MODELLING AND IMPLEMENTATION OF A PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE USING A DSP DEVELOPMENT ENVIRONMENT

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1 MODEING AND IMPEMENTATION OF A PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE USING A DSP DEVEOPMENT ENVIRONMENT S. Van Haute, G. Teröre, K. Hameyer, R. Belmans Katholieke Universiteit euven, Belgium Abstract. A permanent magnet synchronous motor rive using a prototype 6 pole kw inset magnet motor is presente. The rive is controlle by a DSP base control boar that can be programme using the MATAB /SIMUINK software. To investigate the influence of saturation, an accurate measurement proceure base on loa tests is escribe. This metho benefits from the I/O features of the evelopment environment. The theoretical performance limits of the motor are etermine using optimal torue control. Finally, aspects of controller esign, simulation an implementation are briefly iscusse. Keywors. Permanent magnet synchronous motor, flux-weakening, igital control, DSP, /-moelling. INTRODUCTION With the introuction of permanent magnets with a high flux ensity as well as a high coercivity in the late eighties, synchronous motors with permanent magnets became an attractive alternative for application in high performance variable spee rives. In the power range of a few kw to several tens of kw, the sinusoial excite permanent magnet synchronous motor (PMSM) is preferre. It has better characteristics than the brushless DC motor with suare wave currents, especially when a large constant power operation is reuire. Furthermore, avantage can be taken of the aitional reluctance torue when irect an uarature reactances have ifferent values. In esigns with inset an interior magnets, usually X is smaller than X. In this paper, a motor rive with a prototype PMSM with inset magnets an flux weakening capabilities is escribe. As the magnetic parameters of inset an interior PMSMs epen on the saturation level, an accurate measurement proceure base on loa tests is evelope. The results are compare to numerical calculations from a finite element moel. For the prototype motor, the theoretical maximum performance over the entire spee range is etermine. For the instantaneous torue control, a commercially available DSP base environment is use. A stanar VSI-PWM invertor with IGBTs is aapte to be commane by the DSP control boar. where ω is the electrical angular spee an ψ M is the permanent magnet flux. The electromechanical torue can be expresse as follows: [ i ( ) i i ] T = pψ () e M This moel neglects rotor amping an iron losses. However, it can be aapte to take stator iron losses into account [1],[]. The prototype motor use in the simulation an experiments is a kw permanent magnet synchronous motor with sinusoial currents. Figure 1 shows the layout of the rotor. This motor type is referre to as a surface-inset PMSM [] an combines some avantages of both surface mounte an interior permanent magnet motors. From the rotor geometry it can be seen that the irect axis inuctance is smaller than the uarature axis inuctance. This results in an aitional reluctance torue as inicate in euation () an allows for maximum torue-per-ampere control an an extene flux weakening range [4]. The phasor iagram for motor operation is shown in figure. The phasor iagram represents a stationary regime, hence effective values for currents an voltages are use (inicate by capitals). PERMANENT MAGNET SYNCHRONOUS MOTOR MODE Permanent magnet synchronous motors are usually moelle in the rotor reference frame, i.e. Park s - moel. In this synchronous reference frame, the PMSM without rotor amper cage is generally escribe by the following set of euations. i u = Ri + ωi t i u = Ri + + ω i + ωψ t M (1) () Figure 1 Stator an rotor geometry of the 6-pole prototype inset PMSM with the rotor -axis aligne with the magnetic axis of the reference stator phase.

2 The / machine moel is base on a sinusoial variation of the inuctance values. Therefore, a Fourier transform is performe an only the constant value an the first harmonic are taken into account (figure 4). Accoring to figure 4, the / inuctances can be written as = σ + ( ' ) (4) = σ + ( ' + ) (5) Figure DETERMINATION OF MAGNETIC PARAMETERS AND INFUENCE OF SATURATION The optimal control of permanent magnet synchronous motors reuires the accurate knowlege of the machine parameters. Generally, the magnetic parameters epen on the saturation level. For machines with interior magnets, all magnetic parameters (, an ψ M ) show a significant variation with loa current []: (i ); (i ); ψ M (i ). Phasor iagram of a PMSM. Due to saturation, also interaction between -axis an -axis (cross-coupling) can occur [5], however, these can be consiere as secon orer effects [6],[]. Moreover, for the inset magnet type PMSM, only an important variation of with i is expecte. Several methos for measuring the / inuctances of permanent magnet machines at ifferent current an thus saturation levels have been reporte in literature [],[7],[8]. They can be classifie in three categories: static tests; loa tests without loa angle measurement; loa tests with loa angle measurement. The leakage inuctance can not be separately etermine from experiments. As a conseuence, the / inuctance values can only be approximate as ' = (6) ' = 9 (7) It can be shown that the theoretical error is of the orer of half the leakage inuctance. A secon metho to etermine an from static tests is base on the / transformation matrix euation. - Inuctance (mh) phase a 5.5 phase b phase c θ - Rotor position (egrees) Figure Measure phase inuctance values as function of rotor position for the motor shown in figure Static Tests In [] it is shown how the parameters for ifferent loa currents can be obtaine combining static an no-loa tests, without measuring the loa angle. However, this reuires the use of a special inuctance brige operating with a DC voltage. As an alternative, it is investigate here if an can be etermine accurately from the phase inuctances. With an orinary inuctance brige, the phase inuctance values are measure irectly at the machine terminals for ifferent rotor positions (figure ). - Inuctance (mh) θ - Rotor position (egrees) 18 σ+' Figure 4 Measure values, constant value an first harmonic of the phase inuctance value as function of rotor position.

3 1 = Tθ ( TT ) Tθ = (8) with the stator inuctance matrix aa ab ac = ba bb bc (9) ca cb cc For an arbitrary rotor position, the three phase inuctance values are measure, as well as the inuctance of two phases in series. ab ac bc 1 = 1 = 1 = ( ) abs aa bb ( ) acs aa cc ( ) bcs bb cc (1) (11) (1) The results are summarize in Table 1. There is a relatively large ifference for the calculate values for between the applie methos. It can be conclue that the investigate methos give only an iea of the magnitue of the inuctances, but are unreliable for accurate moelling the motor. oa Tests It has been shown in [Chalmers85] an [Stumberger97] that accurate inuctance values from loa tests, incluing the variations ue to saturation, can only be obtaine after a consierable amount of measurement ata processing to reuce the effect of ranom errors. The proceures escribe in [Chalmers85] an [Stumberger97] are moifie, reuiring less measurements an measurement ata processing without loosing accuracy. The measurement set-up is shown in figure 5 an uses the same DSP environment as for the control, which is escribe later in this paper. The machine uner test is riven by a DC machine an operates as a generator. The originality of the proceure lies in the fact that all ata necessary to reconstruct the phasor iagram, incluing the loa angle δ, are obtaine from the registration of the voltage, the current waveforms an an encoer signals uring one or two perios (figure 6). The inuctance values are calculate using the funamental currents an voltages. The ata from the igital power analyzer are average ata over several TABE 1 - / inuctance values obtaine from static tests Inuctance via irectly measure an 9 via an 9 from first harmonic via inuctance matrix (mh) 8,7 9,4 7,5 (mh) 11,57 11,9 11,99 Figure 5 Measurement set up to etermine the / moel inuctance values from loa tests. θ - Rotor position (ra) π u phase voltage (V) t (s) Figuur 6 Rotor position, measure terminal voltage an calculate funamental voltage for the reference phase of the PMSM (f=5 Hz, 7,6 A, δ=-4, ). perios an serve only as a check. Mixing these values with values obtaine from the capture waveforms coul introuce errors in the final results. Curve fitting to evaluate saturation influence on parameters is only necessary on the final results an not in the intermeiate calculation steps, as reuire in [Stumberger97]. The results for the machine with inset magnets are summarize in Table an Table. The recalculate inuctances from the measurement ata are in general higher than the values obtaine from numerical calculations using the flux linkage metho [5]. This is because the latter o not inclue the en wining leakage. TABE - Inuctance values an torue calculate from measurements at ifferent currents an loa angles. I (A) δ ( ) (mh) (mh) T e (Nm),9-1,5 8,8 14,8-5,6 5,5 -,1 8,8 15-7,1 7,6-4, 8,9 15,1-9, 8,1-4, 9 14,9-9,7 TABE - Inuctance, loa angle an torue values obtaine from numerical calculations (inset magnet motor). I (A) δ ( ) (mh) (mh) T (Nm),9-1,4 8,4 14,87-5,4 5,5-9,44 8,5 14,87-7,5 7,6-8,65 8,8 14,88-9,5 8,1-4,71 8,6 14,88-9,68

4 Theoretical, the ifference for an must be ientical. However, in Table an are calculate from the measure ata which inclue the effect of stator core losses. Ajusting the phasor iagram [Honsinger98] an recalculating the motor parameters results in slightly higher inuctances, with a larger increase in than in. It can be seen that for this specific prototype motor, the inuctances are constant, inicating that the level of saturation in -axis an -axis remains constant. However, in [1] it is shown that it can occur that for a similar rotor esign, the - axis inuctance ecreases as -axis current increases ue to the saturation in the stator. This strongly affects the performance an control of the motor. PERFORMANCE CHARACTERISTICS USING FUX WEAKENING The optimal control of PMSMs with < takes avantage of the reluctance torue by introucing a negative irect axis stator current component. This results in a maximum torueper-ampère trajectory in the i - i plane (figure 7), given by the following euation: U DC ω r = (16) ψ M πp I Nx + The maximum spee becomes theoretically infinite when ψ M = I N = i max (17) The factor in (17) as well as / an / in (14), (15) an (16) are ue to the use of the power invariant form of the Park transformation. Introucing the voltage limite maximum power curve, without regaring the current limit [11], the current can be reuce at very high spees when ψ M / < I N. In this case, the control trajectory yieling maximum output at all spees is inicate in figure 8. Calculate results for the prototype motor are shown in figure 9. The results are obtaine using The motor parameters are summarise at the en of this paper. i ψ Mi = i (1) For stationary operation, the current is limite by the rate motor current I r resulting in rate torue The motor voltage is limite by the power electronic inverter. This implies that for a given rotor spee, the current vector must lie within a corresponing bounary. When stator resistance is neglecte, this limiting curves are ellipses ecreasing in size when rotor spee increases [4]. Figure 7 Constant torue hyperbolas, maximum torue-per-ampère trajectory, current limit circle, voltage limit ellipses an optimum current trajectory when ψ M/ > i max. ( / π) U pω r DC i + i ψ + M (14) As a conseuence, rate torue can not be maintaine above the spee at which the voltage limit ellipse intersects the maximum torue-per-ampère trajectory. This spee is the base spee of the motor. ω rb = πp i b U + DC i b ψ + M (15) Reucing the current along the maximum torue-per-ampère trajectory above base spee results in a fast ecrease of output torue. As an alternative, the operating point can be force to leave the maximum torue-per-ampère trajectory along the current limit circle resulting in further flux weakening at maximum current (figure 7). The high spee operating region is consierably extene using the flux weakening algorithm. The maximum spee is reache when all stator current is in the irect axis an is given by Figure 8 i - (A) Optimum current trajectory when ψ M/ < i max. ω base ω max T/A max i (A) Figure 9 Torue hyperbolas, voltage limit ellipses, current limit circle, maximum power an maximum torue-per-ampère trajectory for the prototype motor. I max T r

5 EXPERIMENTA SET-UP The motor control is implemente using a DSP base controller boar with aitional I/O features an an encoer interface (SPACE DS11). This is a MATAB /SIMUINK base evelopment environment. The laboratory test rive further consists of a host PC for the controller boar, an IGBT inverter an the prototype motor, current sensors an an incremental encoer (figure 1). The heart of the controller boar is a TMSC1 igital signal processor. A slave processor is use to perform the igital input an output signals an generate the PWM signals. The controller boar can be irectly programme using MATAB /SIMUINK. Motor currents are measure using EM sensors an fe to the control boar. These signals shoul be be filtere either analog or igital. Due to the parasitic capacitive currents an the fact that the analog filters can not be place close to the inputs of the A/D converters, igitally filtering is preferre here. Phase shift introuce by the filter can be correcte if necessary by aapting the transformation angle from the stator to the rotor reference frame. The position is measure using an incremental encoer. The inverter use is a moifie stanar VSI-PWM inverter with IGBTs. Only an interface to galvanically isolate the control boar from the inverter is ae. The PWM switching signals are fe irectly from the slave processor to the inverter using a high performance optical link, allowing to keep the inverter an rive several meters from the PC with the control boar. The optimal torue control algorithm etermines reference values for irect an uarature axis currents. The PWM generation scheme implemente in the slave processor is base on phase voltage reference values. Therefore, these reference values are etermine using a ecoupling network an the inverse Park transformation. Both subharmonic PWM generation as a space vector moulation are implemente. Figure 1 shows a block scheme of the experimental set-up. The otte frame inicates the functions implemente on the controller boar. The PWM freuency is chosen to be 1 khz. The current sample perio has to be a multiple of the PWM perio or can be eual when the DSP can hanle the algorithm at that spee. CONTROER DESIGN AND SIMUATION To esign the controllers an simulate the entire rive, it is necessary to take the power electronic converter into account. A power electronic system can be moelle in ifferent ways, or, as often encountere, not moelle at all. The level of moelling to be consiere epens on the purpose of the simulation. For control esign purposes, the invertor can be simply moelle by a elay. It is shown that for the subharmonic PWM a general elay time of T p / is aeuate, where T p is the PWM perio [1]. As the rive is controlle by a DSP, it is to be consiere as a sample ata system. There are ifferent approaches to moel these systems [1], [1]. One possibility is to use a iscrete moel [14], using the z-transform an to carry out the controller esign in the z-omain. To enable the use of freuency response methos, a secon transformation is necessary (bilinear transformation). Alternatively, carrying out the initial esign using continuous methos can serve as a guie for a irect iscrete esign. The performance of a system when it coul be realise with continuous harware, is a target for how well the igital system shoul perform an assists in selecting the sample rate. As shown in [1], uner certain conitions a sample ata or iscrete system can be treate as a pseuo-continuous system. This has the avantages with respect to the applicability of optimal control formulations. The effect of A/D an D/A converters, as well as the execution time of the control algorithm itself are taken into account by using euivalent continuous transfer functions. The esigne optimal controllers can be irectly converte to their iscrete euivalents. Figure 1 Experimental set-up. Functions implemente on the DSP-control boar are inicate by the ashe line.

6 Simulations of the rive are performe using MATAB /SIMUINK. Classical controllers, i.e. PID are use for the rive. Combine with the pseuo-continuous moelling, this has the avantage that well-known optimisation criteria can be applie. CONCUSIONS A permanent magnet excite synchronous motor rive is presente, using a inset magnet 6-pole prototype motor with <. Methos to experimentally etermine the / magnetic parameters from both static an loa tests are investigate. The results from static tests have shown to be rather inaccurate. The best results are obtaine using loa tests with simultaneous registration of phase voltages, currents an rotor position an reconstruct the phasor iagram using the funamental values. The theoretical limits of the rive consiering rate motor current an voltage inverter limit are resume. The optimal torue control is implemente using a MATAB /SIMUINK base DSP evelopment environment, using an optic fiber link to control the IGBT inverter. Various PWM algorithms can be programme. Finally, aspects of moelling a sample ata system an esigning the controllers using both continuous an iscrete methos are iscusse.. Appenix PROTOTYPE PMSM DATA Number of poles p 6 Power P kw Rate spee n r 19 rpm Rate current I r 1,6 A Rate torue T r 15, Nm Stator resistance R,76 Ω -axis inuctance 8,8 mh -axis inuctance 15 mh Magnet flux ψ M,56 Vs Acknowlegements The research is supporte by Flaners' Secretary of Economy. The authors are also grateful to the Belgian Fons voor Wetenschappelijk Onerzoek Vlaaneren for its financial support of this work an the Belgian Ministry of Scientific Research for granting the IUAP No. P4/ on Couple Problems in Electromagnetic Systems. The research Council of the K.U.euven supports the basic numerical research. BIBIOGRAPHY [1] Honsinger, V.B.: Performance of polyphase permanent magnet machines. IEEE Trans. Power Apparatus an Systems, 99, 198, [] Mellor, P.H., Chaaban F.B., Binns, K.J.: Estimation of parameters an performance of rare-earth permanent-magnet motors avoiing measurement of loa-angle. IEE Proceeings-B, 18, 1991, -. [] Sebastian, T., Slemon, G.R.: Operating limits of inverter riven permanent magnet motor rives. IEEE Trans. Inustry Applications,, 1987, 7-. [4] Jahns, T.M., Kliman, G.B., Neumann, T.W.: Interior permanent magnet synchronous motors for ajustable spee rives. IEEE Trans. Inustry Applications,, 1986, [5] Sneyers, B., Novotny, D.W. ipo, T.A.: Fiel weakening in burie permanent magnet AC motor rives. IEEE Trans. on Inustry Applications, 1, 1985, [6] Chalmers, B.J.: Influence of saturation in brushless permanentmagnet motor rives. IEE Proceeings-B, 19, 199, [7] Chalmers, B.J., Hame, S.A. Baines, G.D.: Parameters an performance of a high-fiel permanent-magnet synchronous motor for variable-freuency operation. IEE Proceeings-B, 1, 1985, [8] Štumberger, B., Kreca, B. Hribernik, B.: Determination of parameters of synchronous motor with permanent magnets from measurement of loa conitions. IEEE-Int. Electric Machines an Drives Conf. Recor, 1997, WB [9] Pahner U., A general esign tool for numerical optimisation of electromagnetic evices, Ph.D. Thesis, K.U.euven, Belgium, [1] Van Haute, S., Henneberger, St., Hameyer, K., Belmans, R., De Temmerman, J., De Clerc, J.: Design an control of a permanent magnet synchronous motor rive for a hybri electric vehicle. Proc. EPE Conf., 1997, , [11] Morimoto, S., Takea, Y. Hirasa, T. Taniguchi, K.: Expansion of operating limits for permanent magnet motor by current vector control consiereing inverter capacity. IEEE Trans.Inustry Applications, 6, 199, [1] Bühler H., Réglage e systèmes 'électroniue e puissance. Presses polytechniues et universitaires, ausanne, 1997 [1] Franklin, G.F., Powell, J.D., Workman, M..: Digital control of ynamic systems. Secon eition, Aison-Wesley, New York, 199. [14] abriue, F., Fu, Y Sente, P. Buyse, H.: Discrete moelling of the fiel oriente control system in VSI fe AC motor rives,. Proc. EECTRIMACS, 1996, Aress of the authors: Katholieke Universiteit euven, E.E. Dept., ESAT/EEN Karinaal Mercierlaan 94 B-1 euven, Belgium

7 References 1. Binns K.J.; Sneyers B.; Maggetto G.; ataire Ph.: Rotor-position-controlle permanent magnet synchronous machines for electrical vehicles, ICEM 8, 198, pp Sneyers B.; Maggetto G.; Van Eck J..: Inverter fe permanent magnet synchronous motor roa electric traction, ICEM 198, 198, pp Jahns T.M.; Kliman G.B.; Neumann T.W.: Interior permanent magnet synchronous motors for ajustable -spee rives, IEEE Transactions on Inustry Applications, Vol. IA-,No.4, 1986, pp [5] Jahns T.M.; Kliman G.B.; Neumann T.W., Interior permanent magnet synchronous motors for ajustable -spee rives, IEEE Transactions on Inustry Applications, Vol. IA-, No.4, 1986, pp Morimoto, S.; Sanaa, M.; Takea, Y.: Optimum Machine Parameters an Design of Inverter-Driven Synchronous Motors for Wie Constant Power Operation, Proc. IAS 94, pp Chang,.; Dawson, G.E.; Eastham, T.R.: Permanent Magnet Synchronous Motor Design: Finite Element an Analytical Methos; ICEM 9, 199, pp Slemon, G. R.; Xian,.: Moelling an Design Optimisation of Permanent Magnet Motors, Electric Machines an Power Systems, vol., no., 199, pp. 71-9;

8 7. Nipp, E.: Alternative to Fiel Weakening of Surface Mounte Permanent Magnet Motors for Variable Spee Drives, Proc. IAS 95, pp Zhong.; Rahman M.F.; im K.W.: Moelling an experimental stuies of an instantaneous torue an fiel weakening control scheme for an interior permanent magnet synchronous motor rive, EECTRIMACS 1996, pp Nasar, S. A.; Bolea, I.; Unnewehr,.E.: Permanent Magnet, Reluctance, an Self-Synchronous Motors, CRC Press, onon Tokyo, Sebastian T.; Slemon G.R.: Operating limits of inverter-riven permanent magnet motor rives, IEEE Transactions on Inustry Applications, Vol. IA-,No., 1987, pp Jahns T.M.: Flux-weakening regime operation of an interior permanent-magnet synchronous motor rive, IEEE Transactions on Inustry Applications, Vol. IA-, No.4, 1987, pp Haji-Minaglou J.-R: Antriebskonzepte mit permanent-erregten Synchronmotoren für en Einsatz im Elektrofahrzeug, PhD-thesis RWTH Aachen, Sneyers B.; Novotny D.W.; ipo T.A.: Fiel weakening in burie permanent magnet AC motor rives, IEEE Transactions on Inustry Applications, Vol. IA-1,No., 1985, pp π 6 θ - Rotor position (ra) u phase voltage (V) t (s) Figuur 6 Rotor position, measure terminal voltage an calculate funamental voltage for the reference phase of the PMSM (f=5 Hz, 7,6 A, δ=- 4, ).