# Wind Turbine Power Curve Modeling with a Hybrid Machine Learning Technique
## 1 Introduction
In [20; 21], support vector regression (SVR) and Gaussian process (GP) were employed to estimate the real WTPCs. Moreover, GP was also used to obtain probabilistic WTPC in [21; 22]. In [23], [PERSON] et al. proposed two Bayesian-based models, heteroscedastic and robust spline regression models, to fit deterministic and probabilistic power curves in different seasons, respectively. They also proposed two asymmetric spline regression models to obtain accurate power curves in different wind farms and different seasons  
Figure 1: A typical wind turbine power curve. in [9]. Besides, monotonic regression [24], K-nearest neighbor model (KNN) [25], adaptive neuro-fuzzy interference system (ANFIS) [26], fuzzy based models [27], and copula model [28] were also taken to solve the problem of power curve modeling. From the above literature review, it can be found that only one power curve model is selected and used to fit the real WTPC with the measured wind data. However, due to the complex expression of WTPC or complex nonlinear relationship between wind speed and power output, one model cannot describe them comprehensively. In many applications, such as wind speed forecasting [29] and load forecasting [30; 31], it has been proven that a combination of several models will perform better than single models. In power curve modeling, there is no paper that takes advantage of different power forecasts generated by several power curve models. Besides, it is reported that there are many outliers in the collected wind data [32; 33; 34]. They have adverse effects on the learning process of power curve models and prevent us from obtaining accurate WTPCs [34]. So, it is essential to process these outliers in the original wind data first. In this paper, a hybrid wind turbine power curve modeling technique is proposed. Firstly, fuzzy c-means clustering (FCM) is employed to detect outliers. In each cluster, if the distance between the sample and cluster center is larger than a threshold, the sample will be signed as an outlier. The outliers will be removed from the original wind data. Secondly, with the above processed wind data, three types of extreme learning machines, original extreme learning machine (ELM) [35], weighted regularized extreme learning machine (WELM) [36], and outlier-robust extreme learning machine (ORELM) [37], are employed to get the power forecasts. Finally, SVR [38] is used to generate the final forecasts, which are the combination of the forecasts obtained from the above three ELM-based models. The performance of the proposed hybrid model is compared with some popular parametric and nonparametric models on different wind turbines. The results show that the proposed hybrid model can produce a more accurate power forecast at a given wind speed, resulting in a better power curve. The organization of the paper is described as follows. Section 1 is the introduction part. Some popular power curve models are introduced briefly in Section 2. Section 3 presents the methodologies related to the proposed hybrid model and the proposed strategy for power curve modeling. The power curve modeling results of different wind turbines are shown in Section 4. Section 5 concludes the whole paper.