J. Electrical Systems x-x (xxx): x-xx. Regular paper. A DSP-Based Space Vector Modulation Direct Torque Control of IPM Synchronous Machines

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1 F. A. Oman A. M. Ohiba F. M. El-Khouly M. M. Khattr J. Elctrical Sytm x-x (xxx): x-xx Rgular papr A DSP-Ba Spac Vctor Moulation Dirct Toru Control of IPM Synchronou Machin In thi papr a nw DTC chm for intrior prmannt magnt ynchronou machin (IPMSM) i propo. Th propo DTC chm having th avantag of low toru rippl a wll a contant witching fruncy. Th incrmnt in th witching fruncy ruir nithr an incra of th ampling fruncy nor high fruncy ithring ignal injction. Hr in th propo chm, a mol ba obrvr i u to gnrat th optimal rfrnc voltag vctor. Furthrmor, a wll vlop pac vctor moulation tchniu i appli to invrtr control in th propo chm uing a DSP-ba harwar, thrby rucing th toru rippl an incraing th witching fruncy which bcom contant. To illutrat th prformanc of th propo control chm, imulation an xprimntal rult ar prnt. Kywor: Prmannt magnt ynchronou motor, Dirct toru control, toru rippl minimization, Digital ignal procor application. 1. INTRODUCTION Th baic concpt of DTC of AC motor riv i to control both tator flux linkag an th lctromagntic toru of th machin imultanouly. Sinc a DTC-ba riv ytm lct th invrtr witching tat uing witching tabl, nithr currnt controllr nor pul-with moulation (PWM) moulator i ruir, a hown in Fig. 1, thrby introucing fat toru ynamic rpon in comparion with th fil orint vctor control tchniu. Howvr, thi convntional DTC approach ha om iavantag uch a; high toru rippl an variabl witching fruncy, which i varying with p, loa toru an th lct hytri ban. On th othr han to ruc th toru rippl; th hytri toru an flux controllr ban mut b ruc to match th ruir toru prformanc, which ruir ruction of th ytm ampling tim an it i ncary to u a vry fat procing controllr. Although th ytm ampling fruncy can b incra in th convntional DTC th invrtr witching fruncy i till low, approximatly l than on thir of th ampling fruncy [1,, 3, ]. Th invrtr witching fruncy can b incra uing a ithring ignal, by aing a limit amplitu high fruncy ignal to th toru an flux rror ignal [5, ]. Although th witching fruncy i incra it i till variabl for mall rror ban. Othr rarch concrn with th iavantag uing multilvl invrtr, thr ar mor voltag pac vctor availabl to control th flux an toru [7, 8, an 9]. Howvr, th approach ruir mor powr vic, which incra th cot of th ytm an mak it mor Elctrical Tchnology Dpartmnt, Bnha Highr Intitut of Tchnology, Bnha Univrity., Egypt Dpartmnt of Elctrical Enginring, Faculty of Enginring, Minoufiya Univrity, Shbin El-Kom, Egypt.

2 complx. In [1, 11], icrt pac vctor moulation DTC approach i u to ruc th toru rippl. Howvr, thr i a complxity of lcting th aitional hytri controllr. On th othr han, pac vctor moulation (SVM) moulator i incorporat with irct toru control for PMSM riv a crib in [1, 13, 1], to provi a contant invrtr witching fruncy an low toru rippl. In [13] a abat controllr i u to gnrat th voltag comman of SVM moulator, which ruir on-lin olution of vry complx uation. In rfrnc [1], a prictiv controllr i u to calculat th comman voltag vctor. Howvr, th prictiv controllr ha th am problm a th abat controllr. PMSM Vc 1,,3 Invrtr Switching Tabl 1,,3 v c v α, v β θ i a 3/ i b i α, i β Toru an Flux Etimator hy. hy. - Figur. 1 Convntional DTC of IPMSM riv ytm. In thi papr, a nw an impl DTC algorithm with fix witching fruncy for IPMSM i propo to ruc th toru rippl. Th wll-vlop SVM tchniu i appli to invrtr control in th propo DTC-ba IPMSM riv ytm, thrby ramatically rucing th toru rippl. Th rmaining ction of th papr ar arrang a follow: Sction II giv th ruirmnt of a tabl DTC IPM riv. Sction III xplain th propo DTC chm. Sction IV contain th imulat an xprimntal rult for both claical an propo DTC chm. Th imulation rult ar carri out by moling th riv ytm uing a Matlab/Simulink. - λ * T *. IPM MACHINE EQUATIONS Th voltag uation of th IPM motor in th rotor rfrnc fram can b writtn a follow: v v T = R ω + p L L Th toru uation i, = whr: 3 P λ L L [ λ pm ω R L L + p L i i Sin δ λ + ω (L L λ pm ) Sin δ ] (1) ()

3 v, v an axi tator voltag; i, i an axi tator currnt; R tator armatur ritanc pr pha; L, L irct an uaratur ax ynchronou inuctanc; ω lctrical rotor p in ra/c; T lctromagntic toru, Nm; P numbr of pol pair; δ angl btwn tator an rotor flux linkag; λ, λ pm tator an rotor flux linkag. From uation (), it i n that th lctromagntic toru can hav fat ynamic rpon by changing δ a fat a poibl. Thi i th bai of DTC for IPM motor riv ytm [1, 3]. 3. PROPOSED DTC BY MEANS OF SVM In th propo DTC ytm, th am flux an toru timator which i u for th convntional DTC i till u in th propo DTC chm a hown in Fig.. Inta of th witching tabl an hytri controllr, an optimal voltag vctor calculator i u to calculat th rfrnc voltag vctor a a function of th toru rror. Th appli voltag vctor an thir uration tim ar lct an calculat uing th SVM moulator. From th block iagram of th propo DTC hown in Fig., it i n that th propo chm hav th mot important avantag of th convntional DTC, uch a fat toru ynamic, by applying th convntional DTC uring th tp chang in th toru comman; thn at tay tat tim of th toru rpon th SVM i appli to inur a rippl ruction occurring at th tay tat toru rpon. T * λ * T τ Φ Switching Tabl Switching Stat Slctor Invrtr Vc IPM λ θ V i, V c 3/ SVM V* Figur. Propo DTC IPM riv. Toru & Stator flux Etimator Optimal Voltag Vctor Calculator

4 Th propo DTC chm can b furthr xplain a follow; at tarting up or at th intanc of th loa chang, almot whn th toru rror i larg, th witching tat lctor lct th witching tat of th convntional DTC witching tabl to gt a fat toru rpon at tarting an at a tp chang in th loa toru comman. Whn th toru rror i within th hytri ban limit, th witching tat lctor, lct th witching tat gnrat by th SVM which guaranty that th witching fruncy i fix an th rippl at th tay tat toru rpon ar ruc. 3.1 Optimal Voltag Vctor Calculator Th optimal voltag vctor calculator (OVVC) i u to gnrat th rfrnc voltag vctor accoring to th toru rror, which i th iffrnc btwn th rfrnc an timat toru. Th principal of opration of th optimal voltag vctor calculator i ba on th machin mol. Th ffctivn of ach non-zro voltag vctor on changing th tator flux linkag an toru i proportional to it amplitu. Thu whn th amplitu of th non-zro voltag vctor incra, th ynamic rpon to th chang of tator flux an toru rfrnc bcom fatr. Howvr, th toru rippl amplitu in tay tat opration grow. On th othr han, whn th non-zro voltag vctor ruc, th ynamic rpon to th chang of tator flux an toru rfrnc bcom lowr. Howvr, th amplitu of th toru rippl in tay tat opration cra. Fig. 3 xplain th ignal flow iagram for th optimal voltag vctor calculator. T 1/k + ω λ - λ + v v Figur. 3 Optimal voltag vctor calculator (OVVC). Th lctromagntic toru uation can b writtn a follow, T = 3 P [ λ pm + ( L L Thn, th toru iffrntial with rpct to i an i can b obtain a: ) i ] i (3) T = 3 P { ( L L ) i i + [ λ pm ( L L During ach ampling prio, T, th two currnt componnt, i an i, can conir a contant valu, o uation () can b approximat by: T = a i + a Whr: 1 i ) i ] i } () (5)

5 a a 1 = = 3 P 3 P ( L [ λ pm L ) i ( L L ) i ] From uation (1), by nglcting th voltag rop acro th tator ritanc, w hav; i = T ( v + ω λ ) / L () i = T ( v ω λ ) / L (7) Subtituting from uation (, 7) into uation (5) on obtain, T = K v + K v + K 1 3 (8) Whr: K K 1 3 = a 1 = ω T / L ( K 1 λ, K K λ = a ) T / L From uation (1), with rpct to th irct voltag componnt, v, at tay tat an nglcting th rop acro th tator ritanc, th following uation can b obtain, v = ω λ (9) Subtituting from uation (9) into uation (8), yil: v = T / K + ω λ (1) From uation (9, 1) it i n that w gt th rfrnc voltag vctor componnt in th rotor rfrnc fram, which ar u to gnrat th ruir rfrnc voltag vctor. Th witching tat an it uration tim ar calculat uing th SVM tchniu. 3. Spac Vctor Moulation (SVM) A hown in Fig. th rfrnc pac vctor V* fin by V*, V* an angl θr, can tak any poition in th x-y plan, whil th invrtr output tak only on of th ix nonzro vctor V1,, V an two zro vctor V & V7. Th pac vctor V* i approximat by th two clot non-zro vctor an on of th two zro vctor. A an xplanation xampl conir th ca whr V* li in ctor- whr th two clot vctor ar V1 an V a hown in Fig.. Th invrtr output mut giv V1, V3 an V or V7 for tim t1, t an t uring ach witching cycl T uch a; T = t t t Th tim t1 an t ar proportional to componnt Vj an Vk rpctivly which ar givn a follow; (11) * t1 = A V Co ( α ) t / (1)

6 t = B V * Sin ( α ) (13) A B = = ( 3 3 / π ) T ( 3 / π ) T U ( 1 ) V 3 U3 ( 1 1 ) V Sctor 1 Uk U * Sctor SECTOR Sctor U α U ( 1 1 V ) U7 Uj U c / 3 VU1 1 ( 1 ) Sctor 3 Sctor 5 Sctor U c / 3 U ( 1 V) 5 VU5 ( 1 1 ) Fig.. 1 Th Poibl Spac Vctor of Invrtr Output. Figur : Th poibl voltag vctor of invrtr output. SIMULATION RESULTS Th ytm prformanc unr th propo DTC tratgy i valuat, an th rult ar compar with th rult obtain by th convntional DTC. MATLAB/SIMULINK mol wr vlop to xamin th convntional an th propo DTC algorithm. In imulation, th ampling tim i 7 µ for both th convntional an propo DTC chm an th witching tim for th propo DTC i 1 µ. Th witching tabl u in [1] i mploy for th convntional DTC. Th witching lay an th forwar rop of th powr witch, th a tim of th invrtr an th non-ial ffct of th PM motor ar nglct in th mol. Th toru ynamic prformanc of th convntional an propo DTC chm at 1 rpm ar compar a hown in Fig. 5 unr th am opration conition. It i n that th toru rippl i ruc by mor than 7 % at no-loa an loa conition in th propo DTC. Alo th two algorithm hav am toru rpon ynamic prformanc uring tart-up an loa chang a illutrat in Fig..

7 Sp (rpm) 1 Toru (Nm) Toru (Nm) Claical DTC Propo DTC Tim (c) Figur5: Toru an p rpon for both chm. Claical DTC Sp (rpm) 1 Toru (Nm) Toru (Nm) Tim (c) Propo DTC Sp (rpm) 1 Toru (Nm) Toru (Nm) Tim (c) Figur: Toru an p rpon for both chm.

8 Howvr, it i alo n that unr th convntional DTC, th toru rpon ha rach th rfrnc toru ± 5% of it valu, whil th toru unr th propo DTC can rach an ttl own at th rfrnc valu. Th p rpon i alo hown for th propo DTC in Fig.. It can b n from th figur that th propo DTC ha achiv a fat p rpon than that for th convntional DTC, about 7 m. Furthrmor claration i hown in Fig. 7 for p ynamic rpon an thir corrponing toru rpon for both algorithm. It i n that th toru rippl ruction i till vali at low an high p rang. A p rvr ynamic i carri out at two iffrnt p rfrnc, ± 5 rpm an ± 1 rpm, to inicat th valiity of th controllr opration at both p irction. Th imulation rult for th p rvring ynamic ar hown in Fig. 8 Sp (rpm) Toru (Nm) Toru (Nm) Convntional Propo Tim (c) Figur7: Sp an toru rpon for both chm. Sp (rpm) Toru (Nm) Tim (c)

9 Sp (rpm) Toru (Nm) Tim (c) Figur8: Propo DTC toru rpon with p rvral, at ± 5 an ± 1 rpm. Alo a comparativ imulation rult btwn th propo DTC algorithm an om othr algorithm ar hown in Fig. 9, whr a rfrnc p of 1 rpm i appli to th motor thn, a loa toru of Nm i appli at t = 1.5 c. Th toru rpon for th claical DTC algorithm i givn in Fig. 9 (a) an th Fig. 9 (b) how th toru rpon for th DTC algorithm with ithring ignal. Fig. 9 (c) giv th toru rpon for th DTC algorithm whr th flux linkag an lctromagntic toru timator i carri out at th ynchronou rfrnc fram (rotor fram), an finally th propo DTC algorithm toru rpon i givn in Fig. 9 (). (a) (b) (c) () Tim (c) Figur9: Comparion btwn th propo algorithm an om othr tchniu

10 5. EXPERIMENTAL RESULTS A DSP control car (-Spac 11) an it intrfac unit ar u to implmnt th Claical an th Propo DTC chm for IPM riv ytm. Aitional harwar car ar u for maurmnt of currnt an th DC-bu voltag, which i ruir for th calculation of th two-pha voltag vctor. An incrmntal ncor i u in orr to carry out th optimal voltag vctor calculation an gnrating th optimal rfrnc voltag vctor. Th u ampling tim i 1 μ c (ampling fruncy 1 khz) an th witching fruncy i 5 khz. A tp chang of 1 rpm i appli to th motor thn a loa toru i a, aftr p rpon rach it tay tat valu, with a valu of about Nm for a crtain tim intrval. Th corrponing flux linkag an toru rpon at tay tat conition for both Claical an Propo DTC chm ar givn in Fig. 1. From Figur 1, th toru rpon of th propo DTC chm introuc a grat toru rippl ruction in comparion to th toru rpon for th claical DTC chm. It alo inicat in Figur 1 that a goo rippl ruction in th flux linkag magnitu rpon. Th timat toru an th corrponing pha currnt rpon ynamic at loaing conition i inicat in Figur 11. Th pak valu for th pha currnt i approximatly. A a inicat in Figur 11, which i corrponing to a root man uar valu of about.8 A at a loa toru of Nm. Alo th p ynamic i conir by applying tp incrmnt an crmnt at th rfrnc p. Th p ynamic rpon for both claical an propo DTC chm ar introuc in Fig. 1. A tp incrmnt in p rfrnc from 5 rpm to 1 rpm at tim ual to 1 c. an two tp crmnt from 1 rpm to 9 rpm, thn from 9 rpm to 7 rpm at tim an 3 c. ar appli. It' inicat that th p rpon for th propo DTC i approximatly rippl fr. Th pha currnt wavform at intanc of th p tranition from 5 rpm to 1 rpm unr no-loa for th claical DTC an th propo DTC i clar in Fig. 13. A hown in thi Fig., th pha currnt of th propo DTC i approximatly inuoial which ruc th currnt harmonic an rippl. Toru ( 1Nm / v.) Toru ( 1Nm / v.) Tim ( m / v.) Tim ( m / v.)

11 Toru ( 1Nm / v.) Currnt ( 1 A / v.) Flux ( 1 wb / v.) Flux ( 1 wb / v.) Tim ( m / v.) Tim ( m / v.) (a) Claical (b) Propo DTC Figur1: Sp an toru rpon for both chm. Tim ( m / v.) Figur11: Toru an pha currnt rpon at Nm loaing.

12 (a) Claical DTC (b) Propo DTC Figur1: Sp ynamic rpon for claical an propo chm. Currnt (.1 A / v.) Currnt (.1 A / v.) Sp ( 3 rpm / v.) Sp ( 3 rpm / v.) Tim ( 5 m / v.) Tim ( 5 m / v.) Tim ( 1 m / v.) (a) th claical DTC Tim ( 1 m / v.) (b) th propo DTC Figur13: Pha currnt rpon with p tranition from 5 rpm to 1 rpm unr no-loa..conclusion In thi papr a nw DTC algorithm for th IPM ynchronou machin ha bn vlop. Th ffctivn of th propo DTC algorithm in rucing th toru rippl wa vrifi by computr imulation an xprimntally on a 3-pha IPMSM rat at 1 kw. Th prnt rult hav montrat that th problm which wr aociat with convntional DTC chm uch a, high toru rippl an variabl witching fruncy hav bn compltly avoi. It i alo intrting that th propo toru controllr ha bn hown to b robut to control th machin flux, allowing atifactory ovrall prformanc of th machin unr tuy. Th vlop algorithm alo offr th propct

13 for optimizing th machin prformanc in a mannr imilar to convntional vctor controllr. APPENDIX Paramtr of th u IPM ynchronou machin ar givn in tabl 1; Tabl 1: Numbr of pol pair, P Armatur ritanc, R 1 ohm Magnt flux linkag, λ pm.75 V.S/ra -axi inuctanc, L 159 mh -axi inuctanc, L 5 mh Pha voltag, V V Pha currnt, I 1. A REFERENCES 1. L. Zhong, an M. F. Rahman, "Analyi of irct toru control in prmannt magnt ynchronou motor riv," IEEE Tran. Powr Elc., Vol. 1, No. 3, May S. Dan, F. Wizhong, an H. Yikang, "Stuy on th irct toru control of prmannt magnt ynchronou motor riv," 5th Intrnational Confrnc on Elctrical Machin, ICEMS, L.X. Tang, M.F. Rahman, Y. Zhiing, an T. Cun, "In-pth rarch on irct toru control of prmannt magnt ynchronou motor," IECON Inutrial Elctronic Socity, IEEE 8th annual Confrnc,.. M.F. Rahman, W.Y. Hu, K.W. Lim, M.A. Rahman, "An invtigation of irct an inirct toru controllr for PM ynchronou motor riv," Powr Elctronic an Driv Sytm, Intrnational Confrnc, S. Frrira, F. Mora, L. Frnano Prira, "Dirct toru control with tator rippl fruncy impo ithring," IEEE Powr Elctronic Tranaction,.. T. Noguchi, M. Yamamoto, S. Kono, I. Takahahi, "Enlarging witching fruncy in irct toru controll invrtr by man of ithring," IEEE Tranaction on Inutry Application, Barbara H. Knny an Robrt D. Lornz (). "Stator an Rotor Flux Ba Dabat Dirct Toru Control of Inuction Machin" NASA/TM-1-111/REV1, 1 Inutry Application Socity Annual Mting. 8. Y.S. Lai, J.H. Chn, "A nw approach to irct toru control of inuction motor riv for contant invrtr witching fruncy an toru rippl ruction," IEEE Tran. Enrgy Convr. 1 (3) (1) H. Ghami, S. Vaz-Zah, "A vry fat irct toru control for intrior prmannt magnt ynchronou motor tart up," Enrgy convrion an managmnt (5) Lixin Tang, Lmin Zhong, Rahman, F., "Moling an xprimntal approach of a novl irct toru control chm for Intrior prmannt magnt ynchronou machin riv," IECON Inutrial lctronic ocity, IEEE 8th annual confrnc.

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