This is a repository copy of Online Control of IPMSM Drives for Traction Applications Considering Machine Parameter and Inverter Nonlinearities.

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1 Ths s a repostory copy of Onlne Control of IPMSM Drves for Tracton Applcatons Conserng Machne Parameter an Inverter Nonlneartes. Whte Rose Research Onlne URL for ths paper: Verson: Accepte Verson Artcle: Hoang, K.D. an Aorth, H.K.A. (2015) Onlne Control of IPMSM Drves for Tracton Applcatons Conserng Machne Parameter an Inverter Nonlneartes. IEEE Transactons on Transportaton Electrfcaton, 1 (4) ISSN Reuse Unless ncate otherwse, fulltext tems are protecte by copyrght wth all rghts reserve. The copyrght excepton n secton 29 of the Copyrght, Desgns an Patents Act 1988 allows the makng of a sngle copy solely for the purpose of non-commercal research or prvate stuy wthn the lmts of far ealng. The publsher or other rghts-holer may allow further reproucton an re-use of ths verson - refer to the Whte Rose Research Onlne recor for ths tem. Where recors entfy the publsher as the copyrght holer, users can verfy any specfc terms of use on the publsher s webste. Takeown If you conser content n Whte Rose Research Onlne to be n breach of UK law, please notfy us by emalng eprnts@whterose.ac.uk nclung the URL of the recor an the reason for the wthrawal reuest. eprnts@whterose.ac.uk

2 TTE-Reg R1 1 Onlne Control of IPMSM Drves for Tracton Applcatons Conserng Machne Parameter an Inverter Nonlneartes K. D. Hoang, Member, IEEE, an H. K A Aorth Abstract In ths paper, an onlne control metho of nteror permanent magnet synchronous machne (IPMSM) rves for tracton applcatons conserng machne parameter an nverter nonlneartes s presente. It s shown that the conventonal technue usng parameter nformaton nstantly extracte from premeasure parameter look-up tables (LUTs) only etermnes the local MTPA operatng pont assocate wth ths specfc parameter nformaton wthout evaluatng the global MTPA achevement. Therefore, global MTPA operaton may not be acheve for conventonal onlne control IPMSM rves wth extreme nonlnear machne parameters (e.g. short-pero overloa operatons). Thus, a moel-base correcton metho usng stator flux ajustment s propose for an onlne uasglobal MTPA achevement. It s also proven that n the fluxweakenng regon, ue to the nverter nonlneartes, a lower than expecte maxmum achevable torue for a emane spee an a hgher than expecte current magntue for a emane torue may be obtane. Hence, an nverter nonlnearty compensaton (INC) metho explotng the voltage feeback loop s ntrouce an ts avantages over the conventonal INC scheme are emonstrate. The propose onlne control metho s valate va measurements on a 10kW IPMSM. Inex Terms Dea-tme compensaton, flux-weakenng control, nteror permanent magnet synchronous machne, nverter nonlnearty, maxmum torue per ampere control. EMF FW FB FF INC INE IVD LPF LUT MTPA OVL PDC NOMENCLATURES Electro-motve force. Flux-weakenng. Feeback. Feeforwar. Inverter nonlnearty compensaton. Inverter nonlnearty effect. Inverter voltage rop. Low-pass flter. Look-up table. Maxmum torue per ampere. Overmoulaton voltage lmtaton. Pulse-base ea tme compensaton. K. D. Hoang s wth the Department of Electronc an Electrcal Engneerng, the Unversty of Sheffel, Sheffel S1 3JD U.K. (emal: k.hoang@sheffel.ac.uk; k..hoang@eee.org). H. K A Aorth was wth the Department of Electronc an Electrcal Engneerng, the Unversty of Sheffel, Sheffel S1 3JD U.K. She s now wth AECOM, Lees, U.K. (emal: hawaa_oryth@yahoo.com). SVM I Space vector moulaton. I. INTRODUCTION Nteror permanent magnet synchronous machnes (IPMSMs) are wely utlze n electrc tracton applcatons ue to ts hgh effcency an we fluxweakenng (FW) capablty [1]-[3]. However, IPMSM parameters are well-known for ther hghly nonlnear characterstcs ue to the magnetc saturaton an crosscouplng effects [4], [5]. Thus, a control technue conserng the machne parameter nonlneartes s essental for IPMSM rves employe for tracton applcatons where short-pero overloa operatons assocate wth extreme nonlnear machne parameters are typcally reure to prove the emane acceleraton or the clmbng capablty. Generally, the lterature n ths topc s very large. Snce torue control moe rves are often reure for tracton applcatons [1], [3], [6]-[9], IPMSM rve uner torue control moe [10]-[15] s the man focus of ths paper. Typcally, operaton of IPMSM rves can be categorze nto two moes [11]: the maxmum torue per ampere (MTPA) control n the low-spee regon to mnmze the machne copper losses; an the flux-weakenng (FW) control n the hgh-spee regon to mantan the emane voltage magntue at the voltage bounary assocate wth the DClnk voltage an the selecte moulaton technue, Fg. 1. Base on the emane torue, both the MTPA an the FW regons can be ve nto two subregons [2]: the contnuous subregon lmte by the rate contnuous current an the scontnuous subregon assocate wth the short-pero overloa operaton, Fg. 1. For IPMSM rves, the FW operaton can be acheve va two man technues: the feeforwar (FF)-base [10]-[13] an the feeback (FB)- base control schemes [14], [15]. In a FF-base FW control IPMSM rve, the FW operatng pont (ntersecton pont between a constant torue curve an a constant voltage curve, Fg. 1) s purposely efne from the emane torue an the achevable stator flux magntue uner a emane spee, Fg. 2. In a FB-base FW control IPMSM rve, for a emane torue, the FW operatng pont s automatcally etermne by ajustng the MTPA stator flux reference va a voltage FB loop to mantan the emane voltage at the hexagon bounary of an over-moulaton voltage lmtaton

3 TTE-Reg R1 2 Fg. 1. Operaton regons of IPMSM rves employe for tracton applcatons. Fg. 2. Typcal control schemes for IPMSM rves. FF-base FW control [10]-[13]. FB-base FW control [15]. (OVL) block, Fg. 2. Because of the unue ntersecton between a constant voltage curve an a constant torue curve, Fg. 1, the FW operaton s always acheve va ths voltage FB-base ajustment espte large parameter varatons [16]. Due to ths avantage, n ths paper, the FB-base FW control metho s consere for the teste IPMSM rve. In practce, for IPMSM rves wth machne parameter nonlneartes, preefne -axs current reference look-up tables (LUTs) compute offlne from the premeasure nonlnear machne parameters wth the emane torue or power along wth the emane stator flux magntue as ther nputs are often utlze [10]-[15], Fg. 2. Although the LUTbase metho s smple to be mplemente, t reures offlne teratve calculaton, an cannot conser the parameter msmatches an varatons [17], [18] urng ts operaton. In aton, the teratve computaton s always an extremely tme-consumng process. On the other han, onlne control technues for IPMSM rves wth nonlnear machne parameters were propose n [19]-[22] where the parameter nformaton s prove as an approxmate lnear functon of -axs current [19], premeasure nonlnear -axs stator flux lnkage LUTs [20] or premeasure nonlnear machne parameter LUTs usng measure -axs currents as ther nputs [21], [22]. In comparson wth the LUT-base metho, onlne control technue proves flexblty for onlne parameter estmaton an upate to enhance the rve system effcency [17], [18]. In the low-spee regon where a number of possble combnatons of -axs currents an ther relevant machne parameters can be employe for a emane torue as shown n Fg. 1, the MTPA operaton s often reure to mnmze machne copper losses. For a gven set of machne stator flux lnkage or parameter nformaton nstantly extracte from the premeasure LUTs, the Newton Raphson s metho was employe n [20], [22] an the Ferrar s metho was utlze n [21] for onlne mplementaton of the numercal MTPA solutons. It s note that for IPMSMs wth nonlnear parameters, each operatng pont n a constant torue curve shown n Fg. 1 s a combnaton of fve specfc values: axs currents, -axs nuctances, an permanent magnet (PM) flux lnkage. Thus, for a emane torue, the conventonal onlne methos n [20]-[22] only efne the local MTPA operatng pont (-axs current references) assocate wth the specfc parameter nformaton (-axs nuctances an PM flux lnkage) nstantly extracte from premeasure nonlnear LUTs. Wthout an teratve process whch s mpractcal to be mplemente onlne, these conventonal onlne methos o not have the capablty of evaluatng the global MTPA operatng pont for a emane torue. Bascally, the nonlnear characterstcs of IPMSMs parameters hghly epen on values of the -axs currents [4], [5]. In the contnuous operaton subregon assocate wth low-operatng currents, Fg. 1, where the nonlnear characterstcs are often not sgnfcantly hgh, the eulbrum operatng pont n the constant torue curve uner the conventonal onlne methos may be locate close to the global optmum operatng pont. Thus, n ths subregon, the global MTPA operaton may often be consere as acheve for the conventonal onlne metho [20]-[22]. However, n the scontnuous operaton subregon assocate wth hghoperatng currents where the IPMSM parameters are wellknown for ther extreme nonlnear characterstcs [4], [5], the global MTPA operaton may not be obtane for the conventonal onlne technue ue to ts ncapablty of evaluatng the global MTPA operatng pont. Therefore, an onlne correcton metho to mantan a uas-global MTPA achevement for onlne control IPMSM rves wth extreme nonlnear parameters s one subject of ths paper. On the other han, for smplcty, the nverter nonlnearty effects (INEs) [23]-[32] on IPMSM rves are often neglecte [10]-[15]. In the MTPA regon where the allowable voltage s stll suffcent for the current controllers to mantan the axs current references uner a emane torue, neglectng of the INEs oes not aversely affect the achevable torue whch s the man concern for tracton applcatons. However, n the FW regon where the machne voltage magntue s mantane at the eal hexagon bounary, Fg. 2, there s always a msmatch between the eal eman an the actual voltage apple to the teste machne ue to the INEs. Conseuently, both performance an effcency of the IPMSM rve n the FW regon may become eterorate. Varous compensaton solutons for the INEs on electrc rve systems n the low-spee regon have been suggeste [23]-[32].

4 TTE-Reg R1 3 However, stuy of the INEs on FB-base FW control IPMSM rves n the FW regon s ute lmte [33] an ths s another subject of ths paper. In ths paper, an onlne FB-base FW control metho of IPMSM rves for tracton applcatons uner torue control moe conserng machne parameter an nverter nonlneartes s presente. It s shown that the global MTPA operaton may not be acheve for conventonal onlne IPMSM rves wth extreme nonlnear machne parameters (e.g. n the scontnuous operaton subregon) ue to ts ncapablty of etermnng the global MTPA operatng pont. Therefore, a moel-base correcton metho usng stator flux ajustment to mantan the eulbrum operatng pont very close to the global MTPA pont for a uas-global MTPA achevement s suggeste an expermentally valate. It s also proven that n the FW regon where the machne voltage s regulate at the eal hexagon bounary va a voltage FB loop, ue to the INEs, a lower than expecte maxmum achevable torue for a emane spee an a hgher than expecte current magntue for a emane torue may be obtane. Thus, an nverter nonlnearty compensaton (INC) scheme explote the voltage FB loop ajustment s propose. Compare wth the prevous stuy [33], n ths paper, much more etal escrptons of the suggeste INC scheme are presente an ts avantages over the conventonal INC scheme [26]-[32] are emonstrate. II. ONLINE FB-BASED FW CONTROL OF IPMSM DRIVES WITH NONLINEAR PARAMETERS UNDER TORQUE CONTROL MODE A. Onlne Control for IPMSM Drves wth Nonlnear Machne Parameters uner Torue Control Moe The mathematcal moel of an IPMSM n the () reference frame can be expresse as follows [22]: ψ ψ s s v = R s ωψ e s + ; v = R s + ωψ e s + (1) t t ψ 2 2 = L + ψ ; ψ s = L ; ψ = ψ + ψ (2) s m s s s 3 Te = p [ ψ m + ( L L ) ] (3) 2 where v,,,, s,s, L, are the transforme () voltages, currents, stator flux-lnkages, an stator nuctances, respectvely; e s the electrcal rotor spee; R s s the stator resstance; m s the permanent magnet flux lnkage; s s the stator flux magntue; T e s the electromagnetc torue; an p s the pole-par number. In the low-spee operatng regon, for a emane torue, the MTPA control technue s often employe to mnmze the machne copper losses [22] Te 2Te ( L L ) MTPA + ψ mmtpa = 0 (4) 3p 3p In a FB-base FW control IPMSM rve [14], [15], the axs current references uner both the MTPA an the FW operatons are compute from the stator flux reference an the emane torue, Fg. 2. Substtutng (2) nto (3) an solvng leas to the mathematcal relatonshp between the - 2 axs current, the torue, an the stator flux magntue [33] a + a + a + a + a = (5) where a4 = L ( L L ), a3 = 2 L ( L L )(2 L L ) ψ, m a2 = [(2 L L ) + 2 L ( L L )] ψ ( L L ) ψ, (c) Fg. 3. Nonlnear parameters of teste IPMSM [22], [33]. L as a functon of an. L as a functon of an. (c) m as a functon of m s a = L L L L, ψm[(2 ) ψm ( ) ψs ] a0 = ψm [2 TL e / (3 p)] ψψ m s. Snce both (4) an (5) are 4 th orer polynomals, the Newton-Raphson teratve metho can be employe [22], [33]. After (4) an (5) have been solve, relevant MTPA for (4) an relevant for (5) can be erve va the torue euaton (3). However, the machne parameters n (1) to (5) of the teste IPMSM are hghly nonlnear an represente as functons of an for both L an L, an as a functon of for m, Fg. 3. These nonlnear parameters are obtane va fnte element stues an then expermentally valate by the measurement metho presente n [5]. It s note that the contnuous rate current of the teste IPMSM s 58.5(A) an the scontnuous maxmum current s 118(A) for 200% capablty of short-tme overloa operaton (see Table I n Secton IV for further etals). As can be seen n Fg. 3, the teste IPMSM s parameters become extreme nonlneartes n the

5 TTE-Reg R1 4 scontnuous operaton subregon (hgh-operatng currents). Conventonally, these nonlnear parameters can be store nto three separate LUTs wth measure an as the relevant nputs to prove the nstantaneous machne parameter nformaton [21], [22], [33]. B. Global MTPA Achevement Problem of Conventonal Onlne Control Technue Fg. 4. Constant torue curves of teste IPMSM. As a functon of an I m. As a functon of an s. By teratng the nonlnear parameters shown n Fg. 3 together wth relevant -axs currents, the teste IPMSM s constant torue curves as a functon of the current magntue I m an -axs current ; an as a functon of the stator flux magntue s an are respectvely llustrate n Fgs. 4 an 4. It s note that each operatng pont n a constant torue curve shown n Fg. 4 s a combnaton of fve specfc values:,, L (, ), L (, ), an m ( ). Base on Fg. 4, two general characterstcs of IPMSM wth parameter nonlneartes are outlne as follows Remark 1: For a emane torue n the low-spee regon, a number of possble combnatons of -axs currents together wth ther relevant machne parameters shown n Fg. 3 can be utlze, Fg. 4. Although only one unue combnaton can be employe to acheve the global MTPA operaton, current magntues of ths global MTPA pont an the other combnatons locatng n the small segment aroun ths global MTPA pont (name as MTPA small segment) are almost smlar (e.g. zoomng of the 70Nm MTPA small segment). If the operatng pont s mantane wthn ths MTPA small segment, a uas-global MTPA operaton wth ts current magntue s almost smlar to that of the actual global MTPA pont can be acheve. Smlar phenomenon can be foun n [5], [10], an [12] for IPMSMs wth nonlnear parameters where almost smlar maxmum achevable torue can be obtane for operatng ponts wth a constant current magntue an fferent current angles (.e. fferent -axs current components wth a constant current magntue) locate n the small segment aroun the global MTPA pont. Remark 2: Uner a emane torue, the reucton of the stator flux magntue va ncreasng of -axs current, Fg. 4, results n a parabolc trenlne for the current magntue of whch the mnmum pont s the global MTPA pont, Fg. 4. Thus, the flux reference varaton wthn the MTPA small segment results n almost smlar current magntue (e.g. zoomng of the 70Nm MTPA small segments). Ths phenomenon s smply base on the general emagnetzaton characterstc of IPMSMs. The conventonal onlne technue for IPMSMs wth nonlnear parameters uner torue control moe s llustrate n Fg. 5, [20]-[22], [33]. Frstly, base on the measure ( k 1) ( k 1) currents an (values n the prevous stage), the relevant parameters L ( k 1), L, an ψ ( k 1) are extracte ( k 1) from the parameter LUTs, Fg. 3. These values are employe to compute the relevant -axs current references MTPA, MTPA, an the stator flux reference magntue, ψ m smtpa, uner MTPA operaton for the emane torue, T e, usng (4). Then, the emane flux magntue reference ψ = ψ ψ, an T are use together wth L ( k 1), s smtpa ( k 1) L an e ( 1), an ψ k n (5) to calculate the current references m apple to the teste IPMSM n the next-stage. In the low-spee regon, MTPA ψ = 0 an therefore, =, an =. However, L, MTPA ( k 1) ( k 1) L ψ = ψ, s smtpa, an ψ ( k 1) m are the prevous-stage parameter nformaton. Both the current-stage an the next-stage parameter nformaton s stll unknown an may be fferent compare wth L ( k 1) ( 1), L k, ( 1) an ψ k m when applyng an to the teste IPMSM ue to the parameter nonlneartes. Actually, t s mpractcal for onlne control technues to etermne the global MTPA operatng pont for a emane torue va the teraton of entre parameters LUTs shown n Fg. 3 together wth ther relevant -axs currents ue to ts extremely tme-consumng process. Thus, wthout the capablty of etermnng the global MTPA operatng pont, the conventonal metho n Fg. 5 can only evaluate the local MTPA operatng pont assocate wth the set of machne parameters L ( k 1) ( k 1), L ( k 1), an ψ nstantly extracte from the premeasure LUTs. In practce, for a emane torue, evaluaton of the conventonal metho n Fg. 5 s mplemente wth fferent set of machne parameters assocate wth the varaton of -axs currents urng the transent pero untl an eulbrum operatng pont n the emane torue curve, Fg. 4, s obtane. For the contnuous subregon, Fg.1, where the parameter nonlnear m

6 TTE-Reg R1 5 Fg. 5. Onlne torue control for IPMSM rves wth nonlnear parameters. Conventonal MTPA control metho. Propose MTPA correcton metho. characterstcs are often not sgnfcantly hgh, Fg. 3, ths eulbrum operatng pont may be locate close to the global MTPA operatng pont. Therefore, n ths subregon, the global MTPA operaton may be often consere as acheve [20]- [22]. However, n the scontnuous subregon, Fg. 1, where IPMSMs are well-known for ther extreme nonlnear characterstcs, Fg. 3, the global MTPA operaton may not be obtane. To emonstrate ths phenomenon, measure results of the teste IPMSM (35.5/70Nm contnuous/scontnuous peak torue, see Secton IV for further results) uner the conventonal onlne control metho, Fg. 5, are also presente n Fgs. 4 an 4. As can be seen, uner shortpero overloa emane torues (T e > 35.5Nm) assocate wth extreme nonlnear parameters, Fg. 3, ts eulbrum operatng ponts are stuate away from the MTPA operaton curve. On the other han, t s obvous n Fg. 4 that when the operatng pont uner a emane torue s not stuate n the MTPA operaton curve, f the stator flux magntue s ajuste along the emane torue curve towar the MTPA small segment an then mantane wthn t, a uas-global MTPA operaton can be acheve. Base on ths prncple an the two aforementone general characterstcs of IPMSMs wth parameter nonlneartes, a MTPA correcton metho s propose, Fg. 5. C. Propose MTPA Correcton Metho for Onlne Control Technue In Fg. 5, frstly, base on the conventonal metho, the ( 1) relevant parameters L k ( k 1), L ( 1), an ψ k of the measure currents ( k 1) an ( k 1) m are extracte from the parameter LUTs an employe to compute the relevant local MTPA references 1, 1, an ψ s1 for the emane torue T e va (4). Then, 1 an 1 are utlze to extract relevant precte L, 1 L 1, an are employe together wth normal current magntue, ψ m1 from the parameter LUTs. These values ψ s1 an T e n (5) to prect the I mno, obtane when applyng ( 1 1 ) to the teste IPMSM. Next, ψ s1 s respectvely reuce an ncrease by a small value (1% n ths stuy) to obtan ψ = (1 εψ ) an ψ s2 s1 = (1 + εψ ). After that, ψ an ψ s3 s1 are respectvely utlze together wth L, ( k 1) ( k 1) L to compute the relevant current references ( 2, 3 ) for s2, an ψ 2, s3 ( k 1) m ) an ( 3, T e va (5). Usng prevously escrbe technue, the precte current magntues applyng ( 2, 2 ) an ( 3, I mre an min 3 I obtane when ) to the teste IPMSM can be respectvely erve. Then, I mno, I mre, an I min (fltere by frst-orer LPF-see the next Secton) are compare together to efne the correctve value k c for the stator flux reference as shown n (6). If ψ = 0 KP( Im NO Im IN ) for ( Im NO > Im IN ) & ( Im NO < Im RE ) ( k ) kc = KP( Im RE Im NO ) for ( Im NO < Im IN ) & ( Im NO > Im RE ) ( k 1) kc for ( Im NO < Im IN ) & ( Im NO < Im RE ) If ψ > 0 ( k ) c =0 (6a) k (6b) Uner the propose correcton metho, the stator flux reference for the uas-global MTPA achevement s ajuste as ( k ) ψ = (1 + k ) ψ (7) smtpa c s1 Accorng to Fgs. 4 an 5, n the low-spee regon wth ψ = 0, the comparng result wth Im NO > Im IN an I mno < I ncates that the global MTPA operaton may not mre be acheve when applyng ( 1, 1 ) to the teste IPMSM as an ncrease of the stator flux reference magntue for the emane torue may result n a lower current magntue. Ths conton also mples that the operatng pont ( 1, 1 ) s locate on the left of the MTPA curve, Fg. 4. Thus, a ( k ) correctve value k = K ( I I ) > 0 s utlze n (7) to c P mno min ncrease the stator flux reference magntue an therefore, lea the operatng pont towar the MTPA curve. On the other

7 TTE-Reg R1 6 Fg. 6. Propose onlne control metho for IPMSM rves. han, the comparng result wth Im NO < Im IN an Im NO > Im RE shows that the global MTPA operaton may not be acheve by applyng ( 1, 1 ) to the teste IPMSM snce a reucton of the stator flux reference magntue for the emane torue may result n a lower current magntue. Ths conton also mples that the operatng pont ( 1, 1 ) s locate on the rght of the MTPA curve, Fg. 4. Hence, a correctve value ( k ) k = K ( I I ) < 0 s employe n (7) to reuce the c P mre mno stator flux reference magntue an therefore, rect the operatng pont towar the MTPA curve. Furthermore, the comparng result wth Im NO < Im IN an Im NO < Im RE ncates that the nstantaneous operatng pont s alreay locate n the MTPA small segment shown n Fg. 4 as both further ncreasng or reucng of the stator flux reference magntue for the emane torue may result n a hgher current magntue. Thus, the correctve value s kept as constant wth ( k) ( k 1) k = k for a uas-global MTPA achevement wth ts c c current magntue s almost smlar to that of the actual global MTPA pont, Fg. 4. In practce, values of K p an n Fg. 5 are selecte va a tral-an-error basc untl a mnmum current magntue for the peak scountnuous torue can be acheve. To obtan a smoothe value k c, a LPF s employe. It s note that the propose metho n Fg. 5 can also be consere for eal IPMSM rves wth constant parameters neglectng the nonlnear characterstcs. In the eal case, as the MTPA operaton s always acheve va solvng (4), the ( k ) propose correcton metho s mplemente wth k = 0. On the other han, when the FW operaton s actvate wth ψ > 0, the stator flux reference magntue s regulate by the voltage FB loop, Fg. 2, not the propose correcton ( k ) metho. Thus, k = 0 for ψ > 0 as shown n (6b). c D. Implementaton of Propose Onlne Control Metho for IPMSM Drves wth Nonlnear Parameters The propose onlne FB-base FW control scheme s presente n Fg. 6 where an are compute base on Fg. 5. For the PI current controller parameters, L AV an c L AV s respectvely the average - an -axs nuctance; c s the controller cut-off freuency selecte as two tmes of the teste IPMSM s maxmum spee (4500rpm). Base on the Space Vector Lmt (SVL) technue [34], an OVL block s utlze to keep the voltage reference magntue V αβ wthn the hexagon bounary assocate wth the measure DC-lnk voltage value, Fg. 7. Frstly, the voltage reference vector V = v + jv s converte from the ( ) to the (xy) reference αβ α β frame to obtan V xy, usng (8). j xy xy x j y αβ V = v + v = V e θ ; θ = [1 + 2( S 1)]( π / 6) (8) where S s the sector n whch V αβ s locate, Fg. 7. If v > ( V / 3), x c Fg. 7. OVL metho. SVL technue [34]. Eulbrum voltage loc lmte by OVL block uner fferent torue emans n FW regon. xy V xy s lmte to V xy as follows V = v + j v = ( V / 3)[1 + j( v / v )] (9) xy x y c y x Then, V xy s transferre back to the ( ) reference frame va (10) to prove the output voltage reference vector of the OVL block, V αβ. When the nput vector j xy αβ α j β xy V = v + v = V e θ (10) V αβ of the OVL block partly locates outse the hexagon bounary [ash-lne segment a 1 -b 1 of the locus C 1 n Fg. 7], the output vector V αβ of the OVL block s lmte at the straght-lne a 1 -b 1 n the hexagon bounary va

8 TTE-Reg R1 7 (8) to (10). In the eal case, V αβ an the voltage apple to the machne va the SVM block n Fg. 6 are entcal. In the low-spee regon, the OVL block s not actvate an the IPMSM rve s operate uner the propose MTPA control metho, Fg. 5. When the operatng spee s ncrease, the voltage magntue V αβ s ncrease accorngly untl the OVL block s actvate. Conseuently, the magntue fference between V αβ an V αβ (fltere by frst-orer LPF wth cut-off freuency as c ) s utlze to generate a stator flux FB reference usng the voltage FB loop as shown n Fg. 6 where a lmter s employe to mantan a postve FB value ( ψ 0 ). The voltage FB controller gans are obtane va a tral-an-error basc. Uner the voltage FB loop ajustment, the stator flux reference ψ s s regulate usng (11) untl a new eulbrum voltage reference locus mantane at the OVL hexagon bounary s obtane. As a result, the FW operaton s automatcally acheve. ψ = ψ ψ (11) s smtpa In Fg. 7, the ash crcle s the nput an the sol locus s the eulbrum output of the OVL block for a emane torue n the FW regon. Uner a emane spee, the voltage reference crcle s expane n accorance wth the ncrease of the emane torue untl ts locus s totally outse the crcumscrbe crcle of the hexagon bounary, e.g. the ash crcle C 3. III. INES ON IPMSM DRIVES AND PROPOSED COMPENSATION METHOD In practce, ue to the INEs nclung the ea-tme, the turn on/off elay-tme, an the nverter voltage rop (IVD) effects [23]-[32], there s always a msmatch between the eal eman an the actual voltage apple to the teste IPMSM. In ths secton, the INEs on IPMSM rves are stue an relevant compensaton methos are propose. A. INEs on IPMSM Drves 1) Dea-tme Effects on IPMSM Drves Bascally, a ea-tme tmng t D s necessary to be ntrouce at the rsng ege of the swtchng sgnals elvere to the two swtchng evces n an nverter leg for shotthrough preventon, Fg. 8, [23]-[32]. Ths ea-tme tmng, together wth the swtchng evce s turn-on elay tmng (t onde ) an turn-off elay tmng (t offde ) result n a eatme msmatch ( v a0de,b0de,c0de ) [23]-[32] between the eal reference ( v a0, b0, c0 ) an the actual phase-to-zero voltage (v a0,b0,c0 ) apple to the machne urng a samplng pero T s, (12). It s note that these effects only exst on the nverter leg performng swtchng operaton (e.g. wth phase-a: 0 < t aon < T s ). Dva0De v a0 va0 sgn( a ) a td + tonde toffde D v b0de = v b0 v b0 V c sgn( b ) = b (12) T s D v c0de v c0 v c0 sgn( c ) c Fg. 8. Dea-tme effects on phase-a. Ieal phase-to-zero voltage. Actual phase-to-zero voltage ue to ea-tme effects. Fg. 9. INEs on voltage apple to IPMSM rves n FW regon. Ieal case. Actual hexagon bounary an eulbrum voltage locus ue to INEs. 1 for 0 < tabcon,, < Ts where abc,, = 0 for ( tabcon,, == 0) or ( tabcon,, Ts) In practce, value of (t OnDe -t OffDe ) n (12) s very small compare wth t D an often neglecte. Durng tmng t D, the phase-to-zero nverter leg voltage epens on the current recton as shown n Fg. 8 for the phase-a leg (v a0 ). 2) IVD Effects on IPMSM Drves In the aforementone stuy of ea-tme effect, the nverter swtchng evces are consere to be eal. In practce, the nverter s nonlnear wth the nverter voltage rops (IVDs) [23]-[32], represente for one nverter leg by a forwar voltage rop, V F, connecte n seres wth an on-state resstance voltage rop, R ON [35] (for smplcty, the IVDs of the swtchng evce an the free-wheelng oe are assume to be smlar). For a balance IPMSM wth star-connecte wnng, the msmatch phase-to-neutral voltages n the ( ) reference frame, v IVD, IVD, ue to the IVD effects are presente n (13), [30]. It s note that values of v IVD, IVD epen on both the current value an the current recton.

9 TTE-Reg R D vanivd Dvα IVD v bnivd v =D β IVD (13) D 0 D v cnivd 2 2 DvanIVD a sgn( a ) VF where v bnivd R ON b sgn( b ) D = + 3 Dv cnivd c sgn( c ) 3) INEs on IPMSM Drves Base on (12) an (13), ue to the INEs, there s always a msmatch between the eal an the actual voltages apple to the IPMSM rves. In the MTPA regon where the allowable voltage s stll suffcent for the current controllers to mantan the -axs current references, neglectng of the INEs oes not aversely affect the achevable torue [26]-[32]. However, for the FB-base FW control rve n the FW regon, Fg. 6, ue to the INEs, a smaller actual hexagon bounary together wth a smaller eulbrum voltage locus apple to the teste IPMSM compare wth the eal cases are obtane, Fg. 9. Ths ssue results n a lower than expecte maxmum achevable torue for a emane spee an a hgher than expecte current magntue leang to extra copper losses for a emane torue. As a result, both performance an effcency of the IPMSM rve n the FW regon may become eterorate. B. Propose Inverter Nonlnearty Compensaton (INC) Metho for IPMSM Drves Bascally, the ea-tme effects can be mtgate by varyng the pulse tmng [23], mofyng the swtchng commutaton [24], or combnng of these two methos [25]. In the lowspee regon where the allowable voltage s stll suffcent, the full INEs can be compensate by ntroucng feeforwar (FF) correctve values represente for the average sturbance voltages ue to the INEs over one swtchng cycle nto the voltage references [26]-[32]. In practce, these correctve values are obtane from the off-lne measurement [26], the manufacturer atasheets [27], [28], or the onlne estmaton technues [29]-[32]. It s note that the stues n [23]-[32] were propose for machne rves n the low-spee regon. Due to the zero-current clamp effects [28] n the extreme lowspee regon, performances of the methos n [26]-[28] whch epen on the current recton nformaton may become eterorate. On the other han, the onlne estmaton technues o not rely on the nverter parameters an the current recton nformaton [29]-[32]. However, accurate machne parameter nformaton s essentally reure. In aton, the onlne technues are often base on the assumpton that the teste machnes are eal wth constant parameters an snusoal back-emf waveforms an therefore, the sturbance voltages an the current harmoncs are only contrbute by the INEs. In practce, ths assumpton may be nconsstent for IPMSM rves wth parameter nonlneartes; especally n the FW regon where the regulaton of the voltage magntue at the hexagon bounary also results n hgh voltage an hgh current stortons. Thus, Fg. 10. Compensaton for ea-tme effects.. Phase-to-zero voltage wth PDC scheme. Flowchart of mofe PDC scheme. Fg. 11. Compensaton for INEs. Conventonal FF-base INC metho. Propose FB-base INC metho. the onlne compensaton schemes for INEs may not be sutable for IPMSM rves n the FW regon. In ths paper, ue to ther fferent mpact levels: at swtchng pulse-level as shown n (12) an at funamental sgnal-level as presente n (13), the ea-tme an the IVD effects are compensate separately, Fgs. 10 an 11. Uner the propose nverter nonlnearty compensaton (INC) methos, Fg. 11, the correctve values for the IVD effects (V F an R ON ) n (13) are extracte from the manufacturer s atasheets. Frstly, t was proven n [23] that by accorngly varyng the pulse tmng t ON wth a value t D base on the phase current polarty at the begnnng of each moulaton pero, the mpacts of the ea-tme effects can be mtgate, Fg. 10. Ths metho name as Pulse-base Dea-tme Compensaton (PDC) was well emonstrate n the low-spee operaton regon. However, n the FW regon, there are swtchng peros when only one nverter leg performs swtchng operaton as scusse n [33], [36]-[38]. Thus, a mofe scheme s ntrouce n Fg. 10 to ensure that n the FW regon, the PDC metho s only mplemente on the nverter leg performng swtchng operaton.

10 TTE-Reg R1 9 In aton, uner well-known overmoulaton technues [36]-[38], when the voltage reference locus s only partly outse the hexagon bounary, Fg. 7, the remanng voltage allowances n the hexagon corners can be explote to ncrease the moulaton nex. Base on ths prncple, v IVD, IVD n (13) can be conventonally ae forwar to the relevant voltage reference components as shown n Fg. 11 (name as FF-base INC metho) [26]-[32] to ncrease the voltage magntue apple to the teste machne usng the remanng voltage allowances n the hexagon corners, Fg. 9, an therefore, mtgate the IVD effects. However, n a FB-base FW control rve, the FW operatng pont s automatcally etermne by the voltage FB loop as aforementone. Thus, a new metho name as FB-base INC scheme s presente n Fg. 11 where the IVD effects are mtgate by ntroucng v IVD, IVD n (13) nto the relevant voltage FB references. Unlke that uner the conventonal FF-base metho, the amene voltage references uner the propose FB-base INC metho are automatcally obtane va the voltage FB loop ajustment. Accorng to Fg. 6, as the new voltage FB reference magntue conserng the IVD effects,, s V αβ INC ncrease compare wth, the stator flux feeback V αβ ψ s reuce. Therefore, the stator flux reference ψ s s ncrease va (11) untl a new eulbrum voltage reference wth a larger locus s acheve. As a result, the IVD effects are mtgate. It s note that when the actual eulbrum voltage reference locus shown n Fg. 9 s fully outse the actual hexagon bounary, the remanng voltage allowances n the hexagon corners for mtgatng the IVD effects are completely explote. However, the separate ea-tme effect compensaton s stll achevable va the mofe PDC metho, Fgs. 10 an 11. IV. EXPERIMENTAL RESULTS The propose onlne control metho n Fg. 6 has been valate n a 5kW IPMSM esgne for tracton applcaton wth capablty of short-tme overloa up to 200% rate torue, Fg. 12, an ts parameters are shown n Table I [22], [33]. The teste IPMSM s couple to a ynamometer (AVL) va a 200Nm ratng n-lne torue transucer, Magtrol TMHS 312, for torue measurement. A magnetc encoer (Renshaw RM44SC0011B20F2F10) s employe to prove the rotor poston nformaton. The rve system s llustrate n Fg. 12 where the propose control algorthms are mplemente by a SPACE system, DS1005. The nverter s realze by an ntellgent power moule, Mtsubsh PM300CLA060, of whch the forwar voltage rop an onstate resstance obtane from the manufacturer s atasheet s 1.1V an 0.01Ω, respectvely. The ea-tme an swtchng freuency of the nverter s respectvely set as 3µs an 8kHz. Durng testng, the spee of the employe IPMSM s mantane by the ynamometer controller an ts emane torue s controlle va the SPACE Control Desk-Real Tme Interface tool n the MATLAB/Smulnk envronment. A (c) Fg. 12. Expermental harware setup [22], [33]. IPMSM couple to ynamometer va torue transucer. Inverter an SPACE control system platform. (c). Osclloscope an power analyzer. TABLE I TESTED IPMSM PARAMETERS [22], [33] DC lnk voltage Pole-pars / Phase resstance Base/maxmum spee Cont./Ds-cont. maxmum current Cont./Ds-cont. peak torue below base spee Cont./Ds-cont. peak power below base spee Peak power at maxmum spee 120(V) 3 / 51.2 (m ) 1350 / 4500 (rpm) 58.5 / 118 (A) 35.5 / 70 (Nm) 5 / 10 (kw) 7 (kw) precson power analyzer (Yokogawa WT3000, ±0.02% basc power accuracy) s use together wth the n-lne torue transucer to measure currents, voltages, torue, an effcences of the rve system, Fg. 12(c). All the measurements are mplemente n the steay state to ensure the accurateness. The measure voltage an current waveforms of the teste IPMSM rve uner the propose control methos for the MTPA (1200rpm, 60Nm) an the FW (4000rpm, 10Nm) operatons s respectvely shown n Fgs. 13 an 13. The moulaton nex values n Fg. 13 [ n Fg. 13 an n Fg. 13] were evaluate wth the actual DC-lnk voltage apple to the teste IPMSM conserng the INEs presente n (12) an (13). The teste IPMSM s fully operate n the FW regon wth entre torue range when ts operatng spee s aroun 1600rpm [22]. Snce the machne

11 TTE-Reg R1 10 Fg. 13. Measure results of teste IPMSM rve. MTPA operaton at 1200rpm, 60Nm. FW operaton at 4000rpm, 10Nm. voltage n the FW regon s regulate at the hexagon bounary, the current waveforms n Fg. 13 are sturbe an non-snusoal compare wth Fg. 13. To emonstrate the propose MTPA correcton metho, measurements of currents an relevant torues responng for step-up loa changes up to 70Nm of the teste onlne control IPMSM rve n the MTPA control regon (1200rpm) wthout an ncorporatng the propose correcton metho, Fgs. 5 an 5, are respectvely presente n Fgs. 14 an 14. Base on Fg. 14, a comparatve stuy on currents values, an I m, for the teste onlne control IPMSM rve wthout an ncorporatng the propose correcton metho are llustrate n Fgs. 15 an 15, respectvely. It s note that for a emane torue, each relevant operatng pont uner fferent control technues s a combnaton of relevant axs currents together wth a specfc set of relevant machne parameters n Fg. 3. These eulbrum operatng ponts are acheve va evaluaton of the employe control technue wth fferent set of machne parameters assocate wth the varaton of -axs currents urng the transent pero untl an eulbrum state s reache. As can be seen n Fgs. 14, 15, 15, an also alreay llustrate n Fg. 4, n the contnuous operaton subregon (T e < 35.5Nm) where machne parameter nonlneartes are not sgnfcantly hgh, uner the conventonal onlne metho, the eulbrum operatng ponts are stll stuate close to the global MTPA ponts. However, when the emane torue s ncrease up to the scontnuous operaton subregon (T e > 35.5Nm) assocate wth extreme nonlnear parameters, the eulbrum operatng ponts uner the conventonal onlne metho, ue to ts ncapablty of etermnng the global MTPA operatng pont, are stuate away from the MTPA operaton curve. On the other han, by ncorporatng the propose correcton metho, a uas-global MTPA operaton can be obtane for the teste onlne control IPMSM rve wth ts eulbrum operatng ponts are mantane very close to the global MTPA ponts n both contnuous an scontnuous operaton subregons, Fgs. 4, 14, 15, an 15. Demane currents assocate wth reure torues uner fferent control technues are presente n Table II where t s shown that the propose correcton scheme can acheve almost smlar current magntue for each emane torue as that wth the offlne LUT-base metho. For further emonstratng the effects of the propose correcton metho, the ncrease of copper losses n percentage of the teste onlne control IPMSM rve ue to not ncorporatng the propose technue s llustrate n Fg. 15(c). As can be seen, n the contnuous subregon where the machne parameter nonlneartes are not sgnfcantly hgh, the ncreases n the current magntues, Fg. 15, an the relevant ncrease n the copper losses, Fg. 15(c), ue to not ncorporatng the propose metho are conserably small (1.59% ncrease n the copper losses for 30Nm emane torue). Therefore, n the contnuous subregon, the global MTPA operaton s often be consere as acheve for the conventonal onlne methos [20]-[22]. Snce the eulbrum state uner the conventonal onlne metho wthout the capablty of etermnng the global MTPA operatng pont s only acheve n a ranom manner, the ncrease of copper losses n the contnuous subregon s vare for fferent emane torues, Fg. 15(c). On the other han, n the scontnuous subregon where the machne parameter characterstcs are extremely nonlnear, wthout ncorporatng the propose metho, effcency of the teste onlne control IPMSM rve may be sgnfcantly eterorate by up to 12.69% ncrease n the copper losses at 70Nm emane torue. Furthermore, measurements responng to step-up an step-own loa changes respectvely shown n Fgs. 14 an 14(c) also well emonstrate the ynamc performance of the onlne control metho ncorporatng the propose correcton scheme. In the FW regon, the man focus of ths paper s the compensaton for the INEs on the teste IPMSM rve usng

12 TTE-Reg R1 11 (c) Fg. 14. Measure results of teste IPMSM rve uner MTPA operaton at 1200rpm. Conventonal scheme, step-up torue response. Propose metho, step-up torue response. (c) Propose metho, step-own torue response. the propose FB-base INC metho. Thus, only selecte results are presente. Further results of the teste onlne control IPMSM rve can be foun n [22] an [33]. In Fgs. 16 an 16, t s respectvely shown that by ncorporatng the conventonal FF-base INC metho, Fg. 11, an the propose FB-base INC metho, Fg. 11, a lower current magntue for a emane torue at a emane spee compare wth neglectng INEs s obtane. On the other han, comparson between Fgs. 16 an 16 emonstrates the avantages of the propose FB-base INC metho over the conventonal FF-base INC metho n the FW regon wth a hgher achevable spee for a smlar torue an current magntue (e.g. at 10Nm, 85A),.e. a hgher achevable power for a smlar current magntue. Base on Fg. 16, copper loss reuctons n percentage for the teste IPMSM n the FW regon by ncorporatng the FF-base an the FB-base INC methos are respectvely presente n Fgs. 17 an 17. It s note that the voltage allowances n the hexagon corners, whch are essental for mtgatng the IVD effects, are reuce when the eulbrum voltage locus s expane ue to the ncrease of the emane torue uner a emane spee; or the ncrease of the emane spee. Thus, the effectveness of

13 TTE-Reg R1 12 Fg. 16. Contour plot of measure phase current magntue of teste IPMSM rve n FW operaton. Wthout an ncorporatng FF-base INC metho. Wthout an ncorporatng FB-base INC metho. (c) Fg. 15. Measure results of teste IPMSM rve uner MTPA operaton at 1200rpm, wthout an ncorporatng propose correcton metho.. values.. Im values. (c). Increase n copper losses (%) ue to not ncorporatng propose metho. TABLE II DEMANDED CURRENTS UNDER DIFFERENT CONTROL METHODS Te (Nm) Iteraton Offlne (A) Im Conventonal Onlne (A) Im Propose Onlne (A) Im both the FF-base an the FB-base INC methos on copper loss reucton s reuce n accorance wth the ncrease of the emane torue or the emane spee, Fgs. 17 an 17. For the propose FB-base INC metho, uner a low- spee an low-torue operatng conton (2000rpm, 5Nm), up to 7% copper loss reucton can be obtane, Fg. 17. However, at a hgh-spee operatng conton (4500rpm, 20Nm), only 1.65% copper loss reucton can be acheve. In aton, the conventonal FF-base INC metho can only respectvely obtan 5% copper loss reucton at 2000rpm, 5Nm an 1.2% copper loss reucton at 4500rpm, 20Nm, Fg. 17. On the other han, uner a emane spee, when the voltage allowances n the hexagon corners are fully utlze, the separate compensaton for the ea-tme effect, Fg. 11, stll can be acheve. It s shown that 1.5% maxmum achevable torue can be obtane at 4500rpm (22.42Nm compare wth 22.1Nm) by ncorporatng the propose FBbase INC metho, Fg. 18. The avantages of the FB-base INC metho over the conventonal FF-base INC metho wth a hgher achevable torue for a emane spee n the FW regon can also be observe n Fg. 18. V. CONCLUSION In ths paper, an onlne FB-base FW control technue of IPMSM rves for tracton applcatons uner torue control moe conserng machne parameter an nverter nonlneartes has been propose an expermentally valate. It has been proven that global MTPA operaton may not be acheve for IPMSM rves uner the conventonal onlne control metho wth extreme nonlnear machne parameters (e.g. n the scontnuous operaton subregon) ue to ts ncapablty of etermnng the global MTPA operatng pont. Thus, a moel-base MTPA correcton metho usng the

14 TTE-Reg R1 13 wll nclue conseraton of machne parameter estmaton an upate to enhance the rve system effcency. ACKNOWLEDGEMENT The authors woul lke to thanks the anonymous revewers for ther valuable comments an suggestons that greatly contrbute to mprove the ualty of ths paper. REFERENCES [1] [2] [3] [4] [5] [6] Fg. 17. Cooper loss reucton of teste IPMSM rve uner INC methos.. FF-base INC metho.. FB-base INC metho. [7] [8] [9] [10] [11] Fg. 18. Maxmum achevable torue of teste IPMSM rve n FW regon wthout an wth INC schemes. ajustment of the stator flux reference has been propose an a uas-global MTPA achevement has been presente. It has been shown that n the FW regon where the machne voltage magntue s mantane at the eal hexagon bounary, there s a msmatch between the eal eman an the actual voltage apple to the machne ue to the nverter nonlneartes. Ths ssue causes a lower than expecte maxmum achevable torue for a emane spee an a hgher than expecte current magntue for a emane torue. Therefore, a FB-base INC scheme explotng the voltage FB loop has been suggeste an ts avantages over the conventonal FF-base INC metho have been emonstrate. Future work to mprove the propose onlne control metho [12] [13] [14] [15] [16] [17] H. Naka, H. Ohtan, E. Satoh, an Y. Inaguma, Development an testng of the torue control for the permanent-magnet synchronous motor, IEEE Trans. In. Electron., vol. 52, no. 3, pp , Jun G. Pellegrno, A. Vagat, P. Guglelm, an B. Boazzo, Performance comparson between surface-mounte an nteror PM motor rves for electrc vehcle applcaton, IEEE Trans. In. Electron., vol. 59, no. 2, pp , Feb T. Myajma, H. Fujmoto, an M. Fujtsuna, A precse moel-base esgn of voltage phase controller for IPMSM, IEEE Trans. Power Electron., vol. 28, no. 12, pp , Dec B. Stumberger, G. Stumberger, D. Dolnar, A. Hamler, an M. Trlep, Evaluaton of saturaton an cross-magnetzaton effects n nteror permanent magnet synchronous motor, IEEE Trans. In. App., vol. 39, no. 5, pp , Sep./Oct K. M. Rahman an S. Ht, Ientfcaton of machne parameters of a synchronous machne, IEEE Trans. In. Appl., vol. 41, no. 2, pp , Mar./Apr F. R. Salmas, Control strateges for hybr electrc vehcles: evoluton, classfcaton, comparson, an future trens, IEEE Trans. Veh. Technol., vol 56, no. 5, pp , Sep M. Ceraolo, A. Donato, an G. Francesch, A general approach to energy optmzaton of hybr electrc vehcles, IEEE Trans. Veh. Technol., vol. 57, no. 3, pp , May F. Yan, J. Wang, an K. Huang, Hybr electrc vehcle moel prectve control torue-splt strategy ncorporatng engne transent characterstcs, IEEE Trans. Veh. Technol., vol. 61, no. 6, pp , Jul L. He, T. Shen, L. Yu, N. Feng, an J. Song, A moel prectve control base torue eman control approach for parallel hybr powertrans, IEEE Trans. Veh. Technol., vol. 62. no. 3, pp , Mar H. W. Kock, A. J. Rx, an M. J. Kamper, Optmal torue control of synchronous machnes base on fnte-element analyss, IEEE Trans. In. Electron., vol. 57, no. 1, pp , Jan B. Cheng an T. R. Tesch, Torue feeforwar control technue for permanent-magnet synchronous motors, IEEE Trans. In. Electron., vol. 57, no. 3, pp , Mar S. Lee, Y. S. Jeong, Y. J. Km, an S. Y. Jung, Novel analyss an esgn methoology of nteror permanent-magnet synchronous motor usng newly aopte synthetc flux lnkage, IEEE Trans. In. Electron., vol. 58, no. 9, pp , Sep S. H. Km an J. K. Seok, Maxmum voltage utlzaton of IPMSMs usng moulatng voltage scalablty for automotve applcaton, IEEE Trans. Power Electron., vol. 28, no. 12, pp , Dec B. H. Bea, N. Patel, S. Schulz, an S. K. Sul, New fel weakenng technue for hgh salency nteror permanent magnet motor, n Conf. Rec. IEEE IAS Annu. Meetng, Oct. 2003, pp T. S. Kwon, G. Y. Cho, M. S. Kwak, an S. K. Sul, Novel fluxweakenng control of an IPMSM for uas sx-step operaton, IEEE Trans. In. Appl., vol. 44, no. 6, pp , Nov./Dec T. S. Kwon an S. K. Sul, Analyss of the effects of the parameter varaton on the flux weakenng controller for mprovng torue capablty, n Proc. 23r Annu. IEEE Appl. Power Electron. Conf. Expo. (APEC2008), Feb. 2008, pp H. Km, J. Hartwg, an R. D. Lorenz, Usng on-lne parameter estmaton to mprove effcency of IPM machne rves, n Proc. IEEE Power. Electron. Spec. Conf., 2002, pp

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Lpo, Pulse wth moulaton for power converters: Prncple an Practce, New York: Wlley-IEEE Press, Khoa Dang Hoang (S 10-M 12) receve the B.Eng. an M.Sc.(Eng.) egrees from Ho Ch Mnh Cty Unversty of Technology (HCMUT), Ho Ch Mnh Cty, Vetnam, n 2002 an 2005, respectvely, an the Ph.D. egree from the Unversty of Sheffel, Sheffel, Unte Kngom, n 2011, all n electrcal an electroncs engneerng. Snce 2011, he s workng as a post-octoral Research Assocate at the Unversty of Sheffel uner several projects focusng on rve-tran esgn an control for the next generaton electrc vehcles. Hs key research nterests nclue power converson, avance control technues for electrcal rves, an analyss an esgn of electrcal machnes. Hawa K A Aorth receve the B.Eng egree n electrcal engneerng from Garyouns Unversty, Benhgaz Cty, Lbya, n 1996, the M.Eng egree n automatc control from Tabbn Insttute for Metallugrca Stues, Caro, Egypt, n 2005, an the Ph.D. egree n electrcal an electronc engneerng from the Unversty of Sheffel, Sheffel, Unte Kngom, n She was a research assstance from 1996 to 2002, an then lecturer from 2005 to 2008 at the Unversty of Omar Al Mukhtar, Al Beea Cty, Lbya. Snce 2014, she s wth AECOM, Lees, Unte Kngom, as an electrcal esgn engneer. Her key research nterests nclue power converson, avance control technues for electrcal rves, PWM technues, an analyss an esgn of electrcal machnes.