# Wind Turbine Power Curve Modeling with a Hybrid Machine Learning Technique
## 3 Proposed Wind Power Curve Model
### Proposed Strategy for Wind Power Curve Modeling  
In our collected wind data, there are many outliers, which may be caused by over dating, pitch malfunction, pitch controller malfunction, wind speed under reading, dirt, bugs or icing on blades, and down rating, and so on. [42]. So, it is essential to detect and remove those outliers in our collected wind data. In this paper, several steps, which are described in Figure 2, are taken to generate accurate wind power curves.  
Step 1: Clustering the collected wind data. Different environmental conditions or different working conditions lead to different patterns and characteristics of the collected wind data. Here, FCM is employed to divide the data into different clusters. The samples in the same cluster may have some common characteristics.  
Step 2: Detecting and removing outliers. In a certain cluster, Mahalanobis distance is employed to measure the distance between the sample and cluster center. Generally, outliers will be far from normal samples, and also farther from the cluster center than normal samples. So, the sample will be considered as an outlier when the distance between the sample and cluster center is larger than a given threshold. Then, the detected outliers will be removed from the data. The Mahalanobis distance can be computed by  
\[M_{dist}=(x-\mu)\Sigma^{-1}(x-\mu)^{\top} \tag{24}\]  
where \(x\) is the sample in the observed cluster, \(\mu,\Sigma\) are the corresponding cluster center and covariance of all samples in the same cluster.  
Step 3: Training ELM-based power curve models. After removing the outliers from the collected data, the processed data is employed to train different wind power curve models. However, one cannot ensure that all outliers are detected and removed from the collected wind data. So, some unobvious outliers may hide in the processed data. It is wise to use robust wind power curve models to eliminate the adverse effect of hidden outliers on the power curve modeling. Moreover, considering the efficiency of ELM, the original ELM and its two robust variants are selected as basic power curve models to describe the nonlinear relationship between wind speed and power output. The number of hidden nodes in ELM-based models greatly affects their performance. So, in their training phases, validation sets are employed to help select the optimal model parameters, which can be obtained when the forecasting error on a validation set reaches its minimum.  
Figure 2: The flowchart of the proposed hybrid model.  
Step 4: Producing deterministic wind power curve. Occasionally, a single model is unable to describe the complex relationship comprehensively. So, in this paper, alongside the wind speed, the wind power forecasts on the validation set obtained in Step 3 are also used as inputs to train a regression model, SVR. Namely, SVR is utilized to approximate the function \(f(\cdot)\) in the following equation,  
\[P_{real}=f\Big{(}S,P^{\prime}_{elm^{\prime}}P^{\prime}_{welm^{\prime}}P^{\prime} _{orelm}\Big{)}+\varepsilon \tag{25}\]  
where \(P_{real}\) is the real wind power, \(P^{\prime}_{elm^{\prime}}\), \(P^{\prime}_{welm^{\prime}}\), \(P^{\prime}_{orelm}\) denote the forecasted wind power obtained by ELM, WELM, and ORELM, respectively, at wind speed \(V\), \(\varepsilon\) is the error term. Then, at any unknown wind speed, the corresponding wind power forecasts can be obtained using the trained SVR. Thus, a deterministic wind power curve can be derived.  
**4. Wind Turbine Power Curve Modeling in Different Wind Farms**  
In this section, to evaluate the performances of different power curve models under various geographical environments, a comparative study is conducted in different wind farms.