Newton-Raphson Based Computation of i d in the Field Weakening Region of IPM Motor Incorporating the Stator Resistance to Improve the Performance

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1 Pge 1 o 6 Newton-Rphson Bse Computton o n the Fel Wekenng Regon o IPM Moto Incopotng the Stto Resstnce to Impove the Peomnce Shh Pevn 1, Z. S 1, n M. Ns Un, Seno Membe IEEE 1. Insttute o Mthemtcl Scences Unvesty o Mly 63, Kul Lumpu, Mlys E-ml: spevn@ssw.um.eu.my zlns@um.eu.my Abstct-Ths ppe pesents hgh pecson clculton o - xs stto cuent, to mpove the peomnce o nteo pemnent mgnet synchonous moto (IPMSM ve ove we spee nge o hgh peomnce nustl ve pplctons. The Newton-Rphson metho (NRM s use o computton o lux component o stto cuent,. Ttonlly, the stto esstnce s neglecte to clculte n the lux wekenng egon. The powe cpctes o the moto n the nvete e consee n evelopng the contol lgothm. The eccy o the popose NRM bse computton o o IPMSM ve s evlute n smulton t eent opetng contons. The peomnce o the IPMSM ve wth the popose NRM metho s lso compe wth the conventonl clculton o. Keywos - Inteo pemnent mgnet moto, Fluxwekenng contol, mxmum toue pe mpee contol, hgh pecson computton, Newton Rphson metho. I. INTRODUCTION The pemnent mgnet synchonous motos (PMSM get p nustl cceptnce becuse o the vntgeous etues such s hgh toue to cuent to, hgh powe to weght to, hgh ecency, hgh powe cto, low nose, n obustness [1]. Unlke n the we-woun excte synchonous motos, oto exctton o the PMSM s pove by the pemnent mgnets. The vnces n PM mtel ulty n powe electoncs hve booste the use o PMSM n electc moto ve o hgh peomnce pplctons such s utomotve, eospce, ollng mlls, etc. Among the PM synchonous motos, the nteo pemnent mgnet synchonous moto (IPMSM wth mgnets bue nse the oto coe shows excellent popetes such s mechnclly obust oto, smll eectve gp, n oto physcl non-slency []. The vecto contol technue s wely use o hgh peomnce contol o n IPMSM ve s the moto toue n lux cn be contolle septely n vecto contol [3]. Thus, the moto cts lke c moto whle mntnng the genel vntges o c moto ove c motos. Pecse contol o hgh peomnce IPMSM ove we spee nge s n engneeng chllenge. Fst n ccute esponse, uck ecovey o spee om ny stubnces n nsenstvty to pmete vtons e some o the mpotnt chctestcs o hgh peomnce ve system use n electc vehcles, obotcs, ollng mlls, tcton n spnle ves [1]. Some o the ve systems lke spnle ves n tcton lso nee constnt powe opeton [4]. The IPMSM ve cn be opete n constnt powe moe (bove the te spee usng the el-wekenng technue. In n IPMSM the. Deptment o Electcl Engneeng Lkehe Unvesty Thune By, Onto P7B E1, Cn E-ml: mun@lkeheu.c ect contol o el lux s not possble. Howeve, the el cn be wekene by the emgnetzng eect o -xs mtue ecton cuent, [3]. Recently the eseches [4-7] contnue the eots to evelop the IPMSM ve system ncopotng the lux-wekenng moe. The eseches evelop sophstcte contol lgothms but otenly gnoe the hgh pecson computton o the lgothm [8]. Mostly they epen on Mtlb/Smulnk lby. Theeoe, thee s nee to nvestgte the othe computtonl methos. Pope lux computton s cucl ssue o moto contol ptcully, t hgh spee conton. In [4] uthos gnoe the stto esstnce to compute the -xs component o stto cuent,, whch mkes the lux wekenng opeton possble. The mn eson s to smply the computton. Howeve, ths esults n mpope lux wekenng opeton o IPMSM. Theeoe, n ths ppe ccute lux estmton o pope el wekenng opeton s evelope ncopotng the stto esstnce o IPMSM. The Newton-Rphson metho (NRM bse numecl computton s use o hgh pecson computton o to enhnce the peomnce o the IPMSM ve ove we spee nge. The peomnce o the popose NRM bse computton o o IPMSM ve s evlute n smulton usng Mtlb/Smulnk [11]. The mplementton o the popose ve system usng gtl sgnl pocesso (DSP bo DS14 s cuently unewy. II. MOTOR MODEL AND CONTROL PRINCIPLE The mthemtcl moel o n IPMSM n the - synchonously ottng eeence me o ssume snusol stto exctton s gven s [1], L = v Rs Pω L Pω t (1 L = v Rs + Pω L t ( T = T + J pω + B ω (3 e L m m 3P Te = ( + (L L (4 whee, v n v e the, xs voltges, L n L e the, xs nuctnces, n e the, xs stto cuents, espectvely; R s s the stto esstnce pe phse, s the constnt lux lnkge ue to oto pemnent mgnet, ω s the ngul oto spee, θ e s the oto poston n electcl /1/$31. 1 IEEE

2 Pge o 6 egees, P s the numbe o pole ps o the moto n p s the eentl opeto, T e s the evelope electc toue, T L s the lo toue, B m s the vscous coecent n J m s the net constnt. The st tem o (4 epesents the mgnet toue ue to the oto pemnent mgnet lux n the secon tem epesents the eluctnce toue ue to the complex ntecton o, xs cuents n nuctnces o the IPMSM. The complexty o the contol ses ue to the nonlne ntue o the toue euton (4 becuse,, L, L, n e not constnts. All these unttes vy ung ynmc opetng contons []. To mke the toue euton lne n the contol tsk ese, usully s set to zeo. Howeve, n n ctul IPMSM nonlne ve, t s nppopte, the ssumpton o = les to eoneous esults. In ths ppe s not consee zeo. The vlue o s clculte om mntnng the mtue voltge n cuent wthn the cpcty o the moto n the nvete. Ths mpoves the peomnce o the ve system s compe to the = technue. A. Flux Contol Below Rte Spee Reeng to the phso gm o Fg.1, the stto phse voltge n cuent cn be elte to the - xs voltges n cuents s, Vˆ = V δ = v + jv ( Î I β = + j = (6 The mxmum vlue o stto phse voltge n cuent e V m n I m, espectvely. Below the bse spee, wth the ssumpton o keepng the bsolute vlue o stto cuent si V X ω s o X I δ β -xs ω s m = E o o L L constnt, cn be clculte n tems o o mxmum toue pe mpee (MTPA contol. Ths s obtne by eenttng (3 n settng t to zeo s [6], = (7 (L L 4( L L + In el-tme, mplementtton o the ve system becomes complex, n t ovebuens the DSP wth expessons n euton (7. In oe to solve ths poblem, usully smple eltonshp between - n -xs cuents, whch s obtne by expnng the sue oot tem o euton (7 usng Mclun sees expnson s (8. In ths cse only o st two tems e consee o smplcty (8 B. Smple Flux Contol Above te Spee Above the te spee, n stey-stte cn be clculte n tems o to mntn constnt stto voltge. Ths s obtne om (1 n ( by neglectng the stto esstnce op s [6], 1 (V m = + L (9 L L P ω whee V m s the mxmum stto phse voltge neglectng the stto esstnce op, ( ( V = v + v (1 v v m o o o o = Pω L (11 = Pω L + Pω (1 Futhe to euce the computtonl buen, Mclun sees expnson (only st two tems e consee cn be pple to euton (9, whch yels: si ω s o m ( genel phso gm V X δ -xs ω s m=e o I = o m L (b phso gm wth =. -xs -xs Fg. 1. Phso gm o IPM synchonous moto: ( genel phso gm, (b phso gm wth = /1/$31. 1 IEEE (1.316 ω (13 ω Above the te spee, the voltge emns constnt s the mgnet lux s wekene by the -xs mtue ecton cuent, n hence, the powe emns constnt n ths egon. Bse on the bove lgothm the block gm o the complete IPMSM ve s shown n Fg.. Euton (9 epesents n ellpse n the - plne, whch nctes tht n ncese n oto spee esults n smlle nges o the cuent vecto s shown n Fg.3. By ppoptely contollng, the mpltue o the temnl voltge s juste to V m. Above the bse spee.e., n constnt powe egon, the voltge emns constnt s the mgnet lux s wekene by the mtue ecton o n oe to ecese the totl gp lux. The lux-wekenng contol not only extens the opetng lmts

3 Pge 3 o 6 o IPMSM ve but lso eleves the cuent egulto om stuton tht occus t hgh spees. The mxmum mpltue o the phse voltge V m whch cn be sustne by the nvete wthout stuton o the cuent egulto s gven s uncton o the c bus voltge V B s, V m = ( / π V B (14 It s seen om eutons (1, ( n ( tht n cse o =, the mgntue o the temnl voltge V nceses wth n ncese n moto spee ω o the -xs cuent. Theeoe, the stuton o the cuent egulto occus t hgh spees o gven toue, when the moto temnl voltge ppoches V m whch my cuse nstblty o the ve o = contol. The numecl vlues o the moto pmetes e shown n the Appenx. V B PWM Invete Bse ve ccut Cuent contolle b c c b IPMSM Encoe sutble o el-tme mplementton. Howeve, some ppoxmton s tken n Mclun sees to compute, whch esults nppopte vlue o the lux. Moeove, n the el wekenng egon, the stto esstnce s neglecte to smply the clculton. Thus, the moto peomnce wll be ecte especlly t hgh spee conton. Theeoe, n ths ppe NRM bse numecl computton o s use so tht the lux clculton wll be moe ccute n hence the moto uns smoothly bove te spee contons. Futhemoe, the stto esstnce s consee to compute n the FW egon. Below the te spee o NRM bse computton o, (7 cn be ewtten s, Accong to NRM, ( = { } = (16 (L L ( n 1 = ( n = ( n ( ( + (17 Below the te spee the clculton o oes not show tht much eence between NRM bse computton n the conventonl computton bse on (7 o, (8. Tht s why uthe nlyss o clculton below the te spee s not pove. The lux clculton bove the te spee s moe mpotnt thn below the te spee n hence the numecl computton o bove te spee s pove below. Vecto otto θ (, ω - ω Spee contolle + ω - ω - t θ Cuent, A I Fg.. Block gm o the complete ve system. It s note tht euton (13 s the key euton o FW contol o the moto bove the te spee o 188. /s. The mxmum ttnble spee o gven set o stto voltges n cuents cn be obtne om euton (9. At mxmum spee, the toue poucng cuent component wll be zeo. Thus the mxmum opetng spee o moto ω mx cn be clculte s, ω mx P( L V V m R m s = I + P( L I + = ( Fo the ptcul 1 hp IPM moto consee n ths ppe, the mxmum ttnble spee s 389 /s [1]. III. NEWTON RAPHSON BASED COMPUTATION OF In secton II the s clculte bse on Mclun sees n oe to euce the computtonl buen so tht t wll be Fg. 3: Locus o stto cuent I t eent spees stng om 188./s to 37./s n step o./s. Above the te spee o NRM bse computton o, the FW metho cn be eevlute om (1 n ( s ollows: ( = ( Pω ( L + + Rs + ( Rs Pω L Vm = (18 whee, V m s the mxmum stto phse voltge wthout neglectng stto esstnce. Fom (17 n (18, bove the te spee one cn get, ( Pω ( L + + R + ( R Pω L V s s m ( + 1 = ( n ( ( ( ( = n Rs R s Pω L + Pω L Pω L + + R s n Cuent, A (19 Bse on the teton the vlue o s clculte the consecutve vlues conveges wth the pecson o ε= /1/$31. 1 IEEE

4 Pge 4 o 6 Tht mens ( n + 1 ( n ε then = (n+1. Fst the vlue o s clculte olne usng the NRM n then polynoml o s uncton o spee s evelope, whch s use o lux wekenng lgothm. Above the te spee the vton o wth eent spees e shown n Fg.4. The vlue clculte bse on smple euton (13 e lso shown. It s oun tht thee s sgncnt eence between the two vlues tht cuses the enhncement n the peomnce. It s lso oun tht clculte bse on (13 s postve o spees bove but ne te spee (188. /s, whch s not mkng the el wekenng opeton. Whees, the NRM bse numecl computton o ncopotng the stto esstnce (R s s lwys negtve n hence ensung the pope el wekenng opeton. Usng the cubc polynoml cuve ttng metho the euton o (compute bse on NRM s uncton o spee s etemne s, =.4ω -.19ω +.89ω 3 (18 Ths euton s use to clculte o el wekenng opeton o IPMSM. The cuve ttng o hghe egee polynoml exhbts b contone. The cuve ttng euton ws checke wth the ele t n the plot s shown n Fg.. It s oun tht the ctul mtches lmost peectly wth the vlues obtne om polynoml (18., A 1 - bse on smple euton ( bse on NRM ncopotng stto esstnce, R s Spee, /s IV. RESULTS AND DISCUSSIONS The peomnce o the popose ve system s nvestgte n smulton t eent opetng contons. Smple esults e gven below. The smulte tnsent esponses o the IPMSM ve o step chnge o commn spee e shown n Fgs. 6 n 7 o the popose n conventonl clculton o [6], espectvely. It s clely seen om Fg. 6( tht the popose NRM bse numecl computton o ensues pope lux wekenng opeton n hence thee s no oveshoot n the spee esponse when the spee ncese om 188. to /s. Whees, t s seen om Fg. 7( tht the spee esponse sues om bg oveshoot ue to the conventonl smple clculton o. Theeoe, the ncopoton o the stto esstnce to clculte bse on NRM s juste. Fo el wekenng opeton s becomng moe negtve when the spee goes bove te spee, whch s shown n Fg. 6(c. The toue component o the cuent eceses bove te spee snce the toue eceses n the el wekenng egon, whch s shown n Fgs. 6(b n 7(b. Fg. 8 shows the esponse o the IPMSM ve t vey hgh spee (3 /s usng the popose NRM bse computton. The moto cn ollow ths hgh commn spee only ue to the pope clculton o. Wth conventonl smple computton o, t ws not possble to un the moto t such hgh spee conton. Thus, the popose technue extens the opetng spee egon o the moto. As the spee nceses the euency o the stto cuent nceses, whch s shown n Fg. 8(c. The 3-phse cuents shown n Fg. 8( ncte the blnce opeton o the moto. A lo stubnce s lso pple to the moto n the coesponng esponses e shown n Fg. 9. It s oun tht the moto cn hnle the lo stubnce whle unnng t hgh spee conton. Theeoe, the popose NRM bse numecl computton o poves pope el wekenng opeton n hence the ve cn hnle the uncetntes such s suen chnge n eeence spee n lo whle unnng t hgh spee (bove te spee conton. Fg. 4: Vton o wth spee, ω O - clculte bse on NRM ncopotng R s bse on polynoml (18, A Spee, /s Fg. : Compson o cuve ttng polynoml wth ctul /1/$31. 1 IEEE

5 Pge o 6 3 Reeence spee 3 3 Reeence spee Spee, /s 1 ( Actul spee Spee, /s 1 ( Actul spee , A 1 (b,, A (b , A - - (c, A (c -7 Fg. 6: Smulte tnsent esponses o the IPMSM ve o step chnge o spee t te lo usng the popose NRM bse computton. Cuent, A Cuent, A Spee, /s Tme, s ( (b (c, b, c, A ( Tme, s Fg. 8: Smulte esponses o the IPMSM ve t vey hgh spee (3 /s conton t te lo usng the popose NRM bse computton Tme, s. Fg. 7: Smulte tnsent esponses o the ve o step chnge o spee t te lo usng the conventonl computton o [6] /1/$31. 1 IEEE

6 Pge 6 o 6 3 popose metho coul be potentl cnte o el-tme el wekenng opeton o IPM moto. Cuent, A Cuent, A Spee, /s Tme, s Fg. 9: Smulte esponses o the popose IPMSM ve o step ncese n powe n el wekenng egon. (b (c ( REFERENCES [1] M. N. Un, T. S. Rwn, G. H. Geoge n M. A. Rhmn, "Peomnce o Cuent Contolles o VSI-Fe IPMSM Dve", IEEE Tnsctons on Inusty Applctons,vol.36, no.6, Nov/Dec., pp [] B. Sneyes, D. W. Novotny n T. A. Lpo, Fel-Wekenng n Bue Pemnent Mgnet AC Moto Dves, IEEE Tnsctons on Inusty Applctons, vol. IA, pp. 3987, Mch/Apl 198 [3] T. M. Jhns, Flux-Wekenng Regme Opeton o n Inteo Pemnent- Mgnet Synchonous Moto Dve, IEEE Tnsctons on Inusty Applctons, vol. IA, pp , July/Aug [4] S. Momoto, M. Sn n Y. Tke, Eects n Compenston o Mgnetc Stuton n Flux-Wekenng Contolle Pemnent Mgnet Synchonous Moto Dves, IEEE Tnsctons on Inusty Applctons, vol. 3, No. 6, pp , Nov./Dec [] R. Dhou, Ne Mohn, Anlyss o Cuent-Regulte Voltge Souce Invetes o Pemnent Mgnet Synchonous Moto Dves n Noml n Extene Spee Rnge, IEEE Tnsctons on Enegy Conveson, vol., No.1, pp , Mch 199. [6] M. N. Un, T. S. Rwn n M. A. Rhmn, "Peomnce o Inteo Pemnent Mgnet Moto Dve ove We Spee Rnge", IEEE Tnsctons on Enegy Conveson, vol. 17, no. 1, Mch, pp [7] M. N. Un n M. A. Rhmn, Hgh Spee Contol o IPMSM Dves Usng Impove Fuzzy Logc Algothms, IEEE Tnsctons on Inustl Electoncs, Vol. 4, No. 1, Feb. 7, pp [8] M. Ns Un n M. I. Chy, On-Lne Pmete Estmton Bse Spee Contol o PM AC Moto Dve n Flux Wekenng Regon, IEEE Tns. on In. Applctons, Vol. 44, No., Sept./Oct. 8, pp [9] Yun Zhng, Longy Xu, Must K. Güven, Song Ch, n Mhesh Ilnl, Expementl Vecton o Deep Fel Wekenng Opeton o -kw IPM Mchne by Usng Sngle Cuent Regulto, IEEE Tns. on In. Applctons, Vol. 47, No. 1, Jn./Feb.. 11, pp [1] M. Azzu Rhmn, Mhn Vlthgmuw, M. Ns Un, n K. J. Tseng, Nonlne Contol o Inteo Pemnent Mgnet Synchonous Moto, IEEE Tnsctons on Inusty Applctons, Vol. 3, No., Mch/Apl 3, pp [11] Mtlb/Smulnk Use Gue, The Mth Woks Inc., Ntck, MA, 9. APPENDIX: MOTOR PARAMETERS 3-Φ, 1 hp, 8 V, 6Hz, P=, L =.444 H, L =.797 H, R=1.93Ω, J m =.3 Kg-m, B m =.8 N-m//s, =.314 volt//s. V. CONCLUSION In ths ppe Newton-Rphson bse numecl computton o lux component o stto cuent, hs been use o pope lux wekenng opeton o IPMSM ve. The cuent, hs been clculte bse on moto moel wthout neglectng stto esstnce. Fo the complete ve the MTPA technue s use below the te spee n el wekenng technue hs been use bove the te spee. Then the peomnce o the ve system hs been nvestgte n smulton usng Mtlb/Smulnk t eent opetng conton. The peomnce o the IPMSM ve wth the popose NRM bse computton o hs lso been compe wth the conventonl [6] smple computton o. It hs been oun om the esults tht the IPMSM ve wth popose clculton o poves bette esponse s compe to the conventonl clculton o. Thus, the /1/$31. 1 IEEE