Stefan Brock, Tomasz Pajchrowski. Poznan University of Technology, Poznan - Poland

Transcription

1 Preprnt of the paper preente on: 7th Int. Conference on Electrcal Drve an Power Electronc, The Hgh Tatra, Slovaka 8 September, o:.684/m9.fghare Energy Effcent Open Loop Control of Permanent Magnet Synchronou Motor for Fan Applcaton Stefan Brock, Tomaz Pajchrowk Poznan Unverty of Technology, Poznan - Polan Stefan.Brock@put.poznan.pl Tomaz.Pajchrowk@put.poznan.pl Abtract The paper eal wth the problem of V/f control of a Permanent Magnet Synchronou Motor wthout wnng umper for fan applcaton. Bae on tablty analy, an atonal tablzng loop ntrouce. Voltage optmzaton wa carre out n orer to mnmze the nput power of PMSM. Smulaton reult confrme the valty of the apple oluton for fan applcaton. Keywor pm motor rve, ajutable pee rve, optmaton I. INTRODUCTION In the lat ecae, the ue of permanent magnet ynchronou motor (PMSM) n moton control applcaton ha gnfcantly ncreae ue to ther feature uch a hgh effcency an hgh power enty []. In ervo applcaton, n orer to acheve hgh ynamc performance n torue, pee an poton repone the fel orentaton houl be apple n a cloe loop control []-[]. The PMSM control reure a poton enor uch a an ncremental or abolute encoer, whch ncreae the cot an ecreae the relablty of the control ytem. Therefore, PMSM enorle control wely ue. Many paper have a ther man focu to elmnate poton enor. One of the metho ue a enorle vector control, whch etmate the rotor poton by ung, for example, the motor electromotve force [4], or by ung a Kalman flter [5,6]. The econ metho V/f control n an open loop wthout rotor poton. In applcaton uch a pump an fan, where a hgh ynamc not reure, a mple V/f control metho can be apple ntea of fel orente control [7]-[]. In many applcaton, nteror-type PMSM wth umpng wnng are ue for open-loop V/f control. Coneuently the ytem table. However ue to hgh cot, PMSM wth umpng wnng are not often ue. PMSM wthout umpng wnng o not enure ynchronzaton between the rotor an tator to the control V/f. It a caue of ntablty of the ytem of PMSM n open loop V/f control. Therefore, atonal gnal are neee to enure ynchronzaton an table operaton n V/f control. In [8]-[], n orer to acheve tablty to control V/f wth PMSM wthout umper wnng, a c-lnk current feeback wa ue. Moreover, a coornate g- frame wa ntrouce n orer to fn the algorthm whch mnmze nput power to the PMSM. In [7], a new metho of V/f control wth PMSM wthout umpng wnng n the rotor propoe. In th metho, tator voltage calculate n orer to mantan contant tator flux. Th allow workng wth contant torue n the full freuency range. To tablze the ytem for the full freuency range, atonal ampng of the rotor reure. Th can be acheve by an approprate moulaton of the freuency of the motor [7]. In th paper, an extenve mulaton tuy for PMSM wthout wnng umper for open loop V/f control wa carre out, where voltage calculate n orer to mantan a contant tator flux. An analy of the tablty wa carre out. It reult how that the PMSM wthout wnng umper untable. An atonal tablzng loop wa ntrouce. Voltage optmzaton wa carre out n orer to mnmze the nput power of the PMSM. Smulaton tue confrme the valty of the apple oluton. They are alo a goo tartng pont for future expermental tue. II. MATHEMATICAL AND SIMULATION MODELS OF PMSM DRIVE The bac euaton of PMSM on - coornate, where the -ax efne along a permanent magnet flux, are efne a: y u = R + - w y () t y u = R + + w y () t where u, u an, are the tator voltage an current component, y, y are flux component an w the motor angular velocty. R the tator retance. The flux properly efne a: y = L + l () m y = L (4) where l the permanent magnet flux an L, L are the m tator nuctance on both ax. In th paper the urface PMSM

2 analyze, for whch L = L = L. Moton of the rve ecrbe by euaton: w J = Te - TL = lm - TL (5) t Loa torue T T k w T L for a typcal fan applcaton efne by: L = + f (6) where coeffcent. T a tatc frcton torue an k f a fan The control ytem egne on the ba of the euaton n the -ax allow very goo ynamc properte of the rve. In th cae, t however neceary to meaure or etmate the poton of the motor haft. In the cae of PMSM control n open loop t avable to convert the rve euaton to the g-ax rotatng ynchronouly wth the upply voltage (Fg. ). After rotaton the euaton () (6) g ug = = R g + L - w L + w lm n (7) t u = u = R + L + w L g + w lm co (8) t where w the upply voltage angular freuency. The relaton between current an voltage n -ax an g-ax efne a: é éco -n ég ê = ê n co ê ë ë ë éu é-n ê u u = ê co ë ë (9) () The loa angle change n tranent tate ue to: t R = w - w () u u e u e m l g L l m L Fg.. Steay tate vector agram of the PMSM g The motor torue eual to: Te = lm ( g n + co ) () III.. STABILITY ANALYSIS OF PMSM DRIVE WITH V/F CONTROL The euaton et (7)-() nonlnear. To analyze the tablty the lnearzaton near the operatng pont realze. For the fxe rotor pee w reure to prouce an eual electromagnetc motor torue: T = T + k w () L f To mnmze the motor current, the - component value of the current wll be: = TL = lm (4) In th cae, the loa angle, whle omttng the voltage rop at the retance, accorng to the agram of Fgure wll be eual to: L arctan l = (5) The tator voltage houl be: m ( ) u = L + l w (6) m The current component value on the, g - axe can be etermne a: é co n n g é é é ê = ê n co ê = ê co - ë ë ë ë (7) In teay tate, the loa angle not change, whch mean that w = w. For the analy of the lnearze moel of the rve wth PMSM, the tate vector x an the nput vector u are ntrouce a: x = é ëdg D Dw D (8) u = é ëdu D D g u w T T (9) For uch an etablhe lnearze moel of the PMSM, fan rve tablty analy wa performe over the whole range of pee. For the numercal analy, the ample rve ata were ue, bae on paper [7]-[]. Fgure how the loc of the pole a a functon of rve pee.

3 Fg.. Loc of the rve pole a a functon of pee. Bae on the analy, two par of pole can be hghlghte n the rve ynamc. The fat one, relate to electromagnetc procee n the motor, table for any pee. The other low par, hown enlarge n Fgure, relate to the electromechancal varable. Th par only table for low pee, up to about % of the rate pee. Above th pee, the pole are n the rght half-plane of the complex plane. Bae on the analy, an orer reucton of the ytem euaton poble. The reuce orer tate euaton ha the form: x & = A x + B u () R R R R where [ ] T x R = Dw D () In a mplfe analy t aume that tator retance can be omtte, an then: éa a A R = ê ë- a = - k w f lm æ lm ö a = ç g co - n + J è L ø () Dw b Stablzaton a a Fg.. Smplfe block agram B b b b R = ê éb b b ë lm co = - J w L lm n = J w L l m = - J n + co g w Dw D ()

4 On the ba of euaton ()-(), the mechancal ubytem block agram of the PMSM rve can be repreente a hown n Fgure. In th cheme, only the nput D w taken nto account. Through th nput, an atonal tablzng gnal to the rve apple. Voltage vector component are electe wth the ntenton of mnmzng loe n the motor. IV. FREQUENCY MODULATION AND VOLTAGE CONTROL METHODS A. Voltage control metho The mulaton tet were carre out n Matlab Smulnk. Durng the tet, the behavor of the pee of PMSM rve wa analyze. In paper [7], a new V/f control metho propoe for a PMSM wthout umpng wnng n the rotor. In th metho the reference tator voltage calculate n orer to mantan a contant flux. Th allow a contant torue n the full range freuency to be obtane. For the calculaton of the magntue of the voltage v the followng euaton wa ue [7]: v = r co ju + e + ( r co ju ) - ( r ) (4) where: j u the angle between voltage (v ) an current ( ) vector e = l m w - electromotve force l m torue contant w r reference pee. The current vector obtane by meaurng three phae current n a fxe coornate ytem ab: = a + b (5) where: = a ( a b c ) - - (6) = ( - b ) (7) b c The term coj u calculate from the euaton: cof where: u o co( f ) o ( fu + ) éa cofu + b u - + = ê ê+ c co ë j u voltage vector angle a, b, c motor phae current. (8) a, b,c j u Calculaton of Calculaton of coj u coj u T + T + Fg 4. The algorthm for calculatng the voltage v w r Calculaton of v In orer to elmnate hgh freuency torton n the current a low pa flter wa ue. The algorthm for calculatng the tator voltage v hown n Fgure 4. B. Stablzng Loop To tablze the ytem for the full freuency range, atonal ampng of the rotor reure. Th can be acheve by an approprate moulaton of the freuency of the motor [7]. The mplfe ynamc moel, preente n ecton ue for the analy. Th moel allow the prectng of how the apple freuency houl be moulate to a ampng to the ytem wth PMSM. In aton, the pee turbance the man caue of the power perturbaton for an operatng pont. Bae on th analy, the apple freuency houl be moulate a: D w = -kd p (9) v e coj u e Calculaton of pe p e Dp e -k= c T + wr w r v Dw e Fg 5. The algorthm for calculatng the freuency moulaton gnal Dw e where Dp e perturbaton of power for an operatng pont. Th value can be expree a an electrcal power gnal after pang through the hgh pa flter æ ö æ T ö D p = ç - p = ç p è T + ø è T + ø e e e where nput power of the PMSM gven by: pe = v cofu () () The algorthm for calculatng the freuency moulaton gnal Dw e hown n Fgure 5. The block agram of the open control ytem V/f wth tablzng loop hown n Fgure 6. V. TUNING OF STATOR VOLTAGE TO ENERGY-OPTIMAL WORKING STATE Optmzaton of the motor n teay tate operaton can be one n the on-lne or off-lne tructure. The on-lne metho bae on the meaurement of power loe, an ue a earch algorthm to tune a control varable to acheve a mnmum lo workng conton. The optmzng controller oe not epen on a lo moel an robut to varaton n the motor parameter, uch a temperature. Correct meaurement of loe unfortunately often ffcult to mplement n practce. The off-lne metho bae on a lo moel of the machne.

5 e ref Steay tate optmzaton DV DC Reference gnal generator w ref Calculaton of V w / V PWM PMSM Dw Calculaton of Dw { Fg 6. Structure of PMSM rve wth tablzng loop an teay tate optmzaton Th approach can be ue when the loe n the machne can be ealy moele n term of nput gnal. Th metho can uually be ealy mplemente ung look up table metho. Th metho propoe n th paper. In a permanent magnet motor wth no core lo, a rve that operate at nearly zero -ax current component wll be optmally effcent. In teay tate, the ampltue of the motor upply voltage nfluence the component of the current, whle a -ax current component etermne by the loa torue. Wth a fan rve there an explct epenence of loa torue on the pee. After a ere of mulaton tet a teay tate optmzaton table create. The reference acceleraton nput ue to etermne the teay tate. The output gnal the fne-grane reference voltage correcton. The optmzaton table bae on power loe n rve. The total power loe cont of wnng loe an core loe. Are loe are calculate n etale motor moel. The reult of optmzaton are hown on fg. 7 an 8. The power loe epen on reference pee an apple voltage correcton. The mnmum value of power loe earch n the table. Fg 7. Power loe veru pee an correcton voltage Fg 8. Look-up table for correcton voltage reang veru reference pee VI. SIMULATION RESULTS A motor mulaton moel wa bult n Matlab bae on tanar motor euaton ()-(6). For utable moelng of the tatc torue, the tatc frcton Karnopp [] moel wa ue. A PWM nverter wa moele a an eal P gan wth atonal elay. At the preent tage of reearch t aume that the current meaurement eal. The reference pee generate by a reference gnal generator wth acceleraton an jerk lmt. To emontrate the effectvene of the propoe metho, ome reult of the mulaton are preente. The tet cont of three phae: tartup, changng pee an brakng. Fgure 9 how the waveform for the ytem wthout the optmzaton block. The rve workng properly. Actual pee cloely follow the reference pee. The freuency correcton gnal prove table operaton. The current component n the -ax relate to the loa torue. Unfortunately the -ax current ncreae the loe n the rve. Fgure how the waveform for the ytem wth the optmzaton block. Uner teay tate conton the -ax current reuce to almot zero. Alo the reucton of the - ax current hown n the ynamc tate. Due to the large gran ze of the optmzaton table there are tepwe change n the current value. Further work houl lea to a reucton of th phenomenon. VII. CONCLUSION The metho of the PM motor control preente n th paper utable for applcaton reurng a low ynamc, lke pump an fan. Th metho oe not ue poton enor or poton etmator. The off-lne optmzng metho apple to acheve mnmum power loe. The metho preente wll be mplemente n a real nutral rve wth low an mle ze fan.

6 Fg. 9 Smulaton reult for a ytem wthout optmzaton. Top: Reference pee (ahe lne) an rve pee (ol lne) Mle: current (ahe lne) an current (ol lne) Bottom: Freuency correcton Fg.. Smulaton reult for an optmze ytem. Top: Reference pee (ahe lne) an rve pee (ol lne) Mle: current (ahe lne) an current (ol lne) Bottom: Freuency correcton ACKNOWLEDGMENT Th work wa realze wthn the project "New generaton of energy-avng electrc rve for pump an coolng fan n mnng nutry, agreement no. POIG...--/9, The Operatonal Programme Innovatve Economy, fnancal perpectve between 7-. REFERENCES [] P. Va, Senorle vector an rect torue control. Oxfor Unverty Pre, 998. [] S. Brock, an J. Dekur, The problem of meaurement an control of pee n a rve wth an naccurate meaurng poton tranucer, th IEEE Internatonal Workhop on Avance Moton Control, pp. - 6, 6-8 March 8. [] T. Pajchrowk, an K. Zawrk, Applcaton of artfcal neural network to robut pee control of Servorve, IEEE Tranacton on Inutral Electronc, vol. 54, no., pp.-7, February 7. [4] Mormoto, K. Kawamoto, M. Sanaa, an Y. Takea, Senorle control trategy for alent-pole PMSM bae on extene EMF n rotatng reference frame, IEEE Tran. In. Applcat., vol. 8, pp. 54-6, July/Augut. [5] D. Janzewk, Extene Kalman flter bae pee enorle PMSM control wth loa recontructon, Veran Corc, Kalman Flter InTech, Venna. [6] S. Bolognan, L. Tubana, an M. Zglotto: Extene Kalman flter tunng n enorle PMSM rve, IEEE Tran. In. Applcat., vol. 9, pp , November/December. [7] P.D. Chanana Perera, F. Blaabjerg, J.K. Peeren, an P. Thogeren, A enorle, table V/f control metho for permanent-magnet ynchronou motor rve, IEEE Tran. In. Applcat., vol. 9, pp , May/June. [8] R.S. Colby, an D.W. Nowotny, An effcency-optmzng permanent magnet ynchronou motor rve, IEEE Tran. In. Applcat., vol. 4, pp , May/June 988. [9] Y. Nakamura, T. Kuo, F. Ihbah, an S. Hbno, Hgh-effcency rve ue to power factor control of a permanent ynchronou motor, IEEE Tran. Power Electron., vol., pp. 47-5, March 995. [] M. Kuch, T. Ohnh, H. Hagwara, an Y. Yaua, V/f control of permanent magnet ynchronou motor utable for home applance by DC-lnk peak current control metho, Internatonal Power Electronc Conference, IPEC, pp ,. [] B. Armtrong-Hélouvry, P. Dupont, an C.C. De Wt, A urvey of moel, analy tool an compenaton metho for the control of machne wth frcton, Automatca, vol., no. 7, pp. 8 8, 994.