Fault Eccentricity Diagnosis in Variable Speed Induction Motor Drive Using DWT

Transcription

1 AMSE JOURNAS-AMSE ETA publication-7-seie: Advance C; Vol. 7; N 3; pp 8- Submitted Oct. 8, 7; Revied Dec. 6, 7; Accepted Dec. 6, 7 Fault Eccenticity Diagnoi in Vaiable Speed nduction Moto Dive Uing DWT * Rouaibia Reda, **Abaoui fayçal, ***Bahi Taha 3 *Faculty of Science and Technology Univeity Mohamed-Cheif Meaadia EER ab Souk Aha, Algeia. (ouaibia.eda@hotmail.com) ** Depatment of Electonic Engineeing Badji Mokhta Univeity ASA ab Annaba, Algeia. (abaoui@univ-annaba.og) ***Depatment of Electical Engineeing Badji Mokhta Univeity ASA ab Annaba, Algeia. (tbahi@hotmail.f) Abtact Thi pape decibe the monitoing and diagnoi of eccenticity fault in vaiable peed induction moto dive. The ued contol technique i the indiect field oiented contol (FOC) fuzzy logic baed contolle to enue the obut peed egulation and to compenate the fault effect. The vaiable peed induction moto can be affected by vaiou kind of fault. Aigap eccenticity i one of the majo defect occuing in uch electic dive; it detection could be ueful fo peventing potential catatophic failue. A dynamic model taking into account the fault i popoed baed on the appoach of magnetically coupled coil to imulate the behavio of eccenticity fault in induction moto. Thi wok peent two appoache fo diagnoi and detection of eccenticity fault and evaluation of thei eveity baed on monitoing of the tato cuent ignal, uing Pak vecto method and dicete wavelet tanfom (DWT) with diffeent appoache to ditinguih healthy a well a faulty condition of the machine. The obtained imulation eult via the popoed technique allow detection and diagnoi of eccenticity fault and identify thei eveity. Key wod Fuzzy logic contolle, Diagnoi, nduction moto, Mixed eccenticity, Dicete wavelet tanfom. 8

2 . ntoduction Nowaday induction machine (M), in paticula, quiel cage M i the mot ued one in indutie equiing high pefomance. Futhemoe, indutial application widely need to vaiable peed M. Howeve, contolling thee electic dive peent ome difficultie due to thei complex and non-linea behavio duing atuation effect and due to thei highly coupled tuctue between flux and toque.we can get aound thee limitation by the ue of field oiented contol theoy (FOC) [.Thi technique efeed a vecto contol, induced lage change in the field of electical dive.the FOC cheme equie the cloed contol of flux and toque cuent (inne loop) and peed contol (oute loop).thi tuctue i divided into two goup: the indiect field oiented contol (FOC) popoed by Hae [ and the diect field oiented contol (DFOC) popoed by Blahke [3. Fo eveal decade, taditional vecto contol uing conventional P contolle wee applied to powe electonic aea and to contol electic machine. Although conventional P contolle howed implicity in deign and tability in pefomance, they ae enitive to load ditubance, paamete vaiation and equie an accuate mathematical model of M. To ovecome the above poblem, an intelligent contolle baed on fuzzy logic contolle (FC) i being ued to enhance the pefomance of M dive. Howeve, the contol pefomance of M i till influenced by uncetaintie failue and fault due to poduction pocee o opeating condition [4, 5. Mot of the fault occuing in the thee-phae M ae due to change in the ai-gap eccenticity. Seveal method have been developed fo the identification of thi kind of fault, oiginally baed on electical monitoing uch a tato cuent monitoing [6, axial flux, intantaneou powe [7, active eactive powe, ai-gap toque monitoing and cuent Pak component [8 followed by themal and vibation monitoing [9. Seveal autho applied moden computing appoache uch a genetic algoithm, wavelet analyi, expet ytem, Neual Netwok [,, and Fuzzy ogic [. Othe popoe olution baed on the on-line condition monitoing method which i applied to heavy poce indutie [3. n thi wok, we peent two method fo detection and iolation of the eccenticity fault in a thee-phae vaiable peed quiel cage induction moto uing an indiect field oiented contol (FOC) uing a fuzzy logic baed peed contolle in ode to maintain good pefomance in degaded mode, that i, in the peence of eccenticity defect.the fit method i baed on fault detection with the evolution of component id and iq cuent in the plan of Pak. The econd method i baed on dicete wavelet decompoition (DWT) [4-6. 8

3 The pape i oganized a follow; fit we peented a bief oveview of the induction machine dynamic model and the function of the vecto contolled dive. Then, the methodology of the fuzzy logic contolle i peented. The application of the Pak vecto appoach and wavelet analyi DWT a diagnotic method, fo ealy fault detection and fo eveity evaluation i invetigated. A compaion of the FOC imulation eult between the eccenticity fault and healthy cae ae peented and dicued. Finally, concluion ae peented in the lat ection.. Dynamical Equation of the nduction Moto The popoed model i baed on a thee-phae M. The cage oto model conit of nb identical and equally paced ba hoted togethe by two identical end ing a hown in Fig.. Fig.. Equivalent Roto meh cicuit Thi appoach offe a compomie in tem of model accuacy and computation time. n addition to that, thi type of model can take into account eveal electomagnetic fault uch a boken ba and eccenticity fault. The Model of the thee-phae induction moto i peented by the ytem of equation: V d[ d[ [ R+ [ + [ () dt dt Which lead to 83

4 84 [ [[ [[ [ [ dt d[ R V dt d + () (3) + 3, nb T T T V V V V V V V V (4) + 3 3, nb T e nb T T (5) The tato eitance and inductance matixe ae (3x3): [ R (6) p p p (7) The pincipal inductance of the magnetizing tato phae i [4: R N p e p.. 4 (8) The total cyclic inductance of a tato phae i equal to the um of the magnetizing and leakage inductance: f p ip + (9).[ [ [ [. [ _ R dt d dt d R V dt d T T

5 The mutual inductance between i and j tato phae i given a: ij p () The oto eitance and inductance matixe ae (nb+) x (nb+): () p Nb e p Nb e Nb Nb e Nb Nb e e e nb. e () Whee the pincipal inductance of a oto meh can be calculated by: p N N R g (3) Theefoe, the total inductance of oto mehe i: + + (4) ip p b e The mutual inductance between non-adjacent oto mehe i and j i defined by: ij b N g R (5) The mutual inductance matix between tato phae and oto meh i (m x nb+) 85

6 l l l 3 l l l 3 l l l nb nb 3nb (6) The mutual induction between the tato phae m and oto meh k i given by: M mk M co( p m + ka) (7) 3 Thee electical equation mut be added to the following mechanical equation: d ( Te Tl + f v. ) dt J d with dt (8) The expeion of electomagnetic toque Te i ultimately detemined by the elationhip below [4: T e [ [ T d [ d [ [ [ [ [ (9) 3. ndiect Field Oiented Contol The mot impotant apect of field-oiented contol applied to M i the decoupling of tato cuent into two component, ued fo geneating magnetizing flux and toque [. The decoupling allow u to contol the M a a imple DC machine with epaate excitation [6. The FOC technique ha imple implementation and i moe eliable what make it widely ued in induty. To achieve field oientation along the oto flux, the diect flux component i aligned in the diection of oto flux φ. φq; φd φ, Vd and Vq. () The advantage of uing a efeence elated to the otating field fame i to have contant magnitude. t then eaie to make the egulation, by acting on the id and iq vaiable. The magnitude and Te ae odeed epaately. Thi eult in: M. id ; () + pt 86

7 M. iq l T. p. M. iq. T e K. i q () (3) Whee ω l: i a lip fequency. Hence, the analogy with DC machine pefomance i clealy etablihed, by keeping the flux contant. The electic toque i found popotional to the iq component, and the flux φ and id component of cuent can be elated to the fit-ode linea tanfe function whee T i a oto time contant. Fig.. how the block diagam of indiect field oiented contol of 3-phae M with a fuzzy logic baed peed contolle. Fig.. ndiect field oiented contol (FOC) block diagam 4. Fuzzy ogic Contolle Fuzzy logic contol (FC) i a linguitic appoach which attempt to imitate human contol tategie in technical envionment built fom the ue if then ule povided by human expet that completely define the behaviou of the ytem. The FC block diagam i hown in Fig 3. 87

8 Fig.3. Fuzzy contol bloc diagam t i compoed of fou majo block: fuzzification, knowledge bae, infeence engine, and defuzzification. Thee ae two input, the fit one i peed eo e(k), the econd i the change of peed eo Δe(k). The output i the toque efeence, calculated at evey ampling time k e( k) w*( k) w( k) (4) e ( k) e( k) e( k ) (5) Whee e(k) i the eo value, ω*(k) denote the efeence peed, ω(k) i the actual peed and Δe(k) i the change of eo at ampling time. Fig4. Membehip function of the fuzzy logic contolle fo the eo (e), the change of eo (Δe), and the output (Δu) 88

9 Membehip function fo input and output vaiable wee nomalized with value vaying between [-, and aociated with the following linguitic vaiable NB (Negative Big),NM(Negative Medium), NS(Negative Small), ZE( Zeo Equal); PS(Poitive Small), PM( Poitive Medium) and PB(Poitive Big) hown in Fig 4. Each of the input and output ae poceed by the infeence mechanim that execute 7x749 ule ummaized in Table: Table. Rule bae fo the fuzzy contolle Δe\e NB NM NS ZE PS PM PB NB NB NB NB NB NM NS ZE NM NB NB NB NM NS ZE PS NS NB NB NM NS ZE PS PM ZE NB NM NS ZE PS PM PB PS NM NS ZE PS PM PB PB PM NS ZE PS PM PB PB PB PB ZE PS PM PB PB PB PB 5. Eccenticity Fault Model Eccenticity fault i moe elated with intenal fault of the machine; it appea when thee i an unequal ai gap between oto and tato. Thee kind of eccenticity can be conideed: tatic eccenticity [4, dynamic eccenticity [3 and mixed eccenticity [8, 9. n tatic eccenticity cae (SE), the ai gap become iegula; theefoe, the minimum ai gap location appea at a pecific fixed poition. t function take inuoidal fom with the angula poition of the tato. Dynamic eccenticity (DE) exit when the axi of otation coincide with the axi of tato but not with the axi of the oto.the minimum ai gap location then change with the oto angula poition and evolve with it. Fo the mixed eccenticity (ME), the two defect (SE) and (DE) ae peent at the ame time and the axi of otation i diffeent fom both axe of tato and oto. n thi wok, we chooe to tudy mixed eccenticity fault. The expeion of the ai gap that eflect thi type of defect i expeed by the following equation: e, ) e + co( ) + co( ) (6) ( d with e: ai gap of the machine; 89

10 a.e: pecentage of tatic eccenticity; d a.e: pecentage of dynamic eccenticity. The fault fequency component of the eccenticity defect ae baed on expeion [9: f ecc f (7) p ( k ) with fecc : eccenticity fault fequency, f :fundamental fequency, k,, n: i a contant and : i the moto lip. 6. Fault Detection Method 6. Pak Vecto Appoach Pak vecto appoach i an eay way to decide if the machine i healthy o not. t mean that the phae cuent (ia, ib, ic) ae to be tanfomed into a two-coodinate ytem with pependicula axe (id, iq) and placed on d-axi and q-axi epectively. n othe wod, tanfoming a thee-dimenional ytem into a two-dimenional (-D) [.The cuent pak vecto component ae function of main phae vaiable which ae: id iq ( i 3 ( i a b ) ) ( i 6 ( i b c ) ) ( i 6 c ) (8) 6. Wavelet Tanfom The wavelet tanfom wa intoduced with the idea of ovecoming the dawback of the Fouie tanfom. The wavelet tanfom aue both time-fequency analyi and time cale analyi with multi-eolution chaacteitic. The continuou wavelet tanfom (CWT) i defined by the following equation t, ( t) (9) 9

11 The paamete τ indicate the tanlation in time, and i a cale paamete, ψ(t) i the tanfoming function, alo known a the mothe wavelet. The tanlation and the expanion tanfom the ignal into anothe timecale. The epeentation fom with malle cale coepond to the high-fequency component [. n the cae of the DWT, the expanion and tanlation paamete and τ ae limited only to dicete value leading to the following expeion: Fig.5. The DWT decompoition ignal j t k, ( t) j j (3) Whee the whole numbe and τ contol the wavelet expanion and tanlation, epectively. Fo pactical eaon, the implet and mot efficient dicetization come by chooing and τo : j, ( t) j t k j ( t k) j j (3) A ignal ia(t) can be decompoed and econtucted by mean of two component: appoximation (aj) and detail (dj), whee appoximation can be intepeted a a high-pa filte (HPF) and detail a a low-pa filte (PF) a hown in Fig 5. Thi mean that the appoximation contain the low-fequency infomation of the oiginal ignal belonging to the inteval [, f/ (j+) and detail contain the high-fequency infomation whoe fequencie ae included in the inteval [f/ (j+), f/ (j). 9

12 Decompoition which ue dicete wavelet tanfom (DWT) of a ignal i caied by a ucceive opeation uing (HPF) and (PF) of the time domain ignal. The econtucted ignal ia (t) can be appoximated uing the DWT by [9-: i + a( t) d + d d n an (3) 6.3 Wavelet Enegy The fault diagnoi i baed on obevation and compaion between the enegy aociated to each level of ignal decompoition. The tato cuent ignal contain infomation included in each fequency band which i eulting fom the wavelet packet decompoition. The enegy value fo each fequency band i defined by [, [5: E j n k D j, k ( n) (33) Whee j: i the level of detail and Djk i the detail ignal at level j and n i the total numbe of ample of the ignal. The enegy value of decompoition level contain neceay diagnotic infomation. The plot of thee value can be ued to diagnoe fault in the quiel cage M and it can alo ae the eveity degee of the fault. Befoe the calculation of the wavelet enegy, the numbe of the decompoition level mut be well defined by the following elationhip [6 [, : f e log( ) f int N + (34) log( ) With f: fundamental fequency and fe: ampling fequency. 7. Simulation and ntepetation The tatic and dynamic pefomance of FOC tategy in the healthy and faulty tate ae evaluated uing the MATAB /Simulink oftwae. Seveal tet wee caied out uch a tatup with low-peed opeation, ated load, and evee tet of peed. 9

13 7. Reult fo Healthy Machine Figue 6(a) and 6(b) how the moto peed and the tato cuent unde healthy condition of the machine. The tet of contol i ealied with an inveion of the peed diection fom + [ad/ to - [ad/ at time t. Thi change of diection of otation poceed with the application of a load toque equal to 3.5N.m at time t. Depite the load vaiation, the peed follow the efeence value, which pove the obutne of thi technique even with vaiation o change of the peed otation diection. Fig. 6. Healthy condition of the moto: (a) Moto peed, (b) Stato Cuent 7. Reult fo Machine with Mixed Eccenticity Fault We applied a mixed eccenticity fault ME5% (SE5% and DE5%) and ME% (SE% and DE%) at tat-up of moto. The figue 7(a-b) and 8(a-b) how the effect of thee defect. Fig. 7(b) and 8(b) diplay the evolution of the tato cuent; fitly we tat with no load and then, at time t, a load toque of 3.5[N.M i applied with the mixed eccenticity fault. A 93

14 hown in thee figue, a ignificant inceae of the ocillation in tato cuent ignal paticulaly between t and t 4 ae due to the peent of the eccenticity defect component. Fig. 7. Faulty moto with mixed eccenticity fault (ME 5%): (a) Moto peed, (b) Stato cuent Fig. 8. Faulty moto with mixed eccenticity fault (ME %): (a) Moto peed, (b) Stato cuent 94

15 n fig. 7(a) and 8(a) we obeve that peed alway emain table and follow the efeence the oto peed follow the efeence value without any ignificant ocillation; the application of mixed eccenticity fault and the load doe not affect the oto peed. Thee eult how that the fuzzy logic peed contolle i obut and peent a tong pefomance. 7.3 Cuent Pak Vecto Analyi Fig. 9. Pak cuent vecto appoach fo healthy and faulty machine The figue 9(a-b-c) how the obtained -D Pak cuent vecto fo both healthy and mixed eccenticity fault cae. n the Fig. 9(a), the cuent patten of pak vecto ha an elliptic hape. Howeve, in the cae of eccenticity fault, the cuent patten hape hown in fig. 9 (b-c) i totally diffeent fom the elliptic one, which indicate the eccenticity fault. t could be een that cuent patten fo the faulty moto i clealy diffeent fom the cuent patten of the healthy moto. Thi clealy how the diagnoi capability of the Pak Vecto appoach. But thi method alone can't give u pecification on eveity fault degee which i a paamount infomation, becaue we have 95

16 not to deal with all the eccenticity fault with the ame manne. Theefoe, we applied dicete wavelet tanfom which allow u to invetigate and then appeciate thi eccenticity fault tenne. 7.4 DWT analyi The decompoition in multi-level of the tato cuent i caied out uing the mothe wavelet Daubechie44 (db44). The level of neceay decompoition ae calculated with the following elationhip: fe log( ) f N int + level log() (35) n the cae of ou imulation, fundamental fequency (f 7 Hz) i obtained diectly by fequency analyi of the tato cuent, and ampling fequency (fe khz). So, the numbe of appopiate decompoition i equal to level. Table indicate the diffeent fequency band of appoximation and detail. Table. Fequency band of appoximation and detail evel Fequency band appoximation Fequency band detail _ Fig., Fig and Fig, how the DWT analyi of the tato cuent ignal given in Fig. 6.b-7b and 8.b (tato cuent phae a). On the othe hand, d, d, and d ae the detail ignal obtained by DWT decompoition with the mothe wavelet db44 at level, in both healthy and faulty cae. 96

17 Fig.. DWT analyi of tato cuent fo the healthy machine A compaion between Fig - and fig, when we applied a load toque at t and changed the diection of otation at t, indicate that in the d level ignal, thee i no much change but thee ae an impotant vaiation in the d and d level ignal containing low band fequency caued by the hamonic of the eccenticity fault. Fig.. DWT analyi of tato cuent fo faulty machine unde (ME 5%) 97

18 Fig.. DWT analyi of tato cuent fo faulty machine unde (ME %) Fig. 3, how the vaiation of the enegy in the fequency band of decompoition of multi wavelet-level in the cae of a healthy machine and with diffeent degee of mixed eccenticity defect: (ME%,ME%,ME 5%, ME %, ME5%,ME % and ME 5%). Fig. 3. Enegy calculation fom tato cuent fo healthy and faulty cae The toed enegy in each level of decompoition, confim the obeved inceae in the ignal of detail and appoximation epecially in the level d and d (ee Table ).Thi i 98

19 coeponding to the band of neighbohood and below of the fundamental f7hz. The effect of the mixed eccenticity default i clealy manifeted by the toed enegy in the level. The inceae diffe accoding to the eveity of the default. t can be een that the diffeence between the healthy and the faulty cae i vey clea, and the inceae of enegy diffe accoding to the eveity of default. Concluion The aim of thi wok i the diagnoi of ai-gap mixed eccenticity fault in vaiable peed induction moto baed on a obut fuzzy logic contolle uing two method. The fit method i baed on the cuent pak vecto; the cuent patten obtained give a clea indication of the peence o not of eccenticity fault in compaion with the healthy cae. The othe complementay method i baed on the dicete wavelet analyi and enegy level. The imulation eult of wavelet tanfomation give the advantageou infomation to decide the faulty ituation, paticulaly in the peence of eccenticity fault. The eult howed that the enegy level inceae imultaneouly with the inceaing degee of the eccenticity fault. Howeve, the enegy in healthy cae alway peent the lowet level. Theefoe, it i concluded that the employed technique can be ued a a eliable tool fo detection of the eccenticity fault a well a the evaluation of it eveity degee. Appendix The machine paamete ued in the imulation ae lited in the table below: Machine paamete Output powe Numeical value Pn. kw Stato voltage V /38V Stato fequency Nominal cuent Nominal peed f 5 Hz n 4.5/.6A Ωn 85t/mn Pole numbe p Stato eitance Roto eitance Roto ba eitance Reitance of end ing egment R7.58 Ω R6.3 Ω Rb.5 mω Re.5 mω 99

20 Roto ba inductance nductance of end ing eakage inductance of tato Mutual inductance Numbe of tun pe tato Numbe of oto ba b. μh e. μh f6.5mh M46.4 mh N6 Nb6 Refeence. S. Chacko, C.N. Bhende, S. Jain, R.K. Nema, Modeling and imulation of field oiented contol induction moto dive and influence of oto eitance vaiation on it pefomance, 6, Electical and Electonic Engineeing: An ntenational Jounal, vol. 5, no.. K. Hae, Dynamic of adjutable peed dive with convete-fed quiel cage induction moto, 968, (Gemany) Ph. D. Dietation, Damtadt, Techniche. 3. F. Blachke, The pinciple of field oientation a applied to the new tanvecto cloed-loop contol ytem fo otating-field machine, 97, Siemen Rev, vol. 34, no. 3, pp M. Aka, Detection of a tatic eccenticity fault in a cloed loop diven induction moto by uing the angula domain ode tacking analyi method, 3, Mechanical Sytem and Signal Poceing, vol. 34, no. -, pp H. Talhaoui, A. Menace, A. Keal, R. Kechida, Fat Fouie and dicete wavelet tanfom applied to enole vecto contol induction moto fo oto ba fault diagnoi, 4, SA Tanaction, vol. 53, no. 5, pp T. Ameid, A. Menace, H. Talhaoui. Hazelli, Boken oto ba fault diagnoi uing fat Fouie tanfom applied to field-oiented contol induction machine: imulation and expeimental tudy, 7, nt. J Adv Manuf. Technol., vol. 9, no. -4, pp A. Chaouch, M. Hai, A. Bendiabdellah, P. Remu, ntantaneou Powe Spectum Analyi To Detect Mixed Eccenticity Fault n Satuated Squiel Cage nduction Moto,3d intenational Confeence on Automation, Contol, Engineeing and Compute Science Ouachtouk, S. Elhani, S. guedia, k. dahil, l Sadiki, Advanced Model of Squiel Cage nduction Machine fo Boken Roto Ba Fault Uing Multi ndicato, 6, powe engineeing and electical engineeing, vol. 4, no J.R. Magdaleno, H.P. Baeto, J.R. Cote, R.M. Capoal,.C.Vega, Vibation Analyi of Patially Damaged Roto Ba in nduction Moto unde Diffeent oad Condition Uing DWT, 6, Hindawi Publihing Copoation, vol. 6, D

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