Sensorless Speed and Position Control of Synchronous Machines using Alternating Carrier Injection

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1 Sensorless Speed nd Posiion Conrol of Synhronous Mhines using Alerning Crrier Injeion Mro Linke, Suden Member, Rlph Kennel, Senior Member, Johim Holz, Fellow Universiy of Wupperl Eleril mhines nd drives hp:// Absr High frequeny rrier injeion is promising pproh solving high performne sensorless drive demnds. Posiion onrol low nd zero speed is only possible using nisoropi effes onsidered in highfrequeny models. The usully open loop rrier signl injeion is imped by nonliner inverer properies like he ded-ime effe. This pper disusses he influene of he ded ime effe on he rrier signl exiion ompring lerning nd revolving injeion priniples. To overome disurbing effes n lerning injeion proedure is proposed using predefined injeion ngle. The pproh redues he effes of he inverer disorion volges. As resul i is possible o rk even smll slienies ypil for surfe mouned permnen mgne synhronous mhines. For proessing he high frequeny urren for posiion esimion, here is no ddiionl hrdwre neessry wihin sndrd drives wih field oriened onrol. The pper presens heoreil nlysis nd experimenl resuls. Index erms sensorless posiion onrol, rrier injeion, ded-ime effe, I. INTRODUCTION I. A. High frequeny rrier injeion Severl proposls hve been mde o use esimion lgorihms for speed deeion nd even for posiion deeion of synhronous mhines low nd zero speeds. Ppers reenly published indie high frequeny injeion mehods beoming more nd more rive [1, 4, 5]. In Surfe Mouned Permnen Mgne Synhronous Mhines (SMPMSM he slienies re smll, beuse he mgnes re disribued rher homogenously on he surfe of he roor. Therefore injeion mehods usully re no pplied o his ype of mhines. These mhines, however, provide smll moun of nisoropy produed by surion of he min flux. This pper desribes high-frequeny injeion sheme o onrol speed nd posiion in Surfe Mouned Permnen Mgne Synhronous Mhines espeilly low sor frequeny nd even sndsill. The high-frequeny es signl is onrolled o be in lignmen wih he nisoropy of he roor - in his se wih he slieny indued by surion - resuling in n mpliude moduled spe veor. A synhronous rking sheme evlues he nisoropy his onep voids omplex demodulion lgorihms whih re sensiive o vriions of mhine prmeers nd ddiionl slienies negleed by he model. The inverer ded-ime effe represens he mjor rrier signl disorion. In hper V hese highly nonliner effes re disussed. In revolving rrier sysems n ellipil rrier volge disorion n be observed leding o misinerpreions of he ul nisoropi mhine properies refleed in he rrier urren. For lerning rrier injeion shemes vriion of he rrier injeion ngle hs been nlyzed o overome he inverer ded-ime effe, whih hs srong imp on he high frequeny rrier signl exiion. The pproh bses on reduing he inverer disorions volges by using he orhogonl esimion xis. I. B. Alerning high frequeny rrier injeion shemes Alerning rrier injeion shemes re ble o rk relibly even smll nisoropies. In differenes o revolving rrier injeion shemes he lerning rrier mehods re ble o deouple differen slieny effes. This is due o he orienion of he orhogonl esimion xis ording o he slieny ligned exiion xis [7]. The pproh in [7] uses so-lled in phse omponen isolor (sepring he nisoropy informion. An djusing proedure is suggesed o ompense he degrding demodulion performne wih inresing rrier phse lgs due o inuries of he inverer nd mesuring equipmen. In differene o [7] he mehod presened in his pper proposed phse sensiive reifier inorporing ddiionlly d- xis urren informion o proess n (online minimized esimion error ngle. Alerning rrier injeion wih displemen of π/4 wih respe o he slieny xis [4], suffers from inverer rrier volge hrmonis genered by he ded ime effe. This effe n be explined by nlysing he urren rjeory rnsiion beween wo swihing seors.

2 II. ALTERNATING CARRIER INJECTION PRINCIPLE The phse ngle of n lerning rrier volge veor u is kep in lignmen wih he esimed d-xis in he dq-roor referene frme (Fig. 1. As onsequene, he modulion hs lmos no effe on he orque produing urren omponen in he q-xis [11]. jq sor jq mgnes III. ESTIMATIN OF THE ANISOTROPY The new mehod generes posiive s well s negive urren sequene omponen, boh onining informion bou he roor posiion. The injeed rrier volge (S jδˆ u = u os ( ω e (3.1 is lwys in lignmen wih he esimed posiion of he nisoropy (esimed vlues re mrked wih h ^: Bsed on his pproh he superimposed rrier signl n be desribed in sor oordines s follows (S jωˆ ( e u = u os ω. (2.1 The rrier frequeny ω is hosen round 2 khz o obin fs response nd o void inerion wih he urren onrol loop. As long s he esimed roor posiion oinides wih he rel roor posiion δ he es signl is omposiion of wo high frequeny es signls s used in onvenionl highfrequeny injeion mehods [2] bu roing in direions opposie o eh oher. As resul only he d-xis is exied by he rrier. The resuling high-frequeny urren i (response of he eleromgnei iruis o he injeion volge u is lso in lignmen wih he min flux. Like he volge he urren n be lso deomposed o posiive nd negive sequene omponen, i - nd i + respeively (Fig. 1. The mpliude of i vries sinusoidlly wih ime. A smll mislignmen beween he rel nd he esimed roor posiion produes n ddiionl high frequeny omponen - j(δˆ δ [ ld + ( lq - ld e ] ( δˆ = sin( ω ldlq i u + u - u ω ω d ω u = u os ( ω Fig.1: Resuling urren signl i s moduled spe veors in roor oordines (2.2 whih n be deeed o feed roor slieny rking lgorihm whih is sensiive even o he smll nisoropies of SMPMSMs [11]. The urren signl (2.2 is no used o esime he roor posiion by lulions. I serves s n error signl h is minimized by he rking sheme in he nex smpling yle. roor ω i - ψ m i This offers n effeive wy o demodule he roor posiion informion. The sin-funion from (3.5 behves proporiond ω δ ˆ = ωˆ. (3.2 The nisoropy in SMPMSM is minly bsed on he surion effe of he min flux; i roes wih he sme frequeny ω s he roor. In differene o he field oriened sysem he subsrip generlly indies n nisoropyligned oordine sysem. Boh oinide in he se of surfe mouned PMSM. A rnsformion of he rrier volge o field oordines is done by muliplying equion (3.1 by e -jδ. This leds o (F j( δ δ ˆ u = u os ( ω e. (3.3 The differenil sor equion n be represened s follows: (F (F j( δ δ ˆ (F d i u = u os ( ω e = lσ (3.4 d Sor resisne, indued volge nd ross oupling of he urrens re negleed in he differenil sor equion [11]. This is only permied if he rrier frequeny ω is muh higher hn he fundmenl frequeny. The rel field ngle δ is he unknown vrible in his equion. The soluion in field oordines of (3.4 is (F u 1 1 i = sin ω os( δˆ δ + j sin( δˆ δ. (3.5 ω lσd lσq Equion 3.5 n be disussed s follows: he rrier urren mpliude i inreses proporionlly o he rrier volge u nd dereses wih inresing rrier frequeny. Moreover, he rrier urren omponen i q is direly proporionl o he ngle error δ.

3 lly o he ngle error δ. Hene, he nex proessing yle is used o orre he direion of rrier signl. IV. SENORLESS CONTROL APPROCH IV. A. Demodulion of he rrier urren Using high frequeny injeion mehods for sensorless onrol, he signl demodulion lgorihm requires high performne in signl proessing. To redue he lulion effor, he high-frequeny urren i (3.5 is rnsferred o referene frme in negive direion pproxime rrier frequeny. This is done by ( ω+δˆ (S -j( ω+ δˆ i = i e (4.1 This rnsformion generes high frequeny urren signl h is esy o demodule wihou referring o mhine prmeers. Assuming he remining negive sequene urren omponens of i re rejeed by low pss filer, rnsformion (4.1 pplied o he urren signls (3.5 resuls in ( lσd + lσq ( ω +δˆ 1 i = p u ω j(2δ-2δˆ j4 lσd lσq. (4.2 ( lσd lσq e I n esily be sepred beuse i is rnsformed by (4.1 o bou wie he rrier frequeny. Equion 4.2 illusres he urren response onining he useful informion bou he mislignmen of he esimed field ngle wih referene o he rel field ngle. I is used s n error esimion ngle δ = δ δˆ. (4.3 The urren response is furher simplified o redue proessing power neessry for demodulion. In he se of smll error esimion ngles he urren response is: - j( σ + ( ω +δˆ 1 l d lσq i p = u (4.4 4 ω lσd lσq ( lσd lσq 2 δ This equion shows he rel omponen of he urren response in he referene frme ording o (4.1 being proporionl o he error ngle δ. This is used o rk he field ngle by losed loop rking sysem (Fig. 2. Fig.2: Signl flow grph of he field ngle esimion sheme bsed on he proposed mehod IV. B. Sensorless posiion onrol of SMPMSM As disussed in hper IV.A, high sophisied demodulion of he rrier response n be repled by rking he error esimion signl (4.3. I is possible o genere lulion quniy represening he mislignmen δ beween he esimed field ngle nd is rel vlue, (4.4. Trking n error signl is robus gins noise nd mesuremen olernes e.g. he limied resoluion of nlog o digil onverers in drive onrollers. As he esimed field error ngle δ is evlued in he proposed mehod insed of he bsolue field ngle iself, he resoluion of he high frequeny urren signl i is less riil. Furhermore, he error signl δ is hnging only slowly in omprison o he smple frequeny. The signl flow grph in Figure 2 illusres he bsruure of he proposed sensorless sheme. The posiive sequene urren hs rel omponen proporionl o he error ngle δ (4.4. This signl is smpled wih he smpling frequeny of he urren onrol loop. The following PIonroller feeds onrolled osillor o ree he esimed field ngle. This resuls in losed loop sruure h orres he field ngle sepwise by eh smpling yle. Hene, high smpling frequeny ensures good nd dynmil fs lignmen wih field xis. The disurbnes of he quired signl re low, hus permiing operion low rrier mpliudes. The prominen dvnge is he rking observer no depending on ny mhine prmeers. To esblish nrrow filer hrerisis, he urren i (Fig. 2 is rnsformed o he esimed field oordine sysem by ( δˆ (S -j( δˆ i = i e. (4.5 This rnsformion resuls only in urren omponens of rrier frequeny ω. This llows using nrrow bnd filers h rejeing ll frequenies exep he rrier frequeny, whih is essenil o esime smll slienies.

4 IV. C. Experimenl resuls The experimenl resuls re obined using ommeril 6- pole SMPMSM servo drive wih 1.2 kw red power. The esimed posiion δˆ is used s feedbk signl for field oriened onrol. The enrl rk of he digrm in Figure 3 represens he posiion error ˆ δ beween he mesured posiion δ nd he esimed posiion δˆ (inresed sle. The swihing frequeny is 8 khz, he rrier frequeny is 2 khz wih pek rrier urren i,.mx of 2 ma. The urren is proessed using he sme 12-Bi A/D onverer lso used for sensing he fundmenl urrens. π -π π/1 π -π -π/ ms Fig. 3: Experimenl resuls: roor posiion δ nd orresponding esimed vribles δˆ, ˆ δ V. DEAD-TIME EFFECT ON CARRIER EXICITATION V.A. Modeling of he Ded-ime effe The mjor disorions of he inverer oupu re used by n inerlok ime T d, prevening emporry shor irui of he DC link when using volge soure inverer. The inerlok ime T d is ypilly higher hn he urn off ime of he individul IGBT. During he inerlok ime he upper nd lower power swihes re urned off, herefore eh hlf bridge oupu poenil is deermined by he se of he freewheeling diodes nd hene by he polriy of he lod urren [6]. This siuion is vlid for fundmenl sor urrens s well s for high frequeny rrier urrens. jim S 3 S 2 δ δ δ Figure 4 shows six disorion volge veors S i loed in omplex plne ording o he sor urren [6]. I n be seen h eh error volge hve he sme mpliude bu hey re displed o eh oher by 6 degrees phse ngle. The six seors deermine he pproprie error volge phse ngle by 1 2 [ sign( i + sign( i + sign( i ] 2 se ( is = s sb s. (5.1 3 The vribles,,b, re he respeive sor phse urrens, = e j2π/3 is he veor roor nd sign represens he polriy of he respeive phse urren ( deiled desripion of his sheme n be found in [6]. This jusifies he definiion of omplex error volge veor. u er Td Toff = se( is = u se( is (5.2 T The normlized error volge veor u er is nonliner funion of he sor urren nd is minly proporionl o he effeive IGBT off-ses T d T off [6]. The six error volges resul in sixh hrmoni of he sor urren. V.B. Disorion of roing Crrier Injeion The revolving rrier exiion represens widely known mehod of sensorless onrol [2]. Usully ll high frequeny rrier mehods re rrnged s n open loop injeion sheme, ssuming inverer lineriy. The disorion phenomen used by he inverer ded-ime is normlly negleed, lhough i n led o serious problems [1]. The fundmenl disorion model disussed bove is lso vlid for high frequeny injeion. However he influene on he rrier signl is differen o he influene on he fundmenl ses. The high frequeny seor rnsiion, inheren o his signl lss, led o high hrmoni error volges u er u s seor S 4 seor 4 seor 5 S 5 S 6 se( S 1 Fig.4: Definiion of he six disorion volge veors S i ording o eh sor urren seor Re α= b α=2 Fig.5: Sor volge u s nd urren rjeory, pplying roing rrier volge u = u e nd jω onsn fundmenl volge u jα s1 = us1e (simulion

5 For symmeril resons he following disussion is foused on seor one nd wo only. All experimenl resuls in his hper re ken using n isoropi mhine. Therefore hey solely presen he undesired modulion effe of he inverer nonlineriy wihou ny imp of he oher effes. i,β,α 2 ma -2 ma 2 A Figure. 5 presens he sor nd volge rjeory inorporing he ded ime-effe, s ypilly presen in sensorless rrier mehods. The usully lrger nd slowly vrying fundmenl urren, is emuled (for illusrion purposes s onsn DC urren wih predefined sor ngle. The superposiion of smll high frequeny rrier urren nd lrge fundmenl urren leds o hrerisil seor rnsiions. The high frequeny volge veor u is superimposed o he fundmenl one, resuling in high frequeny urren rjeory i shown by he fundmenl DC urren summing up o he sor urren (see Fig 5. i,α -2 A 2 ma -2 ma ms α=3 b α=4 Fig.7: Mesured disorions of he filered rrier urren omponens i α i β resuling from he ded-ime effe, (f s = 6 khz, T d =5 µs u s lion effe of he rrier volge rjeory u is visible. I depends direly on he high frequeny urren rnsiion nd is srongly nonliner. Therefore he mximum influene beween boh seors n be expeed 3 degrees fundmenl urren ngle As he high frequeny urren ouhes he seor boundry defined in Fig. 4, he high frequeny volge ges disored by n error volge u er (see Fig. 5b. The error volge is deduible onsidering equion (5.1. A srong ellipil modu- β 18 α=3 b α=4 Fig.6: Sor volge nd urren rjeory u s,, pplying roing rrier volge u = u e nd jω fundmenl onsn volge u jα s1 = us1e (simulion Figure 6 poins ou he ellipil modulion effe onsidering he fundmenl urren phse ngles α of 3 nd 4 degrees. The mximum rrier volge disorion kes ple 3 degrees fundmenl urren phse ngle s expeed. Consequenly he ellipil rrier disorion bses on n error volge u er wih rrier frequeny ω, hene no eliminble by ny filer. Figure 7 illusres he onsequenes of disored rrier volge rjeory (inresed ded-ime for beer illusrion. The rrier urren ges moduled ylilly whenever one of he fundmenl phse urren omponens psses zero. This modulion effe is hrdly seprble from desired nisoropi mhine modulion effes beuse of he frequeny sper re very lose ogeher. β seor 3 seor 2 q seor 3 seor 2 q S 3 S 2 i ϕ inj = π /2 S 3 S 2 i ϕ inj = π/3,1 d,1 d S 1 α S 1 α seor 1 seor 1 injeion ngle ϕ inj = π/2 b injeion ngle ϕ inj = π/3 Fig. 8: High frequeny rrier urren rnsiion during seor hnges wih differen injeion ngles ϕ inj ording o he fundmenl sor urren 1

6 V.C. Disorion of lerning rrier injeion Smll slienies require highly sensiive esimion mehod, whih mus be robus gins prsii nisoropies like inverer lmping effes. Resuls shown below mke ler h he orienion of he injeed lerning volge ording o [11] provides n imporn ddiionl degree of freedom. This n be undersood by sudying he seor hnge in Fig. 8. The ded ime effe generes six differen error volge veors S 1 -S 6 depending on he ul sor urren. Regrding seor 1 nd 2 s n exmple, i is obvious, h he high frequeny lerning urren rjeory deermines high frequeny error veor rnsiion during he seor hnge (Fig. 8. The urren rjeory, however, depends direly on he injeion ngle ϕ inj of he high frequeny signl ording o he fundmenl urren 1. This resuls in n lerning high frequeny volge disorion signl wih rrier frequeny. In he se of Fig. 8 he error volge u er n be deomposed ino onsn DC-volge erm ording o he men vlue of boh disorion volges S 1,S 2 (negleing he vriion of he DC-erm during one fundmenl period nd he lerning erm ( rrier frequeny ording o he differene of S 1,S 2. S S1 + S 2 S1 S ( 2 er = u + re( ω ( u Wih respe o is frequeny he lerning erm (re is no seprble by filers. Therefore he imp on he rrier signl n be redued only under he following hree ondiions: minimizing he inverer inerlok ime minimizing he rnsiion ime beween wo seors properly used rrier injeion ngle ϕ inj The firs wo mehods re no under he onrol of he design engineer nd herefore obviously less pplible. The ls poin n be used o deermine predefined injeion ngle ϕ inj o minimize he imp of he disorion volge u er. The disorion volge observed in synhronous dqreferene frme s in Fig. 8 depends on he injeion ngle ϕ inj nd n be luled ording o (5.3 by veor rnsformion. Fig. 9 illusres he volge disorion in he d- nd q-omponen differen injeion ngles. I is imporn o relise h here exiss periodilly moduled q-xis rrier volge u q even when he high rrier exiion is injeed in he d-xis only. The disorion volge omponen u err,q is srongly inresed depending on he injeion ngle. A orre high frequeny rrier urren response i,q moduled by mhine nisoropies n herefore only be expeed for undisored volge rrier omponens u q. This is nerly gurneed for n injeion ngle of α, sβ u q α, sβ u q 2.5 A 3 V - 3 V 6 V - 6 V A 2.5 A 3 V - 3 V 6 V - 6 V A ms Injeion ngle ϕinj= π/2 The disorion effe of he error volge u er influenes he rrier volge omponens u q, u d depending on he inje ms b injeion ngle ϕinj = π/3 Fig. 9: Disorion of he high frequeny rrier volge omponens u q, u d during one fundmenl period (due he inverer ded ime effe differen injeion ngles ϕ inj (simulion ϕ inj = π/2. (Crrier exiion wih he injeion ngle ϕ inj = heoreilly lso resuls in minimum disorion. Bu experimens onfirm h his n hrdly be relized. i,q,α i,β 2 ma -2 ma 2 A -2 A 2 ma -2 ma ms Fig.1: Mesured disorions of he filered rrier urren omponens i d i q resuling from he ded-ime effe, (f s = 6 khz, T d =5 µs, ϕ inj = π/2

7 ion ngle. However, he relive disorion of he d- omponen is very smll beuse i oinides wih he min exiion direion. The q-omponen, generlly used for nisoropi mhine idenifiion, is highly sensiive o volge disorions. Therefore disorions used by inverer nonlineriies should be voided in his xis by mens of proper injeion ngles ϕ inj. Figure 1 onfirms he heoreil resuls onerning he minimum disorion effe in he q-omponen using n injeion ngle of ϕ inj = π/2. Even hough here is modulion of he d- rrier urren he q-rrier urren remins nerly unffeed. Under lod ondiions he fundmenl mhine urren is perpendiulr o he min field (no field wekening nd he rrier urren is ligned wih he min field xis. Therefore he injeion ngle is lose o π/2. Hene he proessed q- rrier urren i q (Fig. 2 is lmos no ffeed by he inverer ded ime effe. This siuion provides high ury in roor posiion esimion visulised in Figure 3. VI. CONCLUSION This pper presens n improved sensorless onrol lgorihm for Surfe Mouned Permnen Mgne Synhronous Mhines using high-frequeny volge injeion. The mehod is suible for relune mhines nd permnen mgne mhines wih buried mgnes, bu i is espeilly designed o rk smll slienies nd o dee he smll differenes in roor nisoropy provided by synhronous moors wih surfe mouned permnen mgnes. The posiion esimion mehod is independen of mhine prmeers s only posiion error is esimed by rking sheme. Speil enion is given o he inverer nonlineriies ffeing he rrier signl. Hene speil injeion sheme using predefined injeion ngles is suggesed. This resuls in minimum rrier disorion wih referene o he orhogonl esimion xis. Experimenl resuls verify inverer nonlineriies being minimized by proper hoie of he injeion ngle. REFERENCES 1. J. Holz, Sensorless Posiion Conrol of Induion Moors - n Emerging Tehnology, IEEE Trnsions on Indusril Eleronis, Vol. 45, No. 6, Deember Rober D. Lorenz, Sensorless Drive Conrol Mehods for Sble, High Performne, Zero Speed Operion, Inernionl Conferene on Power Eleronis nd Moion Conrol- EPE-PEMC, Kosie J.K H, S.K. Sul, K. Ide, I. Muroki, K. Swmur, Physil Undersnding of High Frequeny Injeion Mehod o Sensorless Drives of n Induion Mhine, IEEE-IAS 2, Conferene Reord of he 2 IEEE Ind. Appl. Conferene, Vol.4 4. J.K. H, S.K. Sul, Sensorless Field-Orienion Conrol of n Induion Mhine by High-Frequeny Signl Injeion, IEEE Trn. On Ind. Appl., Vol. 35. No.1, Jn./Feb A.Consoli, F. Russo, A. Tes, Low- nd Zero-Speed Sensorless Conrol of Synhronus Relune Moors, IEEE Trns. On Ind. Appl., Vol.35, No.5, Sep./O. 1999,pp J. Holz: Pulsewidh Modulion for Power Converers, Proeedings of he IEEE, Vol. 82, No. 8, Aug. 1994, pp P.L. Jnsen, Sensorless Roor Trking of Induion Mhines wih Asymmeril Roor Resisne, Pen Number: 6,1237,258, My 3, 2, USA, 8. L.A.S. Ribeiro, M.W. Degner, F. Briz, nd R.D. Lorenz, Compring Crrier Frequeny Curren nd Volge Injeion for he Esimion of Flux, Posiion, nd Veloiy in Sensorless AC Drives, Proeedings of IEEE-IAS Conf., O , 1998, S. Louis, pp N. Teske, G. M. Asher, M. Sumner, nd K. J. Brdley: Suppression of Surion Slieny Effes for he Sensorless Posiion Conrol of Induion Moor Drives under Loded Condiions, IEEE Trnsions on Indusril Eleronis, vol. 47, no. 5, pp , O N. Teske, G. M. Asher, K. J. Brdley, nd M. Sumner: Anlysis nd Suppression of Inverer Clmping Slieny in Sensorless Posiion Conrolled Induion Mhine Drives, Conf. Re. IEEE-IAS Annul Meeing, no. 36, Chigo, USA, Sep./O M. Linke, R. Kennel, J. Holz: Sensorless posiion onrol of Permnen Mgne Synhronous Mhines wihou Limiion Zero Speed, 28h Annul Conferene of he IEEE Indusril Eleronis Soiey IECON 2, Sevill/Spin, Nov. 5-8, 22.