# Solar Irradiance Forecasting Using Dynamic Ensemble Selection
## 1 Introduction  
Energy production plays a major role in modern societies, impacting the economy and the development of several countries [1]. Over the past years, energy production has primarily relied on the employment of fossil fuels, which are still the main energy production source [2]. However, fossil fuels are one of the primary emission sources of CO2, which also contributes to greenhouse effects and global warming [3]. Moreover, it is a non-renewable energy source, and it is being consumed more than it is produced. Alternatively, solar energy is an important renewable energy source that produces on average \(1.74\times 10^{17}\) W in 1 year, which is meets energy demands worldwide [4]. Solar energy is considered a promising alternative to fossil fuels. However, it has intermittent and volatile characteristics due to factors, such as precipitation, temperature, wind velocity, andatmospheric pressure [5, 6]. These volatile characteristics can produce voltage fluctuations, possibly leading to instability in the power grid if they are not taken into account [7]. Moreover, the integration of traditional power systems with renewable power sources requires a precise balance between the demand and supply of power [6, 8]. If the energy demand surpasses the energy supply, destabilization of the power grid can occur, resulting in power quality degradation or even grid damage. Conversely, if the demand is lower than the supply, energy will eventually be lost, and wastage can occur because of the possible high costs associated with the storage of solar energy [7]. Considering the prediction of the demand and supply, the strategic section of energy plants decides whether energy is purchased. Prediction errors can lead to extra charges for the final consumer [9]. Therefore, accurate forecasting of solar irradiance plays a major role in power grid systems, estimation of reserves, scheduling, congestion management, use of produced energy in the energy market, and reduction of energy production costs [5, 9, 10]. Traditional statistical methods, such as the autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA), are popular due to their simplicity and a well-defined Box and Jenkins methodology is used to select a suitable configuration of the model [11]. However, ARIMA models assume a linear correlation structure between forecasts and past data, which may underperform in the presence of nonlinear patterns. Considering that real-world data is often composed of a combination of linear and nonlinear patterns [12], and solar irradiance data present intermittent and volatile characteristics, the ARIMA models may perform worse than other methods in the literature [5, 13]. In contrast to linear statistical models, forecasting methods based on machine learning are more suitable for mapping nonlinear patterns [13] in data. Machine learning methods, such as artificial neural networks (ANNs) and support vector machines (SVMs), are flexible data-driven models and have been used in the irradiation forecasting context [13]. However, machine learning-based models can also present problems related to model misspecification, overfitting, and underfitting [14, 15, 16], which leads to a poor generalization capacity [17]. To overcome the limitations of single and machine learning models, one possible strategy is to combine the forecasts of several models through the employment of ensembles to improve the system's accuracy [18]. This strategy is promising because it reduces the risk of selecting an inappropriate model. In addition, it has the flexibility of the use of different combination strategies and different model generation methodologies [19]. Ensemble learning strategies are often composed of three stages: generation, pruning, and combination [19, 20]. The ensembles can be classified according to the base learners being homogeneous or heterogeneous. Homogeneous ensembles are composed of the same learning algorithm while heterogeneous ones are often composed of different ones [19].