System Identification on Alstom ECO100 Wind Turbine

Transcription

1 System Identification on Alstom ECO00 Wind Turbine Carlo E. Carcangiu Alstom Wind 78, Roc Boronat Barcelona, Spain Stoyan Kanev ECN Wind Energy P.O. Box, 75LE Petten, the Netherlands Michele Rossetti Alstom Wind 78, Roc Boronat Barcelona, Spain Iciar Font Balaguer Alstom Wind 78, Roc Boronat Barcelona, Spain ABSTRACT Control algorithms for wind turbines are traditionally designed on the basis of linearized dynamic models. On the accuracy of such models depends hence the performance of the control, and validating the dynamic models is an essential requirement for achieving the optimum design. The aim of this wor is to identify, at different wind speeds, the dynamic model of a wind turbine in operation. Experimental modal analysis is the selected technique for system identification, and band-limited pseudo-random excitation signals are summed to the controlled inputs of the wind turbine system. Fairly good match is found in frequency and damping ratio for a frequency range up to Hz. The time domain validation indicates in all cases reasonable model quality. The frequency domain comparison carried out for selected wind speeds shows close overlap around the first tower fore-aft and side-to-side frequencies, even though some discrepancies are found at first drive train frequencies. Keywords: System Identification, Experimental Modal Analysis, PRBS, Wind Turbine Control. INTRODUCTION Control algorithms for wind turbines are traditionally designed on the basis of linearized dynamic models. On the accuracy of such models depends hence the performance of the control, and validating the dynamic models is an essential requirement for achieving the optimum design. The aim of this wor is to identify, at different wind speeds, the dynamic model of a wind turbine. Experimental modal analysis EMA system identification has been applied on the Alstom Eco00 Wind turbine in order to extract modal information at different operational conditions. Proper band-limited pseudo-random binary excitation signals PRBS have been carefully arranged to avoid the induction of undesired significant

2 loads on the tower and rotor, taing also into account the constraints of the actuators. Experimental modeling is an orthogonal approach to first principles physical modeling, where the phenomena observed in reality are modeled by using measured data from the operational wind turbine. To this end, system identification techniques are used to fit the parameters of a suitable mathematical model to the measured data as good as possible. For wind turbine applications, experimental modeling has only received limited attention in the literature. The application of exciter methods, where rather unrealistic direct and measurable excitation on several points on the blades is assumed, was investigated by Bialasiewicz []. Recently, research on modal analysis was performed within the framewor of the European research project STABCON - Stability and control of large wind turbines'', where both simulation studies and experimental results were included [2][3]. The simulation studies are based on blade excitations that are difficult to perform in practice. More realistic excitation signals were investigated at Risø National Laboratory, by using the blade pitch and generator to excite with harmonic signals the first two tower bending modes, even though the measurement of the decaying response was proved to be unsuitable for an accurate estimation of the damping [3]. The identification of openloop drive train dynamics from closed-loop experimental measurements on a fixedpitch variable-speed wind turbine is presented in [4], for control algorithm design purposes. Because the experimental modeling is based on data collected from a wind turbine during operation, i.e. with the controller operating, closed-loop system identification must be applied. Prior to the current wor, a detailed review has been hence carried out of the available closed-loop identification CLID approaches to wind turbine model identification, listed below: method [5], Indirect method [5], Joint Input/output method [5], Closed-loop instrumental variable method [6], Tailor made instrumental variable method [7], Closed-loop N4SID subspace identification [8],

3 Parsimonious subspace identification method [9], Subspace identification based on output predictions [0]. Initial studies using simulation data from both linear and nonlinear aeroelastic simulations have indicated the methods, and as most promising for wind turbine applications, with the method often outperforming the other methods. For that reason, and for the sae of space limitation, only the method is summarized in Section 2.. In order to identify accurate i.e. unbiased input-output models using the abovementioned system identification methods, it is necessary that the inputs are additionally excited by signals that are uncorrelated with the wind. How this can be achieved without introducing unacceptable additional loads will be discussed in Section 2.2. Moreover, special attention has also been paid on data-driven model validation, for which purpose several techniques have been developed and summarized in Section 2.3. A number of model validation methods are presented in Section 2.4. The experimental tests results are included Section 3, splitting tower and drive train modes. 2 METHODOLOGY 2. 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 turbine operates in closed-loop. The starting point of the method is the selection of a suitable model structure. For wind turbine applications, a simple auto-regressive-with-exogenous-input ARX model is proved to be sufficient. The ARX model has the following form A p. y = B p. u + e where y l R is a generalized output vector, u m R is the input vector, e l R is some unnown generalized disturbance signal representing the influence of the wind on the output measurements, is the moment of time, and A P R lxl and B lxm P R are matrix polynomials dependent on the unnown parameter P

4 A P = I + A q B P = B P = + B q [ A K, A, B K, B ], 0 na + A q 0, 2 + B q 2 2 nb + L+ A 2 na + L + B q nb na q, nb, 2 Above, q denotes the bacward time shift operator, i.e. y = y q. The goal is to estimate the model parameters p given input/output data{ u, y } N =. This is achieved in the following way. Given the ARX model structure, the one step ahead predictor for the output vector is formed yˆ = P. ϕ, ϕ = vec[ y, K y na, u, K, u nb] 3 where vec M is the vectorization operator which stacs the columns of a matrix into one vector. This predictor model is used for constructing the prediction error = y yˆ = y Pϕ 4 To estimate the unnown parameter matrix P, the following prediction error criterion is minimized with respect to P N V P = N 2 = An analytical expression can be obtained for the parameter matrix P that minimizes the prediction error criterion by using the fact that for given matrices of appropriate dimensions, the following expression holds X. Y. Z = Z T X. vec Y. 6 hence

5 = = = = N T T T N T P vec I y I N P vec I y N P vec P vec P V ϕ ϕ ϕ 7 giving = = = N T T N T T T y I N I I N P vec ϕ ϕ ϕ 8 The identified ARX model is then parameterized by this optimal parameter matrix P. It can be theoretically shown that the identified model is unbiased under reasonable assumptions [5]. 2.2 Excitation signal design Figure - System identification setup A schematic system identification setup is depicted in Figure. Typical inputs are the collective blade pitch angle θ and generator setpoint T g, and outputs are generator speed Ω and tower fore-aft v nod and sidewards v nay velocities or accelerations. The blocs K g and K θ in the feedbac loops represent the generator

6 and the pitch controllers, respectively, which are not required in the identification methods, presented in Section 2.. Time series of these typical inputs and outputs allow the identification of the transfer functions from θ to v nod, from T g to Ω, and from T g to v nay, from which the tower fore-aft, tower side-to-side and drive train dynamics can be analyzed. The frequency range where the models can be accurately identified depends on the bandwidth of the excitation signals: r θ on the blade pitch and/or r g on the generator. When the frequency and damping of the first tower mode need to be identified, the bandwidth should at least include the expected first tower frequency. When the first drive-train mode is needed, the excitation bandwidth must at least include the first drive-train frequency. Hence, the proper choice of excitation signals is ey-important for achieving informative experiment under reasonable amount of excitation. Two opposite objectives exist indeed, and a trade-off should 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 spectrum. On the other hand, the system limitations such as hardware limits, loads, etc. impose the use of low-energy, narrow bandwidth excitation. The design of excitation signals should therefore prescribe that a the signals remain within the hardware limits, b the additional loads are as small as possible, and c the dynamic models are still accurately identified. For the considered wind turbine specifically, the excitation signals r θ and r g have been designed in such a way, that no unacceptable loads are induced, the excited pitch demand has acceptable speed and acceleration, and the electric power remains within acceptable limits. To this end, the pitch excitation signal r θ is designed as a pseudo-random binary signal PRBS with amplitude of 0.5 degrees, filtered with a low-pass FIR filter with cutoff frequency of Hz, and an elliptic bandstop filter with 20 db reduction, db ripple, and stop-band of 30% around the expected first tower frequency 0.32 Hz. In this way, the pitch excitation does not excite the region around the expected first tower frequency, as well as frequencies above Hz.

7 the generator excitation signal r g is also designed as PRBS signal, but uncorrelated with the one used for pitch excitation, and with an amplitude of 3% of the rated signal, filtered with a lowpass FIR filter with cutoff frequency of 2 Hz, so that the excitation is concentrated in the frequency region up to 2 Hz. Simulations made with an aeroelastic code have demonstrated that these excitations do not introduce significant increment in loads. 2.3 Modal parameters estimation Once a model of the wind turbine is identified, there are different ways to extract modal parameters, such as the first tower and drive-train frequencies and damping. One way to do that is by performing model reduction on the identified mode, to reduce the model order, such as there is only one mode in a specified interval of interest where the frequency is expected to lie. For the considered wind turbine, the selected interval is [0.25, 0.40] Hz for the tower, and [0.7, ] Hz for the drive train. The retained mode is the mode with the largest participation factor. The frequency and damping of this mode are then selected from the reduced system. 2.4 Model validation methods Model validation is the process of deciding whether an identified model is reliable and suitable for the purposes for which it has been created. The following model validation methods have been used to chec the accuracy of the identified model: Variance-accounted-for VAF: this is a model validation index often used with subspace identification methods. Given the measured output y and the output predicted by the one step ahead predictor y ˆ, the VAF criterion is defied as VAF y y ˆ σ, = σ u 9

8 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 usually considered to represent a very accurate model. Prediction error cost PEC: this is the value of the prediction error cost function, defined above. The smaller the value, the better the model accuracy. Auto-correlation index R : when a consistent model estimate is made, the ix prediction error should be a white process, so that its auto-correlation function R τ should be small for non-zero τ, whereτ denotes the discrete time step. bnd For a given confidence level α e.g. α = 99%, a bound R α can be derived bnd such that for an accurate model the inequality R τ R α should hold for all τ. The index Rix is then computed as the square sum of the distance between bnd each value of the correlation function R τ and the bound R α, where only the values outside the bound are used. Cross-correlation index u R ix : in the closed-loop situation the prediction error will be correlated with future values of the input, but should be uncorrelated with past inputs when the model is consistent. The cross-correlation function R τ should u then be limited in absolute value for τ. The index u R ix is computed similarly to R ix. It is important to point out that the data set used for validating the models should be different from the data used for obtaining the model, as otherwise wrong conclusions could be drawn. When the data length is short, a rule of thumb is to use two thirds of the data for identification, and the remaining one third for validation. 3 RESULTS 3. Preliminary simulations Time domain closed-loop system identification methods CLID are applied to both simulations, used to verify loads and to chec identification methodologies, as well as to measurement data from an Alstom ECO00 wind turbine using PRBS signals as defined in Section 2.2.

9 Figure 2 and Figure 3 show the PRBS excitation signals added to the collective pitch and generator demand following the scheme presented in Figure. 0.5 basic and filtered PRBS signal on pitch angle basic filtered Amplitude [dg] time [s] 0 PSD 4 pitch speed 20 pitch acceleration ,0 0. frequency [Hz] time [s] time [s] Figure 2 - PRBS excitation signal on collective pitch. 500 basic filtered Amplitude [Nm] time [s] 50 PSD frequency [Hz] Figure 3 - PRBS excitation signal on generator.

10 As explained in Section 2, closed-loop identification techniques are used to identify open loop models. Given the identified models, the corresponding frequency and damping of the first tower fore-aft and side-to-side mode and the first drive train mode of the open-loop wind turbine can be computed at different wind speeds. Time and frequency validation methods are used to evaluate each method. As first step, closed-loop identification techniques are applied to excited input/output data from aeroelastic simulations. Simulations show that no significant loads were induced on the turbine, the excited pitch demand had acceptable speed and acceleration, and the electric power remained within acceptable limits. As second step, studies on the closed-loop identification methods are carried out using simulation data. Since no information about the controller and the exact excitation signals used r ө and r g is provided, the, and appear to be the most promising methods for wind turbine applications. 3.2 The measurement campaign The same closed-loop identification techniques are applied using real excited input/output data collected from measurements on Alstom ECO00 3MW wind turbine. The measurement campaign was performed at below rated wind speeds, varying between 4 and 8 m/s. The control inputs, collective pitch demand and generator demand, have been simultaneously excited with the PRBS signals in order to obtain the transfer functions from these inputs to the outputs generator speed and tower top fore-aft and sideward velocities. The input/output measurement data collected are summarized in Table. Table - Signals stored from the real wind turbine Generator speed Ω rpm Tower top fore-aft acceleration v fa m/s 2 Tower top fore-aft acceleration v sd m/s 2 Excited blade pitch angle demand ө deg Excited generator torque T g Nm Wind speed at nacelle V nac m/s

11 Experience shows that woring with tower top velocities improves the quality of the identified models around the first tower modes. Hence, for the estimation of the tower modes, the outputs v fa and v sd are integrated to velocities v nod and v nay. Four measurement time series are selected, each taen during partial load operation. Due to the fact that each of these four measurements cases contains some irrelevant information from the identification point of view, they have been concatenated. As indicated in the Table 2, Test and 2 have the same mean wind speed. Hence, Test data can be used for model identification, while Test 2 can be used as validation data at m/s. The same holds for Test 3 and 4, where the mean wind speed is m/s. Table 2 - Measurement time series from the real wind turbine Test case Data length Mean V nac Purpose Test 459 s m/s Ident. m/s Test 2 30 s 4.8 m/s Valid. m/s Test 3 65 s 6.2 m/s Ident. m/s Test s 6.5 m/s Valid. m/s 3.3 Tower First fore-aft mode identification In order to estimate the tower first fore aft modal frequency and damping, the transfer function from pitch angle demand to the tower top fore-aft velocity v nod is identified. For identification the test set Test and test 3 are used. In Figure 4 the Bode plots are compared of the identified models at m/s with the linearized model obtained from the aeroelastic code indicated as Lin. mod. at 5 m/s. From Figure 4, it can be also observed that the identified models are reasonably close to the models around the first tower frequency. Given the identified models, the corresponding frequency and damping are computed as explained in Section 2.4. The modal frequencies and logarithmic decrements, computed from the identified modes are compared to those obtained from the linearized models at 5 and 7 m/s Table 3.

12 Figure 4 - Bode plot of the identified tower fore-aft models at mean wind speed of m/s and linearized model at 5 m/s. Transfer: Collective pitch angle demand Nacelle x-velocity. Table 3 - Frequency and logarithmic decrement of the tower first fore-aft mode Wind [m/s] Method Freq [Hz] Log.decr [%] 5.0 Lin. Mod Lin. mod The validation results, based on sets Test 2 and Test 4, are summarized in the Table 4, indicating that all models have comparable high accuracy.

13 Table 4 - Validation results for identified models of the tower first fore-aft. Wind [m/s] Method VAF PEC x0-5 R ix u R ix x Tower First side to side mode identification Similarly, to estimate the tower first side to side modal frequency and damping, the transfer function from generator demand T g to the tower top side to side velocity v nay is identified. In Figure 5 the bode plots of the identified models at m/s with linearized model at 7 m/s are shown. Figure 5 - Bode plot of the identified tower side to side models at mean wind speed of m/s and linearized model at 7 m/s. Transfer: Generator torque Nacelle y-velocity.

14 A close overlap is observed between the identified models and the linearized model. Those similarities are quantified in terms of frequency and logarithmic decrement in the Table 5. The time domain validation results are shown in Table 6. Table 5 - Frequency and logarithmic decrement of the tower first sideward mode Wind [m/s] Method Freq [Hz] Log.decr [%] 5.0 Lin. mod Lin. mod Table 6 - Validation results for identified models of the tower first sideward mode Wind [m/s] Method VAF PEC x0-5 R ix u R ix First drive train mode Finally, the first drive train frequency and damping are estimated from the identified transfer function from the generator demand T g to the generator speed Ω. In Figure 6 the Bode plots of the transfer functions identified with the, and method are shown, compared to the linear model obtained from the aeroelastic code.

15 Figure 6 - Bode plot of identified first drive train models at mean wind speed of m/s and linearized model at 7 m/s. Transfer: Generator torque Generator speed As reported in Table 7, the identified drive-train frequency is about 0% higher than the linearized model. Comparing the linearized model obtained with the aeroelastic code to the identified model using method, a better estimation is obtained. In any case, the drive train frequency is not clearly evident in the input-output data. Table 7 - Frequency and logarithmic decrement of the first drive train mode. Wind [m/s] Method Freq [Hz] Log.decr [%] Lin. mod Lin. mod

16 In contrast with the frequency domain results showed in Table 7, the Time domain validation methods shows excellent results Table 8. Table 8 - Validation results for identified models of the first drive train mode Wind [m/s] Method VAF PEC x R ix u R ix An explanation for those differences could be either that the drive-train frequency is not well represented in the data due 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 linearized model obtained from the aeroelastic code. Further experiments needs to be performed to clarify the reasons of such discrepancies. 4 CONCLUSIONS Theory and results of an innovative experimental system identification method for estimating modal parameters of a wind turbine in operation is presented. In the mentioned method, additional excitation signals on the controllable inputs of the turbine pitch and/or generator are needed. These signals are designed in such a way that accurate models are identified, but preventing the occurrence of extra loads on the wind turbine. In order to validate the identified open-loop models, both time-domain validation methods and frequency-domain comparisons to linearized aeroelastic models are made. After preliminary simulations with aeroelastic models, an experimental campaign has been carried out on the ECO00 3 MW wind turbine for different below-rated operational conditions. Fairly good match is found in frequency and damping ratio for a frequency range up to Hz. The time domain validation indicates in all cases reasonable model quality. The frequency domain comparison carried out for selected wind speeds shows close overlap around the first tower fore-aft and side-to-side frequencies, even though

17 some discrepancies are found at first drive train frequencies. Further experiments need to be performed to clarify the exact reason of this divergence by either increasing the generator excitation amplitude or by de-activating the drive-train filter in the controller. The estimated modal parameters can be used for either improving the existing control loops, for achieving additional functionality by designing new control strategies for fatigue reduction or for updating the existing FEM and multibody models. ACKNOWLEDGEMENTS This wor has been partially performed by ECN Wind Energy within the SenternNovem long-term research project SusCon: a new approach to control wind turbines EOSLT0203, and partially within the InVent project-accó CIDEM COPCA. REFERENCES [] Bialasiewicz, J. 995: Advanced System Identification Techniques for Wind Turbine Structures. Report NREL/TP , NREL. Prepared for the 995 SEM Spring Conference, Grand Rapids, Michigan, USA. [2] Marrant, B. and T. van Holten 2004: System Identification for the analysis of aeroelastic stability of wind turbine blades. Proceedings of the European Wind Conference & Exhibition, pp [3] Hansen, M.H., K. Thomsen, P. Fuglsang and T. Knudsen 2006: Two methods for estimating aeroelastic damping of operational wind turbine modes from experiments. Wind Energy, 9--2: [4] Nova, P., T. Eelund, I. Jovi and B. Schmidtbauer 995: Modeling and control of variable-speed wind-turbine drive-system dynamics. IEEE Control Systems, 54: [5] Ljung, L. 999: System Identification. Theory for the User. Prentice Hall. [6] Van den Hof, P. and X. Bombois 2004: System Identification for Control. Delft Center for Systems and Control, TU-Delft. Lecture notes, Dutch Institute for Systems and Control DISC

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