Magnetic Lossess Simulation in PM SM Drive by FE: Harmonic Superposition by Method of Locked Rotor

Transcription

1 Magnetc Lossess Smulaton n PM SM Dve by E: Hamonc Supeposton by Method of Locked Roto Robet Kaczmaek, Jean-Claude Vanne, Wan-Yng Huang To cte ths veson: Robet Kaczmaek, Jean-Claude Vanne, Wan-Yng Huang. Magnetc Lossess Smulaton n PM SM Dve by E: Hamonc Supeposton by Method of Locked Roto. EPQU 00, 00, Bacelone, Span. pp.-4, 00. <hal-00469> HAL Id: hal Submtted on 6 eb 008 HAL s a mult-dscplnay open access achve fo the depost and dssemnaton of scentfc eseach documents, whethe they ae publshed o not. The documents may come fom teachng and eseach nsttutons n ance o aboad, o fom publc o pvate eseach centes. L achve ouvete pludscplnae HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau echeche, publés ou non, émanant des établssements d ensegnement et de echeche fanças ou étanges, des laboatoes publcs ou pvés.

2 Magnetc Lossess Smulaton n PM SM Dve by E: Hamonc Supeposton by Method of Locked Roto Robet KACZMAREK, Wan-Yng HUANG and Jean-Claude VANNIER Dept. Enege Supélec 99 Gf su Yvette, ance obet.kaczmaek@supelec.f Abstact The PWM-suppled pemanent magnet synchonous machnes ae exposed to magnets heatng due to hamonc felds whch otate n elaton to oto. The coespondng losses can be calculated by E smulaton fo each fequency, wth supeposton of all components of the losses. In cetan condtons thee dmensonal modellng s equed to get enough pecson. Howeve, tme-steppng 3D fnte element methods coupled wth moton equatons can lead to excessve computatonal tme. Then a locked oto appoach wth cuent sheet otatng may be nteestng. In ths case howeve, the supeposton doesn t eally wok unless specal pocedue s appled. Magnetc loss dsspaton cannot be coectly calculated wth smple supeposton of ndvdual felds, e.g. the th and th hamonc otatng n opposte decton. Ths s because the esultng feld has an altenatve component wth dsspatve effects dependng on ts poston. They wll be moe mpotant f the component oscllates n the mddle of magnets and less mpotant n the mddle of gap between them. Keywods-pemanent magnet synchonous machne; hamoncs; supeposton ; fnte elements ; 3D modelng I. INTRODUCTION Pemanent magnet synchonous machne (PMSM, wth ts smplcty, hgh effcency even at low speeds, stong powe densty and elatvely low t of mantenance can be sutable choce fo an AC nvete dve. Usual way of teatng non snusodal supply condtons s supeposton of hamonc components, patculaly fo toque and magnetc losses calculaton. Analytcal methods ae often vefed by fnte element (E modelng and smulaton, as hgh pecson s equed wth goously smooth toque applcatons o wth mnmal sze machne desgn. In the latte case losses n magnets ae of concen, because unde PWM voltage supply the eddy cuent losses may sgnfcantly se magnets tempeatue. Ths can be pevented by magnets fagmentaton, an opeaton mechancally delcate. Wth E applcaton the poblem of choce between D and 3D packages s cucal. Tadtonally, when machnes can be consdeed as essentally adal flux devces wth stay flux n the end wndngs beng neglgbly small [] then the D tmestepped smulaton [-4] s pecse enough fo paamete evaluaton and toque calculaton. Ths axom can not always be appled to PM SM whee accuacy of calculaton of magnets losses depends to a lage extent on magnets dmensons. The D smulaton assues good pecson n case of magnets wth ato of axal and tangental lengths exceedng ten []. Ths condton howeve may be elevant n case of actual machnes whee pepaaton and mountng of long and thn magnet peces on oto s suface s delcate opeaton. Then 3D smulaton can be equed. Hee the tme-stepped fnte elements smulaton becomes excessvely tme consumng. A soluton to ths poblem comes wth locked oto and hamonc MM otatng aound t. Actual machne beng desgned wth quas snusodal wndng dstbuton, the hamonc analyss s concened wth tme hamoncs of ode and, and 3 etc. Calculaton of magnets losses on oto sde mples then hamoncs -/6 th, - / th etc. Howeve, supeposton of ndvdual losses may dffe substantally fom losses dsspated by composed felds. In ode to fx condtons fo supeposton to wok, we stat wth hamonc felds analyss n stato and n oto efeence fame. II. SLIDING AND COMPOSED MM A. Stato efeence In nvete-fed PM SM the amatue cuents ae usually non snusodal, wheeas the spatal dstbuton of magnetomotve foce can be assumed as snusodal n stato efeence fame fxed (θ0 n geometcal axs of wndng dstbuton of phase a. Ths axs ponts to maxmum of the ne expesson fo MM of phase a (: a ( θ na b ( θ nb c ( θ nc ( θ ( θ 0 ( θ 40 If we stat countng tme fom the moment the fundamental cuent n wndng a s at ts peak value (

3 a v a ( t ( t V ( ωt ( ωt ϕ ( then we fnd peak value of the fundamental composed magneto-motve foce at θ0 (θ,t a (θ,t b (θ,t c (θ,t (3 In ths moment the oto axs s laggng the stato axs, and obvously also the fundamental MM, by the machne ntenal angle δ (g.. o futhe analyss we take the th and the th amatue cuent hamoncs (4: a b c a b c ( t ( t ( t ( t ( t ( t ( ωt φ ( ωt φ 0 ( ωt φ 40 ( ωt φ ( ωt φ 0 ( ωt φ 40 wth ntal phases φ and φ measued n elaton to the coespondng hamonc voltages, whch ae all n-phase wth supply PWM voltage and, obvously, wth ts fundamental component. These cuents fom a pa of felds, of classcal fom of snusodal dstbuton along the a gap, otatng n elaton to stato at, espectvely, -ω : 3nI ( θ t and ω : ( ω φ θ 3nI ( θ ( ωt φ θ (6 At t0 the (θ has ts maxmum n θ-φ and (θ at θφ (g.. (4 g.. The fundamental, the th and the th hamoncs of MM n elaton to stato, epesented hee by ts a wndng at t0. Roto s consdeed wth one pa of poles and magnets ndcated n black. We should now elate all these quanttes to oto. B. Roto efeence In oto efeence fame we wll see these felds as ceated by phase cuents of, espectvely, negatve and postve sequence (: ( t ( t ( t ( t ( t ( t φ6 φ6 0 φ 40 6 φ 6 φ 6 0 φ 40 6 these cuents cculatng n vtual 3-phases wndngs fxed on the oto n poston of δ ahead of the otos axs; at t0 ths poston s that of the stato a wndng. Then the oto elated MMs have the fom (8: n n n ( θ δ ( θ δ 0 ( θ δ 40 ( (8 The phase φ n cuent expesson beng nothng moe than ntal angles, we have φ -6 φ and φ 6 φ. Ampltudes don t change, nethe, when passng fom stato to oto efeence fame and so we have I and I -. The magneto-motve foce 6 esultng fom the postve sequence cuents can be epesented by vecto otatng ove oto suface at 6ω :

4 3nI 6 ( θ, t φ 6 ( θ δ (9 and smlaly fo negatve sequence cuents we have MM otatng at -6ω : 3nI 6 ( θ, t φ6 ( θ δ (0 At t0 the -6 has ts maxmum n θ δ ϕ 6 and 6 at θ δ ϕ6. They concde wth dsposton of, espectvely, the th and the th stato elated components (g.. Wth th and th cuent hamoncs havng dffeent ampltudes, fo example I - > I, the esultng MM s composed of one oscllatng and one sldng component 6nI ( θ, t φ 6 φ6 6ωt 3n ( I I φ 6 φ 6 ( θ δ ( φ ( θ δ Wth the oscllatng pat gowng, the dependence of losses on ts angula poston wll gow. We wll now establsh a law on ths dependence as well as condtons on the PM loss supeposton. III. 6 SURPLUS COEICIENT OR LOSSES AND ENERGIES We assume eddy cuent dsspaton as the only PM losses. Consequently, we take them as popotonal to squae of MM, ths popotonalty beng chaactezed by new loss coeffcent C (. o one sldng MM t wll be C T T 0 θ dθ dt ( wth θ - ntegaton aea of magnet s extent on oto ccumfeence. In case whee magnets cove two thds of each pole we get loss coeffcents coespondng to -6 and 6 In case of dffeent ampltudes of cuents I δi the composed MM s a sum of oscllatng and sldng components. The coespondng loss coeffcent can be epesented as C n I 6n δi n I δi 9 3n I ( I δi (δ wheeas the coeffcents of ndvdual losses ae n I 6n δi C C n I δi (4 Wth these coeffcents we can defne an analytc suplus paamete Δ a whch gves a measue of excess of losses calculated fo oscllatng MM n compason to sum of losses of ts two sldng components: 9 3n Δ a C [ C C ] ( I I δi (δ ( Except fo two postons of the oscllatng feld, the losses of the latte don t equal the sum of losses and supeposton method can gve eoneous esults. In ode to evaluate ths eo we ntoduce a elatve suplus coeffcent SC a, wth ndex a fo analytc : wth SC ( Δ a ( C C 3 3 (δ k 4 a _ I I I I (6 I I ΔI k ( I I ΔI 0.ΔI ( I I 0. I I It confms theoetcal assumpton that the sldng component, pesent n the composte M, lowes the suplus coeffcent. As a matte of fact, the peak value of k coesponds to puely oscllatng MM. The equaton ( suggests also that any ato I - /I gves the same coeffcent that ts nvese (g.. 6 n I 6 n I C _ and C (3 Both ae ndependent of the angle δ. Ths wll not be the case of loss coeffcent C chaactezng the oscllatng MM composed of -6 and 6.

5 g.. The loss suplus coeffcent s the same fo a gven cuents ato and fo ts nvese. Smulaton by E. Ampltude of the loss suplus SC vaes between % and % fo cuent ato between 4 and ; the eo of supeposton dmnshes when the oscllatng pat of MM becomes less. We can expect that f the magnet coves totally the oto suface, then the supeposton of losses geneated by sldng felds gves coect esults. The losses don t depend then on poston of oscllatng components. The E smulaton confms ths (g. 3. IV. INLUENCES O LOAD Load dependng cuents modeate ampltudes of analytc suplus paamete Δ a (. Actually, cuents se wth load, and so does the angle δ. The most dsspatng poston of oscllatng flux coesponds also to low, no-load value of cuents, wheeas wth δ nea 90,.e. n low dsspatng poston, cuents ae hgh. Losses ae obvously hghe n low dsspaton poston. Ths modeaton doesn t change the elatve suplus coeffcents SC. Beng developed fo the th and the th hamoncs, t can be easly calculated fo hghe fequences, lke th and 3 th, 9 th etc. V. CONCLUSION When locked oto method s appled to PM hamonc losses then the losses supeposton can deceve f adequate decomposton of feld nto sldng and oscllatng felds s not opeated. Eo of losses estmaton ses wth squae of MM, and so t s moe mpotant fo lage machnes. The poblem wll dsappea wth futue use-fendly E packages pemttng easy and effcent electo-dynamc modelng and smulaton of oto n movement and stato suppled wth non snusodal voltage. Ths, howeve, doesn t seem to be nea futue. VI. REERENCES g. 3 Wth magnets coveng /3 of the oto ccumfeence losses depend on poston of oscllatng feld, wheeas wth oto entely coveed by magnets (/ they don t. Smulaton by E. [] T. Hekkla, Pemanent magnet synchonous moto fo ndustal nvete applcatons analyss and desgn, PhD dssetaton, Lappeenanta Unvesty of Technology, nland, 00, avalable at : os.pdf [] J. Neg, M. Nemela, J. Pyhonen, J. Patanen, EM calculaton of oto losses n a dedum speed dect toque contolled PM synchonous moto at dffeent load condtons, IEEE Tans. on Magnetcs, vol. 38, no., Septembe 00, pp [3] C.C. M, G.R. Slemon, R. Bonet, Mnmzaton of on losses of pemanent magnet synchonous machnes, IEEE Tans. on Enegy Conveson, vol. 0, no., Mach 00, pp. -. [4] C. M, G.R. Slemon, R.Bonet, Modelng of on losses of pemanentmagnet synchonous motos, IEEE Tans. on Industal Applcatons, vol. 39, no. 3, May/June 003, pp [] Z.Y. Wang, Analyse et mesue de petes dans le oto d une machne synchone à amants pemanents pou en optmse la stuctue, PhD dssetaton, Supelec, ance, 00