SLIDING MODE DIRECT TORQUE AND ROTOR FLUX CONTROL OF AN ISOLATED INDUCTION GENERATOR INCLUDING MAGNETIC SATURATION

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1 Rev. Rou. Sci. Techn. Électotechn. et Éneg. Vol. 61, 2, pp , Bucaet, 216 SLIDING MODE DIRECT TORQUE AND ROTOR FLUX CONTROL OF AN ISOLATED INDUCTION GENERATOR INCLUDING MAGNETIC SATURATION ADEL ABERBOUR 1, KASSA IDJDARENE 1, ABDELMOUNAÏM TOUNZI 2 Key wod: Diect toque and oto flux contol (DTRFC), Sliding ode contol, Autonoou induction geneato, Magnetic atuation. Thi pape peent a contol yte of an iolated quiel cage induction geneato (IG), whoe tato winding ae connected to a PWM invete/ectifie, uing diect toque and oto flux contol (DTRFC) algoith baed on the liding ode appoach. Unlike the conventional vecto contol chee, the popoed contol tategy peit to diectly contol the flux and toque without eoting to the uually ued cuent contol loop. The thee phae induction geneato i odeled though a diphae appoach and the agnetic atuation phenoenon i included both in the IG odel and in the contol algoith via a vaiable agnetizing inductance, baed on expeiental tet. The contol yte hould keep the dc voltage aco the capacito contant and equal to the efeence value, egadle of change in the oto peed and load. 1. INTRODUCTION The deand fo electical enegy i apidly gowing woldwide. On the othe hand, foil fuel eouce will be depleted and the envionental pollution i inevitable which ake the ankind look fo altenative enegy eouce. Beide, the enewable enegy ouce ae poiing olution. Aong thee olution, wind enegy i the wide ued one [1]. Squiel cage type IG i widely ued in wind powe application. It capability to opeate a a geneato without extenal powe upply allow it ue in tand alone powe geneation yte without any eactive powe fo the gid. Thi inteet i enhanced though it any advantage ove othe type of electic geneato uch a obutne, low pice and aintenance fee opeation. In the cae of tand alone opeating, induction geneato ae uually excited by thee ac capacito connected aco thei tato teinal and then known a elf excited induction geneato (SEIG). Thi excitation ethod i the cheapet and iplet technique but it ha eveal liitation. Indeed, the agnitude and fequency of the tato voltage ae vey enitive to the vaiation of the otation peed and the load. Diffeent yte configuation and contol tategie ae popoed in the liteatue in ode to ovecoe thee poble [25]. Aong all contol ethod fo SEIG, diect toque contol (DTC) i conideed paticulaly inteeting being independent of achine oto paaete. It baic chee i chaacteized by the abence of coodinate tanfoation, cuent egulato and PWM ignal geneato. It i iple, obut and allow a good toque contol. Howeve, the peence of hyteei contolle fo flux and toque lead to toque and cuent ipple and vaiable witching fequency fo the PWM convete. Vecto contol algoith ae alo conideed in SEIG powe geneating yte [25]. Geneally, thi contol technique take a cacaded configuation and fou contolle ae ued (uually popotional integal (PI) contolle; extenal loop fo the flux and the dc voltage contol and inne loop fo the cuent contol [3]. The witching ignal fo the PWM convete ae then calculated uing a PWM ignal geneato. In oe cae, only two contolle ae ued fo flux and dc voltage contol while the cuent ae contolled uing hyteei contolle [2, 5]. Howeve, the ue of hyteei contolle lead to cuent ipple and vaiable witching fequency. In the othe ide, the ue of fou contolle lead to a coplicated and bulky contol chee. Note that a lage nube of olution have been popoed in ode to fulfill two ain objective: obtaining a pecie and quick contol of the flux and toque and eduction of the coplexity of the algoith involved in the vecto contol yte. In thi pape, we popoe a vecto contol tategy whee the oto flux and toque ae contolled in a diect anne without eoting to the uually ued cuent contol loop. Only two contol law ae ued and yntheized by the liding ode (SM) appoach. The choice of thi appoach ha been otivated by the peence of witche in the PWM convete. Change in the tate of the witche caue vaiation in the topology of the contolled yte. A the SM i a vaiable tuctue contolle, it i oe uitable fo yte with vaiable topology, which i the cae of the tudied yte. In addition the liding ode contol i chaacteized by it obutne, high dynaic and it i inenitive to the yte uncetaintie [6, 7]. Uually, in conventional SEIG vecto contol yte, the non-linea behavio of the induction achine agnetic ateial i not taken into conideation, o the agnetizing inductance i kept contant [2]. Howeve, it can lead to a eiou poble of accuacy and eliability, even oe in the cae whee the efeence of the flux i vaiable and the agnetic atuation occu. Theefoe, in ode to get a oe accuate pediction of the induction achine behavio and a good pefoance of the dive, and ovecoe the weakne of the involved etiato, the agnetic atuation phenoenon i taken into account in the dynaic odel of the IG and updated online in the contol yte. 2. CONTROL STRUCTURE The tudied yte, hown in Fig. 1, i contituted of a quiel cage thee-phae induction geneato (IG) connected echanically to a wind tubine though a gea box and 1 Univeité de Bejaia, Faculté de Technologie, Laboatoie de Technologie Indutielle et de l Infoation (LTII), 6, Algéie, E-ail: abebouadel@yahoo.f, idjdaene@yahoo.f. 2 Univeité de Lille, Laboatoie d Electotechnique et d Electonique de puiance (L2EP), 1, 59655, Fance, E-ail: ounai.tounzi@univ-lille1.f.

2 2 Contol of iolated induction geneato including atuation 143 Fig. 1 Syte and contol chee. electically to a PWM ectifie/invete. The dc ide of the latte i connected to a capacito, a battey to tat up the yte if no enant voltage i available and a diode which decouple the battey fo the ectifie/invete a oon a the dc voltage geneated i highe than the one of the battey. The load R i equivalent to the global load een fo the dc ide. The block diaga of the contol chee i alo hown on the ae figue INDUCTION MACHINE MODEL Uing tato and oto fluxe a the tate vaiable, the induction achine odel can be witten in the ynchonou efeence fae a follow: dφ 1 d L ω στ στl dφ 1 q Φd V d ω στ στl Φ q V q = +,, (1) dφd 1 Φd ( ωω ) στl στ Φq d Φq 1 ωω ( ) στl στ whee Ф d, Ф q and Ф d, Ф q ae the d and q-axi tato and oto flux coponent epectively. V d and V q ae the d and q-axi tato voltage coponent. τ and τ ae the tato and oto tie contant, with τ = L /R and τ = L /R, R and R ae tato and oto eitance. L and L ae the tato and oto elf inductance, L i the agnetiing inductance. Beide, σ i the leakage coefficient with σ = 1L 2 /(L L ), ω and ω ae the tato pule and oto peed expeed in electical adian pe econd. The agnitude of the tato flux, oto flux and tato voltage can be witten a follow: whee Φ = Φ + Φ Φ = Φ + Φ V = V + V d q d q d q Φ = L i + L i Φ = L i + L i Φ = L i + L i Φ = L i + L i d d d q q q d d d q q q We can alo intoduce the agnetizing cuent along the d and q-axi, uch a: i = i + i i = i + i d d d q q q = d + q and i i i. To expe L with epect to i, eveal appoache can be ued whoe iplet one i the polynoial appoxiation. ( ) n j j j=,. (2) (3) (4) L = f i = a. i, (5) whee a j epeent the polynoial coefficient. The wavefo of the agnetizing inductance i obtained though tet at no load fo diffeent voltage agnitude. Figue 2a and 2b how a copaion between eaueent and appoxiated value of a agnetizing inductance veu i.

3 144 Adel Abebou, Kaa Idjdaene, Abdelounaï Tounzi 3 Note that, in the following we aue that the efeence fae otate at the peed of the oto flux, o that, Ф d = Ф and Ф q =, and the efeence deivative with epect to tie ae neglected. Theefoe, by diffeentiating each liding uface fo (6) with epect to tie and ubtituting coeponding elation fo (1) yield: dsφ dφ 1 = kφ + ( Ri d ωφ q) Vd, στ σττ σττ (9) Fig. 2a Magnetizing inductance veu agnetizing cuent (expeiental). Fig. 2b Magnetizing inductance veu agnetizing cuent (iulation) DTRFC DESIGN USING SLIDING MODE APPROACH Accoding to the liding ode theoy, the fit deigning tep conit in defining the witching function (liding uface). It i eential that the tie deivative of the witching function depend diectly on one of the vaiable input of the tate odel which ae, in ou cae, the diphae tato voltage coponent V d and V q. Theefoe, the witching function of the oto flux S Ф and electoagnetic toque S Te ae defined a follow: * d * ( ) ( ) SΦ = kφ Φ Φ + Φ Φ d t, * STe = Te Te whee Ф * and T e * ae oto flux and electoagnetic toque efeence epectively. The electoagnetic toque T e i given a follow: T p = ( Φ Φ Φ Φ ), e q d d q k Ф i a poitive coefficient. It value i choen by the deigne, knowing that a high value of the latte lead to quick epone of the oto flux. The econd tep of the DTRFC deign conit to find the global contol law fo each liding uface. It geneal foula i given a follow: (6) (7) V = Veq + Vn, (8) with V eq i the o-called equivalent contol voltage whoe ain ule i to aintain the contolled vaiable on the liding uface but it i not intended to attact it towad the liding uface, thi tak i devoted to the dicontinuou contol coponent V n. dste 1 1 p p = + Te + ΦωΦd ΦVq. (1) στ στ The equivalent contol law fo each oto flux and electoagnetic toque can be found by eolving the equation below: ds Φ ds = and Te =. (11) Then, we obtain: σlτ dφ 1 1 Vd_ eq= kφ + ΦdωΦ q Φ, (12) στ στ σlτ V 1 1 = + Φ +ωφ q_ eq q d στ στ. (13) To find the coplete voltage vecto, the dicontinuou te ut be added to the equivalent contol. It peit to contol the concened vaiable outide the liding uface. Thu, the tie deivative of oto flux and electoagnetic toque witching function ut be conideed in the voltage vecto foula, uch a: * σl τ Vd = Vd _ eq * Vq = Vq _ eq pφ dsφ ds Te, (14) with V * d and V * q ae the global contol law of oto flux and electoagnetic toque epectively. The final tep conit in finding a elationhip, between the witching function and thei coeponding tie deivative, that allow attacting the oto flux and electoagnetic toque towad the liding uface. Thi elation i obtained by uing a eaching condition [8], uch a: dsφ dste SΦ < and STe <. (15) Then, the dicontinuou contol ut be deigned in uch a way that peit to keep a diffeent ign fo the witching function and it deivative. So, the following choice ae ade: dsφ =gφign ( SΦ) cφsφ. (16) dste =gteign ( STe ) cteste Plugging coeponding elation fo (16) into (14) lead to the DTRFC contol law below:

4 4 Contol of iolated induction geneato including atuation 145 σl τ V = V _ g ign S c S, (17) ( Φ ( Φ ) Φ Φ ) * d d eq V V _ g ign S c S. ( ( ) ) * q = q eq Te Te Te Te pφ (18) The paaete (g Ф = 12, c Ф = 2, g Te = 5 and c Te = 2 ) ae choen optially by obeving the behavio of the contolled vaiable, baed on citeia of high dynaic behavio and low ipple, i.e. the paaete choice ha to be a good copoie between a all value which can lead to low toque dynaic and low ipple and a too high value which can lead to a high toque dynaic and high ipple. Note that, in the cae of thi pape, the tate vaiable ae expeed in a efeence fae otating at the peed of the oto flux, o that, Ф d = Ф and Ф q =. Theefoe, the uually ued etiato in the conventional flux oiented contol ae alo valid in the tudied tategy. The oto flux, electoagnetic toque, the ynchonou fequency and the tato flux coponent can be etiated a follow [2]: Li d L Li q Φ=, Te= p Φiq, ω= + p Ω 1+τ L τφ Φ d =σ Li d+ Φ and Φ q=σli q L, (19) whee i the tie deivative opeato. A can be een fo (19), all the etiato depend on the agnetizing inductance. Then, the fact of conideing it contant can lead to eiou poble of accuacy. Hence, in ode to get a good pefoance of the dive, the agnetizing inductance i updated online in the contolle. The accuacy can be ipoved oe by adding the non-linea behavio of the oto eitance with epect to the tepeatue, indeed, Ф, Ф d and ω depend on the oto tie contant. But thi i not within the cope of thi pape. 3. SIMULATION RESULTS The logic contol ignal of the PWM convete ae calculated by uing the pace vecto odulation (SVM) technique. The detail about it ipleentation can be found in [9]. The noinal paaete of the induction achine ae lited in the appendix. In thi pape, the dc voltage efeence value i put equal to V * dc = 57 V. Thi will lead u to an voltage of about 23 V in the ac ide. The efeence oto flux i inveely popotional to the peed (flux weakening ode): ω Φ = ω * at Φ_ at, (2) whee, Φ -at and ω at ae the ated oto flux (Φ -at.7 Wb) and ynchonou peed, epectively. Thi tategy would allow avoiding a high atuation of the tuctue when the otation peed i beyond the ynchonou peed. Note that, a liitation ut be ipoed to the contolled oto flux in ode to avoid high atuation level when the peed i weak, a can be deduced fo (2). Fig. 3 Dc voltage. Fig. 4 Roto flux. The value of the load eitance R i initially equal to 7 Ω which i the value that allow the achine to geneate a ignificant powe elated to the opeating condition. At t = 2 the eitance i inceaed to R = 1 Ω, then it i deceaed to it initial value at t = 3. The otation peed i initially kept at it ynchonou peed (75 p). A tep inceent of 1 % i done at t = 4. Then at t = 5, a tep deceae of 2 % i applied. Figue 3 how the tie wavefo of the dc voltage that i well contolled. A can be een, the dc voltage i uch oe enitive to load ditubance than peed ditubance. Figue 4 how the oto flux epone. It i well contolled and how a vey quick epone obtained fo K Ф = 1. In the ae figue, we alo how the oto flux locu in the α-β efeence fae. Figue 5 how the electoagnetic toque tie wavefo. It tack vey well it efeence value. We can alo obeve the ipact of the load and otation peed vaiation on the electoagnetic toque. Fig 6 how the liding uface of the oto flux and electoagnetic toque. A can be een, they ae both foced to zeo. Finally, Fig. 7 and 8 how the agnetizing cuent tie and the value of the agnetizing inductance obtained fo the conideed opeation A thi inductance depend on the agnetic atuation level, we can note the influence of the load vaiation at t = 2 and t = 3. Thi can be diectly linked to the agnetizing cuent i vaiation (Fig. 7). At t = 4, the agnetizing inductance inceae due to the deceae of the oto flux which i ipoed by the inceae of the peed at contant load. The invee effect i obviouly obeved at t = CONCLUSIONS In thi pape, DTRFC baed on vecto contol concept and yntheized by the liding ode appoach of an autonoou induction geneato i tudied. Thi tategy peit a diect contol of flux and toque without eoting to the uually ued cuent contol loop. Thu, the coplexity of the contolle i educed. In addition, the

5 146 Adel Abebou, Kaa Idjdaene, Abdelounaï Tounzi 5 adaptation of the agnetizing inductance peit to avoid the weakne of the involved etiato. Finally, the iulation eult howed the effectivene of the popoed DTRFC tategy, o it can be conideed a a poiing altenative to the exiting olution in the field of enewable wind enegy yte. Fig. 5 Electoagnetic toque. APPENDIX Paaete of the induction achine: P N = 5.5 kw, U N = 23/4 V, I N = 23.8/13.7 A, 5 Hz, Ω N = 69 p, J =.23 kg. 2, d =.25 N. ad 1, R = Ω, R = Ω, p = 4. Received on July 23, 215 Fig. 6 Sliding uface. Fig. 7 Magnetizing cuent. Fig. 8 Magnetizing inductance. REFERENCES 1. M. Cheng, Y. Zhu, The tate of the at of wind enegy conveion yte and technologie: A eview, Enegy Conveion and Manageent, 88, pp , K. Idjdaene, D. Rekioua, T. Rekioua, A. Tounzi, Vecto contol of autonoou induction geneato taking atuation effect into account, Enegy Conveion and Manageent, 49, pp , D. Seyou, C. Gantha, Teinal voltage contol of a wind tubine diven iolated induction geneato uing tato oiented field contol, IEEE tanaction on indutial Application, 23, pp S. Haadi, N. Hidoui, L. Sbita, A DTC SEIG dive chee fo an iolated wind tubine buck yte, Intenational Confeence on Contol, Deciion and Infoation Technologie (CoDIT 13), 213, pp M. Bašić, D. Vukadinović, M. Polić, Fuzzy DC-voltage contolle fo a vecto contolled tand-alone induction geneato, Intenational Jounal Of Cicuit, Syte And Signal Poceing, 7, 3, pp , A. Keboua, M. Abid, Hybid fuzzy iliding ode contol of a doublyfed induction geneato in wind tubine, Rev. Rou. Sci. Techn. Électotechn. et Éneg., 57, 4, pp , A. Boucheta, I.K. Bouehane, A. Hazzab, B. Mazai, M.K. Fellah, Fuzzy-ilding ode contolle fo linea induction oto contol, Rev. Rou. Sci. Techn. Électotechn. et Éneg., 54, 4, pp , M. Adjoudj, M. Abid, A. Aiaoui, Y. Radani, H. Bounoua, Sliding ode contol of a doubly fed induction geneato fo wind tubine, Rev. Rou. Sci. Techn. Électotechn. et Éneg., 56, 1, pp , T.J. Fu, W.F. Xie, A novel liding-ode contol of induction oto uing pace vecto odulation technique, ISA Tanaction, 44, pp , 25.

7. Inverter operated induction machines

7. Inverter operated induction machines 7. Invete opeated induction machine Souce: Siemen AG, Gemany Dept. of Electical Enegy Conveion Pof. A. Binde 7/1 Invete-fed induction machine Fequency convete (invete) geneate thee-phae voltage ytem with