Sensor Less Speed Measurement Of Im

Sensorless Speed Measurement of Induction Motors Roberto Micheletti Department of Electrical Systems and Automation, University of Pisa Via Diotisalvi. 2 1-56126 P i s , Italy

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Abstract The paper deals with the accurate slip measurement of induction motors. The proposed procedirre uses a non-invasive slip nieaszirement scheme based on digitalfilferingand dvnamic parameter estimation. The slip measurement is carried ouf M'ithout speed sensor and is deduced analvzing the magnetic field harnionics spectruni in pro1imit.v of the induction motor. First the enif induced waveform, taken from U searching coil, is filtered rising algorithms based on the discrete Fourier transform. Then the stator frequencb and rotorfiequency are obtained b? comparing thefiltered voltage with a mathematical model using an optimization procedure. The model's parameters are varied until an adequate match is obtained with the filtered voltage. Experiniental resulrs are presented to validate this method.

K@xQ&

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Digital filtering, JndiJrtion mofors, Slip

measurement. 1. INTRODUCTION Induction motor drives are now being more and more in process industry because of the application of the field oriented control strategy. However, the performance of such control method depends strongly on the accuracy of the motor parameters uscd in the vector controller. It is well known that the variation of the rotor resistance and rotor constant time has a most dominant effect on the control performance. Unfortunately the rotor resistance depends widely on the rotor temperature and on the slip frequency, resulting in the deStruction of the decoupled condition of the flux and torque. In recent years many studies are then carried out to overcome this situation. Estimation methods to get rotor parameters use extended Kalman filter approach [I], observer technical [2] and adaptive system [3]. It is actively proceeding to research for speedsensorless vector control which estimates rotor speed and slip

frequency without speed sensor. The slip frequency detection is carried out utilizing rotor slot harmonics [4], [ 5 ] or sensing and exploiting the stator current [ 6 ] . This paper presents an algorithm for the accurate measurement of the slip frequency based on digital filtering and dynamic parameter estimation method [7]-[9]. The slip frequency measurement is carried out without speed sensor and is deduced analyzing the magnetic field harmonics spectrum in proximity of the induction motor. First the emf induced waveform, taken from a searching coil, is filtered using algorithms based on the discrete Fourier transform. Then the stator frequency, rotor frequency and consequentially the slip frequency are obtained by comparing the filtered voltage with a mathematical model using an optimization procedure. The model's parameters are vaned until an adequate match is obtained with the filtered voltage. The parameters that affect the performance of the algorithm are essentially the data window size, the sampling rate and the characteristics of the filter. Mathematical development of the algorithm is presented and the effects of key parameters that affect the performance of the algorithm are discussed. A representative set of experimental results are presented. The proposed method can be reliably applied in rotor parameter identification in steady state conditions and running test.

11. ESTIMATION ALGORITHM OF STATOR AND ROTOR FREQUENCY The stator frequency f, and rotor frequency f, are obtained with the same procedure by comparing the respective filtered voltages with a mathematical model using an optimization method.

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-a=Eo .

After filtering operation, we obtain a set of "n" samples of the stator (rotor) voltage. The filtered voltage can be approximated by a sinusoid

AA

'

-a=Eo . aR

-a=Eo aw

'

(7)

There results after rearrangement v(t)=Vsin(at+O)

(1)

gy,"(f.\)4Ja1=

where V a n d 0 are amplitude and phase,respectively. By rcwriting the voltage in terms of quadrature components "(1) = A sin wt + B cos wt ="(A, B, w, t)

(2)

with

0 = tan -'(B/A) Expanding v(t) in a Taylor series in the neighborhood

of given values A a , Bo, (rh of parameters A, B, w gives

where the higher order terms of the expansion are ignored and n = (A0 , BO,%). The principle of operation of the estimation technique is based on the comparison between the real values of the filtered voltage and the estimation values of the model. Thus the problem consists in determining the parameters A, B, w able to minimize the error between sampled values and estimation values. The total square error, at instant 4. is

Solution of (8) gives the corrections AA, AB and Aw necessary for updating parameters A , B and w for each iteration step. This recursive technique permits t o obtain the unknown stator and rotor frequency with good accuracy. Finally the slip frequency is given by

s = fJf

expressed as

where vr(ts) and v(ts) represent the sampled outputs of the real system after filtering and the model reference at time t,,respectively. Substitution of (4) into ( 5 ) yields

Iterative methods are well known for their sensitivity to the initially guessed values of the unknowns. The initial values used for the model reference are determined as follows. The initial value of o, is obtained using the first five samp les of the input voltage

?

The total square error is minimized by solving the partial derivatives of (6) relative to A, B, w evaluated at Ao.Bo,oh

(9)

e-

3 [2v(tI+2T&v(t J-v(t, +4TJ] 2[v(t l+T J+43t ,+2TJ +v(t ,+3Tsd

The initial values of system:

(10)

and & are determined solving the

v ( t , ) = A a s i n w , t , + Bocosw,t, (11)

v(tl +Ts)=Aosin[(rh(t, + T s ) l + B o c o s [ ~ ( t +Ts)l ,

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111. RESULTS The measurement algorithm has been verified to investigate the validity of this technique. The rated values of the induction motor used in the experiments are given in Table I . Table 1 Rated values of a tested induction motol Power Volta e Y Current (U) Fre uenc Revolution er minute (rimin)

the emf component at the stator frequency (emf at stator frequency component). The second one is a lowpass filter with cutoff frequency set to 2 Hz. The output of the lowpass filter is the emf component at the rotor frequency (emf at rotor frequency component). The emf at stator and rotor frequency components with motor loaded at 1480 rpm are shown in Fig. 2.

21.5 A

The slip frequency measurement is carried out analyzing the waveform of the induced emf, taken from a searching coil, due to the magnetic field in proximity of the induction motor. Fig. 1 shows the waveform of the induced emf with motor loaded at 1480 rpm; the slip frequency is s=1.33%, corresponding to a rotor frequency of 0.667 H z . Useful estimates o f the slip frequency are obtained using about 114 cycle of the emf at stator and rotor frequency, therefore the proposed procedure could be compatible with control purposes. The searching coil is put on the frame of the induction motor.

,,me ( 5 )

Fig. 2.Emf at stator and rotor frequency with motor loaded at 1480 rpm

Fig. 3 shows the waveform of the induced emf with motor loadedat 1470 rpm; the slip frequency is s=2.00%,

emf (V)

04

M September, 2003

0.3

emf (v)

0.2 0.1 00

4.1 0.2

0.3 0.4

0 11818 d o 8 ab,. x.wr

10

x (8Yf0,)

30

20 em,

time (E)

Fig. 1. Waveform of the induced emf with motor loaded at 1480

m.

0 (,,le a07 ad,. x - v a

30

20

10

x (aYtO))

em,

xime I S )

Fig. 3. Waveform of the induced emf with motor loaded at 1470 Then this waveform is filtered using algorithms based on the discrete Fourier transform. The filtering operation is obtained with two eighth order IIR filters. The first one is a bandpass filter with a center frequency of 50 H z and bandwidth 4 Hz, whose output is

m.

The emf at stator and rotor frequency components with motor loaded at 1470 rpm are shown in Fig.4.

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s o l y

. .

,

~

4-6 Septeinbev, 2003

. .

,

,

. ,

Next pictures show the waveforms of the induced emf and the emf at stator and rotor frequency components with, motor loaded at 1450 rpm and slip frequency ~ 3 . 3 3 % .

0.4,

I

4.44 0

I

I

I

emf ( V I

I

I

I

I

I

i

I 40

I

\ 50

(I1

,,me

Fig. 4. Emf at stator arc rotor frequency with motor loaded at 1470

m.

I

I

in

Figure 5 and 6 show the waveforms of the induced emf and the emf at stator and rotor frequency components with motor loaded at 1460 rpm and slip frequency s=2.67%.

I

I

I

I

30

20

(mem06adl, x."srX(a"to,l

:qo-3

em,

,"(SI

Fig. 7. Waveform of the induced emf with motor loaded at 1450 run

Fig. 5. Waveform of the induced emf with motor loaded at 1460 rpm

-> 0 . j 1

. .

.

.

~

. .

~

~

,

0

02

0 4

06

0 8

I2

1

,\me

14

1 5

18

2

(S)

Fig. 8. Emf at stator and rotor frequency with motor loaded at 1450 rpm

:

4

0 0

Fig. 6. Emf

, 02

L

01

"

" 06

' 0 8

~

'

'

I 12 ,,me (3)

.

1 3 4

1 5

1 8

z

at stator and rotor frequency with motor loaded at 1460 rpm

The delay introduced by the filtering operation is approximately 0.5 s. Tests have been carried out for different values of the slip frequency in the range from s = 1.33% to s = 3.33% with sampling frequency set to 800 Hz. The elaboration for generating new values of A, B, and o at each iteration step is carried out on a data window of about 1/4 cycle o f the respective filtered voltages; these values o f sampling frequency and data window size have been selected in order to increase the speed of convergence and to improve the accuracy.

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The initial values ofparameters%, Ao,Bo are estimated as mentioned in previous section; only six iteration steps are required tu get to the convergence. Results for the stator and rotor frequency and for the slip measurement, in the range from s = 1.33% to s = 3.33%, are shown in Fig.9 and Fig. IO, respectively

4 4 September, 2003

0.040

E

2

0.030

0.020 0.010

0.000 ..

-0.010~ 50.003 50.002 50.001 50.000 49.999 49.998 49.997

5

6

E

-0.020

Revolution per minute

-; b

b) Percent error

1480

1470

1460

1450

Revolution per minute

The proposed system operated satisfactorily for any value of the slip frequency in the previously mentioned range; the error was in any case within + 0.03 Yo.

a) Stator frequency

-

E.2 000 1 5 1.500 c

IV. CONCLUSION

0

g 1.000 0

-b

0.500

p 0.000 J 1480

1470

1460

1450

Revolution per minute b) Rotor frequency

Fig. 9. Result for the stator and rotor frequency in the range from s = 1.33% to s = 3.33%

-e-

-

theoretical

-E-

experimental

3.500

3.000 2.500 2.000 0 1.500

-

l n1.000

0.000 0.500

Fig. 10. Result for the slip measurement in the range from from 5 = 1.33% to s = 3.33%

A new digital approach for the accurate measurement o f the slip frequency o f induction motors has been presented. The non invasive procedure based on digital filtering and dynamic parameter estimation has been shown to work effectively over a nearly wide range of speed and loading conditions. The slip frequency measurcment is carried out without speed sensor and is deduced utilizing the magnetic field in proximity of the induction motor. The system apparatus consists of a searching coil, an ADC hoard and a PC; the measurement system needs only a signal from a searching coil (induced emf) to be digitally filtered using algorithms based on the discrete Fourier transform. Useful estimates o f the slip frequency are obtained using about 114 cycle of the emf at stator and rotor frequency. Sampling rate, data window size and the characteristics of the filter are critical parameters that affect the performance of the algorithm. The accuracy of the slip measurement, in the previously mentioned range o f the slip frequency, is not affected by the load applied to the motor nor b y any consequent changes to the motor parameters. The proposed technique is accurate, simple and l o w cost; moreover it allows in-field measurement of the slip frequency of induction motor even in hazardous environments and it can be reliably applied in rotor parameter identification in steady state conditions and running test. Experimental tests confirmed the validity of the proposed procedure.

1

1480

1470

1460

Revolution Per minute

a) Slip measurement

1450

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REFERENCES [ I I Y.R. Kim. S.K.Sul, M.H. Park: Speed SCIISO~IUSS vcctor ~ o n t r u of l induction motor using extended Kalman. IEEE 7rons. On Indsrin. Applicolions. Sep.-Oct. 1994. pp. 1225-1233. [2] H . Kuhota K. Matrurr. T. Nakano: DSP -based speed adaptive tlux ahserver of induction motor. IEEE T".OPII n d t r r t ~Applicolioni. ~ Mar: Apr. 1993. pp. 344-348. [?I G. Yang. T.H. Chin: Adaptive-speed identification scheme fora vectorcontrolled speed sensorless invener-induction motor. IEEE Trans. On Indnstrv Applicolions. Jul.-Aue. 1993. pp. 820-825. [4] M. Ishida. K. Iwata: A new slip frequqncy detectorofan induction motor utilizing rotor slots h a m m i c s . IEEE Trans. On I n d m y Appiicotiom, Ma). June 1984. pp. 575-582. [SI K.D. Hum. T.G. Hahetler: A comparison of spectrum estimatioii techniques far sensorless speed detection in induction machines. IEEE FOLT On l n d n r i ~Applicarionr. ~: vol. 33. n. 4. 1997. [6] R Beguenane. M.E.H. Benbouzid. F.A. Capolina: On-lineidmdtication of induction motor rotor parameters from terminal signals. ElCro-mlMan. v01.3. no.2. April-June 1996. pp. 51-57. [7] R . Pintelon. J . Schoukens: An improved sine-wavefimngpmdwehr characterizing data acquisuiitian channels. IEEE Tram. @EInsmmw"o,t and Meorsrmrent. April 1996. pp. 588-593. [8] R. Micheletti. R. Pieri: Non-invasive slip measurement ofinduction motors. IEEE It?strtrmentotionand Meosweatmi 7 e P d n u l u ~Conference W T C 2 0 h l . Budapest.May21-23. 2001. vol. I , pp. 1988-61 [9] R. Micheletti. R. Pieri: Accurate measuring method for the slip of asynchronous motors, 12Ih IMEKO 7C4 lniernnriosol S w q " n n i Electrical Meosirrenienr ond lnsrrirnienroriorr ,Zagreb. Croatia. September 25-27. 2002. "

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