sensor less speed measurement of im

8/14/2019 Sensor Less Speed Measurement of IM

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Sensorless Speed Measurement of Induction MotorsRoberto Micheletti

Department of Electrical Systems and Automation, University of PisaVia Diotisalvi. 2 1-56126 Pi s , Italy

Abstract - The paper deals with the accurate s lipmeasurement of induction motors. The propos ed procedirreuses a non-invasive slip nieaszirement scheme based ondig i ta lf i l f er ingand dvnamic para me ter estimation . The slipmeasurement is carried ou f M'ithout spee d sensor an d isdeduced analvzing th e magnetic f iel d harnionics spectruniin pro1imit.v o the induction motor. First the enif inducedwaveform, taken from U searching coil, is filtered risingalgorithms based on the discrete Fourier transform. Thenth e s ta tor frequencb an d rotor f iequency are obtained b?comparing thefiltered voltage with a mathematical modelusing an optimization procedure. The model's parametersare varied until an adequate match is obtained with thefiltered voltage. Experiniental resulrs are presented tovalidate this method.

K@xQ& - Digital filterin g, JndiJrtion mofo rs, Slipmeasurement.

1. INTRODUCTIONInduction motor drives are now being m ore and m ore in

process industry because of the application of the fieldoriented control strategy. However, the perform ance of suchcon tro l method depends s t rong ly on the accuracy o f themotor parameters uscd in the vector co ntroller.

It is well known that the variation of the rotor resistanceand rotor constant time has a most dominan t ef fect on th econtrol performance. Unfortunately the rotor resistancedepends widely on the rotor temperature and on the slipfrequency, resulting in the deStruction of the decoupledcondition of the flux and torque.In recent years many studies are then carried out toovercome this situation. Estimation methods to get rotorparameters use extended Kalman filter approach [ I ] ,observer technical [2] and adaptive system [3].

It i s act ively p roceed ing to research fo r speed senso r lessvector control which estimates rotor speed and slip

frequency wi thou t speed sensor . The s l ip f requencydetection is carried out utilizing rotor slot harmonics [4], [ 5 ]or sensing and exp lo i t ing the s ta to r cu rren t[ 6 ] .

This paper presents an algorithm for the accuratemeasureme nt of the slip frequency bas ed on digital fil teringand d ynamic parameter estimation me thod [ 7 ] - [ 9 ] .The slip frequency measurement is carried out withoutspeed sensor and is deduced analyzing the magnet ic f ie ldharmonics spectrum i n proximity of the induction motor.First the emf induced waveform, taken from a searchingcoil, is filtered using algorithms based on the discreteFourier transform.Then the s ta to r f requency , ro to r f requency andconsequentially the slip frequency are obtained bycomparing the filtered voltage with a mathematical modelusing an optimization procedure. T he model 's param etersare vaned until an adequate match is obtained with thefiltered voltage.

The parameters that affect the performance of thealgorithm are essentially the da ta window size, the samplingrate an d the characteristics of the filter.

Mathematical development of the algorithm is presentedand the effects of key parameters that affect theperfo rmance of the algorithm are discussed .A representative set of experimental results arep resen ted .

The proposed method can be reliably applied in rotorparam eter identification in steady s tate conditions andru n n in g t es t .

11. ESTIMATION ALGORITHM OF STATORAND ROTOR FREQUENCY

The s ta to r f requency f, and rotor frequency f, areobtained with the same procedure by comparing therespective filtered voltages with a mathematical modelusing an optimization method.

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a E a E a E- = o . - = o . - = of ter f i l tering operat ion , we ob tain a set of "n " sampleso f the s ta to r ( ro to r) vo l tage. The f i l tered vo l tage can be AA ' a R ' aw (7 )approximated by a sinusoidThere resu l ts af ter rearrangement

v ( t ) = V s i n ( a t + O ) (1 ) gy,"(f.\)-Ja1=w h ere V an d 0 a re am p l it u d e an d p h ase , r e sp ec t iv e ly .By rcwri t ing the vo l tage in terms of quadratu re

componen ts"(1) = A sin wt + B c o s wt ="(A, B , w, t) (2)with

0 = t an - ' (B /A )Expand ing v ( t ) in a Tay lo r ser ies in the neighborhoodof g iv en va lu es A a , Bo, rh of parameters A, B, w g i v e s

where the h igher o rder terms of the expansion areignored and n = (A0 ,B O , % ) .

The p r incip le o f operat ion of the es t imat ion techn ique isbased on the compa rison between the real values of th ef i l tered vo l tage and the es t imat ion values of t h e m o d e l .Thus the p rob lem con sis ts in determin ing the parametersA,B, w ab le to min imize the erro r between sampled values andest imat ion values . The to ta l squar e erro r , a t in stan t 4. isexpressed as

where v r(ts) and v ( ts) rep resen t the samp led ou tpu tsof the real system after fil tering and the model reference attime t, , respectiv ely.

Substitution of (4 ) i n to ( 5 ) y ields

The total square error is minimized by so lv ing thepartial derivative s of (6 ) relative to A, B, w ev a lu a t eda t A o . B o , o h

So lu t ion of (8) g ives the co rrect ions AA , AB an d Awnecessary fo r updat ing parameters A, B and w fo r eachi teration s tep . Th is recurs ive techn ique per mits t o ob tain theunknown s ta to r and ro to r f requency wi th go od accuracy .Finally the slip freque ncy is given by

s = fJ f (9)I terative methods are well known fo r thei r sensi t iv i ty to

the in i t ia l ly guessed values of the unknowns. The in i t ia lvalues used fo r the model reference are determined asfollows. The initial value of o, s ob tained using the f i rs tfive samp le s of the inpu t vo l tage

3 [2v(tI+2T&v(t J-v(t, +4TJ]? e- 2[v(t +TJ+43t ,+2 TJ +v(t ,+3Tsd (10)

The initial values ofsystem:v ( t , ) = A a s i n w , t ,+ B o c o s w , t ,v (t l + T s) = A os i n[ ( rh ( t, + T s ) l + B o c o s [ ~ ( t , T s)l

an d & are determined so lv ing the

(11)

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111. RESULTSThe measurement algorithm has been verified toThe rated values of the induction motor used in theinvestigate the validity o f this technique.experiments are given in Table I .

Table 1 Rated values of a tested induction motolPowerVolta e YCurrent (U) 21.5 AFre uencRevolution er minute (rimin)

The slip frequency m easurement is carried out analyzingthe waveform of the induced emf, taken from a searchingcoil, du e to the magnetic field i n proximity of the inductionmotor.

Fig. 1 shows the waveform of the induced emf withmotor loaded at 1480 rpm; the slip frequency is s=1.33%,corresponding t o a rotor frequency of 0.667 H z .Useful est imates o f the sl ip frequency are obtained usingabout 114 cycle of the e mf at stator and rotor frequenc y,therefore the proposed procedure could be compatible withcontrol purposes.The searching coil is put on the frame of the inductionmotor.

emf (V)0 40.30.20.10 0

4 . 10 . 20. 30 . 411818d o 8 ab,. x.wr x (8Yf0 ,)0 10 2 0 30em,

time (E)

Fig. 1. Waveform of the induced em f with motor loaded at 148 0m.Then this waveform is filtered using algorithms based

on the discrete Fourier transform.The filtering operation is obtained with tw o eighth orderIIR filters. The first one is a bandpass filter with a centerfrequency of 50 H z and bandwidth 4 Hz, whose output is

the emf component at the stator frequency (emf at statorfrequency component) .Th e s e c o n d o n e is a lowpass filter with cu toff frequencyset to 2 Hz. The output of the lowpass filter is the emfcomponent at the rotor frequency (emf at rotor frequency

component) .The e mf at s tator and rotor frequency components withmotor loaded at 1480rpm are show n in Fig. 2.

,,me 5 )

Fig. 2.Em f at sta tor and rotor frequen cy with motor loaded at 1480rpm

Fig. 3 shows the waveform of the induced emf withmotor load eda t 1470 rpm; the slip frequency is s=2.00%,

emf (v )

0 10 20 30(,,le a07 d,. x - v a x ( a Y tO ) ) em, xime I S )Fig. 3. Waveform ofthe induced emf with motor loaded at 1470m.

The em f at s tator and rotor frequency components withmotor loaded at 1470 rpm are shown in Fig.4.

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s o l y ~ , . . , . . , . ,

,,me ( I 1Fig. 4. Emf at stator ar c rotor frequency with motor loaded at 1470m.

Figure 5 and 6 show the wav efo rms o f the induced emfand the em f at sta to r and ro to r f requency comp onen ts wi thmotor loaded at 1460 rp m and s l ip f requency s=2.67%.

Next pictures show the waveforms of the induced emfand the em f at s ta to r and ro to r f requency componen ts wi th ,motor loaded at 1450rp m and slip frequency ~ 3 . 3 3 % .

em f ( V I0.4, I I I I I I I I i

4 .44 I I I I I(mem06adl, x."srX(a"to, l em ,

I I I I \0 i n 20 30 40 :qo-3 50

, " (S I

Fig. 7. Waveformof the induced emf with motor load ed at 14 50run

Fig. 5. Waveform of the indu ced emf with motor loaded a t 14 60 rpm-> 0 . j 1 . . . ~ . ~ . . ~ ,

-: 4 0 , L " " ' ~ ' ' . 10 0 2 0 1 0 6 0 8 I 1 2 3 4 1 5 1 8 z

,,me (3)Fig. 6. Emf at stator and rotor frequency with motor loaded at 146 0rpm

0 02 0 4 0 6 0 8 1 I 2 1 4 1 5 1 8 2,\me (S )

Fig. 8. Emf at stator and rotor frequency with motor loaded at 14 50rpm

The delay introduced by the filtering operation isapproximately 0.5 s.Tests have been carried out for d ifferen t values o f theslip 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, an do t each iteration step i s carried out on a data window ofabout 1 /4 cycle o f the resp ective filtered voltages; thes evalues o f sampl ing f requency and data window size havebeen selected in o rd er to increase the speed of convergenceand to improve the accura cy .

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The in i tia l values o fp ara me ter s% , A o , B o are estimatedas mentioned in prev ious sect ion ; on ly s ix i terat ion s teps arerequ ired tu ge t to t h e co n v erg en ce .Resu l ts fo r the s ta to r and r o to r f requency and fo r the s l ipmeasurement, in the range from s = 1.33% to s = 3.33%, ar eshown in Fig.9 and Fig. I O , respect ively

..50.0035 50.0026 50.00150.000E 49.999- 49.998;9.997

1480 1470 1460 1450Revolution per minute

a) Stator frequency- 2 000 1E.5 1.500c00g 1.000

0.500b-p 0.000 J1480 1470 1460 1450

Revolu t ion per minu te

b) Rotor frequencyfrom s = 1.33% to s = 3.33%Fig. 9. Result for th e stator and rotor frequency in th e range

-e- theoretical -E- experimental3.5003.000- .5002.000- 1.500

ln1.0000.000.5001

480 1470 1460 1450Revolu t ion Per minu te

a) Slip measurem ent

0.0400.030E 0.0202 0.0100.000

-0.010~-0.020

Revolution per minute

b) Percent errorFig. 10.Result for th e slip measurement in th e range fromfrom 5 = 1.33% to s = 3.33%

T h e p ro p o sed sy s t em o p e ra t ed sa t i s f ac to r i l y fo r an yvalue o f the s l ip f requency in the p rev iously men t ionedrange; the error was in any ca se within + 0.03 Yo.

IV. CONCLUSIONA new digital approach for the accurate measurement o f

the s l ip f requency o f induct ion moto rs has been p resen ted .T h e non invasive p rocedure based on d ig i ta l f i l ter ingand dynamic parameter es t imat ion has been shown to workeffectively over a nearly wide range of sp eed an d lo ad in gcond i t ions .

The s l ip f requency measurcment i s carr ied ou t wi thou tspeed sensor and is deduced utilizing the magnetic field inproximity of the induct ion moto r . The system apparatusconsis ts o f a search ing co i l , an AD C hoard and a PC; themeasurement system needs on ly a s ignal f rom a search ingcoil (induced emf) to be digitally filtered using algorithmsbased on the discrete Fourier transform. Useful estimates o fth e slip f requency are ob tained using abou t 114 cycle o f theemf at stator and rotor f requency . Sampling ra te , datawindow size and the characteristics of the filter are criticalparameters that affect the performance of the algorith m.The accuracy o f the s l ip measurement , in the p rev iouslyment ioned range o f the slip frequency, is no t affected bythe load app l ied to t h e m o to r n o r b y an y co n seq u en tchanges to the mo to r parameters.The p roposed techn ique is accurate , s imple and lowcost; moreover it allows in-field measurement of the slipfrequency o f induct ion moto r even in hazardousenvironments and it can be reliably applied in rotorparameter iden t i f icat ion i n s t ead y s t a t e co n d i t i o n s an drunn ing tes t .Experimental tests confirmed the validity of theproposed p rocedure.

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REFERENCES[ I I Y.R. Kim. S.K.Sul, M.H. Park: Speed SCIISO~IUSScctor ~ o n t r u l finduction motor using extended Kalman. IEEE 7rons . On Indsrin.Appl i co l ions . Sep.-Oct. 1994. pp . 1225- 1233 .[2 ] H . Ku h o ta K. Matrurr. T. Nakano: DSP -based speed adaptive tluxahserver of induction motor. IEEE T". PIn d t r r t ~ ~pplicolioni. Mar:Apr . 1993. p p. 344-348 .[? I G. Yang. T.H. Chin: Adaptive-speed identification scheme fora vector-controlled speed sensorless invener-induction motor. IEEE Trans. OnIndnstrvApplicolions. Jul.-Aue. 1993. pp . 820- 825 .[4 ] M. shida. K. Iwata: A new slip frequqncy detectorofa n induction motorutilizing rotor slots h a m m i c s . IEEE Trans. On I n d m y Appiicotiom,Ma).June 1984. pp . 575- 582 .[S I K. D. Hu m . T.G. Hahetler: A comparison of spectrum estimatioiitechniques far sensorlessspeed detection in induction machines. IEEE FOLTOn lndnri~~:pplicarionr. vol . 33. n. 4. 1 9 9 7 .[6] R Beguenane. M.E.H. Benbouzid. F.A. Capolina: On-lineidmdticationof induction motor rotor parameters from terminal signals. ElCro-mlMan.v01.3. n o . 2 . April-June 1996. pp. 51-57.[7 ] R . Pintelon. J . Schoukens:An improved sine-wavef imngpmdwehrcharacterizing data acquisuiitian channels. IEEE Tram.@Ensmmw"o,tand Meorsrmrent . Apr i l 1996. pp . 588-593.[8 ] R. Michele tt i . R. Pieri: Non-invasive slip measurement ofinductio nmotors . IEEE It?strtrmentotion nd M e o s w e a t mi 7e P d n u l u ~ o nf eren ceW 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 ofasynchronous motors, 12Ih IMEKO 7C4 lniernnriosol S w q " n n i "Electrical Meosirrenienrond nsrrirnienroriorr , agreb. Croatia. September25- 27 . 2002 .

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sensor less speed measurement of im

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