Comparison of a Cascade and Feedback Linearisation Scheme for DC Link Voltage Control in a Grid Connected Wind Turbine

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1 Re. Energ. Ren. : Power Engneerng () 9-38 Comparson of a Cascae an Feeback nearsaton Scheme for nk Voltage Control n a Gr Connecte Wn Turbne Alan Mullane, G. ghtboy an R.Yacamn Electrcal an Electronc Engneerng Department, Unersty College Cork, Cork, Irelan. Abstract Ths paper compares cascae an feeback lnearsaton controllers for c lnk oltage control of back to back IGT nerter res. The cascae controller s mplemente usng an nner loop controllng an, an an outer loop controllng the lnk oltage. It s shown that the lnear cascae controller wll only guarantee the esre close loop response at a specfc operatng pont. A feeback lnearsaton controller s then eelope. Usng ths controller results n a stable system across the operatng space. The feeback lnearsaton controller s apple to a arable spee wn turbne moel, an satsfactory control of the nk oltage s achee. Résumé Dans cet artcle, nous présentons une étue comparate entre eux types e contrôleurs, en cascae et feeback, pour le contrôle e la fférence e potentel en moe contnu es composants nerseurs IGT. e contrôleur en cascae est ms en œure employant une boucle nterne pour la commane es courants et, et une boucle externe pour le contrôle e la fférence e potentel. D après les résultats, l apparaît ue le contrôleur en cascae lnéare ne pourra assurer une réponse en boucle fermée satsfasante u a un pont opératon spécfue. C est pouruo, le contrôleur Feeback lnearsaton a été ms au pont. utlsaton e ce contrôleur a onne leu a un système stable. Ans, le contrôleur Feeback a été applue a la turbne a tesse arable une Eolenne; es résultats satsfasants ont été obtenus uant au contrôle e la fférence e potentel. Keywors : Controller Cascae Feeback lberalzaton IGT Inerter Wn turbne.. INTRODUCTION The purpose a wn turbne s to conert the power n the wn nto the mechancal-rotatonal power of the wn turbne. Ths s then conerte usng an electrcal machne nto electrcal energy, whch s usually supple onto the gr at the strbuton leel. The scheme beng examne here s the use of a arable spee turbne, connecte to an nucton generator. The generator s not connecte rectly onto the gr, but nstea through a oltage source conerter. The oltage sourc e conerter conssts of two back to back nerters connecte a a lnk. Ths setup allows electrcal energy at an arbtrary freuency to be supple to the gr at gr freuency. Wth ths system, maxmum energy can be extracte from the wn by aryng the spee of the turbne for a range of wn contons. Ths energy can then be supple to the gr at gr freuency through the oltage source conerter []. The control strategy for the conerter s space ector moulaton. The attracte features n usng a back to back confguraton wth a space ector moulaton scheme are, gtal calculaton of swtchng tmes, b-rectonal power flow, controllable power factor an ncrease lnk utlzaton compare to other technues an t allows moern control strateges to be apple to arable spee problems [7]. The objecte of the supply se conerter s to keep the lnk oltage constant, regarless of fluctuatons n lnk current. Two controllers are examne to achee ths objecte. Control of the lnk oltage usng PI controllers has been reporte by many researchers [9],[]. Howeer moern control technues such as feeback lnearsaton hae only recently been apple to PWM conerters. The applcaton of a feeback lnearsaton technue for control of lnk oltage n a gr connecte wn turbne wll be examne n ths paper. Ths paper wll compare a cascae controller an a feeback lnearsaton controller for the control of lnk oltage of a back to back IGT re. The frst type of controller examne, uses a cascae confguraton, PID controllers control the an axs currents, an an outerpid controller controls the lnk oltage [9]. The secon scheme uses a feeback lnearsaton technue, where the nonlnear system s lnearse usng the nput-output feeback lnearsaton metho an from ths a controller s esgne for the lnk usng lnear control theory [4]. 9

3 A.Mullane et al. The fluctuaton of the lnk current s proe by a arable spee wn turbne connecte through the secon nerter to the lnk. Changes n wn spee cause a sturbance of the lnk oltage [8].

2 3 A.Mullane et al. The fluctuaton of the lnk current s proe by a arable spee wn turbne connecte through the secon nerter to the lnk. Changes n wn spee cause a sturbance of the lnk oltage [8]. A etale smulaton of ths nonlnear system has been eelope usng Matlab/Smulnk [6]. oth controllers hae been teste an ther effecteness n rejectng sturbances n examne.. CASCADE CONTRO OF INK VOTAGE From fgure ( t) ( t) R ( t) () a a a a t Fg. : Gr se conerter confguraton When the other phases are also nclue, the fferental euatons escrbng the aboe system can be represente usng the transform as Therefore o o ( T ) o o T T R T () t o o ( T ) o o T R (3) t Now T t o ( T ) ω t o o ω (4) the, an components can be rewrtten as ( s ) R ( s R) ( s R) ω ω e e (5)

3 UPEC : Comparson of a Cascae an Feeback nearsaton. 3 A block agram representaton of a current controller for the zero current component s shown n fgure. A smlar controller can be esgne for the be replace by ' to ge Fg. : zero seuence current controller component. The ( s ) R term n the euaton aboe can ω ' (6) Where ' (7) ( s R) The controller for the current component s esgne to proe the correct reference. If we re-examne euaton 6, wth a controller present, nput to the conerter must be n terms of so usng the reference ' such that goes to the ' wll re to ts reference. Howeer the ω terms, the correct ' alue s conerte nto a for the conerter. A smlar eraton of the current controller for the component results n the block agram shown n fgure 3.Wth the nner loop controller, the controller for can be eelope. Fg. 3: Cascae control of lnk oltage usng current controllers n the nner loop

4 3 A.Mullane et al... Power balance between lnk an output se of conerter The total power n the lnk s gen by neglectng losses ths euals the total phase power on the three phase se of the conerter, an for a balance system can be shown to eual P ( ) (8) 3K where K s a scalng term use n the transformaton. Also form fgure C t c (9) P () () c Wrtng P n terms of an ges t P ( ) () C Wth the reference frame algne to the oltage n fgure, the an terms n euaton 8 sappear an the power euaton reuces to. P ( ) (3) 3K The nonlnear moel of the lnk euatons results. t C ( ) 3K (4) Ths moel can be lnearse about an operatng pont to prouce the lnear moel shown n fgure 4 Fg. 4: near moel of lnk euatons

5 UPEC : Comparson of a Cascae an Feeback nearsaton. 33 The frst term n ths block agram accounts for the current taken from the capactor ue to the component of the re. The secon term accounts for the current ae to the capactor ue to the current flowng from the turbne to the c lnk. The thr component accounts for the current change ue to c oltage araton [5] ths component 4 shows a poste feeback, whch may cause stablty problems. Usng 69, K, C, 3 V an 5 A, a controller was esgne for the lnear moel shown n fgure 4 usng the rootlocus metho. The controller was esgne to reject a current sturbance an return the c lnk oltage to ts setpont n 5ms. The lnear controller was then teste on the nonlnear moel by applyng steps n the loa current from 5 A to 7A n 5A ncrements. As the loa current was ncremente, the plant was lnearse about each new operatng pont an the close loop pole locatons usng the orgnal controller were plotte. Fgure 5 shows the close loop pole locatons as the operatng pont changes. As the loa current ncreases, the close loop pole locatons are seen to moe from ther esre postons n the left han plane, towars the rght han plane of fgure 5. Once the poles hae crosse to the rght han plane, an unstable system results. Fg. 5: Close loop pole locatons for ncreasng usng cascae control Ths phenomenon can also be seen n fgure 6, where the orgnal lnear controller has been apple to the nonlnear moel, an the loa current ncrease n 5A ncrements, form to 5A. The system goes unstable for hgher alues of loa current as expecte from the root locus plot. Fg. 6: lnk oltage response to ncreasng steps n loa current wth cascae controller

6 A.Mullane et al FEEDACK INEARISATION The goal of the nput-output lnearsaton technue s to try to obtan, usng state feeback an transformaton, a lnear relatonshp between a new nput efne as, an the output of the plant y. Ths s outlne n fgure 7 below, where the measure sturbance s also cancelle. Fg. 7: Feeback lnearse system confguraton The basc metho to acheng nput output lnearsaton s to fferentate the output functon y untl the nput u appears an then esgn the nput to cancel the nonlnearty. The formal approach to nput-output lnearsaton s shown n many texts [][3]. 3.. Feeback lnearsaton for lnk oltage control From Euatons 5,,8 earler the followng fferental euatons escrbng the prmary ynamcs of the system can be wrtten ( ) C K C R R 3 ω ω & & & (5) These euatons are of the form p u p x g u x g x f x ) (... ) ( ) ( & (6) ( ) ( ) x h y x h y p p M (7) The outputs we wsh to control are

7 UPEC : Comparson of a Cascae an Feeback nearsaton. 35 y (8) y (9) It shoul be note that the, fferental geometrc approach to feeback lnearsaton n [] was apple to systems of the form x & f (x) g(x) u where f ( x ) s a nonlnear functon of the states only. The term n euaton 5 s a nonlnear functon of both the states x, an the sturbance. Ths wll be accounte for n the fferentaton of y. The fferental geometrc approach howeer, s applcable for the eraton of y. Here p so ths yels, f j p ( ) ghj u y& h () j y & 3 3 ( ) ( ) f h g h gh { R e ω R y& ω u (). as expecte (see system euaton aboe). One of the control nputs, u has appeare. Now calculate y usng the same metho. C 3CuK ( ) y& (3) The control nputs hae yet to appear so euaton must be fferentate agan. The approach shown n [] must. be mofe as s also a arable. To account for ths, the partal erate of y wth respect to must also be obtane. Calculatng ths erate, the euatons may be rewrtten n matrx form as y& u A E && y u The nerse of the E matrx s E The controller s sngular when Now f u s selecte as 3CK et[ E ] (6) 3C K () (4) (5)

8 36 A.Mullane et al. u E u the followng euatons result y& & y&& && [ A] Now by choosng the alues of an we can shape the error ynamcs. Frst examne e e& y& ref y& (9) We esgn the error ynamcs to be conergent an stable e& (3) k e Ths s achee by choosng of as For the other nput & ref (3) y ke y& k e& k e (3) ref 3 Ths controller was mplemente usng Smulnk an the error ynamcs esgne to reject a sturbance n the c lnk current n ms.. (7) (8) Fg. 8: lnk oltage response to ncreasng steps n loa current usng feeback lnearsaton control Fgure 8 shows the response of the c lnk oltage usng the feeback lnearsaton controller an the nonlnear moel eelope earler. The same loa current steps as use for the cascae confguraton, were use to test the controller. The controller was also teste usng the loa current supple form a arable spee wn turbne smulaton, the results of whch are shown n fgure 9

9 UPEC : Comparson of a Cascae an Feeback nearsaton. 37 Fg. 9: Feeback lnearsaton control of lnk oltage for a arable spee wn turbne: (a) wn sgnal (b) lnk current (c) lnk oltage

10 38 A.Mullane et al. 4. CONCUSION Ths paper escrbes the eelopment of cascae an feeback lnearsaton controllers for c lnk oltage control n back to back IGT nerters. The It can be seen that the lnear cascae controller wll only guarantee the esre close loop response at the operatng pont for whch the controller was esgne. In the real system as the parameters an change, the transfer functon for the system also changes, an the controller can no longer guarantee the same close loop response. As the moel changes, the close loop poles moe an t s possble that the system moel eates so much, that the close loop poles moe to the unstable regon. Therefore usng the cascae confguraton, control oer the c lnk oltage can only be guarantee f the sturbance or set-pont changes, cause the system to eate lttle from the operatng pont for whch the controller was esgne. The feeback lnearsaton controller howeer results n a stable system across the operatng space use n the test. The c lnk oltage returns to ts set-pont n 5ms as the operatng pont changes. The feeback lnearsaton controller was also apple to a arable spee wn turbne moel, an satsfactory control of the nk oltage was achee. Acknowlegements - The support from the Electrcty Supply oar (ES) s gratefully acknowlege. Also the author woul lke to thank Smon Grmes of ES for hs useful comments. REFERENCES [] Jean-Jacues E. Slotne, Apple Nonlnear Control, Prentce-Hall, Englewoo Clffs, New Jersy, eton, 99. [] Segfre Heer, Wn Energy Conerson Systems, Wley, 996. [3] Hassan K. Khall, Nonlnear Systems, Prentce-Hall, Upper Sale Rer, New Jersy, eton, 996. [4] Dong-Choon ee, -bus Voltage Control of Three-Phase AC/ PWM Conerters Usng Feeback nearzaton, IEEE Transactons on Inustry Applcatons, 36(3):86 833, May/June. [5] eopolo Rossetto ug Malesan, AC//AC PWM Conerter Wth Reuce Energy Storage n the nk, IEEE Trans. on Inustry Applcatons, 3():87 9, 995. [6] Chee-Mun Ong, Dynamc Smulaton of Electrc Machnery, Prentce Hall, 998. [7]. Dewan R. Wu, Analyss of an ac-to-c Voltage Source Conerter Usng PWM wth Phase an Ampltue Control, IEEE Transactons on Inustry Applcatons, 7(): , 99. [8] R. Che, Intellgent Control for Wn Energy Con erson Systems, Wn Engneerng, (): 6, 998. [9] R. Pena, Doubly Fe Inucton Generator Usng ack-to-ack PWM Conerters an ts Applcaton To Varable Spee Wn Energy Generaton, IEE Proc. Electr. Power Appl., 43(3):3 4, May 996. [] Y.Iwaj S.Fukua an T.Aoyama, Moellng an Control of Snusoal PWM Rectfers, Proc. EPE, pages 5, Sept. 993.

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