Dynamic motor parameter identification for high speed ... - IEEE Xplore

486

IEEE Transactions on Energy Conversion, Vol. 14, No. 3, September 1999

Dynamic Motor Parameter Identification for High Speed Flux Weakening Operation of Brushless Permanent Magnet Synchronous Machines Uwe Schaible, Student Member, IEEE

Barna Szabados, Senior Member, IEEE

Power Research Laboratory McMaster University Hamilton, ON, CANADA

Power Research Laboratory McMaster University Hamilton, ON, CANADA

Abstract: An experimental investigation is conducted to determine the behaviour of brushless PM synchronous machine parameters in the high speed flux weakening operating range. Real-time operating characteristics are determined for two commercially available 4 Nm interior PM synchronous machines. Special computer assisted measuring techniques are employed using an experimental vector controlled drive, capable of providing sinusoidal excitation waveforms at up to 8000 rpm. Perturbation analysis is performed on the measured data and results are applied to a variation of the classical d-q axis equivalent circuit model. The experimental results are repeatable and show a significant variation in the machine parameters as a function of the torque angle. Magnetic non-linearities are also identified and accounted for through recomputation of the machine model over a wide range of operating points. The authors demonstratethat all tests can be performed with no previous knowledge of manufacturer proprietary information or results from finite element simulation.

efficiency levels when compared with conventional id= 0 control [ 11-[4]. Proper implementation of flux weakening control requires the knowledge of synchronous machine parameters. The most common parameters required for the implementation of such advanced control algorithms are the classical simplified model parameters: L, - the direct axis selfinductance, Ln- the quadrature axis self- inductance, and Ymag the permanent magnet flux linkage. Prior knowledge of the previously mentioned parameters, and the number of pole pairs p , allows for the implementation of torque control through the use of current vector control and the generalized synchronous machine torque expression, shown in (1).

Keywords: Parameter estimation, permanent magnet machines, current control, microcomputers, electric variables measurement.

The required parameters determine the linearized representation for the d-axis reactance X,, q-axis reactance X,,, and magnet excited voltage EO. Such representation is used to provide a linearized machine model from which control rules such as voltage limit ellipses and maximum torque-per-ampere trajectories can be calculated [ 11. The non-linearity of certain types of salient-pole synchronous machines has made it difficult to apply these control rules. Previous work has shown that the synchronous machine parameters can be highly non-linear and can vary significantly as the machine is loaded [SI-[9]. Hence, modelling of L,, Lq,and Ymag as fixed values over the machine’s entire range of speed and loading results in an inaccurate and less effective implementation of flux weakening in advanced torque control applications. The research presented in this paper is a result of the difficulty encountered by the authors in developing a high performance vector controlled drive for the high speed operation of commercially available brushless PM synchronous machines. The lack of both manufacturer proprietary information and the results of finite element simulation is overcome by conducting special computer assisted measuring techniques on a laboratory test setup. The conducted tests account for magnetic nonlinearities and demonstrate the ability to perform repeatable analysis of any brushless PM synchronous machine over its entire operating range.

I. INTRODUCTION

S

INUSOIDAL back-EMF brushless PM synchronous machines are receiving much attention due to their high speed, power density and efficiency characteristics. New rotor configurations, and the commercial availability of high field strength neodymium-iron-boron magnets has reduced the cost of such machines to a level where they can now provide a significant, yet affordable, performance improvement in many variable speed applications. Unfortunately, manufacturers of such commercially available machines provide very little information for drive designers wishing to implement high performance torque control. Advanced high speed salient-pole synchronous machine drives use vector control in the synchronously rotating reference frame to actively vary the d-axis armature current as a function of loading and speed. Such operation, commonly referred to as ‘flux weakening’, allows for higher speed, torque, and PE-342-EC-0-12-1997 A paper recommended and approved by the IEEE Electric Machinery Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Energy Conversion. Manuscript submitted July 2, 1997; made available for printing December 12,1997.

11. EXPERIMENTAL INVESTIGATION

A . Test Setup Two commercially available brushless PM synchronous machines were purchased from the same manufacturer. Both machines were specified as having a sinusoidal back-EMF, balanced on all three phases. A summary of the manufacturer supplied technical specifications is provided in Table I. 0885-8969/99/$10.00 0 1997 IEEE

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487

TABLE I MANUFACTURER SUPPLIED TECHNICAL SPECIFICATIONS Machine A

Machine B

Max. Operating Speed (rpm)

8000

6000

Max. Cont. Power (W)

2290

1490

Max. Stall Torque (Nm)

4.1 1

3.95

Line-Line Resistance (62)

0.27

0.57

Line-Line Inductance (mH)

1.86

2.30

Back-EMF (Vo Itskrpm)

24.9

19.9

0.235

0.235

FerriteCeramic

Neodymium-

Parameter

Torque Sensitivity (N.m/A mp) Permanent Magnet Type

Microprocessor

1 k

;mj

Data

__t

Va,

Irms

Acquisition System

P

Shaft Position

Vector Controlled

Drive

Iron-Boron

Machine B was recommended as a suitable replacement for the now obsolete Machine A. No further control-specificinformation was available from the manufacturer, either due to a lack of availability or due to its proprietary nature. The basic block diagram of the test setup is shown in Fig. 1. A conventional brushed dc machine is coupled, through a speed reducer, to the Machine Under Test (MUT). Loading of the MUT is accomplished by configuring the dc machine as a separately excited generator and varying its field current as it generates into a resistive load bank. A microprocessoris used to interface with the user and allows for manual control of the MUT's phase current vectors. The MUT operatingpoint is set by simultaneouslyvarying the machine load and the current vector command sent by the microprocessor to the vector controlled drive. The current vector command magnitude I*mag and angle I*a are adjusted through user manipulation. Inputs to the microprocessor include real-time information about the machine speed (a),the true r m s phase voltage (Vm), true rms phase current (I,,,,,), and the average power consumed (P). The real-time information is recorded at different operatingpoints as the MUT is tested. Phase current and voltage inputs to the MUT are measured with respect to a fixed reference frame through use of a data acquisition system. A real-time snapshot of the MUT excitation waveforms is acquired to supplement the operating point information recorded by the microprocessor. A shaft position encoder is connected to the rotor of the test machine and is used to provide the marker pulse (M,,) from which the reference frame is established. The position encoder is also used to provide rotor position information to the vector controlled drive. B. Control Methodologv

Sinusoidalback-EMF is a characteristic obtained frombrushless permanent magnet machines incorporating a buried or interior permanent magnet rotor configuration [4]. This type of rotor configuration can cause the reluctance to be greater along the d-axis flux paths than along the q-axis flux paths, translating into a higher q-axis inductance (LJ than d-axis inductance (LJ. Hence, the second term in (l), also known as the reluctance torque component, can be exploited to produce positive torque

Field Control

U

Machine

w -

Fig. 1. Test setup for parameter identification

Vdl

Vidl

d-axis Fig. 2. Fundamental frequency phasor diagram in addition to the main magnetizing torque, only if there is a negative d-axis current component (id). Flux weakening operation is possible by using vector control that produces such positive reluctancetorque through the active manipulationofthe input current phasor in the second quadrant of the synchronously rotating d-q axis reference frame. Machines A andB were specified as having a sinusoidalbackEMF. It is assumed that the test machines have interior permanent magnet rotors and also the saliency to cause Lq to exceed L,. A phasor diagram for the near rated load flux weakening operation of a brushless PM synchronous machine is shown in Fig. 2. The angle 6,is used to represent the torque angle of the machine. Current phasor Is,is offset by an angle a, from the q-axis to establish a negative d-axis current component.

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0 -32 r

0

40

80

120

160

200

8 240

280

320

360

1

0

1000

2000

3000

4000

Mechanical Degrees

Specified Cont. Torque Range

Fig. 3. Machine A measured waveforms at 7500 rpm and rated load 20,

5000

6000

7000

8000

Speed (rpni) Tested Elec. Torque Range

Fig. 5 . Machine A specified and tested torque range

(90

4 h

g

3

0

e2 E I

.20

L

0

0

40

80

I20

160

200

240

Mechanical Degrees

280

320

1-90

0

1000

2000

Fig. 4. Machine B measured waveforms at 7500 rpm and rated load

3000

4000

5000

6000

7000

8000

Speed (rpm)

360

0 Specified Cont. Torque Range

Tested Elec. Torque Range

Fig. 6 . Machine B specified and tested torque range

Hence, a positive reluctance torque would be developed for an interior permanent magnet machine. It is desired to operate Machines A and B in this manner. The phasors shown in Fig. 2 consist of only the fundamental frequency components, denoted by subscript 1, and can be derived from measurable input quantities to the MUT. The effects of higher order harmonics on the MUT's torque production can be neglected by maintaining near sinusoidal current and voltage excitation waveforms. Conventional synchronous machine drives employ sinusoidal waveform excitation at speeds up to 3500 rpm, after which the excitation is switched to a simpler six step square wave scheme [lo]. The authors have constructed a 7.5 kVA vector controlled drive which is capable of supplying low harmonic sinusoidal excitation for high speed machine operation up to 8000 rpm.

Having established the synchronously rotating d-q axis reference frame, the VSI is reconnected to the MUT and the dc machine is reconfigured as a separately excited generator. The reference currentphasor magnitude rmW and angle I"=is varied to place the actual current phasor to the MUT at desired positions relative to the d- and q-axis. I*,,,agand 1'- can be set to produce the Maximum Torque ConversionEfficiency (MTCE) for a specific loading by monitoring the ratio between the operating speed and the product between the input phase current and voltage. Tests are conducted by establishing the MTCE operating points at different loadings while maintaining a constant speed. A realtime snapshot of the MUT's excitation waveforms is obtained from the data acquisition system for each MTCE operating point. Speed, voltage, current and power information is simultaneously recorded by the microprocessor.

C. Test Procedure

D. Measured Results

Reconstruction of the MUT's phasor diagram begins with the establishment of its q-axis. The dc machine in Fig. 1 is reconnected to operate as a motor and drive the MUT over the desired operating range. The MUT is operated as a generator and its open circuit terminal voltage is measured by the data acquisition system. The fundamental component of the terminal voltage is reconstructed from the measured data, and plotted with respect to the fixed reference frame obtained from the marker signal. The angular displacement of the crest of the reconstructed sinusoid with respect to the marker is used to establish the q-axis, and thereby the d-axis.

The real-time snapshots of the excitation current and voltage waveforms for 7500 rpm, rated load operation of Machines A and B are shown in Figs. 3 and 4. In both cases, the total harmonic distortion factor of the waveforms is less than 10%. All waveforms are measured with respect to the marker at 0 mechanical degrees. The q-axis is assumed to remain fixed with respect to the marker, allowing the fundamental frequency diagram to be reconstructed at any operating point. Tests were conducted on both machines for constant speed operation between full load and no load. The tests were repeated at intervals of 500 rpm, spanning the high speed range of 3500

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Fig. 10. (a) d-axis equivalent circuit (b) q-axis equivalent circuit

0

5

20 Torque Angle (delta) IO

15

25

-30 30

Fig. 8. Machine B measured data and polynomial fits at 5500 rpm

to 7500 rpm. Figures 5 and 6 show a comparison between the manufacturer specified continuous torque capabilities, and the actual electrical torque measured during the tests. The results show that the continuous torque capabilities of Machine A have been overstated by the manufacturer.

III. ANALYSIS OF MEASURED RESULTS A . Phasor Diagram Reconstruction Phasor diagram reconstruction provides the necessary data required to identify load dependent trends in the d-q axis representation of the excitation waveforms. Significant errors can be developed through inaccurate determinationof the Fig. 2 phasor diagram angles 6 and a. Accurate analysis is possible by computing a Fourier analysis of the excitationwaveforms over a complete mechanical revolution. Phasor angles S and a are determined by measuring the electrical angle of the peak of the fundamentaland adjusting for the q-axis. Phasor magnitudes are determined by calculating the measured waveform's distortion factor and adjusting the microprocessormeasured true rms value for that waveform. Reconstruction of Fig. 2 is completed by using an empirical relationship to calculate the value of the frequency and temperature dependent stator resistance Rs. The d-q axis transformed excitation waveform magnitudes are plotted against their calculated electrical torque angle S. A relationshipbetween the excitation inputs and the corresponding electrical torque angle is established by fitting a polynomial through the measuredpoints. The polynomial fits resulting from the measured data of a 5500 rpm loading test on each machine are shown in Figs. 7 and 8. All of the polynomial fits are repeatable to within the 5% measurement error inherent with

this investigation. Machine A has a discontinuity at 6~35'. The discontinuity is detected through a sudden change in the trend of I*, at the MTCE. The discontinuity characteristic shown in Fig. 7 is repeatable and is believed to be caused by a change in the reluctance of the flux path in the machine. As the machine undergoes increased flux weakening at higher speeds and loadings, certain critical sections along the flux path come out of saturation. The torque angle at the discontinuity shifts from a higher angle of 6 ~ 4 8 to " a lower angle of k 2 0 " as the speed setpoint is increased from 4000 to 7500 rpm. No discontinuities are observed at 3500, 4000 and 7500 rprn. The lack of discontinuites at these speeds indicates that for the tested load range, the critical flux path sections remain unsaturated at 7500 rpm, and fully saturated at speeds 5 4000 rpm. Machine B has no discontinuities over the entire operating range. The difference between the two machines is most likely caused by the use of higher field strength neodymium magnets in Machine B. Machine B's critical flux path sections remain unaltered, even when it is subjected to higher levels of flux weakening.

B. Data Modelling The general machine model for a brushless PM synchronous machine consists of only a highly simplified representation of the actual operation of the machine. The static parameter model assumes lossless operation without the effects of magnetic saturation and non-linearities. Acceptable results are possible when using this model at lower speeds and over a nan-ow speed range. The effects of core losses and non-linear behaviour do become more prevalent at higher speeds and over a wide speed range. Core losses must be included when modelling the higher frequency PM synchronous machine operation. Fig. 10 shows the d- and q-axis equivalent circuits used to model high speed operation. The model includes copper losses which are represented by resistance R,. Core losses are represented by including a loss component proportional to the machine's internal voltage Vi [3][6]. A resistance Rc is included for this

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Fig. 14. Machine B computed parameters at 3500 rpm

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Torque Angle (delta)

Fig. 1 I. Machine A computed parameters at 3500 rpm

0

5

50

40

36

60

Torque Angle (delta)

Torque Angle (delta)

Fig. 15. Machine B computed parameters at 5500 rpm

Fig. 12. Machine A computed parameters at 5500 rpm 48

Eo

Eo 36 -24

Xd

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IO

20

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Torque Angle (delta)

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Torque Angle (delta)

Fig. 13. Machine A computed parameters at 7500 rpm

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Fig. 16. Machine B computed parameters at 7500 rpm 5

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3500 rpm 3.

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5500 rpm

I .

0

10

20

30

40

50

60

Torque Angle (delta) Fig. 17. Machine A calculated electrical torque at MTCE

0

5

IO

15

20

25

30

Torque Angle (delta) Fig. 18. Machine B calculated electrical torque at MTCE

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491

investigation. All vector controllablelosses are accountedfor in this model, however, the model does not account for stray load losses such as those incurred by circulating flux in the machine's back-EMF harmonics. C. Parameter Identification Evaluation of the general torque expression, given by (I), requires the knowledge of the unknown parameters X,, Xq,and E,. Mathematical analysis of the Fig. 10 d- and q- axis equivalent circuits yields (2) and (3). Rc =

i q Xq Ra

Vd

observed for both machines.

D. Dynamic Parameter Utilization The measured parameters show that the manufacturer supplieddata in Table I is insufficient for high performance flux weakening operation of the test machines. The variation of the machine parameters indicates the need to re-write (1) to account for the actual operating conditions of the brushless PM synchronousmachine. A dynamicparameter equivalent of (1) is given by (6), as derived from the Fig. 10 equivalent circuits.

- Xq Vq

- id& - Xq iq (3)

iod

= id

-(

vd

- Rs id Rc

)

The desired unknown parameters can be calculated by assuming that the parameters remain constant for small changes in the operating point. Polynomial fits, such as those in Figs. 7 and 8, are used to predict a new operating point at 6, by perturbing the torque angle 6 , with a small perturbation angle A6 = 0.1O [8][9]. Setting X,=Xd, =X,, Xq=Xq1=Xq2, and Eo=Eo,=E, over a small change in 6 yields the desired parameters through (4) and (5), with back substitution into (2) and (3). x q

=

vdl-

AVdz-Ra(id1- A i d 2 ) iqi - A iqz

where: A=

(4)

V,I - iqi RS

K,2 - ivz RS

Vqi-Vqz+ Rs(ioq2-ioqi)

xd =

K (iod 2 - iod I)

(5)

Perhirbation analysis results are shown in Figs. 11 thru 16 for 3500, 5500, and 7500 rpm operation. The characteristics indicate that the q-axis reactance (XJ remains almost linear and constant with torque angle for both machines. The magnet exited voltage (Eo) varies considerably for Machine A, yet remains approximately linear and constant with torque angle for Machine B. The difference is mainly due to less fluctuation in the flux path reluctance of Machine B for variations in speed and loading. A wide variation in the d-axis reactance (X,) can be

Equation (6) is used to calculate the dynamic parameter electrical torque for the two machines, as shown in Figs. 17 and 18. The T,(S,w) characteristic can be used to form a look-up table in a high performance MTCE control algorithm. Simplificationof ( 6 )can be made for machines such as Machine B, where X, and Eocan be approximatedas constant values with changes in torque angle 6. The results clearly indicate that this simplificationcannot be extended to Xd.

Iv.

CONCLUSIONS

The preceding investigation has successfully demonstrated the ease and repeatability of the proposed parameter identification method. All tests can be performed using only the input excitation waveforms to the test machine, without results from finite element simulation, and without previous knowledge of manufacturer proprietary information. The test results clearly indicate a significant variationin the contxolparameters required for high speed flux weakening operation ofbrushless permanent magnet synchronous machines. Incompletemanufacturer supplied data can be supplemented with the results from this investigation. The proposed parameter identification method can be used by machine drive designersto collect data for use in high performance flux weakening vector control algorithms. Flux weakening control schemes that assume a constant L,, fail to properly utilize the reluctance torque component of salient pole synchronous machines. Dynamic characterizationof the control parameters enables full utilization ofthe reluctance torque. Such utilization provides the benefits of higher torque and efficiency over the entire specified speed and torque operating range, It also enables machine designers to identify previously immeasurable performance characteristics and optimize their designs for specific operating torque regions.

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V. REFERENCES [ 11 T.M. Jahns, “Motion Control with Permanent-Magnet AC Machines”,

Proc. IEEE, vo1.82, no. 8 , August 1994, pp. 1241-1252. [2] S.R.MacMinn and T.M. Jahns, “Control Techniques for Improved HighSpeed Performance of Interior PM Synchronous Motor Drives”, IEEE Trans. Indusfry Applications, vol. 27, no. 5, September 1991, pp. 9971004. [3] S. Morimoto, Y. Tong, Y.Takeda, and T. Hirasa, “Loss Minimization Control of Permanent Magnet Synchronous Motor Drives”, IEEE Trans. IndusfryApplicafions,vol.41, no. 5, October 1995,pp. 511-517. [4] T.M. Jahns, G.B. Kliman, and T.W. Neumann, “Interior Permanent Magnet Synchronous Motors for Adjustable-Speed Drives”, IEEE Trans. Industry Applications, vol. IA-22, no. 4, July 1986, pp. 738-747. [SI V.B. Honsinger, “The Fields and Parameters of Interior Type AC Permanent Magnet Machines”, IEEE Trans. Power Apparafus nnd Systems, vol. 101, no. 4, July 1986, pp. 867-875. [6] A. Consoli and A. Raciti, “Analysis of Permanent Magnet Synchronous Motors”, IEEE Trans. Indusfrial Electronics, vol. 27, no. 2, March 1991, pp. 350-354. [7] M.A. Rahman and P. Zhou, “Analysis of Brushless Permanent Magnet Synchronous Motors”, IEEE Trans. IndusfrialElecfronics,vol. 43, no. 2, April 1995, pp. 256-267. [E] M.A. Rahman and P. Zhou, “Accurate Determination of Permanent Magnet Motor Parameters by Digital Torque Angle Measurement”, Journal ofApplied Physics, vol. 76, no. IO, November 1994, pp. 68686870. [9] P. Zhou, M.A. Rahman, and M.A. Jabbar, “Field Circuit Analysis of Permanent Magnet Synchronous Motors”, IEEE Trans. on Magnetics, vol. 30,no. 4, July 1994, pp. 1350-1358. [IO] B.K. Bose, “A High Performance Inverter-Fed Drive System of an Inknor Permanent Magnet Synchronous Machine”, IEEE Trans. Industry Applicafions,vol. 24, no. 6, November 1990, pp. 987-997.

VI. BIOGRAPHIES Uwe Sehalble (S’91) received the B.Eng. & Mgt., M.Eng., and Ph.D. degrees from McMaster University, Hamilton, Ontario, Canada,in 1992,1994, and 1997,respectively. He is currently lecturing in the area of realtime microprocessor systems and is conducting research at McMaster’s Power Research Laboratory in the area of solid state variable frequency drives for high speed machines. He is also actively involved with the development of industrial research partnerships between McMaster and industry in the field of power electronics and power systems. Barna Szabados (S’67-M’71-SM187)received the Diplama d’Ing6nieur ENS1 from the University of Grenoble in 1967, and the Master’s and Ph.D. degrees in electrical engineering from McMaster University, Hamilton, Ontario, Canada, in 1969 and 1971 respectively. Currently, he is Professor of Electrical and Computer Engineering at McMaster University and Director of McMaster’s Power Research Laboratory. He is working in the area of solid state converters, field representations in electrical apparatus and electromagnetic interference, and local area networking in a factory environment. All these projects are done in tight cooperation with industrial partners, Westinghouse Canada and General Motors. He holds positions on several committees. Dr. Szabados is a member of several international professional societies.