2.8 Semi-empirical methods

Ångström-Prescott (AP) is a model used to estimate the global solar irradiation as a function of solar radiation at the earth's surface and daily sunshine duration [15]. Akarslan et al. [16] presents five semi-empirical solar radiation forecasting models based on the AP approach. These models utilize solar irradiance historical data along with the extra-terrestrial irradiance and the clearness index for hourly forecasting of solar radiation. Models 1–2 use historical samples of solar radiation and clearness index, whereas models 3–5 utilize the extra-terrestrial irradiance in addition to historical values of solar radiation and clearness index. The evaluation results show that including the extra-terrestrial irradiance data in the model enhances the forecasting accuracy.

#### 2.9 Combination of k-means, DT, and SVM-C

A hybrid framework is proposed in Ref. [17] to model and forecast hourly global solar radiation data. This approach includes two different phases and uses data mining techniques in each step. K-means clustering technique is used in the first phase to identify the type of days. In the second phase, the decision trees (DT), artificial neural networks, support vector machine regression (SVM-R), and support vector machine classification algorithms (SVM-C) are combined with regression algorithms to obtain the daily clearness index and the meteorological parameters to forecast hourly global solar radiation. The results of the evaluation indicate that the proposed method satisfies the desired accuracy.

#### 2.10 Machine learning-based methods

Five machine learning models, including adaptive forward-backward greedy algorithm (Fo-Ba), leap-Forward, forecast and variable selection by spike and slab regression (spikeslab), bagging wrapper for multivariate adaptive regression splines (Bagged MARS) using generalized cross validation (gCV) pruning, Cubist, and bagEarthGCV are presented in Ref. [18] for the solar irradiance prediction. The Fo-Ba algorithm is an efficient sparse learning and feature selection method with applications in optimization problems. The spikeslab model is a prediction and variable selection approach based on spike and slab regression. Bagged MARS approach computes an Earth model for each bootstrap sample of the original training set. In addition, the generalized cross validation approach is used for regularizing parameter selection in geophysical diffraction tomography (GDT). The abovementioned models are evaluated and compared for different forecasting horizons from 1 h ahead to 48 h ahead. The evaluation results show that the spikeslab and Cubist models have more accurate and consistent performance for different forecasting horizons.

#### 2.11 Combination of SOM and wavelet neural networks

Wavelet neural network is the combination of wavelet analysis and neural networks to address the over fitting issue of single network models. Reference [19] develops a novel short-term PV generation forecasting method by combining SOM algorithm and wavelet neural networks. The SOM method is applied for clustering the weather data and recognizing the future weather type. The wavelet neural network is utilized to build the prediction models for each cluster sample. The proposed method is proven to culminate in highly accurate forecasting.
