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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Advanced control concepts' taking place on Wednesday, 12 March 2014 at 11:15-12:45. The meet-the-authors will take place in the poster area.

Jordi Hernández Albà ALSTOM Energías Renovables España S.L. and Universitat Politècnica Catalunya, Spain
Co-authors:
Jordi Hernández Albà (2) F P Marc Guadayol Roig (1) Vicenç Puig Cayuela (2)
(1) ALSTOM Energías Renovables España S.L. and Universitat Politècnica Catalunya, Vilanova i la Geltrú, Spain (2) Universitat Politècnica de Catalunya, Barcelona, Spain

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Abstract

Wind estimation using EKF and comparison with experimental data

Introduction

A realistic value of wind speed could be very useful to improve the performance of wind turbine controllers, either for scheduling or as an extra feed forward term. In addition, it could also be useful for fault diagnosis and fault-tolerant control of the wind turbine [5]. The objective of this work has been to design and implement a standard Extended Kalman Filter (EKF) based on simplified nonlinear models and compare the performance with experimental wind speed measurements. Although the EKF uses a simple model, the agreement with experimental data is significant, and shows great potential for a wind estimator.

Approach

Estimation of wind speed has already been addressed by several authors. The authors of [1], [2] use a detailed structural model to derive a wind speed estimator. Additionally, [3] also discusses the computation of wind estimation indirectly from the estimation of the aerodynamic torque. The wind speed is then obtained by inverting a nonlinear function.
Although more complex methods have been proposed for wind estimation [1], [2], the present work will only try to estimate the effective wind corresponding to a coherent wind over the rotor and compare such estimations with field measurements. The models used are in line with the type of models used for wind turbine fault diagnosis [5]. Although this is a highly idealized condition, it allows us to describe accurately enough the main dynamics needed for wind estimation using the EKF approach. The model consists of a flexible drive train, rotor inertia and a nonlinear model of the steady aerodynamics with constant wind speed over the whole rotor. The nonlinear equations of the proposed model are the following:

where the subindex G stands for generator, R for rotor and S for shaft. ω is the angular velocity, Q is torque, I is the inertia and B is the damping. Finally, Ks is the shaft stiffness.
Although we could have used a continuous (or hybrid) EKF implementation [4], it is much simpler to try an Euler forward discretization and then apply a discrete-time EKF. The main advantage of such approximation is the simplicity of implementation. With such discretization, the previous equations become:

The nonlinear functions are functions of the power coefficient Cp(λ, β), which is a function of the tip-to-speed ratio λ and the collective pitch angle β. This coefficient is implemented as a 2D look-up table. The EKF also requires the derivatives of such nonlinear functions. Computing the derivatives is a little bit more involved, due to numerical noise. In this paper, derivative computation has been addressed fitting to a look-up table that contains the numerical derivatives.

Main body of abstract

To assess the validity of the formulation and also to tune the weights of the EKF, turbulent simulations using a nonlinear aeroelastic code have been run. However, these simulations were atypical: they used a coherent wind speed but with longitudinal turbulence corresponding to the Normal Turbulence Model (NTM) of the IEC 61400-1 standard. The motivation for such a particular wind speed was to first test the EKF performance in an ideal situation. Note that although the wind speed is simplified, the structural detail of the aeroelastic code is much higher than the simplified model used by the EKF. Although such conditions are an obvious simplification, they have been useful to:
Verify that the nonlinear aeroelastic model can be conveniently modeled, at least for our purposes, by the equations {1}.
Verify that the whole EKF is working properly.
Tune appropriate design weights, which appear in the form of variance noises in the EKF. To make this tuning easier and allow an easy adaptation to different wind turbines, the system has been previously scaled to nominal values.
The results with such ideal conditions are excellent, but this is not a surprise because of the specific characteristics of the wind field used in the simulation. Figure {3} show the estimation of the rotor speed. Clearly the estimation follows very well the real (simulated) rotor.

More interesting is the comparison between the estimated wind speed and the simulated one (figures {{4}, {5}}). The agreement again is excellent.


However, the main objective of the project was to assess if such wind estimations could be used in a real turbine, at least as a secondary measurement. Before showing such comparisons, it is instructive to review our assumptions:
Coherent wind speed. Acceptable agreement is only expected in regions of operation without strong wind asymmetries (low wind shear, low wind misalignment, etc.).
No model mismatch.
The comparison has been done using data from an ALSTOM Haliade 150. A representative result is shown in figure {6}. The wind estimation is compared to a wind measurement from a sonic anemometer mounted on the nacelle.

Even with such strong assumptions, there is a reasonable agreement between measured wind speed and estimated wind speed. In particular, the wind estimation follows quite well the low-frequency component of the wind measurement. The main differences lie in the high frequency range. The “high” frequency noise observed in the wind speed measurement is mostly related to the 3p effect and the 1st fore-aft tower movement. The 1st fore-aft motion could possibly be estimated by the EKF if a model of the 1st mode of tower motion had been included in the model. There are additional differences, which may be explained by the locality of wind measurement and the simple model used by the EKF. Even in this case, the wind estimation is quite good, and it seems possible to consider the application of such estimation by the wind turbine controller. In fact, in order to apply these results in a real turbine, the EKF has been directly implemented in the wind turbine controller, leading to the possibility to use it in the field.

Conclusion

This work discusses state estimation of a wind turbine using nonlinear models. State estimation is one of the basic components, sometimes forgotten, of many advanced control strategies. Many of them rely on the knowledge of hidden states. It is also very interesting from the point of view of fault detection, and most notably, fault isolation. At the same time, good performance of the estimator is an indirect indication of a correct model, which is always very comforting for the wind turbine designer.
The first step has been to use a simplified but nonlinear model of the wind turbine, which assumes a constant axial wind speed over the rotor. This is a common model in the wind turbine control literature but has several limitations. Even with such, aeroelastic simulations show a significant agreement between the simulated and estimated wind speed over the whole range of operation, at last with a coherent wind field. This confirms the idea that EKF can be a powerful tool in wind turbine control design.
Of more interest is the comparison between measured and estimated wind speed. Although the comparison is limited by a high number of uncertainties, the results show a promising agreement between them. This is also very reassuring from a design point of view, because it is implicitly confirming the accuracy of the nonlinear model used by the nonlinear aeroelastic code.
The good fit between estimated and measured wind speed can be profitably used by the wind turbine controller, either to improve wind turbine performance, to improve controller scheduling or for to fault detection.


Learning objectives
EKF is a powerful to estimate unknown wind turbine states and disturbances.
Comparison between measured and estimated values of wind speed is promising, even with the strong assumptions that have been made.
More detailed models are necessary to obtain more consistent wind estimation. The performance of an EKF must be assessed with a statistically significant sample of experimental data.



References
[1] S. Kanev and T. Engelen, "Wind turbine extreme gust control," Wind Energy, vol. 13, pp. 18-35, 2010.
[2] C. Bottasso y A. Croce, «Cascading Kalman Observers of Structural Flexible and Wind States For Wind turbine Control,» Milano, Italy, 2009.
[3] K. Östergaard, P. Brath y J. Stoustrup, «Estimation of effective wind speed,» de The Science of Making torque from Wind, 2007.
[4] P. Novak, T. Ekelund, I. Jovik y B. Schmidtbauer, «Modeling and Control of VAriable-Speed Wind Turbine Drive-Train dynamics».
[5] Odgaard, P. F., Stoustrup, J., & Kinnaert, M. (2013). Fault-tolerant control of wind turbines: a benchmark model. IEEE Transactions on Control Systems Technology, 21, 1168–1182.