A New Model for IPMSM with Rotating High Frequency Voltage Injection

Transcription

1 A New Model for PMSM with Rotating High Frequeny oltage njetion S. Damkhi, MS. Nait Said,and N.Nait Said 3 Department of Eletrial Engineering, Batna Univerity,Algeria ihemd@ymail.om,n_naitaid@yahoo.om Department of Eletrial Engineering, Batna Univerity,Algeria mednaitaid@yahoo.fr Abtrat Controlled ynhronou mahine drive without mehanial peed enor at the motor haft have the attration of low ot and high reliability. The eliminating of the peed enor require the etimation of peed from the mahine itelf. At tandtill and low peed only the high frequeny ignal injetion method (HFSM able to give aurate poition etimation. The HFSM exploit the mahine alieny property whih ontain the information about the rotor poition or flux poition and trak it by injeting a high frequeny exitation. For applying thee method the mahine drive mut be preented the alieny, a the interior permanent magnet ynhronou mahine (PMSM preent an inherent alieny in it rotor, the appliation of HFSM i available. Thi paper preented a high frequeny PMSM model adopted for enorle ontrol appliation. Thi model i obtained by add the rotating high frequeny ignal voltage to fundamental upply. The effet of injeted ignal to the performane of PMSM are tudied and analyzed in thi paper through the imulation tet.. ntrodution nterior permanent magnet ynhronou mahine (PMSM i very popular in indutry beaue of their good performane, high effiieny and power denity. However for PMSM ontrol appliation the ue of poition enor to meaure the rotor poition angle an be inreaed the ot and redue the reliability of ytem. Extenive reearh ha been direted toward enorle ontrol of PMSM and everal approahe are reported in the literature. PMSM poition enorle ontrol tehnique are laified in two ategorie: method baed on fundamental model [,] and method baed on patial alieny [3,4,5].The method baed on fundamental model, etimate the rotor poition from mahine fundamental equation, preent good performane in middle and high peed region. However at frequeny near to zero, the voltage drop on the tator reitane annot be negleted while the bak emf beome lower and lower, vanihing any poibility of having ontinuou low or zero peed operation and limit the appliation of method baed on fundamental model [6]. n order to improve the poition etimation in low peed range the eond type of method are appeared. The patial alieny baed method are often referred to a high frequeny ignal injetion method (HFSM, in whih high frequeny ignal i uperimpoed on tator upply. The applied ignal interat with the rotor alieny or magneti aniotropy of the mahine and the reulting urrent or voltage i proeed to extrat the rotor poition information. Thee method an operate over a wide peed range, inluding zero peed, and an ahieve parameter independent poition etimation [7]. The type of injeted ignal that have been propoed in literature an be laified into three main ategorie. The firt one i injetion high frequeny arrier ignal(rotating arrier injetion urrent or voltage, pulating arrier injetion urrent or voltage the eond injetion a tranient ignal(tet voltage vetor injetion uperimpoed on fundamental PMWthe third tandard PMW withing exploit the withing of fundamental PMW waveform[8]. The appliation of HFSM require the exitene of alieny in the mahine. Sine the PMSM ha an intrini alieny (the diret d-axi indutane i ubtantially different from the quadrature q-axi indutane, o it ha natural potential to be ued for enorle etimation at tandtill and low peed. n thi paper a new model of PMSM baed on pulating high frequeny ignal injetion i preented. The rotating injetion i arried out by the appliation of a balaned et voltage. The interation between the rotating injeted ignal and alieny preented in the PMSM i deteted in urrent repone. Simulation tet i applied for preenting the effet of rotating injeted ignal on the performane of PMSM.. The model of PMSM under fundamental voltage exitation The equation voltage and flux linkage in the tationary referene frame (, are: R o( r in( r R L - Lo( r - Lin( r m ( ( ld lq ld - lq L, L (3 R : i tator reitane, m : i the amplitude of permanent magnet flux linkage. p p -Lin( r L L o( r 57

2 ,, : are voltage, urrent and flux linkage of the tator repetively, L : i the average tator indutane, L : i the differential tator indutane, l d and l q are the diret-axi and quadrature-axi ynhronou indutane, r : i the rotor poition in eletrial degree, p : i differential operator. w Subtituting ( in (: R d R dt d o( r dt in( m r L -L o( r -L in( r -L in( r L L o( r (4 Fig.. Rotating vetor injetion in the tationary referene frame [] A onequene of injeting of rotating voltage The eletromagneti torque and ytem motion equation an be expreed by (5 and (6 repetively. ( Te p * (5 d T T J r e - l (6 dt From (4, (5,(6 we an elaborate the model of PMSM under fundamental exitation, however for enorle ontrol at tandtill operation thi model beome not uitable therefore a new PMSM model baed on high frequeny exitation will be preented. 3. The model of PMSM under high frequeny voltage exitation n order to elaborate the model of PMSM appropriate for enorle ontrol at low peed range. A peritent high frequeny exitation (.5 khz i ued to feed the PMSM. The peritent high frequeny exitation an be rotating or pulating; rotating if it onit a balaned et voltage, pulating if it injeted only in a phae or onit of three idential voltage[9].thi paper will be onerned with rotating voltage injetion. Thi type onit to injet a balaned polyphae voltage vetor rotating at a high frequeny. The polyphae arrier voltage an be etablihed a in (7 and i illutrated in Fig.. j t - e, repreent the amplitude and the frequeny of the injeted vetor voltage, repetively. (7 -The mahine repond with an ellipti urrent Fig.; -The ellipe i orrelated with the aniotropie preented in the mahine; -The rotor poition information i inluded in the high frequeny urrent. i Fig.. Ellipti urrent repone [] Uing (7 a injeted ignal, the model given by (4 an be implified by onidering the following aumption [,, 3]: - The frequeny of the injeted ignal i high to the -The tator reitane R an be negleted ompared to the high frequeny reatane -At low peed the bak-emf i negligible. So the mathematial model of PMSM in HF voltage exitation an be written a: - - j L -L o( - in( r L r - - in( o( L r L L r - (8 57

3 The HF urrent repone for rotating HF voltage injetion an be dedued from (8 a: ( L - - j - (9 L i the tator tranient indutane matrix in tationary frame The alulation of ( L allow writing (9 a: - - j L Lo( r Lin( r L in( r L -Lo( r - - ( ( L - ( L l q l d ( Subtituting (7 in ( the total expreion of reulting HF urrent i Mahine parameter Maximum peed Table.Mahine parameter value (rpm mahine alue parameter l d 4.44(m H Number of pole pair l q 79.57(m H R. ( f f.34(wb J. ( kgm 4.. PMSM without high frequeny ignal injetion n the firt time the imulation tet orrepond to imulate PMSM without HF ignal injetion, the PMSM i fed by 7, 5 ( rm balaned et tator voltage pulate at 5 (Hz.t run at no-load ondition. Fig.3 and Fig.4 how the peed and eletromagneti torque repone, it i evident from thee figure that the peed and eletromagneti torque repone reah the main value at teady tate without any oillation. 4 j - ipe ( t j( - t ine r ( 3 L ip, i jldl n q L jldlq t an be notied from ( that the reulting HF urrent ontain both poitive and negative equene omponent. The firt omponent alled the poitive-equene omponent i p proportional to the average tator tranient indutane and ontain no information on poition r. The eond omponent alled negative-equene omponent i n proportional to the differential tator tranient indutane and it ontain information on the poition r. We an remark alo if the mahine i no alient ( l d lq o L, the negative equene omponent i zero o no information about rotor poition. A onequene the HFSM require the preene of alieny in the mahine. The demodulation of negative omponent allow extrating the rotor poition whih an be ued in enorle ontrol of PMSM.A deribed previouly the injeted HF ignal voltage indued the HF urrent haraterized by two omponent. To illutrate the effet of the preene of indued HF urrent on PMSM a imulation tet will be applied. 4. Simulation reult For evaluating the performane of PMSM with and without injetion of high frequeny ignal the modelling imulation tet i aomplihed. The PMSM parameter are given in Table. Rotor peed[rad/s] Torque[N.m] Fig.3. Rotor peed repone without HF injetion Fig.4. Eletromagneti torque repone without HF injetion Due to the preene of alieny ( ld lq in PMSM the tator tranient indutane beome not ontant. t depend on the rotor poition it trajetory preent an elliptial hape a hown in Fig

4 mag[l] Re[L] Fig.5. Stator ndutane Trajetory From Fig.5 it an be oberved that the PMSM preent an intrinially alieny whih an be exploited for etimating the rotor poition, thi alieny an be traked by high frequeny ignal injetion. Thi preent the aim of next tet of imulation. 4.. PMSM with high frequeny ignal injetion n thi etion the PMSM i upplied by high frequeny voltage uperimpoed to the tator voltage upply. The PMSM i operated at no load with, ( rm, (Hz a high frequeny rotating voltage uperimpoed to, ( rm, ( Hz normal upply tator voltage. Fig.6 how the upply tator voltage in tationary referene frame. Stator Current- a[a] Fig.7. Spetrum of tator urrent a with HF ignal injetion and the alienie preented in the mahine it pulate at f - fr(hz.t ontain the information on rotor poition it i ued for extrating the rotor poition, rather the other harmoni whih an be eliminated by filtering. The Fig.8 how the effet of additional HF ignal that reate a HF ripple in the eletromagneti torque but ha almot no effet on the motor peed..5.5 fe f-fr Frequeny[Hz] f Torque[N.m] S[] Time[e] Fig.6. Supply oltage The injetion of high frequeny voltage ignal reate the harmoni whih appear in both urrent and flux repone. Generally the harmoni preented in repone urrent are uing to extrat the poition of rotor peed in enorle ontrol. n our ae the harmoni preent in the urrent are uffiient to lear the affet of high frequeny ignal injetion. The Fig.7 how the tator urrent petrum with HF ignal injetion. t an be een from Fig.7 that a three harmoni appeared the firt one orrepond to the main frequeny of tator upply fe ( Hz. The two eond harmoni are due to the injeted HF ignal voltage; the firt one preent the poitive equene omponent it pulate at f ( HZ it ha high amplitude ompared to the eond omponent (negative equene, whih i the reult of the interation between the HF Rotor peed[rad/s] Fig.8. Eletromagneti Torque and rotor peed with HF ignal injetion A deribe previouly the onequene of injeted HF ignal voltage the new tator ourant i indued, preented a the negative omponent and poitive omponent. The effet of HF ignal voltage appeared learly in eletromagneti torque and 574

5 tator urrent rather than in peed repone. 5. Conluion Reently new enorle method are appeared, thi method alled high frequeny ignal injetion method (HFSM. t relie on the ue of uperimpoed ignal to normal upply thi ignal an be voltage or urrent, a known at low frequeny the method baed model failed. The (HFSM i able to provide the information about the rotor poition at zero frequeny and tandtill. Thee method require the preene of alieny in the mahine. A the PMSM preent an intrinially alieny the appliation of thee method i eay. n thi paper a new approah of modelling of PMSM i preented, thi approah relied on the injeted of HF ignal rotating voltage. When we injet a ignal voltage to the normal upply an indued urrent i produed in tator. Simulation tet uing an additional HF rotating voltage ha been performed. Apart from the reulting urrent ontained two omponent one of thee omponent alled negative equene inluded the information about a rotor poition whih ha no parameter dependant and an be ued in enorle ontrol. The HF injeted ignal ha no effet on rotor peed. [] Ralph M. Kennel, Senorle Motor Drive, Eletrial Mahine and Drive Wuppertal Univerity. [] S.Taniguhi, S.Wakao, T.Yoneyama, " Poition enorle ontrol of Permanent Magnet ynhronou Motor at low peed range uing harmoni voltage injetion", Conferene Power eletroni and appliation European Proeeding,7,pp.-7. [] M.P.Chaudhary,.Patel, J.G.Jamnani, "Senorle vetor ontrol of PMSM drive uing heterodyne tehnique", nternational Conferene EEE optimization of Eletrial and Eletroni Equipment Proeeding, 8, pp [3] P.Balazovi, R.Filka, "Senorle PMSM ontrol for H-axi wahing mahine drive", Conferene EEE Power Eletroni Speialit Proeeding,8 pp Referene [] S. Morimoto, K. Kawamoto, M. Sanada, and Y. Takeda," Senorle ontrol trategy for alient-pole PMSM baed on extended EMF in rotating referene frame", EEE ndutry Appliation Conferene, 36 th AS Ann. Meet.,, pp [] B. Nahid-Mobarakeh, F, Meibody-Tabar, F. M. Sargo," Bak EMF etimation-baed enorle ontrol of PMSM: Robutne with repet to meaurement error and inverter rregularitie", EEE Tran. ndutrial Eletroni, ol. 43, No., pp , 7. [3] H. Kim, and R. D. Lorenz, " Carrier ignal injetion baed enorle Control method for PM ynhronou mahine drive", EEE ndutry Appliation Conferene, the 39 th AS Ann. Meet., 4, ol., pp [4] S. Kim, Y.-C. Kwon, S.-K. Sul, J. Park, and S.-M. Kim," Poition enorle operation of PMSM with near PWM withing frequeny ignal injetion", 8 th CPE ECCE Proeeding, Aia, May-June, pp [5] J.-H. Jang, S.-K. Sul, J.-. Ha, M. Ohto, and K. de, " Analyi of permanent magnet mahine for enorle ontrol baed on high frequeny ignal injetion", EEE Tran. ndutry Appliation,ol. 4, ue 6,pp , 4. [6] A.Conoli,G.Sarella,G.Selba,S.Royak,M.M.Harbaugh, "Saturation Modulation in oltage Zero Sequene-Baed EnoderleTehnique. Part : mplementation iue",eee EMDC Proeeding, San Antonio, TX,MAY 5-8,5,pp.7-3. [7] Wang Jianmin, Tian Shixia, "Analyi of Stator Reitane Effet in Carrier Signal njetion Baed Senorle Control of Permanent Magnet Synhronou Mahine", Conferene CEEAC Proeeding, November, pp [8] C. Caruana, Senorle ontrol of AC Mahine, Univerity of Malta, Nottingham Summer Shool: 8. [9] G.Bottiglieri,A.Conoli,T.Lipo,"Modeling of Saturated ndution Mahine With njeted High-Frequeny Signal", EEE Tran. on Energy onverion,ol. 43, No., pp ,