In the last decade the energy demand is exponentially increased, hence its management is vital to defend the planet earth [1-3]. The use of renewable energy (wind, solar, wave and biomass) is one of the strategies [4], together with energy savings [5] and efficiency improvements in the energy production and management [6-7], for a sustainable development. In the last years, various strategies have been implemented by several countries to promote the renewable energy [8-10].
PV systems and wind turbines are clean, inexhaustible, and environment-friendly renewable energy options. Nevertheless, the large-scale integration of renewable energy, as PV, into the electricity system presents some limitations, as the variability of the renewable sources [11]. This randomness influences the efficiency of the electric grid.
In this context, it is of great interest the development of energy models and in particular of forecasting models, which represent an efficient support for electricity suppliers, to plan, manage and dispatch the electrical installed power plants [12]. In the literature, different forecasting methods were developed. Among the different prediction methods, Artificial Neural Networks (ANNs) were extensively used in different fields, for example to forecast the electricity load [13–14].
Elman neural network was implemented in [15] for the wind power forecast and a comparison between the ANNs, ARMA (Auto Regressive Moving Average) and ANFIS (Adaptive Neuro-Fuzzy Inference Systems) models was performed in [16]. Regarding the photovoltaic power, an overview of the Artificial Intelligence techniques, applied for modeling, prediction, simulation, optimization and control of the photovoltaic systems was illustrated in [17].
In [18] ANNs were applied to obtain the energy production and the V–I curve of a PV module for a pair of determined values of irradiance and cell temperature. In [19] short-term solar energy predictions were performed and the performance of ordinary LSR (least-square regression), regularized LSR and ANN models were compared. It was observed that improvements can be obtained by an ensemble of forecasts of different models and by proper selection of input data segments.
Generally, the PV forecasting models can be mainly classified into three types. The first type estimates the produced power by using the values of solar irradiance. In a second type of models the current and the past values of the output power are used in order to predict the future ones. The third type of models is a combination of the first and the second one; it can forecast indirectly the produced power based on the present and the past values of power, and meteorological parameters such as air temperature, solar irradiance and relative humidity.
Regarding the models based on solar radiation, several previous works implemented a two-stage approach. In the first stage, the solar irradiance on different time scales is evaluated and used to estimate the PV power. Empirical models can be used to estimate solar irradiation from different available data: measured data of solar irradiance [20], sunshine duration [21], clearness index [22-23], and meteorological parameters [24-25].
Other approach performs the solar radiation thought artificial neural network (ANN). In [26] a feed-forward ANN model (Multilayer Perceptron) was implemented using the ambient temperature and the measured daily solar irradiance values. A solar radiation forecast technique based on fuzzy and neural networks together was developed in [27], the forecast results followed the real values very well under different sky and temperature conditions. In [28] the hybrid ARMA/ANN model showed better performance than the stand alone ANN to predict hourly global radiation for five places in Mediterranean area using data issued from a numerical weather prediction model. In [29] ANN outperformed other statistical models (autoregressive and fuzzy logic models) in the prediction of half daily values of global solar irradiance with a temporal horizon of 3 days.
Instead of using a two-stage approach, various approaches have been developed to directly forecast the PV power output. In [30] a simplified strategy based on a radial basis function network (RBFN) was proposed to forecast 24-h ahead of the PV system. In particular measured exogenous data as temperature, precipitation amount, irradiance period and humidity were used as inputs of the ARMAX model to forecast the 1-day ahead power output of a grid connected PV system in the Colane island of Macau Special Administrative Region (SAR) [31].
One of the main limits of ANN methods is an excessive training data approximation, aimed to increase the out-of-sample forecasting errors. Hence new time series forecasting models have been developed based on Learning Machines using Support Data Machines (SVMs) methods that allow resolving the over-fitting problem and achieving high performance with lower computational cost than ANN model based on back-propagation algorithms [32]. In previous study, the SVM was used to forecast the solar radiation [33-34], electricity load prediction [35] and to evaluate the photovoltaic power production [36]. Reformulations to the standard SVMs are known in the literature as Least Squares Support Vector Machines (LS-SVM) method that simplifies the complex models to solve linear system, with lower computation complexity than SVMs models [37] and performance comparable to that of the standard SVM [38]. A hybrid statistical model based on Least Square Support Vector Machines (LS-SVM) with Wavelet Decomposition (WD) was performed in [39] to predict the output power of a PV system in Mediterranean climate. The authors demonstrated that LS-SVM with WD outperformed traditional ANN.
Furthermore, a promising and relatively unexplored sub-model of ANN is the neural network known as Group Method of Data Handling (GMDH). The GMDH is an inductive learning algorithm that allows finding a relation between input and output variables, selecting an optimal structure of the model or network, through quadratic regression polynomials with two input variables, known as Partial Descriptions of data (PDs) [40]. The input variables are automatically selected and the model structure is automatically configured. This approach of the self–organizing is based on the sorting of possible variants, allowing to find the best solution [41]. The inductive networks have the advantages of faster model development than the neural networks. The GMDH technique was applied in various fields. Xu et al. [42] implemented GMDH in forecasting electric load demand, it outperforms ARIMA for short term load forecast. In [43] the GMDH neural network outperformed the traditional time-series and regression-based models also in the medium-term energy demand forecast. In the field of renewable energy, this model was used in [44] for predicting the mean 1 hour ahead hourly wind speed at Dhahran, Saudi Arabia. The results underlined improvements with respect to several machine learning approaches reported in the literature. In [45] the abductive network was applied to predict global solar radiation in the Kingdom of Saudi Arabia (KSA) based on sunshine duration, month number, latitude, longitude, and altitude of the location.
Recently hybrid GMDH-type algorithm (GLSSVM) has been applied in several fields with significant improvements of the forecasting accuracy respect to GMDH and LS-SVM methods [46] or to other statistical models as ARIMA and ANN [47]. The possibility to forecast the building energy consumption implementing the GLSSVM model was discussed in [48].
Hybrid GLSSVM methods are relatively new and unexplored for the forecast of renewable power, regardless of the advantages that it showed in other fields. In this context in the present paper a novel hybrid GLSSVM model is applied for the prediction of hourly PV output power. The predictions were performed for a 960 kWp photovoltaic system installed in South-East of Italy, using historical data and compared with stand-alone GMDH and LS-SVM methods.
Finally, in order to improve the performance of the forecasting models, we compared one-step prediction strategy with different multistep forecasted strategies. The one-step-prediction gives the forecasted value at the time instant immediately following the latest data, while the multistep prediction starts from the historical values of time series and apply the model step by step to predict future values [49]. Multistep forecast could be direct or iterative [50] or a combination of both [51]. In the first at different time instants, the values can be forecasted all at once. In iterative method, the predicted value at the previous time horizons is the input at the successive time horizons [50].