Speed Control of a Doubly Fed Induction Motor using Fuzzy Logic Techniques

Transcription

1 Intenational Jounal on Electical Engineeing and Infomatic - Volume 2, Numbe 3, 2010 Speed Contol of a Doubly Fed Induction Moto uing Fuzzy Logic Technique D. Ben Attou and Y. Bekaka Depatment of Electical Engineeing, El-Oued Univeity Cente. dbenattou@yahoo.com, youcef1984@gmail.com Abtact: Thi pape peent a compaion between a fuzzy logic contolle and a conventional IP contolle ued fo peed contol with a diect tato flux oientation contol of a doubly fed induction moto. The effectivene of the popoed contol tategy i evaluated unde diffeent opeating condition uch a of efeence peed and fo load toque tep change at nominal paamete and in the peence of paamete vaiation. Simulation eult how that the fuzzy logic contolle i moe obut than a conventional IP contolle againt paamete vaiation and uncetainty, and i le enitive to extenal load toque ditubance with a fat dynamic epone. Keywod: diect tato flux oientation contol, doubly fed induction moto, fuzzy logic contolle, Fuzzy PI contolle, conventional IP contolle. 1. Intoduction Due to many feedom degee, the Doubly Fed Induction Machine (DFIM) peent eveal advantage a well a moto application in high powe application uch a taction, maine populion o a geneato in wind enegy conveion ytem like wind tubine, o pumped toage ytem [1]. The DFIM ha ome ditinct advantage compaed to the conventional quiel-cage machine. The DFIM can be fed and contolled tato o oto by vaiou poible combination. Indeed, the input command ae done by mean of fou pecie degee of contol feedom elatively to the quiel cage induction machine whee it contol appea quite imple. The flux oientation tategy can tanfom the non linea and coupled DFIM-mathematical model to a linea model conducting to one attactive olution a well a unde geneating o motoing opeation [2], [3]. Seveal method of contol ae ued to contol the induction moto among which the vecto contol o field oientation contol that allow a decoupling between the toque and the flux, in ode to obtain an independent contol of toque and the flux like DC moto [4]. Theefoe, decoupling the contol cheme i equied by compenation of the coupling effect between q-axi and d-axi cuent dynamic [4]. With the field oientation contol (FOC) method, induction machine dive ae becoming a majo candidate in high-pefomance motion contol application, whee evo quality opeation i equied. Fat tanient epone i made poible by decoupled toque and flux contol. The mot widely ued contol method i pehap the popotional integal contol (PI). It i eay to deign and implement, but it ha difficulty in dealing with paamete vaiation, and load ditubance [5]. Recent liteatue ha paid much attention to the potential of fuzzy contol in machine dive application. In the aea of the contol of the electic machine, the eeach wok ae oiented moe and moe towad the application of the moden contol technique. Thee technique involve in a vetiginou way with the evolution of the compute and powe electonic. Thi allow to lead to the indutial pocee of high pefomance. Thee technique ae the fuzzy contol, the adaptive contol, the liding mode contol etc [6]. 179

2 D. Ben Attou, et al. Fuzzy theoy wa fit popoed and invetigated by Pof. Zadeh in The Mamdani fuzzy infeence ytem wa peented to contol a team engine and boile combination by linguitic ule. Fuzzy logic i expeed by mean of if-then ule with the human language. In the deign of a fuzzy logic contolle, the mathematical model i not neceay. Theefoe, the fuzzy logic contolle i of good obutne. Owing to it eay application, it ha been widely ued in induty. Howeve, the ule and the membehip function of a fuzzy logic contolle ae baed on expet expeience o knowledge databae [7]. In thi tudy, we ugget a contol cheme to achieve the goal of peed egulation with diect tato flux oientation contol DFIM dive and fuzzy logic contol (Fuzzy-PI). 2. Machine STATE-EQUATIONS The electical model of the DFIM i expeed in a (d-q) ynchonou otating fame. The contol i done unde the following conideation [8]: An input-output cuent decoupling i et fo all cuent; The (d-q) fame i oiented with the tato flux; Due to the lage gap between the mechanical and electical time contant, the peed can be conideed a invaiant with epect to the tate vecto. Unde thee condition, the electical equation of the machine ae decibed by a time vaiant tate pace ytem a hown in (1):. X = AX. + BU. (1) Y = C. X With, T X = id iq id iq U= V V V V d q d q T a1 aω + ω a3 a5ω a ω ω a1 a5ω a3 A ω = a4 a6ω a2 + ω, σ ω a6ω a4 ω a2 σ C = Whee: B b1 0 b3 0 0 b1 0 b3 =, b3 0 b2 0 0 b3 0 b2 1 σ R R R M R M M a =, a1 =, a2 =, a3 =, a4 =, a5 =, σ σ L σ L σ LL σ LL σ L a 6 M 1 1 M M =, b1 =, b2 =, b3 =, σ = 1 σ L σ L σ L σ LL LL 2 180

3 Speed Contol of a Doubly Fed Induction Moto The mechanical equation i expeed by (2): d Ω J = Ce C f Ω (2) dt The electomagnetic toque i given by [8]: PM Ce = ( φq. id φd. iq) (3) L 3. Diect Stato Flux Oientation Contol In thi ection, the DFIM model can be decibed by the following tate equation in the ynchonou efeence fame whoe axi d i aligned with the tato flux vecto [9], [10]: dφq φd = φ ; = φq = 0 (4) dt * φ i d = (5) M i q L * = C (6) e PM φ * dθ R. M = ω = i + V dt * q q / φ L 2 M di d M M V = R + i + σl + V φ σl ( ω ω) i LT dt L LT d d d d q Subtituting the equation (5) in equation (8), we obtain: di d M Vd = Rid + σl + Vd σl ( ω ω) iq (9) dt L (7) (8) V 2 M di q M M = R + i + σl + V ωφ LT dt L L + σl ( ω ω) i With: L L T =, T = R R. q q q d d (10) 4. Stato Flux Etimato Fo the DSFOC of DFIM, accuate knowledge of the magnitude and poition of the tato flux vecto i neceay. In a DFIM moto mode, a tato and oto cuent ae meauable, the tato flux can be etimated (calculate). The flux etimato can be obtained by the following equation [10]: φ = Li + Mi (11) d d d φ = Li + Mi (12) q q q 181

4 D. Ben Attou, et al. The poition tato flux i calculated by the following equation: θ = θ θ (13) In which: θ = ω dt, θ = ωdt, ω = PΩ. 5. Fuzzy Logic Contolle The tuctue of a complete fuzzy contol ytem i compoed fom the following bloc: Fuzzification, Knowledge bae, Infeence engine, Defuzzification. Figue 1 how the tuctue of a fuzzy logic contolle. Figue 1. The tuctue of a fuzzy logic contolle The fuzzification module convet the cip value of the contol input into fuzzy value. A fuzzy vaiable ha value, which ae defined by linguitic vaiable (fuzzy et o ubet) uch a low, medium, high, low whee each i defined by gadually vaying membehip function. In fuzzy et teminology, all the poible value that a vaiable can aume ae named univee of dicoue, and fuzzy et (chaacteized by membehip function) cove whole univee of dicoue. The hape fuzzy et can be tiangula, tapezoidal, etc [11]. A fuzzy contol eentially embed the intuition and expeience of a human opeato, and ometime thoe of a deigne and eeache. The data bae and the ule fom the knowledge bae which i ued to obtain the infeence elation R. The data bae contain a deciption of input and output vaiable uing fuzzy et. The ule bae i eentially the contol tategy of the ytem. It i uually obtained fom expet knowledge o heuitic; it contain a collection of fuzzy conditional tatement expeed a a et of IF-THEN ule, uch a: R (i) : If x 1 i F1 and x 2 i F2... and x n i Fn THEN Y i G (i), i = 1,...,M (14) Whee: (x 1, x 2,..., x n ) i the input vaiable vecto, Y i the contol vaiable, M i the numbe of ule, n i the numbe fuzzy vaiable, (F 1, F 2,...F n ) ae the fuzzy et. Fo the given ule bae of a contol ytem, the fuzzy contolle detemine the ule bae to be fied fo the pecific input ignal condition and then compute the effective contol action (the output fuzzy vaiable) [11]. The compoition opeation i the method by which uch a contol output can be geneated uing the ule bae. Seveal compoition method, uch a max-min o up-min and max-dot have been popoed in the liteatue. 182

5 Speed Contol of a Doubly Fed Induction Moto The mathematical pocedue of conveting fuzzy value into cip value i known a defuzzification. A numbe of defuzzification method have been uggeted. The choice of defuzzification method uually depend on the application and the available poceing powe. Thi opeation can be pefomed by eveal method of which cente of gavity (o centoid) and height method ae common [11]. A. Fuzzy-PI Contolle The fuzzy contolle i baically an input/ output tatic non-linea mapping, the contolle action can be witten in the fom [13]: u = k e. e + k ce. c e (15) The Fuzzy-PI output i: y = k p. u + ki. u (16) Whee: k e i the gain of the peed eo, k ce i the gain of the change of peed eo, k p i the popotional facto; k i i the integal facto, e i the peed eo, ce i the change of peed eo, u i the fuzzy output. The Fuzzy-PI contolle in a vecto-contol of DFIM i ued a peented in Figue 2. Figue 2. Block diagam of vecto-contol of DFIM uing Fuzzy-PI contolle B. Knowledge Bae Popoed Figue 3 and 4 how epectively the tiangle-haped membehip function of eo (e ) and change of eo (ce ). The fuzzy et ae deignated by the label: NB (negative big), NM (negative medium), NS (negative mall), Z (zeo), PS (poitive mall), PM (poitive medium), PB (poitive big), NVS (negative vey mall) and PVS (poitive vey mall). Figue 3. Membehip function fo input e 183

6 D. Ben Attou, et al. Figue 4. Membehip function fo input ce Figue 5. Membehip function fo output Figue 5 how the popoed membehip function fo output vaiable. In thi pape, the tiangula membehip function, the max-min eaoning method, and the cente of gavity defuzzification method ae ued, a thoe method ae mot fequently ued in many liteatue [11]. The infeence tategy ued in thi ytem i the Mamdani algoithm. Table 1. Linguitic Rule Table e NB NM NS Z PS PM PB ce NB NB NB NB NM NS NVS Z NM NB NB NM NS NVS Z PVS NS NB NM NS NVS Z PVS PS Z NM NS NVS Z PVS PS PM PS NS NVS Z PVS PS PM PB PM NVS Z PVS PS PM PB PB PB Z PVS PS PM PB PB PB 184

7 Speed Contol of a Doubly Fed Induction Moto All the membehip function (MF) ae aymmetical becaue nea the oigin (teady tate), the ignal equie moe peciion. Seven MF ae choen fo e and ce ignal and nine fo output. All the MF ae ymmetical fo poitive and negative value of the vaiable. Thu, maximum 7х7 = 49 ule can be fomed a tabulated in Table I, [12]. 6. Reult and Dicuion The DFIM ued in thi wok i a 0.8 kw, whoe nominal paamete ae epoted in appendix. The Fuzzy-PI contolle in a DSFOC dive ytem a peented in Figue 2. The Figue 6 peent the block diagam of fuzzy logic contol of the DFIM uing MATLAB/SIMULINK. A hown in thi figue, the peed loop ue a fuzzy logic contolle (Fuzzy-PI) and the tato flux i contolled by PI contolle. The block command ytem by PI contolle i the vecto contol, which to poduce the quadatue-axi oto cuent efeence which contol the moto toque. The moto flux i contolled by diect-axi oto cuent efeence. Block Pak inveion i ued to convet voltage efeence V d and V q into voltage efeence V a, V b and V c fo intoduce in PMW invete. Moto toque, oto cuent, flux and peed ignal ae available at the output of the Model of DFIM. Figue 6. Block diagam of fuzzy logic contol of the DFIM uing MATLAB/SIMULINK A. Load Vaiation In the fit tet, a cyclic change of diffeent load toque level ae ubjected to the moto at cetain time and a following: Time = [ ]; Toque = [ ]; T he epone of peed, toque, tato flux and oto cuent ae hown in Figue 7. The Fuzzy-PI egulato how the good pefomance to achieve tacking of the deied tajectoy. At thee change of load, the Fuzzy-PI egulato eject the load ditubance vey apidly with no ovehoot and with a negligible tatic eo a can be een in the epone of peed (ee Figue 7). The decoupling of toque-flux i maintained in pemanent mode. We can ee the contol i obut fom the point of view load vaiation. 185

8 D. Ben Attou, et al. In ode to compae the pefomance of Fuzzy-PI egulato with anothe egulato in the ame tet, the Figue 8 how the imulated eult compaion of taditional IP (Integal Popotional) and Fuzzy-PI egulato of peed contol of DFIM unde load vaiation. The Fuzzy PI contolle baed dive ytem can handle the udden change in load toque without ovehoot and undehoot and teady tate eo, wheea the IP contolle ha teady tate eo and the epone i not a fat a compaed to Fuzzy PI contolle. Thu the popoed contolle ha been found upeio to the conventional IP contolle. (a) (b) (c) (d) Figue 7. Reult of peed (a), toque (b), tato flux (c), and oto (d)roto cuent unde load vaiation Figue 8. Simulated eult compaion of IP and Fuzzy-PI egulato of peed contol of DFIM unde load vaiation. 186

9 Speed Contol of a Doubly Fed Induction Moto B. Speed Reveal of Rated Value In the econd tet, peed eveal of (157, -157 ad/), with a load of 5N.m applied at t = 0.6. Figue 9 peent the epone of peed, toque, tato flux and oto cuent veu time unde peed efeence eveal. The peed follow it efeence value without ovehooting. Figue 10 how the eult unde the teady tate and the tanient condition i.e. tep change in load toque at t=0.6 and peed eveal tage at t=1 fo the Fuzzy PI contolle and conventional IP contolle fom which it can be ee that the peed eached the ated value in vey hot peiod fo the Fuzzy PI contolle.. (a) (b) (c) (d) Figue 9. Reult of peed (a), toque (b), tato flux (c), and oto cuent (d) unde eveal peed Figue 10. Simulated eult compaion of IP and Fuzzy-PI egulato of peed contol of DFIM unde eveal peed. 187

10 D. Ben Attou, et al. C. Robut Contol fo Diffeent Value of Roto Reitance In ode to veifie the obutne of Fuzzy-PI egulato unde moto paamete vaiation, we have imulated the ytem with diffeent value of the paamete conideed and compaed to nominal value (eal value), one cae i conideed: The oto eitance vaiation (inceae at 50 % of nominal value oto eitance). Figue 11 how the epone peed, toque and tato flux in the tet of obutne fo diffeent value of oto eitance. The eult indicate that the Fuzzy-PI egulato i inenitive to the oto eitance change, which eult in the no influence on the toque and tato flux. Fo the obutne of contol, an inceae of the eitance doe not have any effect on the pefomance of the popoed contolle. The fuzzy contol give to ou contolle a geat place towad the contol of the ytem with unknown paamete. (a) (b) (c) Figue 11. Tet of obutne eult fo oto peed (a), toque (b), and tato fue(c) fo diffeent value of oto eitance: nominal cae and +50% 188

11 Speed Contol of a Doubly Fed Induction Moto 7. Concluion In thi pape, we have popoed a fuzzy logic contolle fo the peed contol of doubly fed induction moto with a diect tato flux oientation contol. The effectivene of the popoed contolle ha been teted on DFIM in compaion with conventional IP contolle unde diffeent opeating condition. The fuzzy PI egulato pove obutne againt oto eitance vaiation and inenitivity to load toque ditubance a well a fate dynamic with negligible teady tate eo at all dynamic opeating condition. Simulation eult have hown coect tato flux oiented contol behaviou and peed tacking pefomance. Appendix i d, i q : Roto cuent component, φ d, φ q : Stato flux component, V d, V q : Stato voltage component, V d R, L,, V q : Roto voltage component. R : Stato and oto eitance, L : Stato and oto inductance, M : Mutual inductance, σ : Leakage facto, P : Numbe of pole pai, C e : The electomagnetic toque, C : The load toque, J : The moment of inetia, Ω : Mechanical peed, ω,ω : The tato pulation, f : The fiction coefficient, T, T : Statoic and otoic time-contant. θ : The electical tato poition, θ : The electical oto poition. Rated Data of the imulated doubly fed induction moto: Rated value: 0.8 KW; 220/380 V-50 Hz; 3.8/2.2 A, 1420 pm. Rated paamete: R = Ω R = Ω L = H L = H M = H P = 2.0 Mechanical contant: J = 0.01 Kg.m 2 f = 0.00 I.S. 189

12 D. Ben Attou, et al. Refeence [1] S. Khojet, E. I. Slama-Belkhodja, M. Pietzak-David, B. de Fonel, A Fault Toleant Opeating Sytem in a Doubly Fed Induction Machine unde Invete Shot-cicuit Fault, /06/$ IEEE, pp [2] S. Did, M. Tadjine and M. S. Naît-Saîd, Robut backtepping vecto contol fo the doubly fed induction moto, The Intitution of Engineeing and Technology, Contol Theoy Appl., 2007, 1, (4), pp [3] S. Did, M. Tadjine, M.S. Nait-Said, Nonlinea feedback contol and toque optimization of a doubly fed induction moto, Jounal of Electical Engineeing, Vol. 56, NO. 3-4, 2005, [4] Chaai, M. Soltani, M. Goa, Compaative tudy between the conventional egulato and fuzzy logic contolle: application on the induction machine, Intenational Jounal of Science and Technique of Automatic contol & compute engineeing IJ-STA, Volume 1, N 2, Decembe 2007, pp [5] Hebet, L. Xu and Y. Tang, Fuzzy Logic Enhanced Speed Contol of an Indiect Field- Oiented Induction Machine Dive, IEEE Tan. Powe Electonic. Vol. 12. NO 5. Septembe 1997, pp [6] Y. Habouche, L. Khettache and R. Abdeemed, Sliding Mode Contol of the Double Fed Aynchonou Machine Applayed by Cuent Souce, Aian Jounal of Infomation Technology 6 (3), pp , [7] B. Allaoua, A. Abdeahmani B. Gabaoui, A. Nai, The Efficiency of Paticle Swam Optimization Applied on Fuzzy Logic DC Moto Speed Contol, Sebian Jounal of Electical Engineeing Vol. 5, No. 2, Novembe 2008, [8] G. SALLOUM, R. MBAYED, M. DE FORNEL B. PIETRZAK-DAVID, Mixed Senitivity H Contol of Doubly Fed Induction Moto, pp , /07/$ IEEE, pp [9] J. Soltani, A. Faokh Payam, M.A. Abbaian, A Speed Senole Sliding-Mode Contolle fo Doubly-Fed Induction Machine Dive with Adaptive Backtepping Obeve, /06/$20.OO '2006 IEEE, pp [10] Y. Bekaka, D. Ben attou, A Sliding Mode Speed and Flux Contol of a Doubly Fed Induction Machine, Electical and Electonic Engineeing, ELECO Intenational Confeence on, 5-8 Nov. 2009, Bua, pp I I-178. [11] Aiaoui, M. Abid, H. Abid, A. Tahou, A. Zeblah, A Fuzzy Logic Contolle fo Synchonou Machine, Jounal of Electical Engineeing, Vol. 58, NO. 5, 2007, pp [12] V. Kuma, R.R.Johi, Hybid Contolle baed Intelligent Speed Contol of Induction Moto, Jounal of Theoetical and Applied Infomation Technology, pp 71-75,

13 Speed Contol of a Doubly Fed Induction Moto D. Ben Attou wa bon on May 24, 1959 El Oued Algeia. He eceived hi Engineening degee in Electotechnic fom Polytechnic National Intitute Algie Algeia in He got Mc degee in Powe Sytem fom UMIST England in In 2000, he eceived hi doctoat d état (PhD fom Batna univeity Algeia). He i cuently aociate pofeo at El Oued univeity cente Algeia in Electical Engineeing. Hi eeach inteet in Planning and Economic of Electic Enegy Sytem, Optimization Theoy and it application and he alo invetigated quetion elated with Electical Dive and Poce Contol. He i membe of the VTRS eeach Laboatoy. Y. Bekaka wa bon on Ap28, 1984 in El Oued Algeia. He eceived hi Engineening degee in Electotechnic fom El Oued univeity cente Algeia in He pepaed hi Mc in Powe Sytem. Hi aea of eeach inteet i mainly Electical Dive and Poce Contol. 191