IMPROVED TRAJECTORY CONTROL FOR AN INTERIOR PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE WITH EXTENDED OPERATING LIMIT

Transcription

1 IMPROVED TRAJECTORY CONTRO FOR AN INTERIOR PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE WITH EXTENDED OPERATING IMIT Abstract M. E. Haue,. Zhong an M. F. Rahman School of Electrcal Engneerng an Telecommuncaton The Unversty of New South Wales Syney NSW 5 Australa E-mal: meh@stuent.unsw.eu.au Ths paper presents analyss of trajectory control for an nteror permanent magnet (IPM) synchronous motor rve uner PWM current control. An mprove trajectory control wth extene spee range has been ntrouce. The scheme allows the motor to be rven wth maxmum-torue-per-ampere characterstc (MTPA) below the base spee an t mantans the maxmum voltage lmt of the motor uner we flux-weakenng an the motor current lmt uner all contons of operaton accurately. Followng the analyss of the trajectory control, the results of extensve smulaton an experment are gven.. INTRODUCTION The IPM synchronous motor possesses specal features for ajustable-spee rves whch stngush t from other classes of ac machnes, especally surface permanent magnet synchronous motor. Because of ts specal rotor confguraton, pole salency an relatvely large armature nuctance, the IPM synchronous motor s also more sutable for an extene spee range operaton by the flux-weakenng control. The maxmum steay state torue of the IPM synchronous epens on the contnuous armature current ratng. The avalable output voltage of the nverter lmts the maxmum spee attanable at ths torue. In tracton an spnle rves, constant power operaton an we spee range are esrable. Wth c motor rves, these are acheve by the approprate reucton of the fel current as the spee ncreases. In IPM synchronous motor, rect control of the magnet flux s not avalable. The ar-gap flux, however, can be weakene by the emagnetzng current n the rect axs [-5]. In ths paper, the armature current control metho expanng the operatng lmts s examne through analyss, moelng an experment.. CONTRO OF IPM MOTOR DRIVE In a PWM current controlle rves, the currents are regulate by PI (proportonal + ntegral) controllers. Tratonally, the current control executes n the statonary reference frame ue to ts smplcty. When the current controllers are vewe n the rotor reference frame, however, t s seen that there exst cross-couplng effects between -axs an -axs varables an back-emf sturbance. It s possble to compensate the back-emf sturbance by usng backemf fee-forwar compensaton. Other avantages of the latter scheme have been reporte n the lterature, for nstance, the cross-couplng effect can be easly compensate. Furthermore, fel-weakenng control becomes easer snce the -axs current s rectly controlle. The current control n the rotor flux reference frame as a means of torue an flux control has been aopte n ths paper. The block agram of a PWM current controlle IPM motor rve s shown n Fg.. 3. CONTRO TRAJECTORIES The voltage an torue euatons of an IPMSM may be expresse n the - reference frame as follows: v r+ p v = r p + + f () 3 T = P [ + ( ) ] () From euaton (), the steay-state phasor agram of an IPMSM shown n Fg. s obtane. In Fg., β an γ are the leang angles of the stator current an voltage vectors from the -axs respectvely an δ s the torue angle. It s clear that the -axs components of the stator current are = I snβ (3) s = I cosβ (4) s where I s s the ampltue of the stator current vector. Substtutng (3) an (4) nto torue euaton (), yels the expresson for the torue n terms of the ampltue of the stator current as follows:

2 * PI-control wth lmt * * Calculaton of * Current control & -ecouplng * * v v Voltage compensaton vc * vc * - * a abc b θ IPMSM PWM nverter Torue, Nm T T e T r Spee observer θ Encoer Fgure. PWM current controlle IPM motor rve. where v s r s s -axs γ β f δ s -axs Fgure. Phasor agram of an IPM motor. 3 3 T = P Iscos β + P ( ) Is snβ (5) 4, -an -axes armature current, v,v - an -axs armature voltage,, - an - axes axs nuctance, f magnet flux, r armature resstance, I s ampltue of the armature current P number of pole pars, p fferental operator /t, T Torue an - rotor spee. The frst term of (5) s the exctaton torue T e an the secon term s the reluctance torue T r. Fgure 3 shows T, T e an T r as functons of the current phase angle β for the motor n Table when the ampltue of the stator current s kept at the rate value. As s seen from the fg. 3, T e s maxmum at β = an T r s maxmum at β = 45 o. Therefore, the total torue, T, s maxmum wthn the range of o < β < 45 o. For the IPM motor, - may be large, so the reluctance torue s no longer neglgble. From the above analyss, to operate an IPM synchronous motor at hgh torue an effcency, shoul be etermne by (4) wth β corresponng to the maxmum torue for a gven stator current. Phase angle, β Fgure 3. Effects of the current phase angle β. 3. Maxmum Torue Per Ampere (MTPA) Trajectory To obtan fast transent response an hgh torue, the current phase angle β must be controlle to evelop the maxmum torue. The relatonshp between the ampltue of the stator current an the phase angle β for the maxmum torue can be erve by settng the ervatve of (5) wth respect to β to zero. 3 3 T = P I ssn β+ P ( ) I s cosβ = (6) β By substtutng euaton (3) an (4) nto euaton (6), one obtans 3 3 PIssn β+ P ( ) Is(cos β sn β) = (7) From euaton (7), one can obtan f = ( ) 4( ) + (8) Euaton (8) mples that the maxmum torue-perampere (MTPA) s obtane f s etermne by euaton (8) for any.. It shoul be note here that the torue s not rectly proportonal to. Ths s why the torue control va current control s calle nrect torue control. 3. Current an Voltage mt Trajectores When an IPM synchronous motor s fe from an nverter, the maxmum stator current an voltage are lmte by the nverter/motor current an c-lnk voltage ratngs respectvely. These constrants can be expresse as s sm I = + I (9) s sm V = v + v V () where I sm an V sm are the avalable maxmum current an voltage of the nverter/motor.

3 Substtutng euaton () at steay state nto euaton (), one can obtan V = ( r ) + ( r + + ) V () s f sm Euaton () can be smplfe as euaton () f the stator resstance s neglecte. Vsm ( ) + ( + ) ( ) () can be calculate from euaton () as (3) f resstance s neglecte. = + = + (3) f Vsm f ( ) where Vsm = ( ) (4) 3.3 Voltage mte Maxmum Output Trajectory The armature current vector 3 ( 3,, 3 ) proucng maxmum output power uner the voltage lmt conton s erve as follow [6]: = (5) Vsm ( ) = (6) ρ V ( ) 8( ) sm ρ + ρ + ρ = 4( ρ ) where, ρ = (7) The current vector trajectory of the voltage lmte maxmum output s shown n Fg. 4. The rotor spee, A Maxmum torue per ampere trajectory Voltage lmte maxmum output = - f/ trajectory A = p G A 3 B D A E C O Voltage lmt trajectory = 5 rpm = base = rpm = 4 rpm= c = 8 rpm= > 8 rpm, A Fgure 4. Control trajectores n - plane. p s the mnmum spee for the voltage-lmte maxmum-output operaton. Below ths spee, the voltage-lmte maxmum-output operatng pont can not be reache, because the voltage-lmte maxmumoutput trajectory ntersects the voltage lmt trajectory outse the current lmt crcle. If ( ) > I, the f sm voltage-lmte maxmum output trajectory s outse the current-lmt trajectory. Therefore, voltage-lmte maxmum-output trajectory nees not to be consere. 4. CONTRO MODE SEECTION The MTPA an current lmt trajectores are nepenent of the rotor spee an are only etermne by the motor parameters an nverter current ratng. However, the voltage lmt trajectory vares wth the change n rotor spee. It s seen that the voltage lmt trajectory s an ellpse, whch contracts when the rotor spee ncreases. When the rotor spee ncreases nfntely, the voltage lmt ellpse becomes a pont on the axs. If ths pont s nse the current lmt crcle, theoretcally, the motor has an nfnte maxmum spee, otherwse, has a fnte maxmum spee. The ntersecton of MTPA, current lmt trajectores s the operaton pont A at whch the motor has the rate current an voltage an wll prouce the rate torue at the base spee. The control moes,.e., maxmum torue-per-ampere an flux weakenng controls, are selecte accorng to the analyss of fg. 4. The -axs commane current * s etermne by the outer control loop an the -axs commane current * s ece by euaton (8) n maxmum torue-per-ampere control moe, or by () n flux weakenng control moe. Whether MTPA moe or the fel weakenng moe shoul be selecte s etermne by the rotor spee an the loa. Accorng to the rotor spee, the motor operaton s ve nto three sectons, that s, below the base spee b, above the crossover spee c an between the base an crossover spees. The crossover spee c s the spee at whch the back-emf voltage of the unloae motor euals to the maxmum voltage. As a result, the control moe s selecte as follows. 4. Operaton below the base spee It s seen n fg.4 that the voltage lmt ellpse corresponng to the operaton below the base spee s larger than the one for base spee. Therefore, f the stator current vector s controlle accorng to the maxmum torue-per-ampere trajectory an satsfyng the current lmt, whch s the trajectory A O, t must satsfy the voltage lmt snce the current vector s nse the voltage lmt ellpse. Therefore, maxmum torue-per-ampere moe s selecte for constant torue operaton.

4 The - an -axs currents, A an A, wth whch the maxmum torue s prouce, are etermne by (8) an (9) when I s = I sm. A = + ( ) 4( ) sm A I Solvng (), one gets f Ism A= + 4( ) 6( ) A= Ism - A () Ths s the operatng pont at whch the motor prouces the maxmum torue an the lmt value of the outer control loop for constant torue operaton s then etermne by (). 4.. Operaton above the crossover spee To run the motor above the crossover spee, the flux f, whch s the flux lnkage along the rotor axs, has to be reuce. Although the flux s alreay reuce wth the MTPA control, the voltage lmtaton s no longer satsfe when the rotor spee s above the crossover spee. The stator current vector s therefore controlle accorng to the voltage lmt trajectory nstea of MTPA trajectory. Thus, an are etermne accorng to the voltage an current lmt euaton () an (9). The lmt value, v an v, of the outer control loop for such a fel weakenng operaton s therefore etermne by these two euatons wth I s = I sm, whch s nversely proportonal to the rotor spee. where v = + ab () a a a = () sm V b= Ism + (3) v= Ism - v (4) When the rotor spee s n the range from c to, s etermne from euaton (3). However, as the rotor spee excees for whch s ve an becomes a complex number. So shoul be calculate as = / for a rotor spee greater f than. The trajectory for = / has shown n fgure 4. If the rotor spee etermne f p, an has to be from euaton (5) an (6) an the current vector moves from A 3 to E (fg. 4) along the voltage-lmte maxmum output trajectory. 4.3 Operaton between the base an crossover spees (8) (3-4) When the rotor spee s n the range from b to c, the control moe s etermne by the loa. If the motor s unloae, t may operate near the crossover spee wth MTPA control. When the motor s fully (9) loae, t has to be controlle accorng to the voltage lmt trajectory rght above the base spee. For nstance, f the motor runs at rpm, the corresponng voltage lmt trajectory s BCO as shown n fg. 4. Thus, f the motor s heavly loae an the current vector s along the trajectory BC, t has to be controlle accorng to the voltage lmt trajectory. Otherwse, the motor can be stll controlle uner MTPA control along the trajectory CO. The etermnaton of the control moe s base on the calculate from both euaton (8) an (3). If the calculate from euaton (9) s smaller than the one calculate from (3), the current vector s controlle to the MTPA trajectory for constant torue operaton. Otherwse, voltage lmt trajectory s use to control the current vector for fel weakenng operaton. The lmt value for the outer control loop s stll etermne by euaton (4). 5. MODEING AND EXPERIMENTA RESUTS Moelng an experment were performe on an IPM synchronous motor. The specfcaton of the motor use s shown n Table. The rate an crossover spees for ths motor are 5 an 4 rpm, respectvely. The samplng tme of the nner control loop s 5 µs an that of the outer control loop s 75 µs. The rve system was mplemente on a TMS3C3 gtal sgnal processor wth a clock spee of 33 MHz. The rotor poston an spee were obtane from an ncremental encoer wth 5 pulses per revoluton. A three-phase nsulate gate bpolar transstor (IGBT) ntellgent power-moule s use for an nverter, whch s supple at a c lnk voltage of 57 V. Fgure 5 shows the moelng results of spee,, an wth respect to a step change n spee reference from to 5 rpm. It s seen from these fgures that the current vector s at the ntersecton of MTPA an current lmt trajectores,.e., pont A urng acceleraton an moves along the MTPA trajectory when the spee approaches ts reference. Snce the loa torue s taken to be zero, the current vector fnally settles own at orgn, O. Fgure 6 shows the ynamc responses wth respect to a step change of spee reference from to 8

5 Spee, rpm Spee, rpm Tme, sec. (a) Spee response., A (a) Spee response., A Tme, sec..4 Tme,sec (b) response., A, A Tme, sec. (c) response, A Tme, sec. (c) respnse. MTPA A Current lmt, A Tme, sec. (c) respnse. MTPA Current lmt O, A () ocus of current vector. Fgure 5. Moelng results for constant torue operaton uner trajectory control r b. rpm. It s clear that the smooth transton between constant torue an fel weakenng controls occurs when the rotor spee excees the base spee (5 rpm). It s also clear that the stator current vector moves along the maxmum-torue-per armature current trajectory when the spee s below the base spee an shfts to the voltage lmt ellpse when the spee ncreases above base spee. Fgure 7 shows the torue an power versus spee characterstcs of the motor. It s seen that fel weakenng occurs once the spee goes above the base spee (5 rpm). It s seen that constant power operaton s possble wth the trajectory control scusse n ths paper., A () ocus of current vector. Fgure 6. Moelng results for flux-weakenng operaton uner trajectory control r > b. T o r u e, N m 3 4 Spee, rpm 8 4 P o w e r, W 3 4 Spee, rpm Fgure 7. Torue an power versus spee. Fgures 8 an 9 show the expermental results for constant torue operaton an flux-weakenng operaton, respectvely. The expermental results conform to the moelng results ute well.

6 6 8 4 Spee, rpm T m e, s e c., A T m e, s e c , A T m e, s e c..5.5, A -, A (a) spee response. (b) response. (c) response. () ocus of current vector. Fgure 8. Expermental results for constant torue operaton uner trajectory control. Spee, rpm 3, A, A, A Tme, sec Tme, sec Tme, sec , A (a) spee response. (b) response. (c) response. () ocus of current vector. Fgure 9. Expermental results for flux-weakenng operaton uner trajectory control. 6. CONCUSION Ths paper analyses the control trajectores for an IPM synchronous motor. The control trajectores, namely the maxmum torue-per-ampere, current an voltage lmt trajectores, have been erve an expresse n terms of an, an then rawn n the - plane. Base on the analyss of these trajectores, the selecton of constant torue an flux-weakenng moes has been scusse. It has been establshe that the maxmum torue-per-ampere trajectory shoul be selecte for constant torue operaton an the voltage lmt trajectory shoul be selecte for flux-weakenng operaton. It has been shown by the moelng an expermental results that flux-weakenng s very well ncorporate n ths rve. The transton between constant torue an flux-weakenng s very smooth. It s also shown that constant power operaton s possble wth the mprove trajectory control scusse n ths lterature. TABE. Parameters of the IPM Motor use. Number of pole pars P Stator resstance r 9 Ω Magnet flux lnkage ϕ f.447 Wb -axs nuctance.3885 H -axs nuctance.4755 H Phase voltage V 4 V Phase current I.6 A Base spee b 5 rpm Crossover spee c 4 rpm Rate torue T b Nm REFERENCES [] B. Sneyers, D.W Novotny, an T. A. po, Fel-weakenng n bure permanent magnet ac motor rves, IEEE Trans. In. Appl., vol., pp , Mar./Apr [] T. M. Jahns, Flux-weakenng regme operaton of an nteror permanent magnet synchronous motor rvem, IEEE Trans. on In. Appl., vol. 3, no. 4 pp , 987. [3] T. Sebastan an G.R. Slemon, Operatng lmts of nverter-rven permanent magnet motorrves, IEEE Trans. In. Appl., vol. 3, pp , Mar./Apr [4] S. Mormoto, M. Sanaa, Y. Takea, Wespee operaton of nteror permanent magnet synchronous motors wth hgh-performance current regulator, IEEE Trans. on In. Appl., vol.3, no.4, pp. 9-96, 994. [5] M. F. Rahman,. Zhong an K. W. m, A DSP base nstantaneous torue control strategy for nteror permanent magnet synchronous motor rve wth we spee range an reuce torue rpples, IEEE Inustry applcatons socety Annual Meetng, vol., pp , 996. [6] S. Mormoto, M. Sanaa, Y. Takea, Expanson of operatng lmts for permanent magnet motor by current vector control conserng nverter capacty, IEEE Trans. on In. Appl., vol., no. 5, 6, pp , 99.