System identification methods on Alstom ECO 100 wind turbine

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1 System identification methods on Alstom ECO wind trbine Iciar Font Balager Alstom Wind Roc Boronat nº 78, 85 Barcelona, Spain com Stoyan Kanev EC Wind Energy P.O. Box, 75LE Petten, the etherlands Dimitri cherniak Brel&Kjaer Sond and Vibration Measrements DK-85 aerm, Denmark Michele Rossetti Alstom Wind Roc Boronat nº 78, 85 Barcelona, Spain lstom.com; Abstract raditionally, the design of control algorithms for wind trbines is performed based on (linearized) models of the wind trbine dynamics. Control performance is strongly dependent on the accracy of these models and for this reason validation of the dynamics is essential for achieving optimal control. he aim of this work is to identify, at different wind speeds, the dynamic model of a wind trbine in operation by means of two different system identification techniqes. his work has been partly performed within the Senternovem long-term research project SsCon: a new approach to control wind trbines (EOSL3) and partly within the InVent project-accó (CIDEM COPCA). Keywords: System Identification, wind trbine. Introdction wo different system identification methods have been applied on a wind trbine so to extract modal information at different operational conditions: Experimental modal analysis, where inpt/otpt signals are measred, and Operational modal analysis, where only otpt signals are measred. On the Experimental modal analysis, the application of band-limited psedo-random binary excitation signals (PRBS) have been careflly designed to avoid the indction of ndesired significant loads on the tower and rotor, taking also into accont the constraints of the actators. When sing Operational modal analysis, no forced excitation is needed and only the (nmeasred) ambient excitation from the wind is sed. However, an elevate nmber of sensors mst be sed to recollect the vibrational responses since the modal parameters are dependent on the modal shape. heoretical backgrond. Experimental Modal Analysis Experimental modeling is an orthogonal approach to first principles physical modeling, where the phenomena observed in reality are modeled by sing measred data from the operational wind trbine. o this end, system identification techniqes are sed to fit the parameters of a sitable mathematical model to the measred data as good as possible. For wind trbine applications, experimental modeling has only received limited attention in the literatre. he application of exciter methods, where rather nrealistic direct and measrable excitation on several points on the blades is assmed, has been investigated in []. Recently, research on modal analysis has been performed within the framework of the Eropean research project SABCO - Stability and control of large wind trbines'', where both simlation stdies and experimental reslts have been reported [, 3]. he simlation stdies are based on blade excitations that are difficlt to realize in practice. More realistic excitation signals were investigated at Risø ational Laboratory, where the se of the blade pitch and generator torqe to excite the first two tower bending modes by harmonic signals and measrement of the decaying response proved to be nsitable for

2 accrate estimation of the damping [3]. he identification of open-loop drive train dynamics from closed-loop experimental measrements on a fixed-pitch variable speed wind trbine for the prposes of control design algorithms is reported in [4]. Becase the experimental modeling is based on data collected from a wind trbine dring operation, i.e. with the controller in operation, closed-loop system identification mst be applied. In this work, a detailed stdy is performed on the application of the following closed-loop identification (CLID) approaches to wind trbine model identification: method [5], Indirect method [5], Joint Inpt/otpt method [5], Closed-loop instrmental variable method [6], ailor made instrmental variable method [7], Closed-loop 4SID sbspace identification [8], Parsimonios sbspace identification method () [9], Sbspace identification based on otpt predictions () []. Initial stdies sing simlation data from both linear and nonlinear aeroelastic simlations have indicated that the methods, and are the most potential ones for wind trbine applications, with the method often otperforming the other methods. For that reason, and for the sake of space limitation, only the method is smmarized in Section... In order to identify accrate (nbiased) inpt-otpt models sing the abovementioned system identification methods, it is necessary that the inpts are additionally excited by signals that are ncorrelated with the wind. How this can be achieved withot introdcing nacceptable additional loads will be discssed in Section... Finally, special attention has also been paid on data-driven model validation, for which prpose several techniqes are developed and smmarized in Section Excitation signal design Figre. System identification setp A possible system identification setp is depicted schematically on Figre. ypical inpts are the (collective) blade pitch angle θ and generator torqe g setpoint, and otpts generator speed Ω and tower fore-aft v nod and sideward v nay speed (or accelerations). he blocks K g and K θ in the feedback loops represent the torqe and the pitch controllers, respectively, which are not reqired in the identification methods, presented in Section... ime series of these typical inpts and otpts allow for the identification of the transfer fnctions from θ to v nod, from g to Ω, and from g to v nay, from which the tower fore-aft, tower sideto-side and drive train dynamics can be analyzed. he freqency region, in which the identified models will be accrate depend on the bandwidth of the excitation signals r θ (on the blade pitch) and/or r g (on the generator torqe). When the freqency and damping of the first tower mode need to be identified, the bandwidth shold at least inclde the (expected) first tower freqency. When the first drive-train mode is needed, the excitation bandwidth mst at least inclde the first drive-train freqency. Hence, the proper choice of excitation signals is of paramont importance for achieving informative experiment nder reasonable amont of excitation. In fact, there are two conflicting objectives, between which a trade-off shold be made. On the one hand, a good excitation for system identification can be achieved by choosing a high energy excitation signal with wide flat spectrm. On the other hand, the system limitations (sch as hardware limits, loads, etc.) necessitate the se of low-energy, narrow bandwidth excitation. he goal is to design

3 an excitation signal in sch a way, that, (a), the signals remain within the hardware limits, (b) the additional loads are as small as possible, and (c), it still allows the identification of accrate models. For the considered wind trbine, the excitation signals r θ and r g have been designed in sch a way, that no nacceptable loads are indced, the excited pitch demand has acceptable speed and acceleration, and the electric power remains within acceptable limits. o this end, the pitch excitation signal r θ is designed as a psedo-random binary signal (PRBS) with amplitde of.5 degrees, filtered with a 3st order lowpass FIR filter with ctoff freqency of Hz, and an elliptic bandstop filter with db redction, db ripple, and stop-band of 3% arond the expected first tower freqency (.3 Hz). In this way the pitch excitation does not excite the region arond the expected first tower freqency, as well as freqencies above Hz. the generator torqe excitation signal is also designed as PRBS signal, bt ncorrelated with the one sed for pitch excitation, and with an amplitde of m (3% of the rated torqe of 6.8 km), filtered with a 3st order lowpass FIR filter with ctoff freqency of Hz, so that the excitation is concentrated in the freqency region p to Hz. Simlations made with an aerolastic code have revealed that these excitations introdce significant increment in loads.... method for closed-loop identification In the direct method [5], a so-called prediction error model identification is applied to the data, collected while the wind trbine operates in closed-loop. he starting point of the method is the selection of a sitable model strctre. For wind trbine applications, a simple atoregressive-with-exogenos-inpt (ARX) model proves to be sfficient. he ARX model has the following form A ( p). y( = B( p). ( + e( () where vector, y( R ( R l is a generalized otpt m is the inpt vector, l e( R is some nknown and immeasrable generalized distrbance signal representing the inflence of the wind on the otpt measrements, k is the lxl moment of time, and A( R and lxm B( R are matrix polynomials dependent on the nknown parameter P: A( = I + A q B( = B P = Above, + B q [ A K, A, B K, B ], q na + A q, + B q nb + L + A na + L + B q nb na q, nb denotes the backward time shift operator, i.e. q y( = y( k ). he goal is to estimate the model parameters p given inpt/otpt data {, y( } k ( =. his is achieved in the following way. Given the ARX model strctre, the one step ahead predictor for the otpt vector is formed yˆ( = P. ϕ(, ϕ( = vec([ y( k ), K y( k na), (, K, ( k nb)]) where vec(m) is the vectorization operator which stacks the colmns of a matrix into one vector. his predictor model is sed for constrcting the prediction error ( = y( yˆ( = y( Pϕ( () o estimate the nknown parameter matrix P, the following prediction error criterion is minimized with respect to P V ( = ( (3) k= An analytical expression can be obtained for the parameter matrix P that minimizes the prediction error criterion by sing the fact that for given matrices of appropriate dimensions, the following expression holds X. Y. Z = ( Z X ). vec( Y). (4) Hence V ( vec( = vec( = giving k = k = ( ϕ ( y( ( ϕ ( vec( ( y( ( ϕ ( vec( ),

4 vec( = k= ( ϕ ( ( ϕ ( k= ( ϕ ( he identified ARX model is then parameterized by this optimal parameter matrix P. It can be theoretically shown that the identified model is nbiased nder reasonable assmptions [5]...3. Modal parameters estimation Once a model of the wind trbine is identified, there are different ways to extract modal parameters, sch as the first tower and drive-train freqency and damping. One way to do that is by performing model redction on the identified mode to redce the model order, sch that there is only one mode in a specified interval of interest where the freqency is expected to lie. For the considered wind trbine in this paper, this interval is chosen as [.5,.4] Hz for the tower, and [.7,] Hz for the drive train. he retained mode is the mode with the largest participation factor. he freqency and damping of this mode of the redced system are then selected...4. Model validation methods Model validation is the process of deciding whether an identified model is reliable and sefl for the prposes for which it has been created. he following model validation methods have been sed to check the accracy of the identified model: y( Variance-acconted-for (VAF): this is a model validation index often sed with sbspace identification methods. Given the measred otpt y( and the otpt predicted by the one step ahead predictor yˆ (, the VAF criterion is defied as σ VAF ( y, y ˆ) = (5) σ where σ y is the variance of the signal y(, and σ - the variance of the prediction error. It is expressed in percentage. A VAF above the 95% is sally considered to represent a very accrate model. Prediction error cost (PEC): this is the vale of the prediction error cost fnction, defined above. he smaller the vale, the better the model accracy. Ato-correlation index ( R ix ): when a R (τ ) consistent model estimate is made, the prediction error shold be a white process, so that its atocorrelation fnction shold be small for non-zeroτ, whereτ denotes the discrete time step. For a given confidence level α (e.g. α = 99% ), bnd a bond R (α ) can be derived sch that for an accrate model the ineqality hold for all bnd R ( τ ) R ( α) shold τ. he index is then compted as the sqare sm of the distance between each vale of the correlation fnction (α ) R (τ ) and the bnd bond R, where only the vales otside the bond are sed. Cross-correlation index ( R ix ): in the closed-loop sitation the prediction error will be correlated with ftre vales of the inpt, bt shold be ncorrelated with past inpts when the model is consistent. he crosscorrelation fnction R R ix (τ ) shold then be limited in absolte vale for τ. he index is compted R ix similarly to. R ix It is important to point ot that the data set that is sed for validating the models shold be different from the data sed for obtaining the model, as otherwise wrong conclsions cold be drawn. When the data length is short, a rle of thmb is to se two thirds of the data for identification, and the remaining one third for validation.. Operational Modal Analysis he ability to obtain modal characteristics of the big strctres and particlarly wind trbines played an important role in the establishment and frther development of operational modal analysis (OMA). here are two significant advantages of OMA when one considers its application to wind trbine. First of all, OMA does not reqire the knowledge of the excitation forces; instead it applies the assmption that the forces are ncorrelated, distribted over

5 the entire strctre and have flat broadband spectra. Secondly, since the tested strctre is in its typical operational regime, all bondary conditions and the load levels are correctly reprodced: these conditions are very difficlt to flfill in the laboratory tests. his especially important for the aeroelastic damping estimation that varies with wind speed, wind direction, rotor speed and the blade pitch. he following expression relates the (linear) response of the strctre to the excitation forces: x ( ω) = H( ω) f ( ω), (6) where x(ω) is the vector of the response spectra, f(ω) is the vector of the excitation spectra and H(ω) is the freqency response fnctions (FRF) matrix. From modal analysis theory, it is known that FRF matrix contains all necessary information to extract modal parameters. Applying simple algebra one can obtain G xx ( ω) = H( ω) Gff ( ω) H ( ω), (7) where G xx (ω) is the response crossspectra matrix and G ff (ω) is excitation cross-spectra matrix. (.) H stands for matrix Hermitian (conjgate transpose). Assming the forces are ncorrelated, distribted over the strctre and having flat broadband spectrm, its crossspectrm matrix becomes (ω) I and H G ff G xx ( ω) H( ω) H ( ω). (8) his proves that, if the excitation assmptions flfilled, the response crossspectrm matrix contains the fll information reqired to obtain (n-scaled) modal model of the system. Excitation de to wind trblence flfills the abovementioned assmptions, which makes the application of OMA to standstill wind trbine a straightforward task. Paper [] proves the feasibility of the method. However, the application of OMA to operational wind trbines is not simple. It is being considered in the next sections.... Violation of the ime invariance assmption One of the fndamental assmptions behind any experimental modal analysis H techniqes is that the strctre nder test mst not change dring the test (so-called strctre invariance). It is not the case for operational wind trbines: the rotation of the rotor mst be somehow taken into accont. he effect of rotor rotation manifests itself in the eqation of motion: the mass, stiffness and gyroscopic force matrices become time-dependent. Formlating and solving the eigenvale problem for this case lead to time-dependent eigenvales and eigenvectors which become meaningless as modal parameters. Fortnately, so-called Coleman coordinate transformation (also known as mlti-blade coordinate transformation) allows one to eliminate time dependency of the system matrices, ths converting the original timevarying eigenvale problem to a timeinvariant one. he modal parameters: modal freqencies, damping and mode shapes are then obtained by solving the corresponding eigenvale problem. Stdy [] extends this approach to experimental modal analysis. Forward Coleman transformation is applied to the data measred on the wind trbine blades, which is then combined with responses measred on the tower. he OMA methods are then applied to the transformed data, reslting in modal freqencies, damping and mode shapes. Backward Coleman transformation is finally employed for the mode shapes for their visalization.... Violation of the excitation assmptions Analyzing interaction between wind trblence and rotating blades [3], it is possible to show that the aerodynamic forces do not flfill OMA assmptions: first of all the forces acting at different parts of the blades are correlated arond fndamental freqency and its harmonics. Secondly the forces have periodic natre which manifests itself by peaks on force freqency spectra. he peaks are located at the fndamental freqency and its harmonics and have thick tails which narrows the regions where OMA assmptions are valid.

6 Amplitde [dg] In [] a carefl experiment planning is sggested as a tool to avoid the freqency regions where OMA assmptions are not flfilled. 3 Reslts 3. Experimental Modal Analysis Reslts ime domain closed-loop system identification methods (CLID) are applied to both simlated data, sed to verify loads and to check identification methodologies, and measrement data from an Ecotècnia wind trbine sing PRBS signals as defined in section... Figre and 3 show the PRBS excitation signals added to the collective pitch and generator torqe demand following the scheme presented in Figre time [s] PSD -,. basic and filtered PRBS signal on pitch angle 4 - pitch speed As explained in section, Closed-loop identification techniqes are sed to identify open loop models. Given the identified models, the corresponding freqency and damping of the first tower fore-aft and sidewards mode and the first drive train mode of the open-loop wind trbine can be compted at different wind speeds. ime and freqency validation methods are sed to evalate each method. As first step, closed-loop identification techniqes are applied to (excited) inpt/otpt data from aeroelastic simlations. Simlations show that no significant loads were indced on the trbine, the excited pitch demand had acceptable speed and acceleration, and - basic filtered pitch acceleration freqency [Hz] time [s] time [s] Figre.: PRBS excitation signal on collective pitch. Amplitde [m] 5 basic and filtered PRBS signal on generator torqe time [s] PSD freqency [Hz] basic filtered Figre 3: PRBS excitation signal on generator torqe. the electric power remained within acceptable limits. As second step, stdies on the closedloop identification methods are carried ot sing simlation data. Since information abot the controller and the exact excitation signals sed (rө and r g from Figre ) is not given, the, and demonstrate to be the most promising methods for wind trbine applications. 3.. he measrement campaign he same closed-loop identification techniqes are applied sing real (excited) inpt/otpt data collected from measrements on Alstom ECO 3MW wind trbine. he measrement campaign was performed at below rated wind speeds varying between 4 and 8m/s. he control inpts, collective pitch demand and generator torqe demand, have been simltaneosly excited with the PRBS signals s in order to make the identification of the transfer fnctions from these inpts to the otpts generator speed and tower top fore-aft and sidewards velocities possible. he inpt/otpt measrement data collected is smmarized in the following table:

7 Generator speed Ω rpm ower top fore-aft acceleration ower top fore-aft acceleration v& fa m/s m/s v& sd Excited blade pitch angle demand ө Excited blade pitch angle demand g deg m Wind speed at nacelle V nac m/s Lin. 5m/s able.: Signals stored from the real wind trbine Experience shows that working with tower top velocities improves the qality of the identified models arond the first tower modes. Hence, for the estimation of the tower modes, the otpts v& and v& are integrated to velocities v nod and v nay. For measrement time series are available, each taken dring partial load operation. De to the fact that each of these for measrements cases contains some irrelevant information from the identification point of view, they haven been concatenated as indicated in the following table. est case Data Mean length (Vnac) Prpose est 459s 5m/s ident.m/s est 3s m/s Valid.m/s est 3 65s 6.69m/s Ident.m/s est 4 983s 6.585m/s Valid.m/s able.: Measrement time series from the real wind trbine As can be seen from the able, est and have the same mean wind speed. Hence, est data can be sed for model identification, while est can be sed as validation data at m/s. he same hold for est 3 and 4, where mean wind speed is m/s. 3.. ower First fore-aft mode identification In order to estimate the tower first fore aft modal freqency and damping, the transfer fnction from pitch angle demand ө to the tower top fore-aft velocity v nod,.is identified. For identification the test set est and test 3 are sed. Figre 4 compare the bode plots of the identified models at m/s with the linearized model (indicated as Lin. mod.) at 5m/s. fa sd Figre 4.: Bode plot of the identified tower fore-aft models at mean wind speed of m/s and linearized model at 5m/s From Figre 4, it can be observed that the identified models are very well comparable to the l models arond the first tower freqency. Given the identified models, the corresponding freqency and damping are compted as explained in section..4. he modal freqencies and logarithmic decrements, compted from the identified modes are compared to those obtained from the linearized models at 5 and 7m/s. Wind [m/s] Method Freq [Hz] Log.decr [%] 5 Lin. Mod Lin. mod able 3.: Freqency and logarithmic decrement of the tower first fore-aft mode he validation reslts, based on sets est and est 4, are smmarized in the following table. Wind [m/s] Method VAF PEC (x -5 ) R ix able 4.: Validation reslts for identified models of the tower first fore aft. As can be seen from able 4, the validation reslts indicate that all models have comparable high accracy. R ix (x - )

8 3..3 ower First side to side mode identification Similarly, to estimate the tower first side to side modal freqency and damping, the transfer fnction from generator torqe demand g to the tower top side to side velocity v nay is identified. ext figre shows the comparison of the bode plots of the identified models at m/s with linearized model at 7m/s First drive train mode Finally, the first drive train freqency and damping are estimated from the identified transfer fnction from the generator torqe demand g to the generator speed Ω. ext figre shows the Bode plots of the transfer fnctions identified with the, and method, compared to the linear model obtained from the aerolastic code. Lin. 7m/s Lin. 7m/s Figre 5.: Bode plot of the identified tower side to side models at mean wind speed of m/s It can be observed the good overlap between the identified models and the linearized model. hose similarities are qantified in terms of freqency and logarithmic decrement in the following table. Wind [m/s] Method Freq [Hz] Log.decr [%] 5 Lin. mod Lin. mod able 5.: Freqency and logarithmic decrement of the tower first sidewards mode he time domain validation reslts are shown in able 6. d PEC Method VAF R R Win [m/s] (x -5 ) ix ix.8 8.9x able 6.: Validation reslts for id entified models of the tower first sidewards mode Figre 6.: Bode plot of the identified first drive train models at mean wind speed of m/s As can be observed in the figre above, the identified drive-train freqency is abot % higher than the linearized model. Wind [m/s] Method Freq [Hz] Log.decr [%] 5 Lin. mod Lin. mod able 7.: Freqency and logarithmic decrement of the first drive train mode. Comparing the linearized model obtained with the aerolastic code with the identified model sing method, better estimation is obtained. In any case, the drive train freqency is not well present in the inpt-otpt data. In contrast with the freqency domain reslts showed in able 7, the ime domain validation methods shows excellent reslts. Wind [m/s] Method VAF PEC (x -3 ) R ix able 8.: Validation reslts for identified models of the first drive train mode R ix

9 Campbell diagram, fll dataset D OW yaw 9 OC OW tilt IW bw 8 IW fw OW yaw OW tilt 7 OC IC O3W Modal freqency, Hz IW bw IW fw I3C p p 3p Wind speed, m/s Figre 7.: Modal freqency as a fnction of wind speed. Letters in the mode name: O otof-plane, I inplane, C -- collective, W whirling; bw backward; fw forward; D drive-train mode; p, p, 3p fndamental freqency and its first two harmonics. A jstification for those differences cold be either that the drive-train freqency is not well represented in the data de to the presence of a drive-train damping filter existing in the control or that in reality, the drive train is less flexible than in the lineraized model obtained from the aerolastic code. Frther experiments needs to be performed to clarify the exact reason of this divergence. 3. Operational Modal Analysis Reslts In order to ensre feasibility of the application of OMA to operational wind trbine, a series of nmerical experiments were condcted. Using commercial aeroelastic software, the acceleration time histories for the following locations were synthesized: - points on the different blade radii; - hb; - points on the different heights of the tower. and then sed as the inpt to commercial OMA software, where the modal parameters were extracted. Figre 7 presents the obtained modal freqency for the rotor-related modes as a fnction of the wind speed (Campbell diagram). ote, sometimes it was not possible to extract some of the modes for specific wind speeds. Confidence intervals (shown as vertical line segments) were fond to be a sefl tool for jdging applicability of OMA to specific operational conditions (wind speed/pitch/rotor RPM). Figre 8 shows the Campbell diagram for modal damping (in-plane and ot-of-plane rotor-related modes). Similar graphs were obtained for the damping, and for modal parameters of the tower-related modes. Using backward Coleman transformation, mode shapes were calclated and visalized (Figre 9); this visalization played an important role in mode identification. Work is crrently ongoing to apply OMA on a real wind trbine. he data was accompanied with the time histories for azimth and pitch angles, rotor RPM, wind speed and direction, etc. he acceleration data from the blades were sbjected to Coleman transformation

10 Modal damping (rotor in-plane modes) vs wind speed 6 Modal damping (rotor ot-of-plane modes) vs wind speed 9 8 IW bw IW fw IC IW bw IW fw I3C 5 OW yaw OC OW tilt OW yaw OW tilt OC O3W Modal damping, % 5 Modal damping, % Wind speed, m/s 5 5 Wind speed, m/s Figre 8. Modal damping as a fnction of wind speed. op: in-plane modes; Bottom: ot-of-plane modes freqency-domain validation is possible de to the lack of information abot the all excitation signals, Freqency domain comparison can be performed sing linearized models at mean wind speeds of 5 and 7m/s. his comparison shows very good overlap arond the first tower fore-aft and side to side freqencies, bt some discrepancies are fond at first drive train freqencies. Frther experiments need to be performed to clarify the exact reason of this divergence by either increasing the generator torqe excitation amplitde or by de-activating the drive-train filter in the controller. Figre 9.: Visalization of mode shape 4 Conclsions heory and reslts of two different system identification methods for estimating modal parameters of a wind trbine in operation have been presented. In the first method, additional excitation on the controllable inpts of the trbine (pitch and/or generator) is needed. hese signals are designed in sch a way that accrate models are identified and no nacceptable trbine loads occr. In order to validate the identified open-loop models, both time-domain validation methods and freqency-domain comparisons to linearized aeroelastic models are made. he reslts show good match in freqency and damping ratio for a freqency range p to Hz. he time domain validation indexes indicate in all cases good model qality. Althogh no In the second method, only otpt measrements were sed. A feasibility stdy has been performed on simlation data in order to investigate the possibility of sing OMA to identify the dynamic characteristics of a wind trbine nder operation. OMA techniqes are applied sing time domain response data obtained from simlations carried ot with an aerolastic code. Response data is obtained at the locations coinciding (or located close to) ftre real wind trbine measrement locations. Reslts presented as Campbell diagrams show promising applicability of OMA techniqes in an operating wind trbine. Major differences between both methods are mainly the freqency range that can be identified, the eqipment needed for implementation and the modal information extracted. he se of PRBS methods, allows extracting the transfer fnctions directly, which are sed in control design. However, limitations on the actators bond the identification freqency range.

11 On the other side, OMA techniqes allow to extract the mode shapes. However, dedicated eqipment is needed to extract the relevant data. At last, sing those methods, the modal parameters estimated can be sed for either improving the existing control loops, for achieving additional fnctionality by designing new control strategies for fatige redction or for pdating the existing FEM and mltibody models. References [] Bialasiewicz, J. (995): Advanced System Identification echniqes for Wind rbine Strctres. Report REL/P , REL. Prepared for the 995 SEM Spring Conference, Grand Rapids, Michigan, USA. [] Marrant, B. and. van Holten (4): System Identification for the analysis of aeroelastic stability of wind trbine blades. Proceedings of the Eropean Wind Conference & Exhibition, pp _benjaminmarrant_.pdf [3] Hansen, M.H., K. homsen, P. Fglsang and. Kndsen (6): wo methods for estimating aeroelastic damping of operational wind trbine modes from experiments. Wind Energy, 9(--): [4] ovak, P.,. Ekelnd, I. Jovik and B. Schmidtbaer (995): Modeling and control of variable-speed wind-trbine drive-system dynamics. IEEE Control Systems, 5(4): [5] Ljng, L. (999): System Identification. heory for the User. Prentice Hall. [6] van den Hof, P. and X. Bombois (4): System Identification for Control. Delft Center for Systems and Control, U-Delft. Lectre notes, Dtch Institte for Systems and Control (DISC) [7] van den Hof, P. and M. Gilson (): Closed-loop system identification via a tailor-made IV method. Proceedings of the 4th Conference on Decision and Control. Orlando, Florida, pp erfiles/gilsonvdhof-cdc.pdf [8] Van Overschee, P. and B. De Moor (997): Closed-loop Sbspace System Identification. Proceedings of the 36th Conference on Decision and Control. San Diago, California, USA. [9] Qin, S. and L. Ljng (3): Closed- Loop Sbspace Identification with Innovation Estimation. Proceedings of the 3th IFAC Symposim on System Identification, pp [] Ljng, L. and. McKelvey (996): Sbspace identification from closed loop data. Signal Processing, 5: [] S. Chahan, M.H. Hansen, D. cherniak (9), Application of Operational Modal Analysis and Blind Sorce Separation / Independent Component Analysis echniqes to Wind rbines, Proceedings of XXVII International Modal Analysis Conference, Orlando (FL), USA, Feb. 9 [] D. cherniak, S. Chahan, M. Rosseti, I. Font, J. Basrko, O. Salgado (), Otpt-only Modal Analysis on Operating Wind rbines: Application to Simlated Data, to appear in Proceedings of Eropean Wind Energy Conference, Warsaw, Poland, Apr.. [3] D. cherniak, S. Chahan, M.H. Hansen (), Applicability Limits of Operational Modal Analysis to Operational Wind rbines, Proceedings of XXVIII International Modal Analysis Conference, Jacksonville (FL), USA, Feb.