Stochastic Estimation Methods for Induction Motor Transient Thermal Monitoring Under Non Linear Condition

Transcription

1 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Hacene Mellah, Hemsas Kamel Eddine To cite this vesion: Hacene Mellah, Hemsas Kamel Eddine. Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition. Leonado Jounal of Sciences, AcademicDiect, 01. <hal > HAL Id: hal Submitted on 19 Dec 017 HAL is a multi-disciplinay open access achive fo the deposit and dissemination of scientific eseach documents, whethe they ae published o not. The documents may come fom teaching and eseach institutions in Fance o aboad, o fom public o pivate eseach centes. L achive ouvete pluidisciplinaie HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau echeche, publiés ou non, émanant des établissements d enseignement et de echeche fançais ou étanges, des laboatoies publics ou pivés.

2 Leonado Jounal of Sciences ISSN Issue 0, Januay-June 01 p Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Mellah HACEN 1*, Hemsas KAMEL EDDINE 1 Depatment of Electical Engineeing, Faculty of Engineeing, Univesity Fehat Abbas of Setif Cité Maabouda, Route de Béjaia / / Algeia. Automatic Laboatoy of Setif, Electical Engineeing Depatment, Univesity of Setif, Algeia. * : has.mel@gmail.com*. * Coesponding autho: (13) ; Fax: (13) Abstact The induction machine, because of its obustness and low-cost, is commonly used in the industy. Nevetheless, as evey type of electical machine, this machine suffes of some limitations. The most impotant one is the woking tempeatue which is the dimensioning paamete fo the definition of the nominal woking point and the machine lifetime. Due to a stong demand concening themal monitoing methods appeaed in the industy secto. In this context, the adding of tempeatue sensos is not acceptable and the studied methods tend to use sensoless appoaches such as obsevatos o paametes estimatos like the extended Kalman Filte (EKF). Then the impotant citeia ae eliability, computational cost ad eal time implementation. Keywods Induction Moto; Themal Modelling; Estimation Techniques; Themal Monitoing. 95

3 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Intoduction Mellah HACEN and Hemsas KAMEL EDDINE The enegy convesion in an electical machine is inevitably accompanied by losses of powe which emege in caloific fom in the cedits pat is constictive machine. When stato winding insulation mateials ae heated beyond thei tempeatue limits by excessive heat fom moto losses, the winding insulation mateials may expeience acceleated and ievesible deteioation, esulting in educed moto life o even total moto failue [1]. To pevent such excessive themal stess and ensue continuous and eliable moto opeation, the National Electical Manufactues Association (NEMA) has established pemissible tempeatue limits fo stato windings of induction machines based on thei insulation classes []. It is commonly assumed that the moto s life is educed by 50% fo evey 10 C incease above its stato winding tempeatue limit. Theefoe, an accuate estimate of the stato winding tempeatue is cucial in ensuing pope moto opeation below its themal limit. Aside fom diect stato winding tempeatue measuement by means of a themocouple o esistive tempeatue detecto (RTD), the themal model based and the induction machine paamete-based tempeatue estimatos ae two majo techniques used in tacking the stato winding tempeatue [1]. Themal Modeling Methods of EM In liteatue specialized one can gatheed the methods of themal modeling of the machines electic unde the thee types following: Simple Modeling fo a Coase Appoach One finds in the liteatue of many simple appoaches in ode to give bonds between the tempeatue to the stato and the tempeatue with the oto. [3], [4] thus pesent an identification method of the oto of electic esistance which does not make it possible unfotunately to conside stato electic esistance These aticles popose two themal appoaches then to bind two esistances of the electic model: 1 The fist method is based on the expeiment of EDF which consides that the oto 96

4 Leonado Jounal of Sciences ISSN Issue 0, Januay-June 01 p has a tempeatue highe of 10C than that of the stato. The second method, based on wok of Kubota, gives a simple elation of popotionality between two esistances calibated on the face values of the make badge. One finds the method of the popotionality in othe aticles like [5].On the othe hand, of late wok wee ealized on model EDF and put a flat as fo its validity fo all the opeating modes [6]. Fine Modeling fo a Pecise Themal Catogaphy It is based on the use of the finite element method with a model geometic and mechanics detailed. Figue 1. Themal catogaphy potion of an asynchonous machine, obtained by finite elements [9] This makes it possible to obtain a complete catogaphy of the tempeatue of the machine (Figue.1). These esults ae vey inteesting since they make it possible to give an idea of the places whee the tempeatue becomes citical accoding to the opeations and answe the poblems of the hot points [7, 8]. Electical Equivalent Supply Netwoks (Nodal Method) [10] [11] Those geneally model the whole of the machine with nodes of tempeatue associated with each mateial used [1]. The identification of this model is thus caied out eithe by finite elements, o by a geat numbe of points of tempeatue measuement within the machine. These models ae geneally vey detailed (Figue ) and thus too complex fo ou application in eal time [1]. 97

5 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Mellah HACEN and Hemsas KAMEL EDDINE Figue. Equivalent themal models of the asynchonous machine [1] As ou goal pincipal is the use of kalman filte, these two types of models ae not exploitable, because these methods do not give the fomalism of state. Simplified Models Othe eseaches sought to simplify the models by gatheing the losses in subsets and by appoximating the tempeatue in an unspecified point by a simple exponential answe which one can simply epesent by a esistance and a heat capacity [13] and [14]. Figue 3. Themal model of the asynchonous machine [13] Themal Modelling of IM In many cases the model is the familia steady-state equivalent cicuit, but fo high pefomance dives a full tansient model of the moto is equied. Effective modeling, and theefoe the effectiveness of dive contol and estimation, is limited by the complexity of the physical pocesses occuing within the moto. Fequency dependence of the oto electical 98

6 Leonado Jounal of Sciences ISSN Issue 0, Januay-June 01 p cicuit, nonlineaity of the magnetic cicuit, and tempeatue dependence of the stato and oto electical cicuits all impact on the accuacy with which the moto can be modeled [15]. The modeling of the IM taking all the eal behavios without Assumptions simplifying being vey difficult o impossible. Fo that one will suppose a model with simplifying assumptions. This pape addesses the thid of these effects (tempeatue dependence) by incopoating a themal model of the moto in the estimation pocess. The fequency dependence of the oto electical cicuit and nonlineaity of the magnetic cicuit ae not included. Tempeatue estimation in the induction moto has been dealt with by many authos see [11], but most of these publications descibe eithe a vey complex lumped-paamete netwok o the finite-element method. A state-vaiable model of the induction moto is equied fo the EKF algoithm. The twin-axis stato efeence fame [15] is used to model the moto s electical behaviou, because physical measuements ae Made in this efeence fame; the well-known linea elationship between esistance and tempeatue must be taken into account fo the stato and oto esistances R ( θ ) = R (1 + α θ ) s s s0 s s R ( θ ) = R (1 + α θ ) (1) 0 O: R s0, R 0 stato and oto esistance at the ambient tempeatue, α s and α them coefficients themal espectively. In the IM taditional models, one eplace R 1 and R by Rs θ and R( θ ) espectively, what can be eaanged in space of state on the fomat: ( ) S pδ i = L L ω i R ( θ ) L i L L ω i + R ( θ ) L i + L V () q 1 m ds s s qs 1 d 1 q m qs ds = Rs s ids + Lm iqs + Lmid + Lm iq + L ds pδ i ( θ ) L ω R ( θ ) L ω V (3) pδ i = R ( θ ) L i L L ω i R ( θ ) L i L L ω i + LV (4) d s s m ds 1 m qs 1 d 1 q qs qs = Lm i ( s ) ds Rs i qs LLmωid + R θ Lmω iq + LVqs δ = LL 1 Lm pδ i ω θ L Whee : The mechanical behaviou can be modeled by: T = bω + j pω + T L ( ) (5) But the electomagnetic toque of the moto T can be epesented in tem of stato and oto cuent components: T = p L ( i i i i ) n m qs d ds q By equality of these two peceding equations, the equation speed of oto in the space (6) (7) 99

7 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Mellah HACEN and Hemsas KAMEL EDDINE of state is: b T L pω = pnlm( iqsid idsiq ) ω + (8) j j The themal model is deived by consideing the powe dissipation, heat tansfe and ate of tempeatue ise in the stato and oto. The stato powe losses include contibutions fom coppe losses and fequency -dependent ion losses [15]. pl = ( i i i i ) R ( θ ) + k ω (9) s qs d ds q s s i O: K i is it constant of ion loss. The oto powe losses ae dominated by the coppe loss contibution if the moto is opeated at a low value of slip so: pl = ( i i ) R ( θ ) (10) d q O: H s, H ae the stato and the oto heat capacity espectively. A simple epesentation of the assumed heat flow is given in Figue. 1. Heat flow fom the oto is eithe diectly to the cooling ai with heat tansfe coefficient k, o acoss the aigap to the stato with heat tansfe coefficient k 3 pl = θ + θ + ( θ θ ) (11) 3 s k H p k Heat flow fom the stato is diectly to the cooling ai,with heat tansfe coefficient k 1 pl = θ + θ ( θ θ ) (1) 1 s s s 3 s s k H p k Fo an induction moto with a shaft mounted cooling fan, the heat tansfe coefficients ae dependent on the oto speed. This dependence has been modeled appoximately by a set of linea elationships k k (1 + k ω ) 1 = 10 1ω k k (1 + k ω ) = 0 ω k k (1 + k ω ) 3 = 30 3ω (13) (14) (15) O: k 10, k 0 and k 30 themal powe tansfe coefficients at the zeo speed. k 1w, k w and k 3w vaiation of themal powe tansfe with speed. Substitution into equations15 and 16 in the equations 13,14,17,18 and 19, and eaanging yields the themal state equations fo the stato and fo the oto: R ( θ ) k k (1 + k ω ) k (1 + k ω ) pθ i i ω θ θ θ H H H H s s i 10 1ω 30 3ω = ( + ) + + ( ) (16) s ds qs s s s s s s 100

8 Leonado Jounal of Sciences ISSN Issue 0, Januay-June 01 p k (1 + k ω ) k (1 + k ω ) pθ i i θ θ θ R ( θ) ( ) 0 ω 30 3ω = + q d + ( s ) H H H The whole of peceding equations (6) a (9), (1), (0), and (1) gives us the model of following state: pδ i = L L ω i R ( θ ) L i L L ω i + R ( θ ) L i + L V (18) q 1 m ds s s qs 1 d 1 q m qs pδ i = R ( θ ) L i + L ω i + R ( θ ) L i + L L ω i + L V (19) ds s s ds m qs m d m q ds pδ i = R ( θ ) L i L L ω i R ( θ ) L i L L ω i + LV (0) d s s m ds 1 m qs 1 d 1 q qs pδ i = L ω i R ( θ ) L i L L ω i + R ( θ ) L ω i + LV (1) qs m ds s s qs m d m q qs b T L pω = pnlm( iqsid idsiq) ω + () j j R ( θ ) k k (1 + k ω ) k (1 + k ω ) pθ i i ω θ θ θ H H H H s s i 10 1ω 30 3ω = ( + ) + + ( ) (3) s ds qs s s s s s s R ( θ ) pθ ( i i ) k (1 + k ω ) k (1 + k 0 ω 30 3ω = + θ + d q H H H (17) ω ) ( θ θ ) (4) s Application of the EKF A econstucto of state o estimato is a system having like enty, the enties and the exits of the eal pocess, and whose exit is an estimate of the state of this pocess. The extended Kalman filte algoithm takes account of pocess and measuement noise in a geneal nonlinea system: x ( k + 1) = Ax ( k) + Bu( k) + w ( k) y ( k) = Cx ( k) + v ( k) (5) MAS (IM) + _ E _KE_MAS Enté e FKE (EKF) Figue 4. Application of EKF in IM When: w(k) v(k) epesents the pocess and measuement noise espectively. A. The pediction stage is: 101

9 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Mellah HACEN and Hemsas KAMEL EDDINE B. The coection stage is: xˆ( k + 1 ) = f ( xˆ( k ), u( k) ) (6) ( ) T P( k + 1) = F( k) P k F + Q (7) ( ) T T 1 ( + ) = ( + ) ( + ) + ( k + k ) = ( k + ) + ( k + ) ( k + ) ( k + 1/ k) = ( k + 1) + ( k + 1) { ( k + 1) ( k + 1) } K k 1 P k 1 C CP k 1 C R (8) P 1 P 1 K 1CP 1 (9) xˆ xˆ K y C xˆ (30) C. Covaiance matices initial Values The matix of covaiance of eo in estimation P and squae of 7 7, tanslated the confidence which we can have in the adopted model, It is given [15] by: p (0) = diag[555511] The matix of covaiance of the noise of state Q quantifies the pecision of the model and allows the dynamic adjustment of the paametes. It is geneally difficult to detemine because the diect obsevation of the state of the system is impossible, it is given in [15] by: Q diag( = [ ] ) The matix of covaiance of noise of measuement R tanslated the level of noise to the measue it is given in [15] by: R 0 = Simulation Result Constant Load The two tempeatues (themal model and estimation) vay at diffeent ates, Because of the diffeences in the losses, themal capacities and the powe tansfe coefficients between the stato and oto. The stato and oto tempeatue in the established mode eached the value 65 C, 7 C espectively but thei value consideed eached 6.3 C and 69.6 C. Figue, 5 shows that defeence between the oto and the stato tempeatue is 10 C 0 veified EDF expeiment (The EDF expeiment which consides that the oto has a tempeatue highe of 10C C 0 than that of the stato) [6]. 10

10 Leonado Jounal of Sciences ISSN Issue 0, Januay-June 01 p Figue 5. The estimation and themal model tempeatue of stato and Roto esult unde the constant load condition Vaiable Load In ode to veify the model pefomance fo vaiable load, some step vaiations of load ae applied (100% 10% 50% 75% of the ated load). Figue 6. Stato tempeatue simulation esult unde the vaiable load condition The Figue.6 and Figue.7 Show the simulation esult of EKF and themal Model 103

11 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Mellah HACEN and Hemsas KAMEL EDDINE tempeatue of stato and oto winding unde the vaiable load condition, the defeence between the themal model tempeatue and EKF is.4 C and.7 C fo the stato and the oto espectively. Figue 7. Roto tempeatue simulation esult unde the vaiable load condition Themal Monitoing Based Model fo Pevention of Heat Damage of Electic Motos Basic assistance of this technique is the efeence [16] whee it is monitoing an intenal tempeatue, but D. Staton [14] shows that the tempeatue distibution is not unifom and also the tempeatue moe citical and estictive and that of the windings. Ou contibution is to exploit the help of Y. Huai [17] in the model pesented in [15]. Figue 8. Diagam of simulation used to monito the opeation of the moto We need to detemine how long the engine can opeate in the given condition without exceeding the specified limit of tempeatue. To solve these poblems we developed a 104

12 Leonado Jounal of Sciences ISSN Issue 0, Januay-June 01 p pogam in Matlab / Simulink, which uses ou themal model. In Figue 8 we show a schematic diagam of simulation used to monito the opeation of the moto. a) themal monitoing of the stato tempeatue b- stato tempeatue (ZOOM) Figue 9. Themal monitoing of the stato tempeatue One applies toque intense and a stato defect to incease the stato tempeatue at limiting tempeatue T LS befoe the oto tempeatue eaches the limit T LR (Figue. 9). Unde these conditions indicated above, the tempeatue in the stato winding tempeatue limit hit stato (T LS = 90 C) afte 68min of engine opeation (Figue. 9). Figue 10 shows that we have applied a couple intense and a oto failue at t = 00min to incease the oto tempeatue to L RT, and we see that the tempeatue in the oto winding eaches the limit tempeatue oto (L RT = 110 C) afte 90min of stating (Figue. 10). 105

13 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Mellah HACEN and Hemsas KAMEL EDDINE a) themal monitoing of the oto tempeatue b) oto tempeatue (ZOOM) Figue 10. Themal monitoing of the oto tempeatue In both cases additional (T S = T LS o T R = T LR ) and the engine will tigge the themal potection of the windings is checked, so we will incease the life of the moto windings. This means that the engine should be opeational fo less than one 68 min to avoid oveheating the stato and less than 58 minutes to the oto. Conclusion Since the sensos can be not vey eliable o expensive, the use of an estimato becomes necessay. The filte of Kalman makes it possible to achieve this goal, because it enables us to estimate and pedict, simultaneously the tempeatue stato and oto stating fom the knowledge of the cuents of food of vaious windings, which is well shown though the esults of simulation obtained. The simulation study demonstates that tempeatue ise 106

14 Leonado Jounal of Sciences ISSN Issue 0, Januay-June 01 p calculation with simplified themal model poposed in this pape is feasible. The eo between the simplified themal model poposed in this pape and the ecent publications is acceptable. The simplified themal model can be used to estimate both steady state and tansient state tempeatue of key positions in high-speed geneato. The oveload unning time calculation poblem can be solved unde the hot condition oveload and cold condition oveload. The simplified themal model is also adapted to the vaious types of geneato and moto, but modeling fo diffeent type geneatos and moto and calculating its model paametes ae a had wok. The use of EKF can not only estimate the stato and oto tempeatues but also allows us to pefom a peventive monitoing technique based on the use of Matlab / Simulink, acting on the contol of the powe souce. The advantage of the themal monitoing of IM and inceased the life of insulation is theefoe asynchonous. Refeences 1. Gao Z., Habetle T.G., Haley R.G., Colby R.S., An Adaptive Kalman Filteing Appoach to Induction Machine Stato Winding Tempeatue Estimation Based on a Hybid Themal Model, IEEE, Infomation Guide fo Geneal Pupose Industial AC Small and Medium Squiel-Cage Induction Moto Standads, NEMA Standad MG1-003, Aug Beguenane R., El Hachemi Benbouzid M., Induction motos themal monitoing by means of oto esistance identification, Electic Machines and Dives Confeence Recod, 1997, p. TD/4.1 - TD/ Beguenane R., Benbouzid M.E.H., Induction motos themal monitoing by means of oto esistance identification, IEEE Tansaction on Enegy Convesion, 1999, 14(3), p Sang-Bin L., Habetle T.G., Haley R.G., Gitte D.J., A stato and oto esistance estimation technique fo conducto tempeatue monitoing, Industy Applications Confeence, 000, Confeence Recod of the 000 IEEE, 000, 1, p Saïd M.S.N., Benbouzid M.E.H., H G Diagam Based Roto Paametes Identification fo Induction Motos Themal Monitoing, IEEE Tansactions on Enegy Convesion, 000, 15(1), Schöning M., Lange E., Hameye K., Development and validation of a fast themal finite element solve, Poceedings of the 008 Intenational confeence on electical machines, 107

15 Stochastic Estimation Methods fo Induction Moto Tansient Themal Monitoing Unde Non Linea Condition Mellah HACEN and Hemsas KAMEL EDDINE IEEE, Saka D., Mukhejee P.K., Sen S.K., Use of 3-dimensional finite elements fo computation of tempeatue distibution in the stato of an induction moto, Electic Powe Applications, IEE Poceedings B, 1991, 138(), p Chauveau E., Contibution au calcul électomagnétique et themique des machines électiques Application à l étude de l influence des hamoniques su l échauffement des moteus asynchones, Thèse de doctoat de l Univesité de Nantes, Boglietti A., Cavagnino A., Staton D., Shanel M., Muelle M., Mejuto C., Evolution and Moden Appoaches fo Themal Analysis of Electical Machines, IEEE Tansactions on Industial Electonics, 009, 56(3), p Okoo O.I., Dynamic and themal modelling of induction machines with non linea effects, Kassel Univesity Pess GmbH, Kassel, 00, ISBN Lazaevic Z., Radosavljevic R., Osmokovic P., A novel appoach fo tempeatue estimation in squiel-cage induction moto without sensos, IEEE Tansactions on Instumentation and Measuement, 1999, 48(3), p Hust K.D., Habetle T.G., A themal monitoing and paamete tuning scheme fo induction machines, Industy Applications Confeence, 1997, Thity-Second IAS Annual Meeting, IAS '97, Confeence Recod of the 1997 IEEE, 1997, 1, p Moeno J.F., Hidalgo F.P., Matinez M.D., Realisation of tests to detemine the paametes of the themal model of an induction machine, Electic Powe Applications, IEE Poceedings, 001, 148(5), p Al-Tayie J.K., Acanley P.P., Estimation of speed, stato tempeatue and oto tempeatue in cage induction moto dive using the extended Kalman filte algoithm, Electic Powe Applications, IEE Poceedings, 1997, 144(5), p Huai Y., Melnik R.V.N., Thogesen P.B., Computational analysis of tempeatue ise phenomena in electic induction motos, Applied Themal Engineeing, 003, 3, p Staton D., Hawkins D., Popescu M., Themal Behaviou of Electical Motos An Analytical Appoach, CWIEME 009 Pape MDL [online] Available at: 108