Applications of the Doubly Fed Induction Machine (DFIM)

Application of the Doubly Fed Induction Machine (DFIM) Autho: Gonzalo Abad 1 Miguel Ángel Rodíguez 2 Gzegoz Iwanki 3 1 Unieity of Mondagon, Spain 2 Ingeteam Tanmiion & Ditibution S.A., Spain. 3 Waaw Unieity of Technology, Poland.

Outline 1. Vaiable Speed Wind Enegy Geneato Sytem. Baic Modeling of the Wind Tubine. Wind Tubine Contol Sytem. Diffeent Configuation Accoding to the Electical Geneato. 2. Doubly Fed Induction Machine baed Wind Enegy Geneato Sytem. Contol Sytem. Baic Numbe of an 1,75 MW Wind Tubine. 3. Indutial olution. DFIM Wind Tubine Manufactue. Diffeent Indutial Solution. 4. Application with Pime Moe Diffeent fom Wind - Reiew. Diffeent Application. 07-09-2009 Application of the Doubly Fed Induction Machine, 2

Vaiable Speed Wind Enegy Geneato Sytem Baic Modeling of the Wind Tubine. H. Camblong, M. Rodíguez Vidal, J. R. Puiggali. Pinciple of a Simulation Model fo a Vaiable-Spedd Pitch- Regulated Wind Tubine. Wind Engineeing, Vol 28, Pg 157-175. Mach 2004. 07-09-2009 Application of the Doubly Fed Induction Machine, 4

Vaiable Speed Wind Enegy Geneato Sytem Baic Modeling of the Wind Tubine. T t = 1 ρ π R 2 3 V 2 C t λ = R ωt V p C p =λ C t P t = 1 ρ π R 2 3 V 2 C p C p k7 k 2 k5 λi = k 1 k3β k4β k6 e λ i 1 λi = λ k 8 0.5 0.4 Powe coefficient C p ß opt =-2 C p_max ß=2 0.06 Toque coefficient C t ß=-2 0.3 0.2 0.1 ß=40 ß=5 0.04 0.02 ß=40 ß=2 ß=5 0 λ opt 0 4 8 12 16 20 λ 0 0 4 8 12 16 20 λ 07-09-2009 Application of the Doubly Fed Induction Machine, 5

Vaiable Speed Wind Enegy Geneato Sytem Wind Tubine Contol Sytem. λ Etimato λ et V β* Ω m_nom Ω m_min T em* Regulato - Ω m T em β V β*=β opt V Max powe tacking Ω m * Tem* Regulato - Ωm T em β V V Ω m_ Nom β* Regulato - T em *=T em_nom k opt - β*=β op t T em * Ω m Ω m H. Camblong, I. Matinez Alegía, M. Rodíguez, G. Abad. Expeimental ealuation of wind tubine maximum powe point tacking contolle. Enegy Coneion and Management Vol 47, Iue 18-19, Noembe 2006, Pg 2846-2858. H. Camblong, G. Tapia, M. Rodíguez. Robut digital contol of a wind tubine fo ated-peed and aiable-powe opeation egime. IEE Poceeding Contol Theoy & Application Vol 153, Iue 1, Pg 81-91. Januay 2006. Ω m 2 ^2 D t_m 07-09-2009 Application of the Doubly Fed Induction Machine, 6

Vaiable Speed Wind Enegy Geneato Sytem Diffeent Configuation Accoding to the Electical Geneato. Wind GEARBOX Doubly Fed Induction Machine Netwok Roto ide VSC Gid ide VSC Tanfome oto filte gid filte Chaacteitic (DFIM): Limited opeating peed ange (-30% to 30%). Small cale powe electonic conete. Complete contol of actie powe and eactie powe exchanged with the gid. Need fo lip-ing and gea box. 07-09-2009 Application of the Doubly Fed Induction Machine, 7

Vaiable Speed Wind Enegy Geneato Sytem Diffeent Configuation Accoding to the Electical Geneato. Wind PM-Synchonou Machine Multi-Pole and Multipole wound oto ynchonou geneato Machine ide VSC Gid ide VSC Netwok tato filte gid filte Tanfome Chaacteitic (MPMG and WRSG): Full opeating peed ange. Full cale powe electonic conete. Complete contol of actie powe and eactie powe exchanged with the gid. Elimination of the gea box. No buhe on the geneato in PMSM. 07-09-2009 Application of the Doubly Fed Induction Machine, 8

Vaiable Speed Wind Enegy Geneato Sytem Diffeent Configuation Accoding to the Electical Geneato. Wind GEARBOX Induction Machine Machine ide VSC Gid ide VSC Netwok tato filte gid filte Tanfome Chaacteitic (SCIM): Full opeating peed ange. Full cale powe electonic conete. Complete contol of actie powe and eactie powe exchanged with the gid. No buhe on the geneato but Need fo gea box. Manufactue: Ecotecnia 47 Vaiable Speed 750 kw (ome pototype) 07-09-2009 Application of the Doubly Fed Induction Machine, 9

Vaiable Speed Wind Enegy Geneato Sytem Diffeent Configuation Accoding to the Electical Geneato. Wind GEARBOX PM-Synchonou Machine Multi-Pole Machine ide VSC Gid ide VSC Netwok tato filte gid filte Tanfome Chaacteitic (PMSM): Full opeating peed ange. Full cale powe electonic conete. Complete contol of actie powe and eactie powe exchanged with the gid. Multipole geneato, pemanent magnet needed in lage quantitie. No buhe on the geneato. 07-09-2009 Application of the Doubly Fed Induction Machine, 10

Contol Sytem. Doubly Fed Induction Machine baed Wind Enegy Geneato Sytem WIND TURBINE CONTROL: - Diided in diffeent contol leel. - Only fit contol leel i tudied in thi tutoial. 07-09-2009 Application of the Doubly Fed Induction Machine, 12

Doubly Fed Induction Machine baed Wind Enegy Geneato Sytem Baic Numbe of an 1,75 MW Wind Tubine. Velocidad (pm) Potencia alida (KW) Facto de potencia Tenión línea (V RMS ) 1 975 100 1.0 690 2 1100 167 1.0 690 3 1450 400 1.0 690 4 1615 600 1.0 690 5 1760 800 1.0 690 6 1800 1000 1.0 690 7 1800 1200 1.0 690 8 1800 1400 1.0 690 9 1800 1700 1.0 690 10 1800 1700 1.0 621 11 1800 1700 1.0 759 12 1800 1700 0.9 inductio 690 13 1800 1700 0.95 capacitio 690 14 1950 1842 0.95 capacitio 690 15 1950 2125 0.9 inductio 690 07-09-2009 Application of the Doubly Fed Induction Machine, 13

Doubly Fed Induction Machine baed Wind Enegy Geneato Sytem Baic Numbe of an 1,75 MW Wind Tubine. Moto 1.5 MW PU Moto 1.4 MW PU V nom 690V 690V I nom 1395 A 1400 A u=n/n 0.36 0.39 V nom 1916 V 1769 V R 0.0015Ω 0.0052 0.0018Ω 0.0065 R 0.0015Ω 0.0052 0.0019 Ω 0.0068 Lh 3.34 m Η 3.68 2.78 m Η 3.07 Lf 95.49 μ Η 0.105 86.58 μ Η 0.096 Lf 66.85 μ Η 0.074 108.23 μ Η 0.119 Rfe 26.2 Ω 91.74 66.28 Ω 232.93 τ 2.27 3 7.23e 1.50 3 4.76 e τ 2.29 3 7.29e 1.56 4.96 e σ 0.047 0.047 0.067 0.067 07-09-2009 Application of the Doubly Fed Induction Machine, 14

Indutial olution. DFIM Wind Tubine Manufactue Gamea G52-58 850k, 80 87 & 90 2MW http://www.gameacop.com/e/poducto/aeogeneadoe/c atalogo-de-aeogeneadoe Acciona AW-70 77 & 82 1500 kw AW-100 109 & 116 3000 kw http://www.acciona-enegia.com/default.ap?x=0002020601&lang=e Ecotecnia (Altom) Eco 74 1670kW, 80 2MW Eco 100 3MW http://www.powe.altom.com/home/new_plant/wind/wind_t ubine/38796.en.php?languageid=en&di=/home/new_pl ant/wind/wind_tubine/ 07-09-2009 Application of the Doubly Fed Induction Machine, 20

Indutial olution. DFIM Wind Tubine Manufactue Veta (NEG MICON): V90 (only USA maket) http://www.eta.com/e/olucione-e%c3%b3lica/aeogeneadoe.apx Geneal Electic: 1.5, 2.5 & 3.6 MW (off-hoe) http://www.gepowe.com/pod_e/poduct/wind_tubine/en/index.htm Sulzon: S 82 88, 1500 & 2100kW http://www.uzlon.com/ RePowe: 2.05, 3.3 & 5MW http://www.epowe.de/index.php?id=12&l=1 07-09-2009 Application of the Doubly Fed Induction Machine, 21

Indutial olution. DFIM Wind Tubine Manufactue Siemen (Bonu): SWT-3.6-107, SWT-2.3-101 http://www.powegeneation.iemen.com/poduct-olutioneice/poduct-package/wind-tubine/poduct/poduct.htm Fuhlaende: FL2500 http://www.fuhlaende.de/index_en.php Nodex N100 2.5MW http://www.nodex-online.com/en/podukte-eice/wind-tubine.html Mithubihi MWT 95, 2.4 MW http://www.mhi.co.jp/en/poduct/categoy/wind_tubine_geneato.html 07-09-2009 Application of the Doubly Fed Induction Machine, 22

Indutial olution. DFIM Wind Tubine Manufactue DeWind D6, D8 & D8.2, 1 & 2 MW http://www.compoitetechcop.com/oucompanie/dewindinc/tabid/145/defau lt.apx 07-09-2009 Application of the Doubly Fed Induction Machine, 23

Application with Pime Moe Diffeent fom Wind - Reiew 22MW adjutable peed geneation unit with DFIG and cycloconete fo Naude Powe Station (Japan) 1987 [1] 80MW adjutable peed pumped toage unit with DFIG and cycloconete at Yagiawa Powe Plant (Japan) 1990 [2] 2x400MW adjutable peed pumped toage unit with DFIG and cycloconete fo Ohkawachi Powe Station (Japan) 1993 [1] 2x350MVA adjutable peed pumped toage unit with DFIG and cycloconete fo Goldithal Powe Station (Gemany) 2003 [3] [1] T. Kuwabaa, A. Shibuya, H. Fuuta, E. Kita, K. Mituhahi, Deign and Dynamic Repone Chaacteitic of 400MW Adjutable Speed Pumped Stoage Unit fo Ohkawachi Powe Station, IEEE Tanaction on Enegy Coneion, Vol. 11, Iue 2, June 1996, pp. 376 384. [2] S. Fuuya, T. Taguchi, K. Kuunoki, T. Yanagiawa, T. Kageyama, T. Kanai, Succeful Achieement in a Vaiable Speed Pumped Stoage Powe Sytem at Yagiawa Powe Plant, Powe Coneion Confeence PCC 93, Yokohama, 19-21 Apil 1993, pp. 603 608 [3] K. Gotenbug, F. Koch, I. Elich U. Bachmann, Modeling And Dynamic Simulation Of Vaiable Speed Pump Stoage Unit Incopoated Into The Geman Electic Powe Sytem, 9 th Euopean Confeence on Powe Electonic and Application EPE 09, Gaz, Autia, pp.10 07-09-2009 Application of the Doubly Fed Induction Machine, 25

Application with Pime Moe Diffeent fom Wind - Reiew 2500kVA ange eie dieel engine baed otay uninteuptible powe upply ytem with lip ing induction machine by Stahine [1] Flywheel baed enegy toage ytem with DFIG decibed in eeal pape [2][3][4][5] Vaiable peed powe ytem with UPS function [6]. [1] http://www.onitepoweinc.com/document/uppliedoc/rotay%20ups%20bochue.pdf [2] Yoon-Ho Kim; Kyoung-Hun Lee; Young-Hyun Cho; Young-Keun Hong, Compaion of hamonic compenation baed on wound/quielcage oto type induction moto with flywheel, IPEMC 2000, Volume 2, 15-18 Aug. 2000 Page():531 536 [3] H. Akagi, H. Sato, Contol and pefomance of a doubly-fed induction machine intended fo a flywheel enegy toage ytem, IEEE Tan. on Powe Electonic, Volume 17, Iue 1, Jan. 2002, Page():109-116 [4] Gang Li; Jing Zhang; Shijie Cheng; Jinyu Wen; Yuan Pan, State Space Fomulation and Stability Analyi of a Doubly-fed Induction Machine with a Flywheel Enegy Stoage Sytem Int. Conf. on Powe Sytem Technology, 2006. PoweCon 2006. 22-26 Oct. 2006 Page():1-6 [5] C. Batlle, A. Doia-Ceezo, R. Otega, Powe flow contol of a doubly-fed induction machine coupled to a flywheel, Int. Conf. on Contol Application, 2004. Vol. 2, 2-4 Sept. 2004 Page():1645-1650 [6] G. Iwanki, W. Koczaa: DFIG baed Powe Geneation Sytem with UPS Function fo Vaiable Speed Application IEEE Tan. on Indutial Electonic. Vol. 55, Iue 8, pp. 3047 3054, Aug. 2008 07-09-2009 Application of the Doubly Fed Induction Machine, 26

Mathematical Model of the Doubly Fed Induction Machine. Autho: Gonzalo Abad 1 1 Unieity of Mondagon, Spain 2 Ingeteam Tanmiion & Ditibution S.A., Spain. 3 Waaw Unieity of Technology, Poland. Miguel Ángel Rodíguez 2 Gzegoz Iwanki 3

Outline 1. Dynamic Model of the DFIM. Simplified Model of the DFIM. Space Vecto Repeentation. αβ Model of the DFIM. dq Model of the DFIM. State Space Repeentation of the αβ Model. State Space Repeentation of the dq Model. 2. Dynamic Model of the DFIM Conideing the Ion Loe. αβ Model of the DFIM Conideing the Ion Loe. dq Model of the DFIM Conideing the Ion Loe. State Space Repeentation of the αβ Model. 3. Dynamic Modeling of the DFIM baed on Symmetical Component Analyi. Baic Definition. DFIM in Balanced Opeation. DFIM in Unbalanced Opeation. 4. Steady-State Analyi of the DFIM. Baic Opeation Mode Attending to the Speed and Powe. Pefomance Analyi. Amplitude, Fequency and Phae Shift Vaiation. Pefomance Analyi. Toque and Reactie Powe Contol. 5. Etimato and Obee Stuctue fo the DFIM. Diectly Meauable and Etimated Magnitude. Stato Actie and Reactie Powe Etimation. Stato and Roto Fluxe Etimato. Stato Flux Etimato fom Stato Voltage. Stato Flux Synchonization fom the Stato Voltage. Stato and Roto Flux Obee. 07-09-2009 Mathematical Model of the DFIM, 2

Dynamic Model of the DFIM Doubly Fed Induction Machine (DFIM). Machine unde tudy: 07-09-2009 Mathematical Model of the DFIM, 4

Dynamic Model of the DFIM Simplified Model of the DFIM. Objectie. - Fit dynamic modelling appoach of the machine. - Oiented to deign contol tategie and alidate pefomance of the machine. 07-09-2009 Mathematical Model of the DFIM, 5

Dynamic Model of the DFIM Simplified Model of the DFIM - 3 winding in the tato (ABC) and 3 winding in the oto (abc). - The winding ae conideed a ideal [1]-[2]. - Oiented to deign contol tategie and alidate pefomance of the machine. [1] W. Leonhad, Contol of electical die. Spinge-Velag, 2001. [2] M.P. Kazmiekowki, R. Kihnan, F. Blaabjeg, Contol in Powe Electonic Selected Poblem, Academic Pe, 2002. 07-09-2009 Mathematical Model of the DFIM, 6

Dynamic Model of the DFIM Electic Equialent Cicuit of the DFIM 3 phae equation fo the tato (Pulation ω ) 3 phae equation fo the oto (Pulation ω ) [1] W. Leonhad, Contol of electical die. Spinge-Velag, 2001. [3] J.L. Rodiguez Amenedo, "Analii dinamico y diefno del itema de contol de aeotubina de elocidad aiable con aeogeneado aincono de doble alimentacion", Ph. Thei, Unieidad Calo III, 2000. 07-09-2009 Mathematical Model of the DFIM, 7

Dynamic Model of the DFIM Space Vecto Repeentation. Refeence fame. 1.- The tato efeence fame (α-β): Aligned with the tato, the otating peed of the fame i zeo, and the pace ecto efeenced to it, otate at the ynchonou peed ω. 2.- The oto efeence fame (D-Q): Aligned with the oto, the otating peed of the fame i the angula peed of the oto ω m, and the pace ecto efeed to it otate at the angula peed ω. 3.- The ynchonou efeence fame (d-q): The otating peed of the fame i the ynchonou peed ω, and the pace ecto efeenced to it doe not otate, i.e. it peent contant eal and imaginay pat. 07-09-2009 Mathematical Model of the DFIM, 8

Dynamic Model of the DFIM Space Vecto Repeentation. Refeence fame. One pace ecto can be epeented in 3 diffeent efeence fame. 07-09-2009 Mathematical Model of the DFIM, 9

Dynamic Model of the DFIM αβ Model of the DFIM. Equialent electic cicuit: Voltage and Flux Space Vecto equation: 07-09-2009 Mathematical Model of the DFIM, 10

Dynamic Model of the DFIM αβ Model of the DFIM. Toque equation (thee ae eeal eion): Stato and oto, actie and eactie powe equation: 07-09-2009 Mathematical Model of the DFIM, 11

Dynamic Model of the DFIM dq Model of the DFIM. Equialent electic cicuit: Voltage and Flux Space Vecto equation: 07-09-2009 Mathematical Model of the DFIM, 12

Dynamic Model of the DFIM dq Model of the DFIM. Toque equation (thee ae eeal eion a well): Stato and oto, actie and eactie powe equation: Equialent equation to the αβ model!! 07-09-2009 Mathematical Model of the DFIM, 13

Dynamic Model of the DFIM State Space Repeentation of the αβ Model. Compact eion: - Fluxe a tate-pace magnitude. - Ueful fo imulation pupoe. Expanded eion: 07-09-2009 Mathematical Model of the DFIM, 14

Dynamic Model of the DFIM State Space Repeentation of the αβ Model. - Cuent a tate-pace magnitude. Expanded eion: Compact eion: 07-09-2009 Mathematical Model of the DFIM, 15

Dynamic Model of the DFIM State Space Repeentation of the dq Model. Compact eion: - Fluxe a tate-pace magnitude. - Ueful fo ealuation pupoe. Expanded eion: 07-09-2009 Mathematical Model of the DFIM, 16

Dynamic Model of the DFIM State Space Repeentation of the dq Model. - Cuent a tate-pace magnitude. Compact eion: 07-09-2009 Mathematical Model of the DFIM, 17

Dynamic Model of the DFIM State Space Repeentation of the dq Model. - Cuent a tate-pace magnitude. Expanded eion: 07-09-2009 Mathematical Model of the DFIM, 18

Dynamic Model of the DFIM Conideing the Ion Loe αβ Model of the DFIM Conideing the Ion Loe. - The ion loe can be appoximated to: P lo =k*f*b 2 - The ion loe ae modelled a a eitance (R fe ) in paallel to the mutual inductance (L h ) of each phae. - R fe i appoximately popotional to the fequency. - Cuent i fe doe not ceate flux. 07-09-2009 Mathematical Model of the DFIM, 20

Dynamic Model of the DFIM Conideing the Ion Loe αβ Model of the DFIM Conideing the Ion Loe. Equialent electic cicuit: 07-09-2009 Mathematical Model of the DFIM, 21

Dynamic Model of the DFIM Conideing the Ion Loe αβ Model of the DFIM Conideing the Ion Loe. Space ecto equation: - Voltage equation (ame a peiou model) - Flux equation (diffeent fom peiou model) - New node equation (oltage and cuent) 07-09-2009 Mathematical Model of the DFIM, 22

Dynamic Model of the DFIM Conideing the Ion Loe αβ Model of the DFIM Conideing the Ion Loe. Toque equation (only equialence with the peiou model): Stato and oto, actie and eactie powe equation: only thi expeion i equialent with the peiou model!!! 07-09-2009 Mathematical Model of the DFIM, 23

Dynamic Model of the DFIM Conideing the Ion Loe dq Model of the DFIM Conideing the Ion Loe. Equialent electic cicuit: 07-09-2009 Mathematical Model of the DFIM, 24

Dynamic Model of the DFIM Conideing the Ion Loe dq Model of the DFIM Conideing the Ion Loe. Voltage, flux and node pace ecto equation 07-09-2009 Mathematical Model of the DFIM, 25

Dynamic Model of the DFIM Conideing the Ion Loe dq Model of the DFIM Conideing the Ion Loe. Toque equation: Stato and oto, actie and eactie powe equation: Equialent equation to the αβ model!! 07-09-2009 Mathematical Model of the DFIM, 26

Dynamic Model of the DFIM Conideing the Ion Loe State Space Repeentation of the αβ Model. - Cuent a tate-pace magnitude. Compact eion: 07-09-2009 Mathematical Model of the DFIM, 27

Dynamic Model of the DFIM Conideing the Ion Loe State Space Repeentation of the αβ Model. - Cuent a tate-pace magnitude. Expanded eion: 07-09-2009 Mathematical Model of the DFIM, 28

Mathematical Model of the DFIM, 07-09-2009 30 Dynamic Modeling of the DFIM baed on Symmetical Component Analyi Baic Definition. Phao complexo: teady tate epeentation o inuoidal aiable (x can be a oltage, cuent o flux) ) e ( Real ) (X e Real ) co( ) ( t j ) t j( ω δ ω δ ω x t X t x = = = ) j( e x = X δ () ( ) () () Π = Π = = 3 4 co ˆ 3 2 co ˆ co ˆ 3 3 2 2 1 1 θ ϕ ω θ ϕ ω θ ϕ ω t U k t x t U k t x t U k t x c b a ( ) Π Π = = = 3 4 3 3 2 2 1 3 2 1 ˆ ˆ ˆ θ ϕ θ ϕ θ ϕ U e k X U e k X U e k X c b a Thee phae ytem

Dynamic Modeling of the DFIM baed on Symmetical Component Analyi Baic Definition. Fotequieu: Repeentation of unbalanced ytem by mean of thee balanced ytem x x x o = 1 3 1 1 1 1 a a 2 1 2 a a x x x a b c a=e 2π j 3 x c unbalanced ytem x a x a, x b and x c the thee phae unbalanced ytem phao, ax x b ax xo the zeo equence component a 2 x 2π/3 2π/3 2π/3 poitie equence x 2π/3 a 2 x 2π/3 2π/3 negatie equence x o x o x o x zeo equence x the poitie equence component x- the negatie equence component 07-09-2009 Mathematical Model of the DFIM, 31

Dynamic Modeling of the DFIM baed on Symmetical Component Analyi Baic Definition. Space ecto : Repeent thee phae ytem in teady o tanient tate x( t) = xα ( t) j xβ ( t) = 2 3 2 ( x ( t) a x ( t) a x ( t) ) a b c B Im a u 3/2 u a 2 u c (t) a u b (t) u a (t) 1 A, Re a 2 C 07-09-2009 Mathematical Model of the DFIM, 32

Mathematical Model of the DFIM, 07-09-2009 33 Dynamic Modeling of the DFIM baed on Symmetical Component Analyi Baic Definition. Relationhip: Space ecto and Phao ( θ ) ω ω = = t j t j e x e x x 0 ) ( ) ( 0 0 ) ( x e x e x x e x e x x x x t x t j t j t j t j = = = θ ω θ ω ω ω 0 ) ( ) ( ) ( = t i t i t i c b a 0 ) ( ) ( ) ( = t t t c b a )) ( ) ( )) ( ) ( ( ) ( ) ( ) ( t jx t x t jx t x t x t x t x = = β α β α Thee wie connection ytem, i.e. not neutal point connection

Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Balanced Opeation. Stato flux, oto flux and open oto oltage Steady tate V = R i dψ dt dψ dt Ψ jω ψ Ψ = Lh Ψ L = L L h dψ dt ( L h jω mψ ) = ( ) L j ω = ω 07-09-2009 Mathematical Model of the DFIM, 34

Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Balanced Opeation. Stato flux, oto flux and open oto oltage ψ Tanient tate () t = R i = ψ f dψ dt kψ o e ( t ) τ t0 τ = L /R Vecto k i calculated in uch a way the flux keep continuou Fo example fo a thee phae dip fom 1 to 2 in t=t 0 ψ ( t > t ) 0 = ψ f k ψ o e ( t t0 ) ( t t0 ) τ 2 ω 2 j 1 t jωt0 τ = e jω jω e e 07-09-2009 Mathematical Model of the DFIM, 35

Mathematical Model of the DFIM, 07-09-2009 36 Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Balanced Opeation. Stato flux, oto flux and open oto oltage Tanient tate h L L Ψ = Ψ ) ( m h j dt d L L Ψ Ψ = ω ( ) ) ) (1 ) (1 ( 0 0 τ ω ω t t e pe e p L L t j t j h o = p p 1 2 = = ( ) t j t j t j h DQ o m t t e e pe e p L L ω τ ω ω = ) ) (1 ) (1 ( 0 0 Roto oltage i much highe than lip of the tato oltage

Mathematical Model of the DFIM, 07-09-2009 37 Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Unbalanced Opeation. Stato flux, oto flux and open oto oltage Steady tate Ψ = j R i ω Ψ = j R i ω ω Ψ α β i R i R i R i R Ψ ω j ω Ψ j ω Ψ t j t j j e j e j j ω ω ω ω ω ω = Ψ

Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Unbalanced Opeation. Stato flux, oto flux and open oto oltage Tanient tate ψ () t = ψ f kψ o e ( t ) τ t 0 = L L h dψ dt Ψ ( jωm ) = k e ( tt ) τ 0 L L h ((2 ) e jω t e jω t ) ( 2 ) = ( ω ω ) / ω m Roto oltage i inceaed in tem (2-) fo negatie equence 07-09-2009 Mathematical Model of the DFIM, 38

Mathematical Model of the DFIM, 07-09-2009 39 Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Unbalanced Opeation. Actie and eactie powe { } * 2 3 ) ( ) ( ) ( i t jq t P t S = = { } ) ( 2 3 Re 2 3 ) ( * β β α α i i i t P = = { } ) ( 2 3 Im 2 3 ) ( * β α α β i i i t Q = = ) ( ) ( ) ( = = = β β α α β α j j ) ( ) ( ) ( = = = β β α α β α i i j i i ji i i i i { } * * * * 2 3 ) ( ) ( ) ( = = i i i i t jq t P t S P P P P D C B A P = Q Q Q Q D C B A Q = ) ( 2 3 } Re{ 2 3 * = = β β α α i i i A P ) ( 2 3 } Re{ 2 3 * = = β β α α i i i B P ) ( 2 3 } Re{ 2 3 * = = β β α α i i i C P ) ( 2 3 } Re{ 2 3 * = = β β α α i i i D P ) ( 2 3 } Im{ 2 3 * = = β α α β i i i A Q ) ( 2 3 } Im{ 2 3 * = = β α α β i i i B Q ) ( 2 3 } Im{ 2 3 * = = β α α β i i i C Q ) ( 2 3 } Im{ 2 3 * = = β α α β i i i D Q Contant tem Ocillating 2ω tem

Mathematical Model of the DFIM, 07-09-2009 40 Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Unbalanced Opeation. Toque { } Ψ Ψ Ψ Ψ = em i i i i p T * * * * Im 2 3 { } ) ( Re 1 2 3 2 2 * * * * = em i i R i i i i p T ω ) ( 2 2 _ = T i i R E ) ( _ T P P P P em E D C B A p T = ω

Dynamic Modeling of the DFIM baed on Symmetical Component Analyi DFIM in Unbalanced Opeation. Toque and eactie powe P = A _ P B _ P C _ P D _ P P = T em ω p 2 B D _ P 2 _ P E _ T 07-09-2009 Mathematical Model of the DFIM, 41

Steady-State Analyi of the DFIM Baic Opeation Mode Attending to the Speed and Powe. Baic Steady-State equation: Powe cue at contant toque: Fou Opeating Mode: Baic elation: 07-09-2009 Mathematical Model of the DFIM, 43

Steady-State Analyi of the DFIM Baic Opeation Mode Attending to the Speed and Powe. One imple appoach to deie the pace ecto location: - The peed of the machine define clockwie o anticlockwie otation of the pace ecto. - The electomagnetic toque define the elatie poition between the oto flux and the tato flux, i.e. motoing o geneating mode of opeation on equation. - The tato oltage pace ecto i alway appoximately 90º hifted with the oto flux ecto. - The oto oltage pace ecto i alway appoximately 90º hifted with the oto flux ecto. - The eactie powe of the tato define the elatie poition between the pace ecto of the tato cuent and tato oltage. - The oto cuent can be calculated fom the flux-cuent equation. 07-09-2009 Mathematical Model of the DFIM, 44

Steady-State Analyi of the DFIM Baic Opeation Mode Attending to the Speed and Powe. Mode 1. Motoing at Hypeynchonou Speed Q < 0 Q > 0 Mode 2. Geneating at Hypeynchonou Speed 07-09-2009 Mathematical Model of the DFIM, 45

Steady-State Analyi of the DFIM Baic Opeation Mode Attending to the Speed and Powe. Mode 3. Geneating at Subynchonou Speed Q > 0 Q < 0 Mode 4. Motoing at Subynchonou Speed 07-09-2009 Mathematical Model of the DFIM, 46

Steady-State Analyi of the DFIM Pefomance Analyi. Amplitude, Fequency and Phae Shift Vaiation. The toque and the peed can be etablihed by a gie oto oltage: - Vaiation of the oto oltage. - No toque contol. - Stability poblem. 07-09-2009 Mathematical Model of the DFIM, 47

Steady-State Analyi of the DFIM Pefomance Analyi. Amplitude, Fequency and Phae Shift Vaiation. Electomagnetic toque pefomance at diffeent oto oltage opeation (2MW, 690V, N/N=1/3 DFIM) - Maximum Toque aailable at diffeent oltage. - Depending on the peed the angle and amplitude mut be changed to each poitie o negatie toque. - Limited pefomance. 07-09-2009 Mathematical Model of the DFIM, 48

Steady-State Analyi of the DFIM Pefomance Analyi. Toque and Reactie Powe Contol. - The contol impoe the oto oltage, fom T em and Q efeence. - Good pefomance. Fomula: 07-09-2009 Mathematical Model of the DFIM, 49

Steady-State Analyi of the DFIM Pefomance Analyi. Toque and Reactie Powe Contol. - Modification of T em and Q efeence not imultaneouly. - Mot eleant magnitude of the machine a function of time. 07-09-2009 Mathematical Model of the DFIM, 50

Steady-State Analyi of the DFIM Pefomance Analyi. Toque and Reactie Powe Contol. 07-09-2009 Mathematical Model of the DFIM, 51

Steady-State Analyi of the DFIM Pefomance Analyi. Toque and Reactie Powe Contol. 07-09-2009 Mathematical Model of the DFIM, 52

Etimato and Obee Stuctue fo the DFIM Diectly Meauable and Etimated Magnitude. Aailable magnitude in geneal: - Stato oltage (αβ fame). - Stato cuent (αβ fame). - Roto cuent (DQ fame). - Speed of the machine (alo poition). Depending on the ued contol tategy, it will be neceay to etimate: - Roto Flux (DTC, DPC). - Stato Flux (Vecto Contol). - Toque (DTC, Vecto Contol) - Stato actie and eactie powe (DPC, Vecto contol). 07-09-2009 Mathematical Model of the DFIM, 54

Etimato and Obee Stuctue fo the DFIM Stato Actie and Reactie Powe Etimation. Fom tato oltage and cuent meauement (implet olution): 07-09-2009 Mathematical Model of the DFIM, 55

Etimato and Obee Stuctue fo the DFIM Stato and Roto Fluxe Etimato fom Cuent Meauement. It i poible to imply etimate the tato and oto fluxe in αβ efeence fame: 07-09-2009 Mathematical Model of the DFIM, 56

Etimato and Obee Stuctue fo the DFIM Stato Flux Etimato fom Stato Voltage. The model of the machine, define a imple expeion to deie the flux fom meaued aiable: Fo the Vecto Contol: Only the angle i equied 07-09-2009 Mathematical Model of the DFIM, 57

Etimato and Obee Stuctue fo the DFIM Stato Flux Etimato fom Stato Voltage. Integato: Poblem with the offet => low pa filte Dicetize: Compenation of mod and angle: 07-09-2009 Mathematical Model of the DFIM, 58

Etimato and Obee Stuctue fo the DFIM Stato Flux Synchonization fom the Stato Voltage. Neglecting the tato eitance oltage dop: 07-09-2009 Mathematical Model of the DFIM, 59

Etimato and Obee Stuctue fo the DFIM Stato and Roto Flux Obee. Flux obee with tato cuent feedback: 07-09-2009 Mathematical Model of the DFIM, 60

Etimato and Obee Stuctue fo the DFIM Stato and Roto Flux Obee. Cloed loop obeation of the fluxe. Ueful alo fo toque etimation: 07-09-2009 Mathematical Model of the DFIM, 61

Etimato and Obee Stuctue fo the DFIM Stato and Roto Flux Obee. Choice of G matix: Obee dynamic: k time fate than the machine dynamic: 07-09-2009 Mathematical Model of the DFIM, 62

Contol Stategie fo Gid Connected DFIM baed Wind Tubine Autho: Gonzalo Abad 1 1 Unieity of Mondagon, Spain 2 Ingeteam Tanmiion & Ditibution S.A., Spain. 3 Waaw Unieity of Technology, Poland. Miguel Ángel Rodíguez 2 Gzegoz Iwanki 3

Outline 1. Intoduction. 2. Scala baed Contol. Voltage Fequency Contol. Block Diagam. Expeimental Rig. Expeimental Reult. 3. Field Oiented Contol (Vecto Contol). Block Diagam. Vecto Contol Oiented to the Stato Flux. Dynamic Diffeential Equation. Contol loop. Flux Etimato. Refeence Fame. PI Contolle Tuning Pocedue. Expeimental Reult. 4. Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC). Clai DTC. Claic DPC. Conceptual Analyi of DPC. 5. Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC). DPC Block Diagam. Claic Contol Block. DPC Block Diagam. PDPC Contol Block. Expeimental Reult. Pefomance Compaion. Pedictie DTC (PDTC). 6. Pedictie DTC and Pedictie DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. Expeimental Reult. 7. Stat-up of the Wind Tubine. Encode Calibation. Gid Synchonization. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 2

Intoduction Doubly Fed Induction Machine (DFIM) baed Wind Enegy Geneation Machine unde tudy: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 4

Intoduction Simplified Model of the DFIM. Objectie. - Fit dynamic modelling appoach of the machine. - Oiented to deign contol tategie and alidate pefomance of the machine. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 5

Intoduction Wind Tubine Contol Requiement. GENERAL CONTROL REQUERIMENTS Quick Flux-Toque o Actie-Reactie Powe Contol (Dynamic Repone). Capacity to Opeate at Vaiable Speed. Reduced Flux-Toque o Actie-Reactie Powe Ripple (Powe Quality). Reduced THD of Cuent (In Some Cae Roto ide Filte Requiement). On Line Implementation Simplicity. Robutne Againt Model Uncetaintie. Reduced Tuning and Adjuting Effot of the Contolle. Good Petubation Rejection. Reduced Ste of the Semiconducto ( Low, Contant Switching Fequencie, etc ) 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 6

Intoduction Doubly Fed Induction Machine Contol, State of the At. Geneal claification of AC Induction machine Contol Technique [3] Vaiable Fequency Contol Scala Baed Contolle Vecto Baed Contolle V/F=Contant Volt/Hetz i =f(w ) Stato Cuent Field Oiented Feedback Lineaization Diect Toque-Powe Contol Paiity Baed Contol Roto Flux Oiented Stato Flux Oiented Diect Toque Space Vecto Modulation Cicle Flux Tajectoy (Takahahi) Hexagon Flux Tajectoy (Depenbock) Diect (Blachke) Indiect (Hae) Open Loop NFO (Jonon) Contant Switching Vaiable Hyteei (Idi) Contant Switching Pedictie DTC-DPC [1] M.P. Kazmiekowki, R. Kihnan, F. Blaabjeg, Contol in Powe Electonic Selected Poblem, Academic Pe, 2002. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 7

Intoduction Doubly Fed Induction Machine Contol, State of the At. Benefit of Pedictie Diect Contol 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 8

Intoduction Doubly Fed Induction Machine (DFIM) baed Wind Enegy Geneation Sytem. Supplying topology unde tudy: Toque and Flux contol Powe flow contol (P & Q ) 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 9

Scala baed Contol. Voltage Fequency Contol Block Diagam. Simplet olution CHARACTERISTICS: - Implementation implicity. - Good powe quality. - No good dynamic epone. - No toque contol. - Contant witching fequency modulato 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 11

Scala baed Contol. Voltage Fequency Contol Expeimental Rig. Laboatoy et-up 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 12

Scala baed Contol. Voltage Fequency Contol Expeimental Reult. P i i Roto i - pectum ω m T em - pectum Stato T em 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 13

Field Oiented Contol (Vecto Contol) Geneal Contol Block Diagam. CHARACTERISTICS: - Tuning of egulato i equied - Good powe quality. - Good dynamic epone. - Toque contol in full peed ange. - Contant witching fequency modulato [2] R. Pena, J.C. Clae and G.M. Ahe, Doubly fed induction geneato uing back-to-back PWM conete and it application to aiable-peed wind-enegy geneation, Poc. IEE. Elec. Powe Appl., ol. 143, no. 3, pp. 231 241. May 1996. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 15

Field Oiented Contol (Vecto Contol) Vecto Contol Oiented to the Stato Flux. - One peed loop. - One eactie powe loop. - Two cuent loop. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 16

Field Oiented Contol (Vecto Contol) Dynamic Diffeential Equation. Vecto Contol Oiented to the Stato Flux Fom the oiginal model equation: Synchonouly otating dq efeence fame aligned with the tato flux ecto 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 17

Field Oiented Contol (Vecto Contol) Dynamic Diffeential Equation. Stato flux: The tato flux and i q detemine the toque: The tato oltage detemine the tato flux: The tato flux and i d detemine the eactie powe: Relation between the oto oltage and cuent: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 18

Field Oiented Contol (Vecto Contol) Contol Loop. Coupling tem: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 19

Field Oiented Contol (Vecto Contol) Flux Etimato. The model of the machine, define a imple expeion to deie the flux fom meaued aiable: Fo the Vecto Contol: Only the angle i equied 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 20

Field Oiented Contol (Vecto Contol) Flux Etimato. Integato: Poblem with the offet => low pa filte Dicetize: Compenation of mod and angle: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 21

Field Oiented Contol (Vecto Contol) Refeence Fame. Coodinate tanfomation: Angle calculation: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 22

Field Oiented Contol (Vecto Contol) PI Contolle Tuning Pocedue. Simplified dq cuent loop dynamic: Cuent PI Contolle: With T i = τ i Cloed loop dynamic: Gain: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 23

Field Oiented Contol (Vecto Contol) Vecto Contol. PI Contolle Tuning Pocedue. Simplified peed loop dynamic: Cloed loop dynamic: Gain: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 24

Field Oiented Contol (Vecto Contol) Vecto Contol. PI Contolle Tuning Pocedue. Simplified eactie powe loop dynamic: Cloed loop dynamic: Gain: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 25

Field Oiented Contol (Vecto Contol) Expeimental Reult. Expeimental tanient (15kW tep) & teady-tate pefomance at 1kHz witching fequency Roto ω m Stato T em 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 26

Field Oiented Contol (Vecto Contol) Expeimental Reult. Expeimental tanient (15kW tep) & teady-tate pefomance at 1kHz witching fequency P i i Roto i - pectum ω m T em - pectum Stato T em 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 27

Claic DTC. Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) DTC (Diect Toque Contol) Block Diagam CHARACTERISTICS: - Implementation implicity. - Vey Fat dynamic epone - No tuning of contolle - Toque contol in full peed ange. - Non-contant witching fequency behaiou [3] Gomez, S.A., Amenedo, J.L.R., Gid ynchoniation of doubly fed induction geneato uing diect toque contol, IECON 02,ol. 4, No. 2002. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 29

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DTC. DTC Space ecto diagam fo two leel conete - Toque expeion: - The tato flux i impoed by the tato oltage: dψ = Ri dt - Keep the oto flux contolled by uing oto oltage ecto (T em contol i alo achieed). 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 30

Claic DTC. Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Roto Flux Vecto Vaiation in Moto Mode: - Relation between oto oltage and flux: - If one oto ecto i injected, the new oto flux: - So the oto flux aiation yield: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 31

Claic DTC. Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Roto Flux Vecto Vaiation in Moto Mode: - Relation between oto oltage and flux: - If one oto ecto i injected, the new oto flux: - So the oto flux aiation yield: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 32

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DTC. DTC oto oltage ecto election (Look-up table) - The oto oltage ecto i choen accoding to: - The ecto whee the oto flux ecto i located. - To coect the toque and flux eo. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 33

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DTC. DTC Toque and Flux waefom - Toque and flux contol. - Non-contant witching fequency behaiou. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 34

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DTC. On-Off Contolle 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 35

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DTC. Toque, Flux and Secto Etimation - Thee ae eeal poibilitie. - Thi i a ey imple eion. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 36

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DPC. DPC (Diect Powe Contol) Block Diagam - Same pinciple a DTC - Vey Simila chaacteitic to DTC [4] Datta, R. and V.T. Ranganathan,, Diect powe contol of gid-connected wound oto induction machine without oto poition eno, IEEE Tan. Powe Electon., ol. 16, no. 3, pp. 390-399, May 2001. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 37

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DPC. Conceptual Analyi of DPC - The tato actie and eactie powe depend on the oto and tato fluxe and the phae hift between them (δ) - The tato eactie powe can be contolled by: - The tato actie powe can be contolled by: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 38

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DPC. Conceptual Analyi of DPC 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 39

Claic Diect Toque Contol (DTC) and Diect Powe Contol (DPC) Claic DPC. DPC oto oltage ecto election (Look-up table) The oto oltage ecto i choen accoding to: - The ecto whee the oto flux ecto i located. - To coect the tato actie and eactie powe eo. Look-up table 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 40

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. Pedictie DPC 2 leel Conete 7 Tak (Block): Block 1-4: Baic Diect Powe Contol Pinciple. Block 5-7: Pedictie Diect Powe Contol Pinciple. [5] E. Flach, R. Hoffmann, P. Mutchle, Diect mean toque contol of an induction moto, in Poc. EPE 97 Conf., 1997. [6] J. K. Kang and S.K. Sul, New diect toque contol of induction moto fo minimum toque ipple and contant witching fequency, IEEE Tan. Ind. Applicat., ol. 35, no.5, pp. 1076-1086, Sept.-Oct. 1999. CHARACTERISTICS: - Implementation implicity. - Fat dynamic epone. - No tuning of contolle. - Contant witching fequency behaiou. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 42

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. Claic Block. Pedictie DPC 2 leel Conete 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 43

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. Claic Block. Pedictie DPC 2 leel Conete 1 ON-OFF Contolle without hyteei band -1 1 ep -1 eq 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 44

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. Claic Block. Pedictie DPC 2 leel Conete Only one actie ecto pe contant witching peiod (h), elected fom a Look-up table 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 45

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. Claic Block. Pedictie DPC 2 leel Conete Two actie ecto pe contant witching peiod (h), elected fom two Look-up table. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 46

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) DPC Space ecto Diagam fo 2 Leel Conete. DPC fit actie ecto election 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 47

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) 3 Vecto pe Switching Peiod. AC machine demand inuoidal waefom. Efficient geneation of AC oltage, with VSC. 3 ecto at contant witching peiod (SV,PWM ) Neaet 3 ecto pinciple: - 2 conecutie actie ecto - 1 zeo ecto 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 48

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. Claic Block. Pedictie DPC 2 leel Conete Fit actie ecto election Second actie ecto 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 49

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. PDPC Contol Pinciple. Pedictie DPC 2 leel Conete Neceay fo duty cycle calculation 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 50

Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 07-09-2009 51 )) ( n t in( V L L L L Q L R L R P dt dp bu h 1 3 2 3 2 = π δ ω σ ω σ ω ω σ σ )) ( n t co( V L L L L L R P L R L R Q dt dq bu h 1 3 2 3 2 = π δ ω σ ω σ ω σ σ ( ) i i P β β α α = 2 3 ( ) i i Q β α α β = 2 3 = dt di i dt d dt di i dt d dt dp β β β β α α α α 2 3 = dt di i dt d dt di i dt d dt dq β α β α β α α β 2 3 Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. PDPC Contol Pinciple. Deiatie Expeion.

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. PDPC Contol Pinciple. lope 1 P (k) P (k1) P _ef lope 3 lope 2 lope 11 Q _ef Q (k) h c1 Q (k1) lope 33 lope 22 - Pedictie hoizon: One witching peiod (h). - At the beginning of the witching peiod: - The ecto equence i elected (AV1, AV2, ZV). - The duty cycle ae calculated (h c1 and h c2 ). - The cot function i minimized. h c2 h Actie Vecto 1 Actie Vecto 2 Zeo Vecto 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 52

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) lope 1 Pedictie DPC Block Diagam. PDPC Contol Pinciple. Minimization Citeia. Powe Ripple (Cot Function): P (k) P (k1) P _ef lope 3 lope 2 lope 11 Q (k) Q (k1) Q _ef lope 33 h c1 h c2 h lope 22 h c1 and h c2 ae calculated in ode to minimize the cot function (powe ipple): Actie Vecto 1 Actie Vecto 2 Zeo Vecto Actie and Reactie Powe Ripple Root Mean Squae Minimization 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 53

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pedictie DPC Block Diagam. PDPC Contol Pinciple. lope 1 P (k) lope 12 P (k1) - Unique analytic olution (non-ecuie). P _ef lope 3 - Implementation implicity. lope 2 lope 11 Q (k) Q (k1) Q _ef lope 33 h c1 lope 22 h c2 h Actie Vecto 1 Actie Vecto 2 Zeo Vecto Actie and Reactie Powe Ripple Root Mean Squae Minimization 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 54

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) PDPC Expeimental Reult. Expeimental tanient & teady-tate pefomance at contant peed and 1kHz witching fequency Roto ω m Stato T em 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 55

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) PDPC Expeimental Reult. Expeimental tanient & teady-tate pefomance at contant peed and 1kHz witching fequency P i i Roto i - pectum ω m T em - pectum Stato T em 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 56

Pedictie Diect Toque Contol (PDTC) and Diect Powe Contol (PDPC) Pefomance Compaion. Pefomance compaion 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 57

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. Pedictie DPC fo Multileel NPC VSC 3 leel NPC Conete 7 Tak (Block): Block 1-4: Baic Diect Powe Contol Pinciple. Block 5-8: Pedictie Diect Powe Contol Pinciple. Block 7: Capacito Voltage Balancing 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 59

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. 3 Leel NPC Voltage Souce Conete 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 60

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Space Vecto Diagam. Cae tudy: Thee leel NPC VSC Implementation implicity: Secto and egion calculation 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 61

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Vecto election Pocedue. Fit ecto election Second and thid ecto election 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 65

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Powe aiation Waefom. Steady-tate tato actie and eactie powe aiation waefom: Stato actie (P ) and eactie (Q ) powe eduction citeia: Duty cycle: With: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 66

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Deiatie Expeion. Slope calculation Contant and ecto 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 67

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. Table election pocedue 3 leel NPC Conete Angle of equialent oltage ecto Region calculation 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 68

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. Table election pocedue 3 leel NPC Conete Fit ecto election Second and thid ecto election 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 69

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. Table election pocedue 3 leel NPC Conete 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 70

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. Table election pocedue 3 leel NPC Conete Medium ecto Equialence of cuent 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 71

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Pedictie DPC Block Diagam. Table election pocedue 3 leel NPC Conete Real ecto definition 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 72

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Expeimental Reult. Steady-tate waefom at nominal powe (15kW) at 2 diffeent peed and 0.5kHz witching fequency CH1: V in compoed CH2: V in imple CH3: i Ch4: i 1250 e/min 750 e/min 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 73

Pedictie-DTC and Pedictie-DPC fo Multileel NPC Conete. Expeimental Reult. Expeimental tacking behaiou pefomance at contant peed and 0.5kHz witching fequency P Q S P and Q S w m Roto i - pectum ω m Stato T em 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 74

Stat-up of the Wind Tubine Oeall Contol Stuctue (Idea taken fom ABB). The Wind Tubine coe the following tate: - Encode Calibation. - Gid Synchonization. - Nomal Opeation Condition. - The cuent contol i maintained. - The cuent efeence ae modified. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 76

Stat-up of the Wind Tubine Encode calibation. Initial (Zeo) Poition of the Encode. DQ efeence fame: - otate at ω m peed. - mut be aligned with the thee phae winding of the oto. The encode in geneal: - It i mechanically coupled to the oto axi. - It zeo poition (index ignal) i not aligned with the zeo poition of the machine. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 77

Stat-up of the Wind Tubine Encode Calibation. Initial (Zeo) Poition of the Encode. Thi phae hift mut be coected!! DQ efeence fame: - otate at ω m peed. - mut be aligned with the thee phae winding of the oto. The encode in geneal: - It i mechanically coupled to the oto axi. - It zeo poition (index ignal) i not aligned with the zeo poition of the machine. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 78

Stat-up of the Wind Tubine Encode Calibation. Initial (Zeo) Poition Coection. The Wind Tubine i dien a follow: - The gid ide conete opeate at nomal condition. - The pitch contol etablihe a contant peed (ω m ). - The oto ide conete contol the oto cuent (i ). Nomally i q =0. - The tato beake i opened, o thee i not cuent in the tato ide (i =0). - Due to the oto cuent, thee i a tato oltage induced ( ). 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 79

Stat-up of the Wind Tubine Encode Calibation. Initial (Zeo) Poition Coection. The cuent i only flowing though the oto: 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 80

Stat-up of the Wind Tubine Encode Calibation. Initial (Zeo) Poition Coection. Stato Flux etimation fom the induced tato oltage and uing θ m : Roto Flux etimation fom the oto cuent: They mut hae equal phae!!! 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 81

Stat-up of the Wind Tubine Encode Calibation. Initial (Zeo) Poition Coection. Angle coection until the fluxe peent the ame phae: When both fluxe ae aligned, the co poduct i zeo. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 82

Stat-up of the Wind Tubine Initial (Zeo) Poition Coection. Block Diagam. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 83

Stat-up of the Wind Tubine Gid Synchonization. Wind Tubine Opeation. The Wind Tubine i dien a follow: - The gid ide conete opeate at nomal condition. To cloe the tato beake: - The pitch contol etablihe a contant peed (ω m ). - mut be ynchonized with l. - The encode calibation ha aleady finihed. - The tanient i minimized. - The oto ide conete contol the oto cuent (i ). - The tato beake i opened, o thee i not cuent in the tato ide (i =0). - Due to the oto cuent, thee i a tato oltage induced ( ). 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 84

Stat-up of the Wind Tubine Gid Synchonization. Contol Loop. By the oto ide of the machine: - The amplitude of the tato oltage induced, mut be equal to the gid oltage. - The phae of the tato oltage induced, mut be equal to the gid oltage. 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 85

Stat-up of the Wind Tubine Gid Synchonization. Amplitude Contol Loop. d component of cuent and oltage modify the amplitude of the induced tato oltage 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 86

Stat-up of the Wind Tubine Gid Synchonization. Phae Contol Loop. q component of cuent and oltage modify the phae angle of the induced tato oltage 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 87

Stat-up of the Wind Tubine Switch to Nomal Opeation. Once the tato oltage i ynchonized: - The tato beake i witched. - The cuent efeence ae witched. - The incoming PI egulato mut be initialized to the actual cuent efeence. In that cae: The tanient i minimized!! 07-09-2009 Contol Stategie fo Gid Connected DFIM baed Wind Tubine, 88