Direct power control based virtual flux using SOGI-FLL estimator for BDFIG-WEC system

Transcription

1 Revue des Energes Renouvelables Vol. 20 N 3 (2017) Drect power control based vrtual flux usng SOGI-FLL estmator for BDFIG-WEC system A. Rahab *, F. Senan and H. Benalla Laboratore de l Electrotechnque de Constantne, LEC Faculté des Scences de la Technologe Unversté des frères Mentour de Constantne 1 An El-bey Constantne, Algére (reçu le 30 Août accepté le 30 Septembre 2017) Abstract Ths paper deals wth the control aspect of the brushless doubly fed nducton generator, 'BDFIG' ncorporatng n a wnd energy converson system, 'WECS'. The control process may dvde n two man parts control of machne sde converter, MSC' and grd sde converter, 'GSC'. Control process adopts drect power control, DPC approach thanks to ts robustness and mplementaton smplcty drect power control permts decoupled regulaton for actve and reactve powers and as well pretty good robustness and performance durng transent and steady state operaton wthout PI regulators and rotatng coordnate transformatons. The regulaton of power flow toward supply network va stator s performed usng conventonal drect power control at level the machne sde converter where the actve power reference sgnal s tunng dependng to the output of the MPPT unt anhe reactve power reference sgnal s set to zero to ensure unty power factor operaton. Meanwhle, control of power flow between grd and grd sde converter, 'GSC' s done usng mproved drect power control based vrtual flux and Second order generalzed ntegrator - frequency locked loop, 'SOGI-FLL' estmator n order to estmate frequency and angular poston of voltage grd vector and as well power flow has been analysed durng varous operaton condtons, 'synchronous, sub synchronous and super synchronous speeds'. The obtaned smulaton results show satsfactory system operaton n terms of robustness and optmum power trackng behavour and good steady state stablty and fnally reasonable settlng tme durng transents. Résumé - Cet artcle trate de la commande du générateur à nducton brushless doublement almenté, 'BDFIG' en ncorporant un système de converson d'énerge éolenne, 'WECS'. Le procédé de commande peut être dvsé en deux partes, la commande du convertsseur côté machne 'MSC' et le convertsseur côté réseau 'GSC'. Le procédé de commande adopte une commande drecte de pussance 'DPC' en rason de sa robustesse et la faclté de son mplémentaton permet la régulaton découplée pour les pussances actves et réactves, ans qu'une bonne robustesse et de bonnes performances en régme transtore et statonnare sans régulateurs PI et en transformatons de coordonnées en rotaton. La régulaton du flux de pussance vers le réseau d'approvsonnement va un stator est réalsé en utlsant un DPC conventonnel au nveau du MSC ou le sgnal de référence de la pussance actve est ms au pont en foncton de la sorte du MPPT et le sgnal de référence de pussance réactve est réglé à zéro pour assurer des opératons de facteurs de pussance untares. En même temps, la commande du flux de pussance entre le réseau et le GSC est réalsé en utlsant un DPC améloré basé sur un flux vrtuel et un ntégrateur généralsé de second ordre-boucle verroullée en fréquence 'SOGI-FLL' afn d'estmer la fréquence et la poston angulare du vecteur de tenson du réseau, auss, le flux de pussance a été analysé dans dfférentes condtons opératores: à des vtesses synchrones, sous synchrones, et super synchrones. Les résultats de smulatons qu ont été obtenus ont montré que le système opérat de manère satsfasante en terme de robustesse et de trackng du pont de pussance * rahababderezzak@gmal.com senan.fouz@gmal.com - benalladz@yahoo.fr 449

2 450 A. Rahab et al. optmum, et possède une bonne stablté en régme statonnare et un temps d'nstallaton rasonnable durant les régmes transtores. Keywords: Wnd energy converson system - BDFIG - MPPT control - Drect power control, DPC - SOGI-FLL - Vrtual Flux Estmaton. 1. INTRODUCTION Wnd power has become ncreasngly popular because of the ncreasng dffculty of the polluton of the Envronment. Enormous efforts have been put n the advancement of WECS, to reduce costs, ncrease the effcency anhe relablty [1-2], wth the sustaned and rapd growth of world economy, the energy demand s ncreasng day by day, but a large amount of fossl fuel s useo leao the envronmental polluton aggravaton. The wnd energy as a clean and renewable energy accords wth the future energy development [3]. The permanent magnet synchronous generator anhe doubly fed nducton generator based of WECS 'PMSG WECS', 'DFIG-WECS' has become the most popular confguraton for wnd energy applcatons on one hand, the DFIG has several advantages ncludng the maxmum power capture over a wde speed range and decoupled actve and reactve power control. It also allows the use of a partally rated converter whch reduces the system cost [2, 4]. The use of brushes and slp rngs assocated wth the rotors of DFIG decreases the robustness of system and ncreases the mantenance cost [2, 5, 6]. The cost of mantenance for tradtonal DFIG based wnd generators ncreasehe pressure to seek other alternatve generator systems. Brushless doubly-fed machnes are the evoluton of the cascaded nducton machne and can be wdely used for medum and large wnurbnes wth lmted speed ranges [2-5]. The 'BDFIG', also known as a self-cascaded generator, s composed of two stator of dfferent pole numbers called stator of power wndng 'PW' and stator of control wndng, 'CW' and a specal rotor wndng. Normally the two stator supples are of varous frequences, one a fxed frequency supply lnkeo the grd va converter, and the other a varable frequency supply derved from two-level bdrectonal converters AC-DC-AC as llustrated n fgure 1. The converters capacty n the control wndng are of almost 25 % of the machnes rated power, whch can operate n a wde speed range ncludng super-synchronous, synchronous and sub-synchronous [4, 7-11], a medum speed machne, enablng the use of a smplfed one or two stage gearbox, excludng the thrd hgh-speed stage, known to be the hghest falure rate part of the gearbox, hence reducng the weght of the overall drve tran and further mprovng relablty, reduced captal and mantenance costs and has sgnfcantly greater LVRT capablty [9, 10]. The 'BDFIG-WECS' retans all the advantages of 'DFIG-WECS' and mproves relablty by removng brushes and slp rngs. Therefore, the 'BDFIG-WECS' shows great potental n future wnd power generaton, especally the large wnurbnes and offshore wnd farm where mantenance costs are hgh. [12-13]. 'BDFIG' modelng s much more complex, whch makes qute dffcult control system desgn. Varous strateges of control have been useo control of machne sde converter, 'MSC' {the scalar current control, drect torque control, fuzzy power control, sldng mode power control, and flux orented control based on rotor flux or stator flux/voltage orentaton} [12]. At present, the vector control s manly adopteo mplement the power decouplng control of 'BDFG' [7, 11, 14]. But the vector control requres the complcated control

3 Drect power control based vrtual flux usng SOGI-FLL estmator for algorthm and hgh performance processor, and greatly depends on the 'BDFG' parameters, whch leads to the poor robustness of the system [4]. The drect torque control, 'DTC' wth the smpler control algorthm, faster dynamc response and better robustness than the vector control has been attempteo apply for the varable-speed constant-frequency 'BDFG' control system [4-6]. But the flux observer of 'DTC' s senstve to the generator parameter varaton and naccurate dentfcaton, whch leads to the bad real-tme of control system. Alternatvely, the drect power control, 'DPC', derved from DTC, can drectly decouple and ndependently control the actve and reactve powers to mplement the power trackng. DPC has a smpler algorthm and less calculaton than DTC, and does not need to observe the flux ampltude, whch can well solve the problem of the bad real-tme of control system caused by the flux observer beng senstve to generator parameter varatons. Therefore, 'DPC' of 'MSC' has been appleo the 'BDFIG' control system[3-5, 12], the three strateges are based on the same prncple wth the only dfference exstng n flux estmaton algorthm. The grd sde converter, 'GSC' control approaches can be classfed, as cted n the lterature as a vector orented control, 'VOC' and drect power control 'DPC' [13], the vector control, 'VC' can be ether based on grd voltage [14-16] or vrtual-flux [17] usng proportonal ntegral (PI) controllers. However, t has some dsadvantages, such as ts dependence on the system parameters varaton, that ts performance largely depends on the tunng of the PI parameters [18]. In order to overcome complcaton due to the current control loops, an effectve control, namely drect power control, DPC has been developed [19], Drect power control, DPC strategy has become one of the hot research topcs n recent Years, because of ts fast dynamc response, smple structure, and hgh power factor, and so on [20, 21]. In general, the control of 'GSC' converter contans more sensors {DC voltage sensor, power grd voltage sensors and AC current sensors}, whch not only ncreases the volume of the system devce, mproves the system cost, but also reduces the system relablty of 'GSC' [21]. The 'GSC' can be seen as a vrtual AC motor, ts vrtual flux-lnkage can be useo estmate the voltage of 'GSC', but n the conventonal vrtual flux estmaton of 'GSC' converter, there exsts a pure ntegral lnk, anhen the estmaton process of vrtual flux s nevtably affected by the ntal value anhe cumulatve devaton of the ntegrator [21-27]. The resoluton of the problems of pure ntegraton, more researchers focus on replacng the pure ntegrator by usng low-pass flters, 'LPFs', the ntal value problem of pure ntegrator can be successfully solved [21, 25-27], however, the problem of ampltude and phase devaton s caused. In order to overcome the nfluence of ntegral ntal value and cumulatve devaton of pure ntegrator, and avohe ampltude and phase devaton caused by frst-order low-pass flter, ths paper proposes a new method for Vrtual Flux estmaton that s nherently capable of handlng these problems, as a result a stable and smooth vrtual flux estmated and sector detecton wth precson. The suggested method s based on utlzng the Second Order Generalzed Integrator, 'SOGI' from [24-26]. Ths paper s organzed as follows- In Secton 2, the descrpton basc prncples of system, 'BDFIG-WEC' chan studed. In Secton 3, the mathematcal model of 'BDFIG', Wnd Turbne anhree-phase grd sde converter, 'GSC' are derved. In Secton 4, presents controls of dfferent parts of the 'WEC' chan, DPC method s useo control of machne sde converter, 'MSC' of 'BDFIG', the maxmum power pont trackng, 'MPPT' method was mplemented for optmal energy capture by the wnurbne, drect power

4 452 A. Rahab et al. control based vrtual flux estmaton, 'VF-DPC' by usng Second Order Generalzed Integrator frequency located loop, 'SOGI-FLL' of 'GSC' converter to control the voltage of the DC Lnk s proposed for smplcty,robustness, and excellent performance. Secton 5 presented some smulaton results and dscusson fnally, the concluson are provded n secton DESCRIPTION OF SYSTEM 'BDFIG-WEC' CHAIN The confguraton of the 'BDFIG-WEC' s show n fgure1 the rotor of the 'BDFIG' s connecteo wnurbne, The man stator Power Wndng 'PW' has pole pars 'Pp' connected drectly to the grhan the auxlary stator {control Wndng, 'CW'} has pole pars 'Pc' fed by a varable voltage and frequency converter, whch only handles a fracton of the rated power, the 'BDFIG' can operate n several mode ways ncludng synchronous, doubly-fed, asynchronous mode [8]. The synchronous mode of operaton of the 'BDFIG' s desrable operaton mode, n ths mode of operaton the shaft speed s ndependent of the machne torque and s gven by: Or Where, P C r (1) P P N r P, P P C fp fp 60 (2) P P C C are angular frequences of the supples to the PW and CW, f and f C are PW and CW supply frequences, P P and P C are ther pole respectvely, P par numbers, respectvely. The postve and negatve sgns ndcate the sequence of stator control wndng exctaton wth respect to the power wndng. Wth the CW shorted ( 0 ) or the control wndng s fed wth dc current, the shaft speed s C defned as the natural speed ( ) gven by: P C n p n (3) P P Fg. 1: Schematc dagram of a 'BDFIG' based wnd power system Fgure 1 also show de power flow n a lossless 'BDFIG' and are lsted n Table 1. [8, 10].

5 Drect power control based vrtual flux usng SOGI-FLL estmator for Table 1: Power Flows n a lossless BDFIG Generator mode Speed 0 r n n r P r P Power wndng, PW Out Out Out Control wndng, CW Out In In 3. MODELLING OF THE WECS 3.1 Wnurbne aerodynamc model In ths paper, we are usehe same model cted n [28, 29] The wnd power s defned as follows P R (4) 2 The aerodynamc power P a captured by the wnurbne s gven by: 1 3 (5) 2 2 a R Cp (, ) P The wnurbne s characterzed by ts curve f ( ), fgure 2, wth s the rato between the tp perpheral speed of blades anhe wnd speed, n ths paper, s supposeo be zero and so R C p C P s only dependeo. C P, power coeffcent,, densty of ar (1.25 kg/m 3 ),, wnd speed, R, turbne rayon. Increasng alloys the reducton of power coeffcent or mechancal power recovered from the axs of the wnurbne show fgure 2. (6) 3.2 Mathematcal model of 'BDFG' The model of the 'BDFG' n the PW flux frame s expressed as, [11]: v v v v 0 0 qsp dsp dsc qsc R R r r d sp Rsp qsp P dsp d dsp Rsp dsp ( P (PP PC ) r ) d dsc Rsc dsc ( P (PP PC ) r ) d qsc Rsc qsc ( P (PP PC ) r ) d dr dr ( P PP r ) qr d qr qr ( P PP r ) dr qsp qsc dsc (7)

6 454 A. Rahab et al. dsp qsp dsc qsc dr qr L L L L L L r r sp sp sc sc dr qr dsp qsp dsc qsc Fg. 2: Power coeffcent vs tp speed rato M M M M M M scr scr spr dr spr qr scr scr dsc qsc dr qr M M The aerodynamc torque s gven by: C em spr dsp spr qsp p M.( ) p M.( ) (9) P spr qsp dr dsp qr c scr dsc qr qsc dr Accordng to the nstantaneous power theory, the actve and reactve powers of the (PW) are defned as: P Q sp sp 3 (Vsdp,Isdp Vsqp.Isqp ) (10) 2 3 (Vsqp,Isdp Vsdp.Isqp ) (11) Model of three-phase PWM converter 'GSC & MSC' The man objectve of grd sde converter 'GSC' s to keep the dc-lnk voltage constant t s controlled usng a 'VF-DPC' based SOGI flux estmaton. (8) Fg. 3: Block dagram for three-phase PWM rectfer The converter can be expressed, n a-b-c reference frame wth followng equatons [20]:

7 e e e a b c Drect power control based vrtual flux usng SOGI-FLL estmator for e R e e a b c d L I I I a b c Va Vb Vc Where, L and R are the nductance and resstance of the chokes, respectvely e a, e b, e c, a, b and c are the electrcal grd voltage and current, V A, V B, V C are the AC sde voltages of the converter, The AC rectfer's voltages V A, V B, V C are defned as: Vdc VA ( 2Sa Sb Sc ) 3 Vdc VB ( Sa 2Sb Sc ) 3 Vdc VC ( Sa Sb 2Sc ) 3 S a, S b and S c are the swtchng states of the rectfer show fgure 8. The relatonshp between the AC sde rectfer currents a, b and c anhe DC bus voltage V dc can be wrtten. Where C dc d V dc a a b b c c L (12) (13) S S S (14) C dc s the dc lnk capactance, L the load current. 4. CONTROL OF THE 'BDFIG-WECS' CHAIN 4.1 Maxmum power pont trackng technque Maxmum power pont trackng 'MPPT' strateges play an mportant role n wnd power converson systems 'WECS' because they maxmze the power extracted from the wnd, anherefore optmze the converson effcency. Fgure 4 shows the Power-Speed characterstcs of the wnurbne, the peak power for each wnd speed occurs at the pont where C s maxmzed. To maxmze the power generated, t s therefore desrable for the generator to have a power characterstc that wll follow the maxmum C lne. pmax p Fg. 4: Characterstcs curve of wnd turbne ( opt 8. 1 ; C pmax ; 0 ) [29]

8 456 A. Rahab et al. Two strateges are used n lterature wth or wthout speed control. In ths paper, we usehe strategy wthout speed control; ths method s superor to others because of ts smplcty and accuracy. The other advantage of ths method s that there s no neeo speed controller and wnd speed sensor [30, 31]. The smplfed representaton of wnurbne model wthout speed control n the form of dagram blocks s gven n fgure5 [30]. Fg. 5: Wnurbne model wthout speed control 4.2 Drect power control 'DPC' OF 'BDFIG' The control dea of DPC s derved from DTC. The DPC prncple dagram of the 'BDFIG' s shown as fgure 6, whch s smlar to DTC, the reference actve power s set by maxmum power trackng strategy accordng to wnd speed. Reference reactve * power Q sp s set zero for kept unty power factor, dp and dq are respectvely the errors of the actve and reactve power. For a MSC three phase two level nverter, there are eght possble voltage vectors {sx actve vectors anwo null vectors}, anhe plane s dvded nto sx sectors, as show n fgure 7b. The flux ampltude * P sp sp of the 'PW' wndng s approxmately constant due to the power wndng s drectly connecteo the power grd, so the actve power P sp can be controlled by changng the rotatonal speed and drecton of the control wndng flux,, referrng to the DTC method, the reactve power can be controlled by sc changng the flux ampltude of the (CW) wndng. Therefore, the swtchng voltage vector selecton table has to be re-establshed accordng to the error sgnals of the actve and reactve powers as well as the secton locaton nformaton of the 'CW' flux, the actve and reactve powers of the 'BDFIG' can be drectly decoupled and ndependently controlled by properly selectng the swtchng voltage vectors [3]. The power wndng 'PW' stator flux and control wndng 'CW' stator flux are estmated by (15), (16). sp ( Vsp Rsp sp ) esp (15) sc ( Vsc Rsc sc ) esc (16) sp

9 Drect power control based vrtual flux usng SOGI-FLL estmator for Voltage vectors effects on actve and reactve powers [4, 5] In ths secton, the relaton between the voltage vectors of the nverter anhe 'BDFIG' output power wll be deduced. For three-phase two-level nverters, there are eght possble voltage vectors {sx actve vectors anwo null vectors}, anhe plane s dvded nto sx sectors, as shown n fgure 7a. The control dagram of 'DPC' strategy of 'BDFIG' s llustrated n fgure 6. The actual output powers P sp and Q sp are frst estmated, anhen compared wth the references P ref and Q ref. The errors are sent to two fxed band hysteress comparators to produce dgtzed sgnals dp and dq. Fnally, the voltage vector s selected from Table 2 accordng to dp, dq anhe poston of sc. Fg. 6: Block dagram of DPC controller for 'CBDFIGs' Fg. 7: (a) Relatonshp between voltage vector and flux vector (b) Voltage vectors generated by the nverter and sector dvson 'CW' flux estmaton Flux estmaton plays an mportant role n hgh-performance electrcal drve systems, ncludng those based on feld orented control 'FOC' and drect control 'DPC' and 'DTC'. The three 'DPC' strateges of brushless doubly fed nducton generator realzed n [4, 5, 12] respectvely, are based on same prncpe wth the only dfference exstng n flux estmaton algorthm. In note 'DPC' strateges n [12], hgh relablty wth the elmnaton of rotor current/poston sensor and rotatng coordnate transformaton, and less parameter ndependent wth the control machne stator resstance.

10 458 A. Rahab et al. The 'CW' stator flux can be obtaned by ntegratng the back electromotve force ' e sc ' equaton (16), however, t s well know that a pure ntegrator suffers from three man problems the frst relateo dc drft, when ntegrated, wll cause the ntegrator to saturate, the second s caused by the ntal condton of ntegraton, may leao a dc offset at the output of the ntegrator. The thrd relateo harmoncs, more detaled n [25, 26]. Basehe same prncpe DPC strateges, n ths paper a new flux estmaton method based on the second order generalzed ntegrator frequency-locked loop 'SOGI-FLL' are presented. More detal for ths method presented n next part. Table 2: The voltage vector control selecton table [3, 31] 4.3Vrtual flux based drect power control 'VF-DPC' for 'GSC' The vrtual flux 'VF' concept whch relates the grd voltage anhe ac-sde nductors to a vrtual ac motor s shown n fgure 9a hence; R and L represent the stator resstance anhe stator leakage resstance of the vrtual motor. The lne-to-lne grd voltages e ab, e bc, e ca would be nduced by a vrtual ar-gap flux. In other perspectve, the ntegraton of the lne voltages leads to a vrtual lne vector L. Fgure 8 shows the basc scheme of 'VF-DPC'. Fg. 8: Vrtual-flux based drect power control 'VF-DPC' scheme The command actve power P ref and reactve power Q ref are compared wth the estmated P and Q values va actve and reactve power hysteress controllers, respectvely. The dgtzed output sgnals S P and S Q anhe VF vector poston ( ) are useo select the approprate voltage vector accordng to the swtchng table defned n [19].

11 Drect power control based vrtual flux usng SOGI-FLL estmator for Power estmaton based on vrtual flux Fgure 9a shows a sngle phase equvalent crcut of the vrtual motor that s connecteo the pont of common couplng of the converter. The lne voltage el represents the machnes Electromotve force. The mans vrtual flux 'VF' calculaton s based on flux defnton (17) anhe voltage loop equaton (18). Fg. 9: (a) Sngle phase equvalent crcut of mans connected three-phase rectfer, (b) Sector selecton for 'VF-DPC' technque [20] L e L dt (17) e L d uconv R L L L (18) In practce, R R can be neglected whch gves hence, the lne vrtual flux vector can be calculated based on the measured lne current L anhe converter voltage uconv. Based on the measured dc-lnk voltage and S c, the rectfer voltages are estmated n as follows [19]: u 2 1 Udc Sa (Sb Sc ) 32 2 V dc anhe converter swtch states S a, conv (19) 1 uconv Udc (Sb Sc ) (20) 2 The vrtual flux components are calculated n statonary ( ) coordnates system as: d L L uconv L dt (21) dl L uconv L dt (22) Then, equatons (23) and (24) are useo estmate the actve and reactve power [20]. P ( ) (23) L L L L Q ( ) (24) L L L L 1 The VF vector poston tan L L L L S b s used n 'VF-DPC' scheme to select the approprate converters voltage vector accordng to the swtchng table defned n [32].

12 460 A. Rahab et al 'SOGI-FLL' flux estmaton a. Structure du 'SOGI' The structure of the SOGI s shown on fgure 10a the frst output ( u ' ) of the SOGI s n phase and wth the same ampltude wth the nput ( u ), the second output ( qu ' ) s shfted of 90 wth the same ampltude, (the letter ' q ' s for ndcatng that ths output s n quadrature wth ( u ' ) the two output can then be used for computng magntude and phase of nput ( u ). k s the dampng factor of the flter, a gan of great value gves a quck response but can affect the accuracy of the flter and a gan of low value can cause a very long transent response. Then, takng nto account all these crcumstances the value optmal of gan k s ( 2 ) [24, 25]. u' k ' S D(S) (S) (25) 2 ' 2 u S k S' 2 q u' k ' Q(S) (S) (26) 2 ' 2 u S k S' Fg. 10: Block dagram (a) 'SOGI-QSG' scheme, (b) 'FLL Block' The transfer functons represented by (25) and (26) for band pass flter 'BPF' and low-pass flter 'LPF', respectvely. The bandwdth of the 'BPF' D (s) and 'LPF' Q (s), can be adjusted by proper tunng of the real postve value of gan k. Hence, the sgnals u ' and qu ' are the outputs of the BPF and LPF, respectvely, wth 90 phase shft between them show fgure11, where the ( ) sets the centre frequency (nomnally 50 Hz). ' Fg. 11: 'SOGI' bode plot: (a) D (s) for dfferent values of k b. Frequency-locked loop 'FLL' (b) D (s) and Q (s) for k 2 and 250 The ntroducton of the FLL allows to adapt the nput frequency of the 'SOGI' wth the frequency of the sgnal s fltered. '

13 Drect power control based vrtual flux usng SOGI-FLL estmator for Of ths fact, the analyss of the transfer functon of the error ( E ) compareo the nput sgnal ( u ) s essental: 2 2 S ' E(S) (S) (27) 2 ' 2 u S k S' The transfer functon of (27) resembles a flter passes band wth a null (gan) at the ' frequency ( ), the Bode dagram of (26) and (27) are represented n fgure 12. Fg. 12: 'SOGI' bode plot: E (s) and Q (s) for k 2 and 250 Accordng to the fgure 12, t s clear that the error sgnal anhe component n ' ' quadrature s n phase when ( ) an s n reverse of phase when ( ). Defnng anew varable equal to the product of the error ( ) by the sgnal n quadrature ( qu ' ), the average value of ths new varable s postve when ( ), zero when ( ' ), and negatve when ( ' ' ' ). Therefore a regulator wth a negatve gan s suffcent to elmnate the DC component of the frequency error By shftng the frequency a a shown fgure10b. In order to overcome the dsadvantage to the use of flters n cascade to estmate the vrtual flows under a network unbalanced and full of harmoncs {The delay, senstvty to the varaton of the frequency of the network, a dynamc and very slow}, The 'SOGI' account as a good soluton for the estmaton of the Vrtual flux Under a dsturbed network. Fg. 13: Estmaton of the vrtual flow by SOGI under deal source

14 462 A. Rahab et al. As already seen prevously, the second output of the 'SOGI' s a sgnal of the same ampltude to that of the nput but shft of 90, So we can use the 'SOGI' to ntegrate (21), (22) and by consequence estmate the vrtual flux [24]. Under a balanced network, the vrtual flux can be estmated by the 'SOGI' as llustrated n fgure SIMULATION RESULTS For the valdaton of the proposed 'DPC' strategy, the system has been modelled and bult n Matlab/Smulnk software envronment anested under varous condtons. The 'BDFIG' based system s about 2 taken about 100 khz. The converter dc lnk voltage s set at 600 V. The control of grd sde converter, 'GSC' ams to mantan a constant dc-lnk voltage, an s controlled usng 'VF-DPC' method based 'SOGI- FLL' vrtual flux estmator. The machne sde converter, 'MSC' s exploteo regulate the power flow va 'BDFIG' stator to the grd usng conventonal 'DPC' strategy. In order to verfy the good performance 2.5 kw power scale ans parameters are gven n [11]. The samplng frequency durng smulaton s and advantages offered by control combnaton of 'DPC BDFIG' machne for 'MSC' and 'VF-DPC-SOGI-FLL' for GSC, startng procedure s not relevant to ths paper and not shown n the results. The system s analysed durng steady-state anransents condtons at two case, wnd step change (sub-synchronous, synchronous and super-synchronous) operaton fgure 14a and varable wnd profle fgure 14b. Fg. 14: Wnd speed (a) Step change (b) Varable wnd profle 5.1 Smulaton case 1: results wth step change of wnd power The wnd speed steps from 8.12 m/s to 11.8 m/s at nstant 1.2 s, and from 11.8 m/s to 15 m/s at nstant 1.6 s as shown n fgure 14a. Accordng to the correspondng optmal speed of 'BDFIG' machne s 525 tr/mn at the start up, 750 tr/mn at nstant 1.2 s, and 975 tr/mn at nstant 1.6 s as shown n fgure 15a Smulaton result of 'DPC-BDFIG' for 'MSC' Fg. 15: Smulaton results of 'DPC-BDFIG' of 'MSC' under speed step

15 Drect power control based vrtual flux usng SOGI-FLL estmator for {super-synchronous mode, synchronous mode, sub-synchronous mode} (a) Speed; (b) PW actve power; (c) PW actve power Fg. 16: Smulaton results of 'DPC-BDFIG' of 'MSC' under speed step {super-synchronous mode, synchronous mode, sub-synchronous mode} (a) 3-phase current waveform of CW stator; (b) 3-phase current waveform of PW; (c) 1 st phase a voltage and current of PW The fgure 14a shows the appled wnd profle for the studed system, an could ensure varous operaton condtons {sub-synchronous mode (525 tr/mn), synchronous mode (750 tr/mn) and super-synchronous mode (975 tr/mn)}). It can be seen, that the generator speed s accurately adjusteo the waveforms of optmal reference speed, whch s obtaned from MPPT. The fgure15-b shows the generated actve power n case of {sup-synchronous, synchronous and sup-synchronous} operaton wth zero value of reactve power as can be seen n fgure 15c. The fgure 15a anhe fgure 15b shows the 'PW' stator actve and reactve powers wth ther respectve references. The 'PW' stator actve power reference s obtaned through the MPPT control algorthm. The reference of reactve power of stator 'PW' s set at zero to ensure a unt power factor n order to optmze the qualty of the energy transmtteo the grd. As well can note that the measured actve and reactve powers of the 'BDFIG' follow ther references perfectly whch means that a good steady state performance has been acheved. It s worth to menton, the mode of operaton s dctated by the sgn of the actve power. Ths last s negatve because the machne acts as a generator. Durng transent speed changes, t s observehat the actve power can successfully track the reference value wth hgh dynamc performance whch demonstrates pretty gooransent state performance. Meanwhle, reactve power remans unnfluenced as shown n fgure 15c, demonstratng excellent decouplng control of actve and reactve power. So brefly, the proposed strategy provded an excellent dynamc behavor under a step change an s notcehat the couplng effect between the actve and reactve power s practcally unobservable. The passage from dfferent operaton mode {sub-synchronous to synchronous to super-synchronous} speed s observeo be smooth wthout any transents n the CW and PW stator current waveforms as shown n fgure 16.

16 464 A. Rahab et al. The fgure 16a anhe fgure 16b show the CW rotor current and PW stator current. The PW stator current has a snusodal shape and wth shftng phase at about The frequency of 'CW' rotor current s changed accordng to the rotor speed. For example to mantan a zero frequency for 'CW' rotor current, the 'BDFIG' machne have to rotate at natural speed {750 tr/m, (1.2 s to 1.6 s)}, n the other hand stator current frequency s ndependent to the rotor speed an s dependng only to the grd frequency. The magntude of 'PW' stator current and 'CW' rotor current are vared n accordance wth the wnd speed changes and correspondng to the amount of actve power PW Smulaton result of (DPC-GSC) SOGI flux Estmator Fg. 17: Smulaton results of 'VF-DPC' based 'SOGI-FLL' flux estmaton of 'GSC' under speed step {super-synchronous mode, synchronous mode, sub-synchronous mode}; (a) 1 st voltage and current of GSC; (b) DC-lnk voltage; (c) actve power of GSC; (d) reactve power of GSC Fg. 18: Vrtual flux and Phase angle estmated by 'SOGI-FLL', (a) Vrtual flux; (b) comparson of the angle between grd voltage and vrtual flux estmated The fgure 17a presents the waveforms of the grd phase voltage and GSC current. It can be seen from ths fgure that the lne currents are very close to a sne-wave. Durng tme nterval of ( t 1s to 1.6 s), the waveforms of grd current and voltage are exactly n accordance to phase, whch explans that the 'CW' stator of 'BDFIG' absorbs actve power from the grd durng sub-synchronous and synchronous modes, whereas, durng tme span of ( t 1.6s to 1.8 s), the waveforms of 'GSC' current and voltage are n

17 Drect power control based vrtual flux usng SOGI-FLL estmator for opposton of phase, so that the 'CW' stator of 'BDFIG' provdes actve power to the grd {hyper-synchronous mode}. The fgure 17c-d show actve and reactve powers of 'GSC'. It can be seen that actve power has been vared as well correspondng to the GSC current whch means dependng to operaton mode. The reactve power s set equal to zero to ensure a unt power factor operaton and as n PW sde reactve power regulaton remans unaffected, demonstratng perfect decouplng control feature of actve and reactve powers. The fgure 17b presents the waveform of the DC lnk voltage. The DC lnk voltage reference s set to 600 V, the measured voltage perfectly follows the reference sgnal wth the excepton of the ntal condtons where the voltage control loop does not have enough tme to react, at 1.6s small varaton of DC-Lnk voltage due to the passage of synchronous mode to the sup-synchronous mode. The fgure 18 presents phase shft between grd voltage angle and vrtual flux angle estmated usng 'SOGI-FLL' method. It can be seen that the phase angle waveform of vrtual flux s smooth and stable, at the same tme, the phase angle of 'VF' lags behnd the grd voltage wth 900. Then the estmated 'VF' can be useo detect the sector used n control of drect power control GSC. Fg. 19: Phase flux angle and 12 sector of 'VF-DPC' estmated usng 'SOGI-FLL' The fgure 19 shows the angle and correspondng sector of vrtual flux estmated usng 'SOGI-FLL' method. Where can observe that the sector dentfed usng the voltage vector s shfted forward wth three ranks when usng the vrtual flux vector. 5.2 Smulaton result wth varable wnd profle Fg. 20: Smulaton results of 'DPC-BDFIG' of MSC under wnd speed profle (a) Speed; (b) PW actve power; (c) PW reactve power

18 466 A. Rahab et al. Fg. 21: Smulaton results of 'VF-DPC' based 'SOGI-FLL' flux estmaton of GSC under wnd speed profle (a) Actve power (b) Reactve power (c) DC-lnk voltage The fgure 14b presents the envsaged wnd speed profle. The fgure 20b-c exhbts the actve and reactve powers flow and as n prevous secton t demonstrates pretty goorackng feature n terms of accuracy anme response. The fgure 21b-c shows the dynamc response of 'BDFIG' wth the avalable generator speed fgure 14b. It can be seen, the actve and reactve powers of GSC can track ther references very well, showng excellent dynamc performance anrackng ablty. The fgure 21d shows that the output DC voltage s regulated an follows the reference voltage command of 600 Volts. The proposed 'FV-DPC-GSC' and 'DPC-MSC' based 'BDFIG' system not only has the good control effect of the power trackng, but also can mplement the varable-speed constant-frequency operaton. 6. CONCLUSION In ths paper, a robust drect power control approach appled for wnd energy converson system 'WECS' based 'BDFIG' machne has been nvestgated. Mathematcal modelng of varous parts of the system s ntroduced and explaned. The control process s done n a coordnated manner between grd sde and machne sde. Whereas, conventonal drect power control has been used for the CW stator sde converter n order to adapt and capture the maxmum power avalable by wnurbne to be fed va PW stator to the grd. The maxmum power pont s defned by an MPPT algorthm whch could provde the reference power sgnal used n the 'DPC PW' stator controller. Meanwhle, grd sde control ssue focus manly to ensure constant DC lnk voltage durng system operaton and as well ensurng bdrectonal power flow between grd and CW stator sde. It s worth to menton that we have been adopted mproved drect power control based vrtual flux and 'SOGI-FLL' estmator to regulate power flow va grd sde converter. Smulaton of system has been performed under varable wnd profle. Obtaned results gave us clear dea about relablty of system n terms of steady state performance and robustness durng transents. Frstly, system coulo manage perfectly the man three operaton modes {synchronous, sub synchronous and super synchronous speeds} where the power flow

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