# Wind Turbine Power Curve Modeling with a Hybrid Machine Learning Technique
## 1 Introduction  
The sense of crisis brought about by the depletion of fossil energy has prompted the global energy revolution [1, 2]. Vigorously developing renewable energy is an important measure to protect the environment and meet the energy demand of social development [1, 2]. Recently, due to the advances in technology, and the stimulation of energy policies and environmental pressures, the proportion of renewable energy in the power system of many countries and regions has been rising [1, 2]. Wind power, as one of the clean and renewable energy sources, has received great attention from all countries in the world [1, 2, 3]. Currently, many researchers focus on studying the performance of different wind turbines due to the large-scale development and utilization of wind energy [1, 4]. Usually, a wind turbine power curve (WTPC) shown in Figure 1 can be used to describe the performance of wind turbines, namely the power output of a wind turbine at a specific wind speed [4]. When wind speed \(V\) is less than the cut-in wind speed \(V_{cut-in}\), the wind turbine does not work and no wind power is generated. When \(V\) is locatedin the interval \([V_{cut-in},V_{ratt}]\), the output power increases as the wind speed increases. The output power reaches a constant, the rated wind power \(P_{rated}\), when the wind speed is larger than the rated wind speed \(V_{rntad}\) but less than the cut-out wind speed \(V_{cut-out}\). The wind turbine will be shut down to avoid defects and damage when the wind speed is larger than \(V_{cut-out}\)[1; 5]. Often, the turbine manufacturer provides a theoretical WTPC, which is measured under ideal meteorological and topographical conditions [6]. However, due to the climate variability in the observed wind farm, the theoretical WTPC cannot describe the performance of a wind turbine accurately [7]. So, it is essential to estimate the actual WTPC from the real operational data of a wind turbine. Accurate WTPCs play important roles in wind power forecasting, wind turbine condition monitoring, wind energy potential estimation, and wind turbine selection, and so forth. [1; 8; 9]. Currently, there are two types of power curve estimation methods, parametric models and nonparametric models [10]. As for parametric models, they often consider the shape of power curves. Therefore, many S-shaped functions are employed to model WTPCs. They are the double exponential-based functions and logistic functions [1]. A simple double exponential function and an adjusted double exponential function were employed to model real WTPCs in [11; 12], respectively. Many types of logistic functions were employed to model WTPCs. In [13], a three-parameter logistic function (3-PLF) was used by the authors to evaluate the performance of the Gamsesa G90-2.0 MV wind turbine. Many researchers suggested using a four-parameter logistic function (4-PLF) to model WTPC [14; 15]. When the variable asymmetry factor is added into the above 4-PLF, a five-parameter logistic function (5-PLF) can be derived. And a 5-PLF can degenerate into a 4-PLF by letting the asymmetry factor equal 1 [1]. In [15; 16], a 5-PLF was used, while authors in [17] employed a logistic function with six parameters (6-PLF) to simulate WTPCs. Even in [10], [PERSON] et al. used a modified hyperbolic tangent (MHTan) with nine parameters to approximate the nonlinear relationship between wind speed and power output of a wind turbine. Unlike parametric models, nonparametric models do not consider the shape of WTPC. They only consider the complex nonlinear relationship between wind speed and wind power. Currently, many artificial intelligence-based models have been employed to learn the above complex nonlinear relationship. In [18], three different types of neural networks, self-supervised neural network, multilayer perceptron, and general regression neural network, were used, and their performances were also compared in power curve modeling. In [19], the authors showed that artificial neural network (ANN) generated a better power curve than some parametric models.