International Journal of Advanced Engineering Technology E-ISSN

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Internatonal Journal o Advanced Engneerng Technolog E-ISSN 0976-3945 Reearch Artcle DESIGN AND SIMUATION OF NONINEAR CONTROER FOR GRID CONNECTED DOUBY-FED INDUCTION GENERATOR Behera Ranjan K, Gao

1 Internatonal Journal o Advanced Engneerng Technolog E-ISSN Reearch Artcle DESIGN AND SIMUATION OF NONINEAR CONTROER FOR GRID CONNECTED DOUBY-FED INDUCTION GENERATOR Behera Ranjan K, Gao Wenzhong Addre or Correpondence (Meber, IEEE Departent o Electrcal Engneerng, Indan Inttute o Technolog, Patna, (INDIA (Senor Meber, IEEE Departent o Electrcal and Coputer Engneerng, Unvert o Denver,Denver, CO, USA ABSTRACT In a wnd power generator ung doubl ed nducton generator (DFIG, the three-phae pule wdth odulaton (PWM voltage ource converter (VSC ued a grd de converter (GSC and rotor de converter (RSC The tandard lnear control law propoed or GSC, o ar, not onl untable agant large-gnal dturbance, but alo ha the proble o tablt due to uncertant o load and crcut paraeter In th paper, a nonlnear controller degned or grd de converter (GSC o a doubl ed nducton generator (DFIG or wnd power applcaton The nonlnear controller degned baed on the nput-output eedback lnearzaton control ethod It hown that the converter can be tablzed globall or handlng large-gnal dturbance The reultng cloed-loop te not onl guarantee a ucent tablt regon (ndependent o the crcut paraeter n the tate pace, but alo exhbt good tranent repone Coputer ulaton are preented to conr the eectvene o the propoed control trateg and the valdt o the ulaton technque KEYWORD Doubl ed nducton generator, eedback lnearzaton controller, grd de converter, wnd power I INTRODUCTION Several ltaton aocated wth the qurrel cage nducton generator and hgh cot o the peranent agnet nchronou generator (PMSG can be overcoe wth the DFIG te preented n Fg Th archtecture the ot coon or utlt cale wnd turbne The DFIG topolog capable o lted varable peed operaton va a par o back to back VSC between the rotor crcut and the pont o coon couplng Each o the VSC tpcall cont o three pule wdth odulated (PWM IGBT-dode baed phae leg The rotor crcut o the DFIG acceed va lp rng or connecton to a voltage ource converter (VSC, whch coonl reerred to a the achne de converter (MSC The tator crcut o the achne connected to the grd va a tepup tranorer, but wthout a power converter nterace The bu o the MSC eed a VSC connected n parallel wth the tator col, coonl called the grd de converter (GSC [] Varou control tratege have been propoed to control the GSC n recent work []-[3] The an objectve n the control o voltage ource converter are to acheve a bdrectonal power low and nu haronc dtorton o nput lne current Soe o the control tratege nclude the phae and apltude control (PAC [4], [5], htere current control (HCC [6], and pretve current control wth a xed wtchng requenc (PCFF [6] The PAC provde a good wtchng pattern to reduce tead-tate current haronc and output voltage rpple Fg DFIG wth bdrectonal pule wdth odulaton converter IJAET/VolII/ Iue III/Jul-Septeber, 0/6-33

2 Internatonal Journal o Advanced Engneerng Technolog E-ISSN However, t ha a current coponent (current oet that appear on the ac de o the converter whch deterorate the lnk current and voltage waveor durng tranent The htere current control ha a at dnac repone, good accurac, no oet, and hgh robutne, but the ajor proble o HCC control that t average wtchng requenc vare wth the lnk current, whch ake the wtchng pattern uneven and rando, thu reultng n addtonal tree on wtchng devce The pretve current control wth a xed wtchng requenc how a at dnac repone and ha a good wtchng pattern that reduce the wtchng devce tree However, t entve to paraeter varaton near control a powerul ethod and a long htor o ucceul ndutral applcaton However, the lnear control ethod rel on the ke aupton o all range operaton or the lnear plant odel to be vald Beond the operaton range, a lnear controller lkel to peror ver poorl or to be untable, becaue the nonlnearte n the te cannot be properl copenated or In the nonlnear control degn, the anal carred out or a gven nonlnear plant to be controlled and peccaton o cloedloop te behavor can be tuded eal [7] In th paper, a nonlnear controller, baed on eedback lnearzaton theor propoed or grd de control o DFIG Th nonlnear controller overcoe the dadvantage o the conventonal lnear controller, keepng the -lnk voltage level wthn ther degn lt, even or the tronger voltage dp reultng ro abnoral grd voltage Moreover, the tud how how the converter current can exhbt tranent due to the poor behavor o tandard PI-baed controller, whch operate ar below ther nonal operatng pont One o the prar advantage o the nonlnear controller that t not dependent on an o the te or load paraeter Coparng the reult o the controller, the nonlnear controller ore robut II FEEDBACK INEARIZATION CONTROER The eedback lnearzaton acheved b exact tate tranor and eedback, rather than b lnear approxaton o the dnac The an dea behnd eedback lnearzaton the repreentaton o the nonlnear te b ean o a tranoraton and eedback n order to be able to obtan a lnear relaton between the nput and output o the te Thu, eedback lnearzaton tre to cancel the te nonlnearte through the nput o the te Ater that, a dered dnac can be poed on the te b addng a new control nput Conder that the ult-nput ult-output (MIMO nonlnear te, n the neghborhood o a pont x 0 gven b: x & = ( x + G( x u ( = h(x ( Th coonl dened a ane te, where x the n tate vector, u the control nput vector (o coponent u, the vector o te output (o coponent, and h are ooth vector eld, and G a n atrx whoe colun are ooth vector eld g Input-output lnearzaton obtaned b derentatng the output untl the nput appear Aue that r the allet nteger uch that at leat one o the nput appear n (r, then ( r r r = h + gj h uj (3 j= r wth h ( x 0 or at leat one j, n a gj neghborhood Ω o the pont x 0 Perorng the above procedure or each output eld ( r ( r r h ( x = + E( x u r h ( x (4 where E(x atrx and nvertble In nonlnear control the relatve degree an portant theoretcal concept, whch related to the nuber o te that the te output ha to be derentated untl the nput u explctl appear n the expreon The nput tranoraton can be wrtten a u = E v v r r h h (5 IJAET/VolII/ Iue III/Jul-Septeber, 0/6-33

3 Internatonal Journal o Advanced Engneerng Technolog E-ISSN whch eld equaton o the ple or ( r = γ (6 Snce the new nput γ onl aect the output at th pont, dered dnac can be poed on the te b the new te nput through proper control degn III NONINEAR CONTRO APPICATION TO GRID SIDE CONVERTER CONTRO The cheatc control block dagra o the GSC hown n Fg Modelng o grd de converter n dq- reerence rae gven n [] In atrx or t can be wrtten a: d dt vd R d+ ω q 0 d vq R q q = + ω d + v v 3 0 ( vqq Cv C q + 0v 0 (7 Conderng d and v a the control output o the te = h ( x = d = h ( x = v (8 d Fg Grd de converter control block dagra Now derentatng the output wth repect to te: d vd R d= d + ω q u (9 dt Where g h =0 and u = v d The relatve degree o th output r = Now or the output, 3 v& = ( vqq (0 Cv C & = h + g( h u+ g ( h ( u 3v v R 3v 3( v = ( + ( & Cv Cv C C q q q q q q q ωd u Cv ( IJAET/VolII/ Iue III/Jul-Septeber, 0/6-33

4 Internatonal Journal o Advanced Engneerng Technolog E-ISSN where g h =0, g h =0, g ( h =0, and u =v q For th output the relatve degree r = The vector relatve degree o the te r=(r, r =(, Now, thee equaton can be rewrtten n atrx or & = A + u E && A u vd R A = d + ω q 3v v R 3v 3( v A = + & q q q q q q ( q ω d ( C v C v C v C C = 0 0 3v Cv q E (3 Matrx E ut be nvertble Now nvertng E 0 E = Cv 0 3vq Thereore the control law gven b [9] u A ( + γ = E u A γ whch lead to the nput output relaton between the output and the new nput γ & = γ && γ A dered dnac repone can be poed ung ollowng: = + λ γ & ( (5 0 γ = & + λ( & & + λ0( & (6 where = d, = d, =v, =v are dered te repone The above equaton cab be wrtten a: e& + e 0 (7 λ 0 = & e + λ e& + λ e 0 (8 0 = where e = and e = ( ( Now (7 and (8 are table or λ 0, λ and λ 0 > 0 Then the exact controller can be orulated a vd R u = ( d +ωq γ (9 Cv 3v v R 3v 3( v u [ ( ( & ] q q q q q q = q+ ω d γ 3v q Cv Cv Cv C C A can be een, ung (9 and (0 can degn be degned wth approprate value o λ 0, λ and λ 0 ( (4 (0 IJAET/VolII/ Iue III/Jul-Septeber, 0/6-33

Internatonal Journal o Advanced Engneerng Technolog E-ISSN 0976-3945 IV SIMUATION AND DISCUSSION To valdate the propoed eedback

converter gven n Table I and eedback lnearzaton controller gven n Table II [8] The controller paraeter λ 0, λ and λ 0 were

hown below Th ecton preent the reult o propoed nput-output eedback lnearzaton controller and coparon wth lnear TABE I GRID SIDE

-lnk voltage wth lnear Fg 5 Grd voltage and current wth lnear Fg 3 Repone o I q, I d and I dre wth lnear TABE II FEEDBACK

5 Internatonal Journal o Advanced Engneerng Technolog E-ISSN IV SIMUATION AND DISCUSSION To valdate the propoed eedback lnearzaton controller or grd de converter control, the ulaton are carred out ung Matlab/ulnk The paraeter o the grd de converter gven n Table I and eedback lnearzaton controller gven n Table II [8] The controller paraeter λ 0, λ and λ 0 were tuned to enure that the dnac repone ater and t ndependent o paraeter o the te The GSC ulated ung MATAB/Sulnk and the reult are hown below Th ecton preent the reult o propoed nput-output eedback lnearzaton controller and coparon wth lnear TABE I GRID SIDE CONVERTER PARAMETERS Input uppl phae 480V (r, 3 ph, voltage 60 Hz DC lnk voltage 800 V S 5 H R S 04 Ω C 680 µf Fg 4 Repone o -lnk voltage wth lnear Fg 5 Grd voltage and current wth lnear Fg 3 Repone o I q, I d and I dre wth lnear TABE II FEEDBACK INEARIZATION CONTROER PARAMETERS Paraeter Value λ λ 6500 λ Fg 6 Grd voltage and current wth lnear IJAET/VolII/ Iue III/Jul-Septeber, 0/6-33

Internatonal Journal o Advanced Engneerng Technolog E-ISSN 0976-3945 A near Controller Intall d-ax reerence current et to zero, then a tep change o 4 A appled at t = and

current aectng q-ax current durng tranent condton However, durng tead tate d and q-ax current control perectl decoupled So the decouplng control o actve and reactve power

peak overhoot Th a lead to al the tablt o the controlled plant The reultant grd de phae voltage and current hown n Fg 5 and 6 Fg 5 how the tranton ro unt power actor to leadng

thereb upplng reactve power to the ource It conred that the current tranent appear durng tranent condton and the ettlng te o the current repone hgh enough Fg 8 Repone o -lnk

6 Internatonal Journal o Advanced Engneerng Technolog E-ISSN A near Controller Intall d-ax reerence current et to zero, then a tep change o 4 A appled at t = and ubequentl a tep change o -4 A appled at t= The reultant plot o q-ax, d-ax and d-ax reerence current ung lnear controller (PI controller hown n Fg 3 It hown that change n d-ax current aectng q-ax current durng tranent condton However, durng tead tate d and q-ax current control perectl decoupled So the decouplng control o actve and reactve power etablhed durng tead tate Fg 4 how the voltage acro the -lnk capactor Although -lnk voltage ettled at the reerence voltage (800 V durng tead tate but durng tranent t exhbt hgh peak overhoot Th a lead to al the tablt o the controlled plant The reultant grd de phae voltage and current hown n Fg 5 and 6 Fg 5 how the tranton ro unt power actor to leadng power actor and Fg 6 how the tranton ro leadng power actor to laggng power actor The nput current waveor how that when the grd de converter operate at leadng power actor, thereb upplng reactve power to the ource It conred that the current tranent appear durng tranent condton and the ettlng te o the current repone hgh enough Fg 8 Repone o -lnk voltage wth nonlnear Fg 9 Grd voltage and current wth nonlnear Fg 7 Repone o I q, I d and I dre wth nonlnear Fg 0 Grd voltage and current wth nonlnear IJAET/VolII/ Iue III/Jul-Septeber, 0/6-33

7 Internatonal Journal o Advanced Engneerng Technolog E-ISSN B Nonlnear Controller The q-ax, d-ax and d-ax reerence current ung nonlnear controller hown n Fg 7 It hown that change n d-ax current not aectng q-ax current durng tranent condton and thu d-ax and q-ax current are perectl decoupled So the decouplng control o actve and reactve power enhanced ung nonlnear controller epecall durng tranent Fg 8 how the voltage acro the -lnk capactor DC-lnk voltage ettled at the reerence voltage durng tead tate and tranent condton; and there no peak overhoot oberved n the waveor The grd de phae voltage and current hown n Fg 9 and 0 Fg 9 how the tranton ro unt power actor to leadng power actor and Fg 0 how the tranton ro leadng power actor to laggng power actor The nput current waveor how that when the grd de converter operate at leadng power actor, thereb upplng reactve power to the ource It conred that there no current tranent appearng durng tranton perod and the repone te at enough When the grd de converter operate at laggng power actor, thereb aborbng reactve power ro the ource, there no current dtorton oberved n the current waveor The ulaton reult conr that the perorance o the controller ndependent o the te paraeter and load and exceed the perorance o extng lnear control te TABE III COMPARISION OF RESUTS Cloe loop dnac near controller Depend on the controller paraeter λ 0, λ and λ 0 Propoed nonlnear controller Depend on C, load paraeter and the controller gan Overhoot 0% Depend on dapng actor Repone te 0008 oad dependent Stead tate error 0% 0% (ord dependent Robutne Ye No (Dnac are load dependent load and paraeter varaton The coparon o the lnear controller wth the propoed eedback lnearzaton controller how that the nonlnear controller gve le error and t ater than the lnear So the nonlnear controller ha wde operatng range and table agant largegnal dturbance The perorance obtaned qute encouragng and t deontrated b the ulaton tud REFERENCES S Heer, Grd Integraton o Wnd Energ Converon Ste, John Wle & Son, TD, Chcheter, England, 998 R Pena, JC Clare, GM Aher, Doubl ed nducton generator ung back-to-back PWM converter and t applcaton to varable-peed wnd-energ generaton, IEE Proc Electrc Power Applcaton, Vol 43, No 3, pp 3 4, Ma Holdworth, X G Wu, J B Ekanaake, and N Jenkn, Coparon o xed peed and doubl ed nducton wnd turbne durng power te dturbance, Proc Int Elect Eng, vol 50, no 3, pp , Ma J W Dxon and B T Oo, Indrect current control o a unt power actor nuodal current boot tpe three-phae recter, IEEE Tran Power Electron, vol 35, no 4, pp , Malean and Roetto, AC/DC/AC PWM converter wth reduced energ torage n the DC lnk, IEEE Tran Ind Appl, vol 3, no, pp 87 9, Mar/Apr R K Behera and S P Da, A utlt rendl hgh power nducton otor drve wth drect torque and lux control, n Proceedng o IEEE Internatonal Conerence on Indutral Technolog, (ICIT 006, Muba, Inda, Deceber 5-7, 006, pp Alberto, Nonlnear Control Ste, 3rd Ed New York: Sprnger Verlag, Mullane, G ghtbod, and R Yacan, Wnd-turbne ault rde through enhanceent, IEEE Tran Power St, vol 0, no 4, pp , Nov E Krezg, Advanced Engneerng Matheatc Wle, J J E Slotne and W, Appled Nonlnear Control Englewood Cl, NJ: Prentce-Hall, 99 V CONCUSION The eedback lnearzaton controller or the GSC preented and hown to be hghl eectve or the elnaton o tead tate error, ncreang the peed o repone, and addng robutne agant IJAET/VolII/ Iue III/Jul-Septeber, 0/6-33

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