Concepts and Properties of Controlled Permanent Magnet Drives

Transcription

1 Concepts an Properties of Controlle Permanent Magnet Drives C. Grabner Abstract The consiere converter-fe permanent magnet motor coul alternatively be operate in two basically ifferent states the vector control moe or alternatively the brushless c, also nown as electronically commutate moe. Several quality aspects concerning the system performance have been comparatively investigate in practical as well as theoretical manner. Focus is thereby given to the numerical analysis an previous evaluation of the well interaction between the novel axially unsewe higher harmonic air-gap wave base permanent magnet motor esign an both completely ifferent control algorithms. I. INTRODUCTION A straightforwar inustrial evelopment process of electrical variable spee rive systems is fortunately assiste by moern commercial calculation tools [1-3]. However, the extensive an almost precise analysis of the interaction of ifferent control algorithms, lie the vector control or the brushless DC moe, within introuce innovative permanent magnet motor topologies, as e.g. the higher harmonic air-gap base esign, is still a big challenge [4-6]. The implemente main software features, the interacting converter harware an the motor itself are almost analyze in the time-omain. c lin c to ac power converter energy conversion T1 T2 T3 C pm-motor loa T4 T5 T6 voltage measuring PWM- gate river current measuring sensor processor communication FEPROM Figure 1. Outline of important evices of the consiere rive system. Manuscript receive March 25, Christian Grabner is with the Research an Development Department of Drive Systems, Siemens AG, Frauenauracherstrasse 80, D Erlangen, Germany, (phone: , grabner.christian@siemens.com).

2 II. REALIZED DRIVE SYSTEM The investigate rive system is mae up of many ifferent harware components [7-9]. The essential internal interaction between the supply c-lin, the c to ac power converter, the motor, the sensor, the controllers an communicating tass is schematically epicte in Fig.1. The power conversion from the constant c voltage lin level to the ac voltage system at the motor is elementary performe by the PWM technology. The motor construction itself is built up for a mechanical rate loa of approximately 1.35 Nm. Depening on the control moe, an encoer or Hall-sensor is use. The communication purposes as well as main current an spee control algorithm are implemente in the processor. III. HIGHER HARMONIC AIR-GAP WAVE BASED PERMANENT MAGNET MOTOR DESIGN The moving rotor with attache permanent magnets is almost characterize by its even number of involve magnetic poles, whereas the fixe novel stator wining esign comprises the same pole number by means of higher space harmonics [10]. Both, stator an rotor esigns are unsewe. A. Design of the permanent magnet rotor Obviously a number of p = 14magnetic pole pairs are generate along the circumferential air gap irection. Favorably, the high pole number allows a very thin yoe construction. The invoe istribution of the magnetic fiel ue to permanent magnet excitation is shown in Fig.2. The series space expansion of the raial flux ensity component Br ( ϕ ) in accorance to r( ) ˆ ϕ B ϕ = B sin +α = 0 2 π (1) yiels several harmonic coefficients ˆB, N with some istinct contributions, as it is obvious from Fig.3. The fourteenth component ˆB 14 = 0.91T in the no-loa spectrum acts thereby as the funamental air-gap wave of the rive. B. Stator esign invoing istinct harmonics In orer to generate the same number of p = 14 rotor pole pairs, a fourteenth harmonic wave in the circumferential air gap flux ensity istribution has to be generate from the stator current excitation. This is avantageously one by the establishe alternating thin an thic tooth structure along the circumferential air gap. Figure 2. Constant magnetic vector potential lines at no-loa for the range ±0.002 Vs/m. raial airgap flux ensity [T] 0,9 0,7 0,3 0, Figure 3. Fourier spectrum ˆB of the raial flux ensity component at no-loa. harmonic orer [1] Figure 4. Constant magnetic vector potential lines in case of stator current injection for the range ±0.002 Vs/m. raial airgap flux ensity [T] 0,9 0,7 0,3 0, harmonic orer [1] Figure 5. Fourier spectrum ˆB of the raial flux ensity component at efault stator current.

3 The numerically calculate istribution of the magnetic fiel ue to the stator current excitation only is shown in Fig.4. From the series expansion (1), the harmonic components ˆB, N of the wie spectrum in Fig.5 are obtaine. There exists a lot of orinal numbers with even ifferent magnitues. However, only the invoe fourteenth component with ˆB 14 = T can interact with the rotor part in orer to generate a nearby constant mechanical average torque. IV. VECTOR CONTROLLED HIGHER HARMONIC AIRGAP-WAVE BASED PERMANENT MAGNET MOTOR The vector control moe operates the permanent magnet motor lie a current source inverter riven machine applying a continuous current moulation [11-13]. Therefore, a very precise nowlege of the rotor position is necessary. This coul be manage by applying an encoer on the rotating shaft. The vector control software is aapte to the harware system which is schematically epicte in Fig.1. A. Mathematical motor moel The practical realization of the control structure is fortunately one within the rotor fixe (, q ) reference system, because the electrical stator quantities can there be seen to be constant within the steay operational state [14,15]. The stator voltage an flux linage space vectors are therefore formulate in the (, q ) rotor reference frame as ψ ( ) Sq u ( ) ( ) ( ) Sq = rs isq + + jω ψsq, (2) ψ ( ) ( ) Sq = li S Sq +ψmq, (3) whereby r S enotes the normalize stator resistance an ω ( ) stans for the mechanical spee of the shaft. Thereby, the relation (3) covers only weasaturable isotropic motor esigns. The inclusion of some basic ientities for the permanent magnet flux space vector in the (, q ) system, namely Mq ψ = 0, ψ Mq = ψ M + j0, (4) reuces the system (2), (3) to the set of equations u ( ) ( ) ( ) ( ) S = rs is + ls is ωlsisq, (5) u ( ) ( ) ( ) ( ) Sq = rsi Sq + ls isq +ωlsis +ωψ. (6) M Unfortunately, both equations (5), (6) are always irectly couple without the exception of stanstill at ω= 0. That fact is very unsuitable in particular for the esign of the current controller. Thus, with regar to the use vector control topology, a more favorable rewritten form of (5), (6) as u ( ) ( ) ( ) = us +ωlsisq =, (7) = ri ( ) ( ) S S + ls is u ( ) ( ) ( ) q = usq ωlsis ωψ M =, (8) = ri ( ) ( ) S Sq + ls isq is commonly introuce. The ecouple structure (7), (8) introuces in Fig.6 fortunately both fictive voltages u ( ), u ( ) q in orer to ajust the controller of both axes inepenently from each other. B. Simplifie bloc iagram of close-loop control The control schema in accorance to (7), (8) is realize in Fig.7 with regar to the - an q- axis notation as a two-step overlai cascae structure. The outer spee cascae allows ajusting a pre-set spee value nef, after getting smoothe by a PT1- element. The output of the PI spee controller is also smoothe by a PT1-element an restricte by the thermal I 2 t-protection in orer to avoi thermal amages. The PI spee controller has a moerate sampling rate an etermines the emane q-current component. The rive is operate with a efault zero -current component in orer to achieve maximal torque output. The actual measure electrical phase currents are transforme to the rotor fixe (, q ) reference system an continuously compare to the emane an q current components at the innermost current cascae structure. With regar to the - an q-axis separation, the generate PI-current controller output voltages u ( ), u ( ) q are almost seen as fictive quantities in Fig.7, from which the e-coupling-circuit given in Fig.6 calculates the real emane stator voltage components u ( ) S, u ( ) Sq afterwars. The PI current controller is processe by a rate of 8 Hz. uq,em u,em ωls is,act ωψm ωls isq,act usq,em us,em Figure 6. Bloc iagram of the ecoupling-circuit.

4 nef PI spee controller nem nact i,em=0 i,em iq,em I 2 T monitoring iq,act PI-q current controller PI- current cont. i,act uq,em u,em ecoupl -ing usq,em us,em iq,act i,act,q a, b, c D conversion,q a, b, c uconverter imeas nmeas γmeas Figure 7. Outline of important evices of the vector controlle permanent magnet motor. 1 C. Electrical current shape an harmonic spectrum The vector control operation within the quasisteay operational state at rate-loa conition an a efault spee value of 400 rpm enforces the time epenent current shape epicte in Fig.8 within the numerical calculation. A irect comparison with the measure course in Fig.9 in real-time conitions shows a very goo agreement an confirms the assumptions an simplifications within the numerical analysis proceure. The series expansion i() t = ˆI sin( 2πf t+β) (9) = 1 of the calculate electrical current from Fig.8 leas the harmonic components Î, N. It is obvious from the spectrum in Fig.10, that only the esire funamental component Î 1 = 3.75A at 93.3 Hz is governing the total spectrum. The vector control in conjunction with the special motor obviously avois aitional harmonic components an restricts therefore unexpecte thermal heating ue to timeharmonic currents. D. Electromagnetic torque an spectrum The numerical calculate time-epenent mechanical torque m(t) is epicte in Fig.11. It results from the series expansion in time m() t = Mˆ sin( 2πf t+λ) (10) = 0 that there exists within the harmonic components ˆM, N 0 almost the esire constant contribution of ˆM0 = 1.3Nm. Taing a closer loo to the calculate mechanical torque in Fig.12, a very istinct unesire harmonic component ˆM6 = 0.1Nm nown as loa pulsation moment exists at Hz. electrical current [A] 7,5 5,0 2,5-2,5-5,0-7, Figure 8. Calculate motor current i(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm. Figure 9. Measure motor current i(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm. One ivision correspons to 2 ms in the abscissa an 2.5 A in the orinate. loa current [A] 4,0 3,5 3,0 2,5 2,0 1,5 Figure 10. Calculate motor current i(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm.

5 loa torque [Nm] Figure 11. Calculate shaft torque m(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm. loa torque [Nm] Figure 12. Fourier coefficients ˆM of the shaft torque for a spee range of 400 rpm an a constant loa of 1.35 Nm. V. BRUSHLESS DC CONTROLLED HIGHER HARMONIC AIR-GAP WAVE BASED PERMANENT MAGNET MOTOR The brushless DC magnet motor is operate with a space current istribution which oes not rotate smoothly but remains fixe in istinct positions within sixty electrical egrees, an jumps suenly to a position sixty electrical egrees ahea [16]. The brushless DC moe is also nown as an electronically commutate motor operation. The current has to be commutate electronically between ifferent phases controlle by iverse switching semiconuctors [17,18]. This is possible ue to three Hall sensors which provie the necessary six electrical commutation information uring the rotor shaft movement. The current magnitue is ept to a require value an the current flows only through two of the three phases coevally. The generate average mechanical torque remains always constant within the sixty egree electrical perios. The brushless DC control algorithm is set up at the harware explaine in Fig.1. A. Mathematical motor moel The machine equations in terms of accoring stator space vector notation is written in a stator fixe reference frame as ψ ( ) Sαβ u ( ) ( ) Sαβ = rsisαβ +. (11) The introuce stator flux space vector in (11) is fortunately written in case of wea-saturable isotropic inuctances as ψ ( ) ( ) Sαβ = li S Sαβ +ψm αβ, (12) whereby a rotor flux space vector of constant magnitue is assume. The governing relation for the brushless DC feature is erive from (11),(12) u ( ) ( ) ( ) S = r SiS + ls is + jωψ αβ αβ M, (13) αβ αβ whereby any transformation into a rotor fixe (, q ) reference system is avoie. B. Simplifie bloc iagram of the close-loop brushless DC control The importe Hall sensor signals, enote after the with γmeas, are transforme to a continuous actual spee value with the ai of a D- element. Due to the low number of six Hall sensors, only very rough spee etection is feasible. The smoothe signal by a PT1 is enote as nact. The actual spee nact is compare with the emane spee nem. The ifference is in Fig.13 applie to the moerate PI spee controller which elivers the require motor current magnitue. This value is further limite by the thermal I 2 T protection, which taes implicit use of the actual measure motor current iact. The innermost loop in Fig.13 serves as current control. The actually measure motor current imeas first passes a bloc, before the obtaine signal iact is processe with an 8 Hz sampling rate of the current-controller. Depening on the ifference between the emane current magnitues iem an the smoothe measure current iact, the necessary motor voltage magnitue uem is calculate with the ai of a PI current controller.

6 PI controller PI controller nef nem iem uem nact I 2 T monitoring iact imeas nmeas D conversion γmeas Figure 13. Simplifie bloc iagram of the close-loop spee an current control. 6,0 C. Current shape an harmonic spectrum The influence of the electrical current commutation from one phase to the other can be clearly seen in the calculate time-epenent course of Fig.14 for rate-loa an the spee of 400 rpm. The measure quantity is given in Fig.15. Direct comparison of calculate with measure courses shows a very goo concorance. The implemente numerical analysis is also very suitable to preict even higher harmonics in the motor current. The complete current spectrum (9) contains the funamental component Î 1 = 3.84A at 93.3 Hz. Moreover, some very istinct peas within the spectrum coul be observe. Several invoe higher harmonics such as Î5 = 0.81A at Hz, Î7 = 0.62A at Hz, Î 11 = 0.31A at Hz an Î 13 = 0.21A at Hz are causing negative effects, such as unesire thermal heating. loa current [A] 4,5 3,0 1,5-1,5-3,0-4,5-6, Figure 14. Calculate motor current i(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm. D. Electromagnetic torque an spectrum The numerical calculate time-epenent mechanical torque m(t) is epicte in Fig.17 for rateloa an a spee value of 400 rpm. It results from the series expansion (10) that there exists within the harmonic components ˆM, N 0 almost the esire constant contribution of ˆM0 = 1.36Nm. The nown unesire torque fluctuations within Fig.17 can be seen more clearly in the harmonic spectrum epicte in Fig.18. Both istinct higher components are foun to be ˆM 6 = 0.12Nm at Hz an ˆM12 = 0.09Nm at Hz. Other contributions to the torque ripple are obviously suppresse. The occurring unesire loa tip effects are well nown to be responsible for eventually unesire noise emission. Figure 15. Measure motor current i(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm. One ivision correspons to 2 ms in the abscissa an 1.5 A in the orinate. loa current [A] 4,0 3,5 3,0 2,5 2,0 1,5 Figure 16. Calculate motor current i(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm.

7 loa torque [Nm] Figure 17. Calculate shaft torque m(t) for a spee range of 400 rpm an a constant loa of 1.35 Nm. loa torque [Nm] Figure 18. Fourier coefficients ˆM of the shaft torque for a spee range of 400 rpm an a constant loa of 1.35 Nm. VI. COMPARISON OF BOTH CONTROL METHODS In case of the well-balance motor construction an a iligent sensor ajustment, the mostly unesire torque fluctuation of the unsewe motor esign still exist within the vector an brushless DC operational moe. In case of some technical applications, this isavantage coul be accepte; otherwise the rotor has to be sewe. However, for many circumstances, the easy unsewe motor construction an the much cheaper brushless DC control moe in conjunction with the higher harmonic airgap wave base motor esign is often favorize. Unfortunately, aitional copper losses an varying iron losses are still reucing the thermal torque spee characteristic. In orer to overcome those circumstances within certain ranges, the vector moe is commonly preferre. VII. CONCLUSION The novel axially unsewe higher harmonic airgap wave base permanent magnet motor technology has been analyze with regar to the close-loop vector as well as brushless DC control metho. The main focus is thereby given to the verification of previously unnown an almost unesire effects, which coul significantly worsen the quality of the complete rive system. The vector control metho enforces only one istinct funamental component in the electrical current consumption, whereas the brushless DC control causes a wie harmonic current spectrum. Unesire loa pulsation effects of the unsewe motor coul be slightly reuce by preferring the vector control metho. The applie transient electromagnetic-mechanical finite element calculation metho with aitionally couple external circuits in the time-omain allows the inclusion of basic control features an is therefore very suitable for a straightforwar an accurate analysis of the complete converter fe speevariable rive system in avance. REFERENCES [1] J.S. Salon, Finite element analysis of electrical machines, Cambrige University Press: Cambrige, [2] M.J. DeBortoli, Extensions to the finite element metho for the electromechanical analysis of electrical machines, PhD Thesis, Rensselaer Polytechnic Institute, New Yor, [3] J.P.A. Bastos an N. Saowsi, Electromagnetic moeling by finite element metho, Marcel Deer: New Yor/Basel, [4]P.F. Brosch, Moerne Stromrichterantriebe, Vogel: Würzburg, [5] W.Leonhar, Control of electrical rives, Springer: Berlin, [6] G.K. Dubey, Funamentals of electrical rives, Alpha Science Int.: Pangbourne, [7] K.B. Bimal, Power electronics an variable frequency rives: technology an applications, IEEE Press: New Yor, [8] K. Heumann, Principles of power electronics. Berlin: Springer Verlag, [9] G. Seguier an G. Labrique, Power electronic converters: c to ac conversion. Berlin: Springer Verlag, [10]T. Böefel an H. Sequenz, Eletrische Maschinen, Springer: Wien/New Yor, [11]P. Vas, Vector control of AC machines, Oxfor University Press: Oxfor, [12]K.G. Bush, Regelbare Eletroantriebe: Antriebsmethoen, Betriebssicherheit, Instanhaltung, Verlag Pflaum: München, [13]W. Nowotny an T.A. Lipo, Vector control an ynamics of AC rives, Clarenon Press: Oxfor, [14]P. Vas, Electrical machines an rives: A space-vector theory approach, Clarenon Press: Oxfor, [15]P. Vas, Parameter estimation, conition monitoring, an iagnosis of electrical machines, Clarenon Press: Oxfor, [16]R. Lehmann, Techni er bürstenlosen Servoantriebe, Eletroni, Vol. 21, [17]T.J.E. Miller, Brushless permanent magnet an reluctance motor rives, Clarenon Press: Clarenon, [18]J.R. Henershot an T.J.E. Miller, Design of brushless permanent-magnet motors, Oxfor university press: Oxfor, 1994.