2. ANALYSIS OF THE CDFIG

Revue es Enegies Renouvelables SMEE 10 Bou Ismail Tiaza (2010 347 358 Analysis an veto ontol of a asae oubly fe inution geneato in win enegy aliations Zohei Ti 1*, Hammou Rajeai 1 an Rahi Abesseme 2 1 LAS, Reseah Laboatoy, Deatment of Eletial Engineeing, Univesity of Setif, Algeia 2 LEB, Reseah Laboatoy, Deatment of Eletial Engineeing, Univesity of Batna, Algeia Abstat - This ae esents eent stuies of the ynami an steay state efomane of the asae oubly-fe inution geneato fo win enegy aliations. The moeling methoology base on ynamial euivalent iuits is given in this ae fo the esign of the CDFIG ontolle, the CDFIG an be an attative altenative to onventional ouble outut woun oto inution geneatos. The system emloys two asae inution mahines to eliminate the bushes an oe ings in the taitional DFIG. In this ase, Casae inution geneatos euie lowe maintenane. In CDFIG both statos of onnete mahines ae aessible. The ontol stategy fo flexible owe flow ontol is eveloe. The ineenent ontol of the ative an eative owe flows is ahieve by means of a tow uaant owe onvete une the lose-loo stato flux oiente ontol sheme. The Matlab simulation softwae is use fo a eliminay investigation of CDFIG. Keywos: Casae oubly fe Inution Geneatos - Vaiable see geneato, Veto ontol - Close loo see Contol - Ative-owe an eative owe ajust, Powe flow iagams - Simulation. 1. INTRODUCTION The exession oubly fe alies geneally to mahines whee eletial owe an be fe o extate fom two aessible thee-hase winings, [11]. Reent eseah [2-8] has eveale that the bushless oubly-fe inution geneato (CDFIG o its funtionally iential twin, the CDFIG, is a ossible altenative to the onventional invete-fe inution mahine ive, eseially in minimizing the oveall ive ost fo limite see ange aliations. Reently the oubly fe inution geneatos (DFIG beame the oula onfiguation in vaiable see win enegy aliations [1]. The eveloment an use of the DFIG mahines was itate by the nee fo wie oeational ange as well as the neessity to allow flexible owe flow ontol, gi integation as well as eonomi easons [2-8]. The use of the DFIG mahines, howeve, inease the long tem ost an omlexity of the win enegy geneation. The isavantage assoiate with the woun-oto inution mahines is that the sli ings an abon bushes have to be systematially maintaine [6, 3]. Tyial faults of sli ings an bushes ae: the inease sufae oughness of the ings o the bush ontat fae, beak out of abon mateial fom the bushes an eeasing ontat essing foes whih lea to inease bush saking an signifiant efomane eteioation [6]. Sine win tubines ae installe in emote laes, the maintenane osts fo suh emote installations ae signifiant, [6, 9]. The ost of maintenane fo taitional DFIG base win geneatos inease the essue to seek othe altenative geneato systems * zohei_ti@yahoo.f ; hajeai@yahoo.f.abesseme@lyos.om 347

348 Z. Ti et al. [3]. One of suh altenatives is offee by the CDFIG as shown in Fig. 1. In this onfiguation, the oto enegy is tansfee by using a seon fational inution mahine (ontol mahine, whih is ietly oule to the main geneato (owe mahine though the bak-to-bak onnetion of oto iuit (o both age [3, 4]. A numbe of stuies have been onute on the efomane moeling of the CDFIG. The esults have been esente in simulation esults only. Fig. 1: CDFIG onfiguation fo win owe geneation The objetive of this eseah is to esent a new bushless tehniue fo the iniet veto ontol of a CDFIG. This metho is suitable fo gi-onnete vaiable see BDFIGs. This ae esents the analysis an the simulate esults using Matlab / SimPoweSystem / Simulink fo ontol of the gi onnete oeation, whee the owe flow is ontolle into the gi. 2. ANALYSIS OF THE CDFIG The CDFIG is base on two DFIMs, mehanially an eletially oule, as it is shown in Fig. 1. The two mahines ae invese ouling seuenes [12], an a igoous analysis (using ieal moels of DFIMs. This is the aim of Setion II, an it allows one to esibe the owe flow though the two mahines in oe to evaluate ualitatively the geneato effiieny. Then, it will also be ossible to isuss on omlementay onstaints elate to the CDFIG esign fo an integation of the two mahines into a single fame [12]. Theeafte, moeling (Setion III is oiente by these eliminay esults, moe atiulaly onening ouling seuene between oto winings. A moel of a ealisti geneato is establishe using a gahial eesentation of the system, aate to the en-use oint of view: an eletial sheme. The eesentation oose in this ae (ynamial-euivalent iuit eesentation is not limite to the lassial ase of sinusoial steay-state oeation but it an be alie to a tansient esition of the system. Then, this moel is use fo the esign of the CDFIG ontolle will be etaile in Setion IV [12]. If the DFIM is onseve, oto winings must be sulie by anothe thee-hase a mahine: Anothe DFIM is intoue, as shown in Fig. 3. It is shown that these two DFIMs an be ietly onnete an finally integate, giving us a omlete bushless solution alle asae DFIM-CDFIM (moe eisely, in this ae, geneato- CDFIG. Notie that the global stutue of the geneato base on a single DFIG an be onseve with the CDFIG: The stato winings of the DFIM N 1 ae onnete to a

SMEE 2010: Analysis an veto ontol of a asae oubly fe inution 349 voltage soue invete, an this invete is sulie by a Pulse With Moulate (PWM etifie onnete to a gi [12]. Moeove, in this ae, mahine esign is not teate, an this at of the oblem intoues sulementay onstaints. If a omat solution is euie as fo win enegy euiment, a single-fame CDFIG (SF-CDFIG an be esigne, intouing aitional onstaints fo the numbes of ole ais in oe to avoi iet magneti ouling between stato winings of the two mahines, as shown in Fig. 2, with N 2 an N 1, [11]. Fig. 2: Examle of SF-CDFIG o BDFIG [11] The stuy esente in the following setion is fouse on the CDFIG. Inee, it is neessay to analyze the behavio of this stutue with invese ouling seuene. This ae is base on a simlifie moel of the DFIM whee oe/ion losses an magneti leakages ae neglete as shown in Fig. 3. Thus, a DFIM is haateize by the following: s + Ω (1 P S P s (2 P s P + (3 s Pm s N Ω S o S (4 s Fig. 3: DFIM in suesynhonous moto/geneato onvention

350 Z. Ti et al. Fig. 4: CDFIG owe flow onvention Aoing to Fig. 4, negleting losses, the mehanial owe P m an P m, the oto owe P an P fo eithe mahine, as well as the gi owe P g, may be exesse as funtions of mahine M an M stato owe P an P an the oto owe P an P an the suly stato voltage feuenies, 2 ( g an the oto feueny. S, S, ( N + N Ωm, 2 π f N Ωm, N Ωm S (5 (6 (7 Pm Pm P P N Ω ( 1 S P P (8 ( 1 S N Ω P P (9 S P P (10 S P P (11 P g P + P (12 The oto owe has the same value fo both mahines, but with oosite olaity, so that P P P. Thus, fom {E. (10} an {E. (11}, the stato owe to the mahines may be exesse as a funtion of the feuenies an. P P (13

SMEE 2010: Analysis an veto ontol of a asae oubly fe inution 351 Fom {E. (12} an {E. (13}, the stato owe of owe mahine may be exesse as a funtion of the gi owe P g an the suly feuenies. P P g (14 P P g (15 Fom {E. (10} an {E. (14}, the stato owe fo ontol mahine, may be exesse as a funtion of the gi owe P g an the feuenies. P m P g (16 P m P g (17 ( P P P g m + (18 m Powe flow iagams of the CDFIG ae shown in Figs. 5a- an 5b-, esetively. Fig. 5: Powe flow iagams: a- tyial fo suesynhonous sees b- tyial fo hyesynhonous sees Fig. 6 shows an illustation of the tansfes of owes of the CDFIG with vaiation see. Fo awing the steay state e hase iuit the slis of two mahines shoul be efine: S P m, S P m (19

352 Z. Ti et al. Fig. 6: P m, P m, P m an P as funtions of see Ω m The steay state CDFIG e-hase euivalent iuit is shown in Fig. 7. Beause the two onsiee mahines ae assume iential the sum of oto esistanes an the sum of oto leakage inutanes ae moele in the oto iuit. Fig. 7: Steay state e-hase euivalent iuit of the CDFIG in voltage ontolle mo, [13, 14] The CDFIG steay-state efomane euations on a e-hase basis ae as follows: V 0 V s s R + s j L j Lm 0 s j Lm Rs + j L S js L m 0 j R s L + j m L s I I I Fig. 8 shows the feuenies of the asae aoing to see. s s (20 Fig. 9 shows the tensions Fig. 8: Feuenies fo the 2/2 ole ai CDFIG feueny f, in oe to maintain a onstant V may vay ootionally to mahine V f atio. M M sulie

SMEE 2010: Analysis an veto ontol of a asae oubly fe inution 353 Fig. 9: Tensions V an V vesus see in the CDFIG [13-15] 3. DYNAMICAL MODEL OF THE CASCADED DOUBLY FED INDUCTION GENERATOR The behavio of eah iniviual mahine (PM an CM is esibe by the following: v v v v s s ( Rs + Ls ( S + j is + Lm ( S + j ( R + L ( S + j i + L ( S + j m ( Rs + Ls ( S + j is + Lm ( S + j ( R + L ( S + j i + L ( S + j {E. (21} an {E. (22} efe to the owe an ontol mahines, esetively. Due to the ole ai iffeene between the two statos, thee exists suh elations between the eletial sees of the oto an statos fo the 50 Hz system, whih ae given in 2 π 50 (23 m i i i i s s (21 (22 m P (24 m ( P + P (25 The behavio of the CDFIG an be esibe in (4 by the ombination of {E. (21} an {E. (22} an noting that i i an υ υ ue to the bak-to bak onnetion of otos. vs vs θ + ( R + L ( S + j i + L ( S + j s s m ( Rs + Ls ( S + j is + Lm ( S + j ( R + L ( S + j i + Lm ( S + j i R + L ( S + j i + L S + j i i ( m ( i s It is assume that the stato has two sinusoially istibute winings with numbe of oles ( P P. Thee ae thee initial efeene fames (shown in Fig. 10: (26

354 Z. Ti et al. a- PW efeene s, s elate to a P ole-ai-tye istibution, whih is use as the oveall efeene fame. b- CW efeene s, s elate to a P ole-ai-tye istibution an loate at a mehanial angula osition of θ aians fom s, s. - Roto efeenes, an, elate, esetively, to a P an P oleai-tye istibutions whih ae loate at a mehanial angula osition of θ C fom s, s. Fig. 10: Thee-hase. CDFIG moel in - efeene fame, [13, 14] In a stana atie, the ynami euation in {E. (26} is usually eesente in the selete - efeene fame. With the assumtion of a stiff gi onnetion, the synhonous efeene fame is selete. The stato fame otates at the see e whih is shown in Fig. 2. Moeove, Fig. 10 also shows the angle elationshi of owe mahine stato, owe an ontol mahine otos an ontol mahine stato to the selete efeene fame. The omlete CDFIG ynami moel in - efeene fame an be given in: Ψs υs Rs is + + Ψs t Ψs υs Rs is + Ψs t θ Ψ R i + t + Ψ θ Ψ R i + t Ψ υs Ψ R s s is + t + Ψs υs Ψ R s s is + t Ψs (27

SMEE 2010: Analysis an veto ontol of a asae oubly fe inution 355 Flux linkages ae efine by: Ψs Ψs Ψ Ψ Ψs Ψs Ls is + L m i Ls is + L m i Lm is + L i Lm is Lm is + L i Lm is Ls is + L m i Ls is + L m i The total eleti T e fo BDFIG is the sum of both mahines: Te ( P ( Ψ i Ψ i + P ( Ψ i Ψ i (28 3 s s s s s s s s (29 2 The eleti toue euation is efine by the fition an total inetia of the owe an ontol mahines: Te ( F + F ( J + J T m L F F m (30 t The omlete CDFIG system efine by {E. (27} {E. (30} esents an auate ynami moel of the geneato the moel an eisely esibe the mahine ynami behavio une stiff gi onnetion. 4. CDFIG CONTROLLER DESIGN The situation beomes moe emaning when a win tubine is euie to oue onstant voltage an onstant feueny owe in a weak gi o non-gi onnete, stan alone situation. Seial ontol stategies have to be evise to attain suh objetives. Veto ontol, intoue by Blashke in 1972, [10]. The eveloe ontol stategy is base on a loos ontol as shown in Fig. 11. Two egulation aths ae imlemente as in the lassial veto ontol shemes: one ontol ath egulates the magnetizing uents an the othe one is eiate to ontol the ative uents. In oe to obtain a goo eoule ontol, the PW flux oientation has been selete ( Ψ s Ψs an Ψ s 0. The obtaine ontol stategy fo the BDFM is simila to the well-known stato fiel oientation ontol use in the DFIM. [11, 13, 14]. 5. SIMULATION RESULTS The CDFIG is fist lae in ieal onitions an is iven to 735 m. We imose an ative owe ste of 4 kw at t 3 s an we obseve the esonse obtaine with the PI ontolle. Also we imose a eative owe ste of 2 kw at t 2 s an we obseve the esonse obtaine with the PI ontolle. Results ae esente on figues 12, 13, 14 an 15. We an notie that the esonse times ae euivalent (about 35 ms. The effet of the ative owe ste on the eative owe shows that the oss-ouling tems. The imat of the ative owe hange on eative owe an on the ontay in the DFTSIG is emonstate in Fig. 8, whee they an be seen that thee only exists a tansient

356 Z. Ti et al. istubane in the eative et ative omonent (at times 2 an 3 s while the steay state oeation ae unaffete. Fig. 9 shows the Powe mahine stato uent. Fig. 11: CDFIG Contolle Stutue Fig. 12: Reative an ative owe eouling Fig. 13: Powe stato uent

SMEE 2010: Analysis an veto ontol of a asae oubly fe inution 357 Fig. 14: Roto uent Fig. 15: Contol stato uent 6. CONCLUSIONS Owing to its geat eliability, CDFIM is an inteesting solution fo win enegy aliations. It has been also shown in this ae that using an aoiate moeling aoah base on ynamial euivalent iuit eesentation; a theoetial an simulation stuy of the CDFIG ynami efomane in lose loo ontol of the geneato ative an eative owes has been esente. The ontol system is base on the fiel oientation inile an the oientation of the owe mahine stato flux with two PI ontolles lae in the owe stato fiel ooinates, whee a bak-to-bak voltage soue onvete was emloye. Moeove, the oose moeling aoah allows the stuy of owe flow. The oose onfiguation an be easily imlemente with fational ontol mahine an futhe with ommon suiel age oto an ual stato winings. REFERENCES [1] S. Mulle, M. Deike an R.W. De Donke, Doubly Fe Inution Geneato Systems fo Win Tubines, IEEE Inusty Aliations Magazine, Vol. 8, N 3,. 26-33, May/Jun. 2002. [2] M. Mahmoum, F. Poities an B. Toufik, Doubly Fe Inution Geneato With Ative Filteing Funtion fo Win Enegy Convesion System, in Poeeings of Euoean Confeene Powe Eletoni Aliations,. 9, Set. 2005. [3] K. Potsenko an D. Xu, Moeling an Contol of Bushless Doubly-Fe Inution Geneatos in Win Enegy Aliations, IEEE Tansations on Powe Eletonis, Vol. 23, N 3,. 1191-1197, 2008.

358 Z. Ti et al. [4] F. Runos, R. Calson, A. Oliveia, P. Kuo-Pen an N. Saowski, Pefomane Analysis of a Bushless Double Fe Cage Inution Geneato, Poeeings of. Noi Win Powe Confeene,.1-8, 2004. [5] G. Boaman, J. G. Zhu an Q.P. Ha, Powe Flow in Doubly Fe Twin Stato Inution Mahines by Web Site. [6] M. Aamowiz, R. Stzeleki an D. Wojiehowski, Steay State Analysis of Twin Stato Casae Doubly Fe Inution Geneato, 5 th Intenational Confeene-Woksho CPE 2007. [7] N. Chilakaati, V.S. Ramsen an V. Ramaswamy, Pefomane Evaluation of Doubly-Fe Twin Stato Inution Mahine Dive with Voltage an Cuent Sae Veto Contol Shemes, IEE Poeeings, Eleti Powe Aliations, Vol. 148, N 3,. 287 292, 2001. [8] D. Basi, J.G. Zhu an G. Boaman, Tansient Pefomane Stuy of a Bushless Doubly Fe Twin Stato Inution Geneato, IEEE Tansations on Enegy Convesion, Vol. 18, N 3,. 400-408, 2003. [9] W. Gainge an N. Jenkins, Offshoe Win Fam Eletial Connetion Otions, Offshoe Win Enegy Netwok [Online]. Available: www.owen.eu.l.a.uk [10] F. Blashke, The Pinile of Fiel Oientation as Alie to the New Tansveto Close- Loo Contol System fo Rotating Fiel Mahines, Siemens Review, Vol. 34, N 2,. 217 223, 1972. [11] J. Poza, E. Oyabie, M.A. Roiguez an I. Saasola, Veto Contol Design an Exeimental Evaluation fo the Bushless Doubly-Fe Mahine, IET Poeeings Eleti Powe Aliations, Vol. 3, N 4,. 247 256, 2009. [12] N. Patin, E. Monmasson an J.P. Louis, Moeling an Contol of a Casae Doubly Fe Inution Geneato Deiate to Isolate Gis, IEEE Tansations on Inustial Eletonis, Vol. 56, N 1,. 4207-4219, 2009. [13] Z. Ti, H. Rajeai an R. Abesseme, On the Dynami an -Steay State Pefomanes of A Veto Contolle DFTSIG In Win Enegy Aliations, CIEME'09, T1.20,. 63, 2009. [14] Z. Ti, H. Rajeai an R. Abesseme, Moeling an Contol of Doubly Fe Twin Stato Inution Geneatos in Win Enegy Aliations, WIERA 2, E001, 30, 2009. [15] N. Patin, Analyse Ahitetue, Moélisation et Commane e Généateus ou Réseaux Autonomes et Puissants, Thèse e Dotoat, Eole Nomale Suéieue e Cahan, 2006.