contol without load, uch that the contibution of the oto coppe loe i negligible. The cuent, oltage and input powe ae ecoded when teady-tate condition ae eached. LOSS MINIMIZATION OF IM DRIVE The impoed dynamic pefomance with minimum lo i the impotant equiement fo the IM die. Theefoe, lo minimization cheme uing GA algoithm [45, 46] } hae been incopoated in the oute loop of the contol cheme. The ecto contol not only ha the adantage of poiding excellent dynamic pefomance, but alo, enable decoupled contol of toque and flux though d-axi (flux-poducing) and q-axi (toque-poducing) cuent in the teady tate. Thi mae the incluion of the lo minimization algoithm imple [4]. The die lo i calculated fom the diffeence between the powe input to the inete and the haft powe output. The efeence flux cuent, i d }i geneated by the optimization algoithm, while the toque component of cuent i acquied fom the peed contol loop. In the tanient tate, when eithe the peed command o the load toque i changed, the nominal alue of the i d come into play.the tanient peed i eaily detected when the peed eo ignal ( e ) eache the maximum alue.5 ad/ and the enegy i 4
optimization algoithm tat ettling the i d to the equied y C x () optimal alue. The optimal alue of i d geneate the optimized equied flux without affecting the output powe. The optimal alue of flux educe the powe lo of the die ytem thu fulfilling objectie of the popoed wo. The detailed chematic diagam fo etimation of peed with lo minimization algoithm i hown in Figue. Figue : Schematic diagam of ecto contolled IM die and efficiency optimization cheme. SYSTEM STABILITY ANALYSIS To cay out the tability analyi of any ytem, the aiable mut be time-inaiant [5]. The IM model in ynchonouly otating e } efeence fame ha been expeed a i d p e p p i d i q e p p p iq 4 d p p5 l d σl p4 l p5 A B i i p d q i i C d q d L whee, p R m L L, p L L L m, L p m 4 and p L R d q (8) Lm L (9), 5 In the tate pace domain, (-) can be epeented a x Ax Bu () y Cx () whee, A, B, C ae obtained fom (8)-(9) and x T i i, u T, y T d q d d q i d i q Lineaizing the tate pace equation aound a table opeating point ay x, the mall ignal epeentation i a () x A x Ax y C I A A x (4) o, x id iq d point. T epeent the opeating Fo checing the feaibility of the algoithm fo oto peed etimation, A i calculated in tem of a; A p C p Uing eqn(5) and (6), the expeion of y in eqn(4) become; id y i q p id (5) (6) i p q I A (7) d c c c c4 Let, c c c c4 I A c c c c4 c4 c4 c4 c44 i The tanfe function of d i and q obtained fom eqn(7) can be epeented a id c4 - pc d I A i q c 4 - p c I A d whee, adj I A C ] and i, j aie fom to 4. [ ij Fom Figue, the following expeion hae been deied: d ω i i i d id (8) (9) i p d d () Δˆ ω G() Δε p i ωˆ Figue : Cloed loop epeentation of peed etimato 5
i i q p p i q i q () whee, i p tanfe function of the peed PI contolle, i p tanfe function of cuent PI contolle, a een fom Figue. To chec feaibility of the algoithm fo peed etimation, A i calculated in tem of with an aim of obtaining id and iq. Fom the mall ignal eo equation,, Δε Δωˆ i epeented a: Δε Δωˆ - G() Δi Δi d d Δω Δω 5 4 () L whee, m q L eid e id iq ; L L i ; d e q id Magnitude (db) Phae (deg) - - - 45-45 -9 4 5 Bode Diagam Gm = Inf, Pm = 4 deg (at 7.48 ad/) Fequency (ad/) (a) Bode Diagam Gm = Inf, Pm = deg (at 6.9 ad/) L m 4 L i d L i q i ; d L L m 5 L i d L i q i d i ; d L The cloed loop tanfe function epeentation (Figue. ) of the peed etimato i obtained a: ωˆ ω whee, G() p p i i G() p i () = i the tanfe function of the PI contolle. Equation can be utilized fo the mall ignal tability analyi with lineaized machine equation fo the popoed algoithm (GS, GA and PSO) baed IM die and i caied out fo both the motoing and egeneating mode of opeation. Since, the atifactoy pefomance of the die in the low peed egion i challenging, hence, die tability tudy at a peed of ad/ i epoted. Figue 4 how the bode plot a gien in the figue caption fo both the motoing and egeneating mode epectiely. It i obeed fom the Bode plot that both the Gain Magin (GM) and Phae Magin (PM) ae poitie; epeenting a table ytem fo the IM die ytem. Phae (deg) Magnitude (db) Phae (deg) Magnitude (db) - - - 45-45 -9 4 5 - - - 45-45 Fequency (ad/) (b) Bode Diagam Gm = Inf, Pm = 4 deg (at 8.5 ad/) -9 4 5 Fequency (ad/) (c) 6
Magnitude (db) Phae (deg) Magnitude (db) Phae (deg) - - - 45-45 Bode Diagam Gm = Inf, Pm = 4 deg (at 8.5 ad/) -9 4 5 - - - -4 45-45 -9 Fequency (ad/) (d) Bode Diagam Gm = Inf, Pm = 5 deg (at 9.9 ad/) -5 4 Fequency (ad/) (e) SIMULATION RESULTS The pefomance of the popoed algoithm fo lo minimization of the ecto contolled IM die i eified in Matlab/Simulin fo aiou tet cae a decibed futhe in thi ection. The imulation eult how the peed, oto flux, tato cuent, and lo epone of the IM die, befoe and afte the optimization cheme ae initiated fo IM die. The detailed pecification of the -phae,. W, IM die i gien in Appendix A. Step change in oto peed Reult of the GS, GA and PSO baed optimization cheme, fo the IM die ae tudied in the motoing mode by a tep change in the efeence peed a hown in Figue. 5. An inceaing tep change in the peed command i applied at eey ec and the efeence and actual peed ae hown fo the whole peed ange in Figue 5(a), Figue 6(a) and Figue 7(a) fo the GS, GA and PSO baed optimization algoithm, epectiely. Thoughout the opeation, a contant toque of 5 Nm i maintained. The flux component of the i ) i hown in Figue 5(b), Figue 6(b) and tato cuent ( d Figue 7(b). Afte eey peed tanient peiod, idi adjuted to the optimal alue by the algoithm. The flux oientation i alo alteed a the i d change and i depicted in Figue 5(c), Figue 6(c) and Figue 7(c). The lo of the IM die ytem i hown in Figue 5(d), Figue 6(d) and Figue 7(d). It can be obeed that without efficiency optimization algoithm in the tanient peiod, the die lo i on the highe ide a compaed to the duation afte optimization algoithm become functional. Alo, the Figue eeal that the PSO baed optimization cheme i moe efficient in minimizing the loe a compaed to the GS and GA baed cheme. 6 5 ω _et Magnitude (db) - - - Bode Diagam Gm = Inf, Pm = 46 deg (at 9. ad/) Speed (ad/) 4 Phae (deg) -4 45-45 5 5 5 Time () (a) -9 4 Fequency (ad/) (f) Figue 4: Bode plot of IM die in motoing mode baed on: (a) GS algoithm, (c) GA algoithm, (e) PSO algoithm, and in egeneating mode baed on: (b) GS algoithm, (d) GA algoithm, (f) PSO algoithm. 7
Roto flux (Wb).5.5.5.5 d Speed (ad/) 6 5 4 ω _et -.5-5 5 5 Time () (b) 5 5 5 Time () (a) i d (A) 4.8.6.4..8 Roto flux (Wb).5.5.5.5 -.5 d.6 5 5 5 Time () (c) - 5 5 5 Time () (b) Total lo (W) 6 5 4-5 5 5 Time () (d) i d (A) 4.8.6.4..8.6 5 5 5 Time () (c) Figue 5: Simulation eult of the IM die with GS cheme fo tep change in oto peed at 5 Nm load toque: (a) efeence, etimated and actual peed, (b) d- and q-axi oto flux, (c) d-axi tato cuent, and (d) total lo of the die. 8
5 4.5.4 Total lo (W) - 5 5 5 Time () Figue 6: Simulation eult of the IM die with GA cheme fo tep change in oto peed at 5 Nm load toque: (a) efeence, etimated and actual peed, (b) d- and q-axi oto flux, (c) d-axi tato cuent, and (d) total lo of the die. Speed (ad/) Roto flux (Wb) 6 5 4 ω _et (d) 5 5 5 Time ().5.5.5.5 -.5 (a) d - 5 5 5 Time () (b) Total lo (W) i d (A)....9.8.7.6.5 5 5 5 Time () 5 4-5 5 5 Time () Figue 7: Simulation eult of the IM die with PSO cheme fo tep change in oto peed at 5 Nm load toque: (a) efeence, etimated and actual peed, (b) d- and q-axi oto flux, (c) d-axi tato cuent, and (d) total lo of the die. Regeneatie mode opeation: Second quadant opeation The pefomance of the IM die ytem in econd quadant i hown in Figue 8, Figue 9 and Figue. The etimated peed follow the actual peed atifactoily Figue 8(a), Figue 9(a) and Figue (a)) fo GS, GA and PSO lo optimization cheme. The optimization algoithm come into play at 5 ec, 5 ec, and 5 ec. The optimal and non-optimal fluxe ae hown in Figue 8(b), Figue 9(b) and Figue (b), epectiely fo afoeaid algoithm. The change in cuent duing the entie time peiod i hown in Figue 8(c), Figue 9(c) and Figue (c). The decement in lo when the optimization technique (GS, GA and PSO) ae woing hown in Figue 8(d), Figue 9(d), and Figue (d). It can be obeed fom the eult that PSO baed optimization cheme i moe efficient in educing the lo than the GS and GA baed cheme. (d) 9
6 6 5 Speed (ad/) 4 - Total lo (W) 4 Roto flux (Wb) -4-6 -.5 ω _et 5 5 5.5.5.5.5 Time () (a) Without With - 5 5 5 4.8.6 Time () (b) d - 5 5 5 (d) Time () Figue 8: Simulation eult of the IM die with GS cheme fo econd quadant opeation at 5 Nm load toque: (a) efeence, etimated and actual peed, (b) d- and q-axi oto flux, (c) d-axi tato cuent, and (d) total lo of the die. Speed (ad/) 6 4 - -4-6 ω _et 5 5 5 Time () (a) i d (A).4..8.6 5 5 5 Time () Roto flux (Wb).5.5.5.5 -.5 Without With d - 5 5 5 Time () (b)
i d (A) 4.8.6.4..8.6 5 5 5 5 4 Time () (c) Roto flux (Wb).5.5.5.5 -.5-5 5 5 Time () 4.8 Without With (b) d Total lo (W) i d (A).6.4. - 5 5 5 (d) Time () Figue 9: Simulation eult of the IM die with GA cheme fo econd quadant opeation at 5 Nm load toque: (a) efeence, etimated and actual peed, (b) d- and q-axi oto flux, (c) d-axi tato cuent, and (d) total lo of the die..8.6 5 5 5 Time () 5 4 (c) Speed (ad/) 6 4 - -4-6 ω _et 5 5 5 Time () (a) Total lo (W) - 5 5 5 Time () (d) Figue : Simulation eult of the IM die with PSO cheme fo econd quadant opeation at 5 Nm load toque: (a) efeence, etimated and actual peed, (b) d- and q-axi oto flux, (c) d-axi tato cuent, and (d) total lo of the die.
In Table lo minimization cheme ae peented fo diffeent peed ange at 5 Nm load toque (in motoing mode) and -5 Nm load toque (in egeneating mode). The Table ummaize the compaatie eult of lo minimization achieed with GS, GA and PSO technique and without optimization technique. Fom the table it i noticed that loe fom PSO i moe educed a compaed to both (GS and GA) the technique. The Compaatie diagam of total lo of the IM die with and without optimization cheme i hown in Figue. Lo (W) 6 55 5 45 4 5 Motoing Mode Conentional cheme PSO baed cheme GA baed cheme GS baed cheme Table : Pefomance Aement of IM die opeation in motoing and egeneating mode with and without GA baed optimization. Spee d (ad/ ) 5 Toq ue (Nm) Lo (W), without optimizat ion Lo (W), with PSO optimizat ion Lo (W), with GA optimizat ion Lo (W), with GS optimizat ion 485 59 8 46 4 4 4 6 4 96 46 8 5 64 55 4 9 5 7 8 96 8 76 85 98 7 8 6 Lo (W) 5 4 5 Speed (ad/) 6 55 5 45 4 5 5 Regenating Mode Conentional cheme PSO baed cheme GA baed cheme GS baed cheme 4 5 Speed (ad/) Figue : Compaion of total die lo fo IM die with GA and GS optimization cheme. 5 86 9 9 5 96 4-5 6 6 5 88 7 54 7 4 4 48 76 4 5 47 74 9 46 CONCLUSION Thi pape peent a compaion between thee diffeent optimization cheme fo high pefomance IM die nown a paticle wan optimization (PSO) genetic algoithm (GA) and golden each (GS) method. The optimization cheme ae applied to impoe the oeall efficiency of IM die. The lo-minimization algoithm ae deeloped conideing the die lo fo all the afoeaid cheme. The pefomance of the IM die ytem conideing PSO, GA and GS algoithm hae been teted in imulation fo diffeent opeating condition. Moeoe, the tability analyi of the IM die ytem in the motoing and egeneating mode of opeation confim a table die opeation fo the cheme. The efficiency optimization algoithm geneate the optimal alue of i d. Hence, coe lo of the die ytem i minimized a the flux leel i optimized. It i found fom the eult that the pefomance of the IM die with the PSO baed optimization
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