# Forecasting of Wind Turbine Synthetic Signals Based on Nonlinear Autoregressive Networks

Cristian Blanco, J. Enrique Sierra-García, Matilde Santos

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Cristian Blanco, J. Enrique Sierra-García, Matilde Santos. Forecasting of Wind Turbine Synthetic Signals Based on Nonlinear Autoregressive Networks. 19th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2023, León, Spain. pp.316-324, 10.1007/978-3-031-34107-6_25. hal-05498071

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# Forecasting of Wind Turbine Synthetic Signals
Based on Nonlinear Autoregressive Networks

Cristian Blanco¹(✉), J. Enrique Sierra-García², and Matilde Santos³

¹ ETSI Informática, UNED, Madrid, Spain
cblanco177@alumno.uned

² Department of Electromechanical Engineering, University of Burgos, Burgos, Spain
jesierra@ubu.es

³ Institute of Knowledge Technology, Complutense University of Madrid, Madrid, Spain
msantos@ucm.es

**Abstract.** The importance and future prospects of offshore wind power generation invite great efforts and investments to make it an efficient technology. A crucial aspect is the development of efficient control strategies, which in many cases require models to identify time accurately the state of the turbine at a given. These models must be simple enough not to increase the computational complexity of the control algorithm while being able to capture the nonlinearity and coupling of the wind devices. In this work, we exploit the possibility of using neural networks to identify a wind turbine control-oriented model to predict its power output. Two nonlinear autoregressive with exogenous inputs models, with different input variables, have been proposed, based on feedforward neural networks. Results are satisfactory in terms of model accuracy of an offshore 5MW WT even ruling out relevant variables.

**Keywords:** NARX neural networks · system identification · control-oriented model · forecasting · offshore wind turbine

## 1 Introduction

Offshore wind energy is experiencing an important growth with an increase of this kind of installation, up to 21% in 2021 [1]. Most of these offshore wind turbines are built in shallow water with fixed foundations, while floating turbines present significant challenges due to their greater complexity [2]. This complexity requires the use of models and control algorithms able to capture all dynamic effects to design and operate optimally the turbines. Besides, these controllers must be computationally cost efficient to operate in real time [3]. The main objectives of wind turbine control are to maintain safe operation, maximize power generation, mitigate fatigue loads on the structure, and avoid fault conditions [2].

Commercial wind turbines typically operate at variable speed, and use different control strategies depending on the operating regime [3]. The use of classical control
technics like PID (Proportional-Integral-Derivative) regulators based on a single input single output (SISO) scheme require multiple control loops to stabilize the structure. For more complex turbines, multiple-input multiple-output (MIMO) strategies that are able to capture the most critical dynamics are a must. It is in this context where the identification of the most important features of the turbine system is an important step, in order to design effective control strategies such as MPC (Model Predictive Control) or State Space based control.

Some researchers have worked on this approach. In [4], a MPC based control strategy to stabilize the power generation and reduce the dynamic loads in the structure of the 5-MW floating turbine [5], in the constant speed operation regime, is proposed. An internal linear model, identified from the results of a highly complex non linear model, is used to predict the system behavior and optimize the control signals. Another approach is to design a digital twin of a 1.5-MW turbine to monitor the state of the structure from the loads estimated with the twin [6]. The authors use a Kalman filter based linear model designed with operational data complemented by nonlinear simulations. This model allows estimating the state of the system at an instant of time with limited information about it. In a similar way, in [7] a monitoring system of a gear box based on data obtained from different wind farms is presented. Different machine learning (ML) and deep learning (DL) methods are used to design predictive models. The model based on deep neural networks performs the best. The use of neural networks to estimate turbine power generation is an interesting topic. In [8] an artificial neural network (ANN) is used to estimate the power generated by a five-turbines wind farm, and to propose optimized angles to reduce the wake effect on the turbines. Long short term memory (LSTM) neural networks have been shown as an effective tool to predict the power generation of the turbines in a wind farm [9]. The training of the networks is done using historical wind data and turbine power generation. In [10] and [11], an effective wind speed estimator based on neural networks is successfully used to improve the performance of a classical controller. These types of networks have also been used in the design of controllers as substitutes of complex and computationally costly strategies [12]. In [13] a blade pitch controller for a 7-MW turbine based on neural networks and reinforcement learning is designed, showcasing the potential of the neural network to both substitute other control strategies, and complement and improve their performance. An example of a MIMO that uses a complex autoregressive model based on simple neural networks is presented in [14], the autoregressive model is used to estimate important state-space variables of the system.

In this paper, the use of nonlinear autoregressive with exogenous input models (NARX) based on artificial neural networks (ANN) to identify nonlinear systems is studied using simulated data of a 5-MW turbine [5]. Two models with different input signals are compared. In the first model, the power generated is estimated at t instant using several key signals, including the wind speed, in past instants. For the second model, the wind speed signal is ruled out. It is considered interesting to compare the performance of both models given that the simulated wind speed data coming from Openfast [15] is usually not available in the typical commercial wind turbine, or the sensor measurement may present uncertainties or faulty behaviour. Therefore, having a model that does not rely on this information is interesting.
The paper is structured with a first section in which the turbine, the software, and the models used in the study are described. The data used to train the neural networks, as well as its structure, are also presented. Next, the tests performed to study the performance of the models and results comparison are presented and discussed. Lastly, the conclusions and possible future lines of study are set out.

# 2 System and Models Description

## 2.1 Wind Turbine Description

The wind turbine used is described in [16]. It is an offshore 5-MW wind turbine with a fixed pillar as support. – shows a summary of the key characteristics of the turbine (Table 1).

<table><caption>Table 1. Wind Turbine Characteristics</caption><tr><td>Rating</td><td>5 MW</td></tr><tr><td>Rotor orientation, Configuration</td><td>Upwind, 3 Blades</td></tr><tr><td>Control</td><td>Variable Speed, Collective Pitch</td></tr><tr><td>Drivetrain</td><td>High Speed, Multiple-Stage Gearbox</td></tr><tr><td>Rotor, Hub Diameter</td><td>126 m, 3 m</td></tr><tr><td>Hub Height</td><td>90 m</td></tr><tr><td>Cut-In, Rated, Cut-Out Wind Speed</td><td>3 m/s, 11.4 m/s, 25 m/s</td></tr><tr><td>Cut-In, Rated Rotor Speed</td><td>6.9 rpm, 12.1 rpm</td></tr><tr><td>Rated Tip Speed</td><td>80 m/s</td></tr></table>

This choice is particularly convenient since reliable simulation data for this turbine can be generated with Openfast software [15] in the validation tests, Test 19 in particular. Openfast is a software developed by NREL (National Renewable Energy Laboratory), formerly known as FAST (Fatigue, Aerodynamics, Structures, and Turbulence), used for wind turbine nonlinear simulation and multidisciplinary analysis.

This study uses data generated by Openfast to train the neural networks. Data of the wind speed is generated using the Turbsim [16], with an average speed of 12 m/s.

## 2.2 Neural Network Models Signals Description

The objective of this work is to study the possibility of modeling the power generation in the wind turbine using neural networks. An analysis of the correlation between the Openfast output channels is carried out and the most representative signals for the case study are selected.

The wind turbines variables considered for the neural model are presented in Table 2. They include the output power as the target, and as possible inputs, we will work with
<table><caption>**Table 2.** Key Signals for the Networks</caption><thead><tr><td>SIGNAL</td><td>UNITS</td><td>OPENFAST CHANNEL</td><td>INPUT/OUTPUT (MODEL)</td></tr></thead><tbody><tr><td>Wind Speed x component</td><td>[m/s]</td><td>Wind1VelX</td><td>Input (1)</td></tr><tr><td>Wind Speed y component</td><td>[m/s]</td><td>Wind1VelY</td><td>Input (1)</td></tr><tr><td>Wind Speed z component</td><td>[m/s]</td><td>Wind1VelZ</td><td>Input (1)</td></tr><tr><td>Blade Pitch</td><td>[°]</td><td>BldPitch1</td><td>Input (1 and 2)</td></tr><tr><td>Rotor Speed</td><td>[rpm]</td><td>RotSpeed</td><td>Input (1 and 2)</td></tr><tr><td>Rotor Torque</td><td>[kNm]</td><td>RotTorq</td><td>Input (1 and 2)</td></tr><tr><td>Generator Power</td><td>[KW]</td><td>GenPwr</td><td>Input/Output (1 and 2)</td></tr></tbody></table>

the wind speed Cartesian components, the angle of the blades (pitch), the rotor speed and its torque.

The output of the networks is the output power. Model 1 uses all the signals to train the networks, whereas in model 2 the wind speed signals are ruled out. The data are generated with an Openfast simulation for 3000 s, with time increments of 50 ms. In the rest of the article the models, for the sake of clarity, will be called model 7-signals, the first model, and model 4-signal the second one.

## 2.3 Neural Networks Description

The networks are feedback neural networks used to create the nonlinear autoregressive with exogenous input model. Figure 1 shows a typical NARX network. In this figure, x(t) is the exogenous input, y(t) is the autoregressive variable, W is the matrix of weights, and b the bias introduced.

The neural networks are generated with Tensorflow [17]. Both neural networks have the same macro structure. It has not been thoroughly optimized, but parameters that yield acceptable results from a set of values tested have been selected. The networks have one input layer of 10 artificial neuron units and an output layer with 1 standard unit, with a ReLu activation function.

The input data for the networks are the state vectors with the selected signals with a time window of a second, i.e. 20 temporal increments of 50 ms each. Thus the input has 20 state vectors. The network output is the estimated generator power.

Figure 2 shows a summary of the networks. The number of parameters of the input layer is the number of state vectors (20), times the number of signals (4/7), times the number of neurons (10), plus the number of outputs of each neuron to the next layer (10), for a total of 810 (4-signals model) and 1410 (7-signals model) parameters. The number of parameters of the output layer is the number of inputs from the previous layer (10), plus the output (1), for a total of 11 parameters.
<figure><img src="image_3.png" /><figcaption>Fig. 1. NARX Network Scheme [18]</figcaption></figure>

<table><caption>Fig. 2. Networks Structure Summary (Top – 7-signals, bottom – 4-signals)</caption><thead><tr><th>Layer (type)</th><th>Output Shape</th><th>Param #</th></tr></thead><tbody><tr><td>dense (Dense)</td><td>(None, 10)</td><td>1410</td></tr><tr><td>dense_1 (Dense)</td><td>(None, 1)</td><td>11</td></tr></tbody></table><p>Total params: 1,421<br>Trainable params: 1,421<br>Non-trainable params: 0</p><table><thead><tr><th>Layer (type)</th><th>Output Shape</th><th>Param #</th></tr></thead><tbody><tr><td>dense (Dense)</td><td>(None, 10)</td><td>810</td></tr><tr><td>dense_1 (Dense)</td><td>(None, 1)</td><td>11</td></tr></tbody></table><p>Total params: 821<br>Trainable params: 821<br>Non-trainable params: 0</p>

## 2.4 System Identification

To perform the system identification, the neural networks have to be trained. It is done using the Openfast generated data over 3000 s, with time increments of 50 ms. That is, there are 60,000 data points for each selected signal. A 60%, 20%, 20% split is performed for training, validation, and test sets. Since it is a time series, this division is done in chronological order. The performance over the test data set is shown in Fig. 3 and Fig. 4.

In Table 3 the values of the MAE (mean absolute error) and RMSE (root mean square error) that have been used as metrics are presented.
<figure><img src="image_4.png" /><figcaption>Fig. 3. Training Results 7-signals</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Training Results 4-signals</figcaption></figure>

<table><caption>Table 3. Training Performance Summary</caption><thead><tr><td>MODEL</td><td>MAE [KW]</td><td>RMSE [KW]</td></tr></thead><tbody><tr><td>7-SIGNALS</td><td>8.94</td><td>11.77</td></tr><tr><td>4-SIGNALS</td><td>4.23</td><td>7.81</td></tr></tbody></table>

As can be seen, both networks show good performance on the training data. Nevertheless, the second model stands out for the smaller errors it presents, even with fewer signals.
## 3 Discussion of the Results

Once the neural networks have been trained, the results of the tests that have been carried out with the two models defined above are presented. To compare the models performance with reliable data, the regression test data no. 19 of the Openfast software is used. This test dataset has data for the signals used in this study for a period of 60 s, with time sample of 50 ms. The data used for testing is different from the training data used during the validation of the networks.

The results of both models test are summarized in Fig. 5 and Table 4. The results are consistent with the training results. Both networks types show good performance.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Predicted generated power with the two models</figcaption></figure>

<table><caption>Table 4. Model 1 Results Summary</caption><thead><tr><td>MODEL</td><td>MAE [KW]</td><td>RMSE [KW]</td></tr></thead><tbody><tr><td>7-SIGNALS</td><td>39.76</td><td>67.60</td></tr><tr><td>4-SIGNALS</td><td><strong>21.93</strong></td><td><strong>40.99</strong></td></tr></tbody></table>

It is worth it to remark that the model with less exogenous inputs shows the best performance. Results are good and errors are within acceptable limits, although bigger than the ones obtained in the training process.

## 4 Conclusions and Future Works

The suitability of nonlinear autoregressive with exogenous inputs models based on feed-forward neural networks to estimate the generator power of a wind turbine is studied. Two models with different input signals are trained and used to compare their performance. The second model, with fewer inputs given that the wind speed is not used,
performs similarly compared to the first model. Both models give good results regarding the prediction of the output power. However, it is an interesting exercise given that the wind speed is a variable that might not be available or may be not reliable.

Even though the results when an abrupt variation of the signal is not desirable, this performance can be improved optimizing the hyper-parameters of the networks or even implementing different mechanisms as a function of these changes [19]. The number of state vectors considered as input to the networks is possibly one of such parameters that might be sensitive to the mentioned behaviour. Moreover, it could be interesting to modify or increase the Openfast signals used as inputs to improve the predictions. Lastly, a future line of study could also be to design a similar model specifically tailored to use as part of a model predictive controller.

**Acknowledgement.** This work was partially supported by the Spanish Ministry of Science, Innovation and Universities under MCI/AEI/FEDER Project no. PID2021-123543OB-C21.

## References

1. Council, G.W.E.: Global Wind Report 2022. GWEC, Brussels (2022)

2. Hu, R., Conghuan, L., Ding, H., Zhang, P.: Implementation and evaluation of control strategies based on an open controller for a 10 MW floating wind turbine. Renew. Energy **179**, 1751–1766 (2021)

3. Wright, A.D., Fingersh, L.J.: Advanced control design for wind turbines Part I: control design, implementation, and initial tests. NREL, Golden (2008)

4. Wakui, T., Nagamura, A., Yokoyama, R.: Stabilization of power output and platform motion of a floating offshore wind turbine-generator system using model predictive control based on previewed disturbances. Renew. Energy **173**, 105–127 (2021)

5. Jonkman, J., Butterfield, S., Musial, W., Scott, G.: Definition of a 5-MW reference wind turbine for offshore system development. NREL (2009)

6. Branlard, E., Jonkman, J., Dana, S., Doubrawa, P.: A digital twin based on OpenFAST linearizations for real-time load and fatigue estimation of land-based turbines. In: Journal of Physics: Conference Series, vol. 1618 (2020)

7. Wang, L., Zhang, Z., Long, H., Xu, J., Liu, R.: Wind turbine gearbox failure identification with deep neural networks. IEEE Trans. Industr. Inf. **13**(3), 1360–1368 (2017)

8. Sun, H., Qiu, C., Lu, L., Gao, X., Chen, J., Yang, H.: Wind turbine power modelling and optimization using artificial neural network with wind field experimental data. Appl. Energy **280**, 115880 (2020)

9. Zhang, J., Yan, J., Infield, D., Liu, Y., Lien, F.-S.: Short-term forecasting and uncertainty analysis of wind turbine power based on long short-term memory network and Gaussian mixture model. Appl. Energy **241**, 229–244 (2019)

10. Sierra-García, J.E., Santos, M.: Improving wind turbine pitch control by effective wind neuro-estimators. IEEE Access **9**, 10413–10425 (2021)

11. Sierra-García, J.E., Santos, M.: Deep learning and fuzzy logic to implement a hybrid wind turbine pitch control. Neural Comput. Appl. **34**(13), 1–15 (2021). https://doi.org/10.1007/s00521-021-06323-w

12. Blanco Fernández, C., Sierra García, J.E., Santos, M.: Control de un laboratorio de control de temperatura mediante redes neuronales recurrentes. XLIII Jornadas de Automática 193–200 (2022)
13. Sierra-García, J.E., Santos, M.: Redes neuronales y aprendizaje por refuerzo en el control de turbinas eólicas. Rev. Iberoamericana de Automática e Informática Ind. **18**(4), 327-335 (2021)

14. Alonso, A., Zabaljauregi, A., Larrea, M., Irigoyen, E., Sanchís, J.: Studying the use of ANN to estimate state-space variables for MIMO systems in a NMPC strategy. In: 17th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2022). SOCO 2022. Lecture Notes in Networks and Systems, vol. 531, pp. 464-473 (2022). https://doi.org/10.1007/978-3-031-18050-7_45

15. Jonkman, J., Musial, W.: Offshore Code Comparison Collaboration (OC3) for IEA Task 23 Offshore Wind Technology and Deployment. NREL, Golden (2010)

16. https://github.com/OpenFAST/openfast. National Renewable Energy Laboratory, https://git hub.com/OpenFAST/openfast. Accessed 1 Sept 2022

17. Abadi, M., et al.: Tensorflow: a system for large scale machine learning. In: OSDI, vol. 16, pp. 265-283 (2016)

18. Habibi, M.R., Hamid, B., Dragicevic, T.: Detection of false data injection cyber-attacks in DC microgrids based on recurrent neural networks. IEEE J. Emerg. Sel. Top. Power Electron. **9**, 5294-5310 (2010)

19. Sierra-García, J., Santos, M.: Switched learning adaptive neuro-control strategy. Neurocom- puting **452**, 450-464 (2021)