1. Introduction
The accurate modeling and forecasting of solar power output in photovoltaic (PV) systems are certainly essential to improve their management and enable their integration in smart grids [
1,
2]. Namely, the output power of a PV system is highly correlated with the solar irradiation and the weather conditions that explain the intermittent nature of PV system power generation. Particularly, the characteristic of fluctuation and intermittent of the temperature and solar irradiance could impact solar power production [
3]. In practice, a decrease of larger than 20% of power output can be recorded in PV plants [
4]. Hence, the connected PV systems to the public power grid can impact the stability and the expected operation of the power plant [
5]. Given reliable real-time solar power forecasting, the integration of PV systems into the power grid can be assured. Also, power forecasting becomes an indispensable component of smart grids to efficiently manage power grid generation, storage, delivery, and energy market [
6,
7].
Long-and short-term forecasting methods are valuable tools for efficient power grid operations [
8,
9]. The success of integrating PV systems in smart grids depends largely on the accuracy of the implemented forecasting methods. Numerous models have been developed to enhance the accuracy of solar power forecasting, including autoregressive integrated moving average (ARIMA), and Holt-Winters methods. In Reference [
10], a short term PV power forecasting based on the Holt-Winters algorithm (also called triple exponential smoothing method) has been introduced. This model is simple to construct and convenient to use. In Reference [
11], different time series models including Moving average models, exponential smoothing, double exponential smoothing (DES), and triple exponential smoothing (TES) have been applied for short-term solar power forecasting. In Reference [
12], a coupled strategy integrating discrete wavelet transform (DWT), random vector functional link neural network hybrid model (RVFL), and SARIMA has been proposed to a short-term forecast of solar PV power. This study showed that the use of the DWT negatively affects the accuracy of solar PV power forecasting under a clear sky. While the quality of the forecast model is improved when using DWT in cloudy and rainy sky weather. In addition, the coupled model showed superior forecasting performance in comparison to individuals models (i.e., SARIMA or RVFL). However, switching between two forecast models is not an easy task, particularly for real-time forecasting. In Reference [
13], a hybrid model merging seasonal decomposition and least-square support vector regression was developed for forecasting monthly solar power output. Improved results have been obtained with this hybrid model compared to those obtained with ARIMA, SARIMA, and generalized regression neural network.
In recent years, shallow machine learning (ML) as non-parametric models, which are more flexible, have been widely exploited in improving solar PV forecasting. These models possess desirable characteristics and can model the complicated relationship between process variables and do not need an explicit model formulation to be specified, as is generally required. In Reference [
14], a hybrid approach combining support vector regression (SVR) and improved adaptive genetic algorithm (IAGA) is developed for an hourly electricity demand forecasting. It has been shown that this hybrid approach outperformed the traditional feed-forward neural networks, the extreme learning machine (ELM) model, and the SVR model. In Reference [
15], an approach for forecasting PV and wind-generated power using the higher-order multivariate Markov Chain. This approach considers the time-adaptive stochastic correlation between the wind and PV output power to achieve the 15-min ahead forecasting. The observation interval of the last measured samples are included to follow the pattern of PV/wind power fluctuations. In Reference [
16], a univariate method is developed for multiple steps ahead of solar power forecasting by integrating a data re-sampling approach with machine learning procedures. Specifically, machine learning algorithms including Neural Networks (NNs), Support Vector Regression (SVR), Random Forest (RF), and Multiple Linear Regression (MLR) are applied to re-sampled time-series for computing multiple steps ahead predictions. However, this approach is designed only for univariate time series data. In Reference [
17], a forecasting strategy combining the gradient boosting trees algorithm with feature engineering techniques is proposed to uncover information from a grid of numerical weather predictions (NWP) using both solar and wind data. Results indicate that appropriate features extraction from the raw NWP could improve the forecasting. In Reference [
18], a modified ensemble approach based on an adaptive residual compensation (ARC) algorithm is introduced for solar power forecasting. In Reference [
19], an analog method for day-ahead regional photovoltaic power forecasting is introduced based on meteorological data, and solar time and earth declination angle. This method exhibited better day-ahead regional power forecasting compared to the persistence model, System advisor model, and SVM model.
Over the last few years, deep learning has emerged as a promising research area both in academia and industry [
20,
21,
22,
23,
24]. The deep learning technology has realized advancement in different areas, such as computer vision [
25], natural language processing [
26], speech recognition [
27], renewable energy forecasting [
4,
28], anomaly detection [
29,
30,
31], and reinforcement learning [
32]. Owing to its data-driven approaches, deep learning has brought a paradigm shift in the way relevant information in time series data are extracted and analyzed. By concatenating multiple layers into the neural network structures, deep learning-driven methods enable flexible and efficient modeling of implicit interactions between process variables and automatic extraction of relevant information from a voluminous dataset with limited human instruction. Various deep techniques have been employed in the literature for improving solar power forecasting. For instance, in Reference [
33], Recurrent Neural Networks (RNNs) is adopted for PV power forecasting. However, simple RNN is not suited to learn long-term evolution due to the vanishing gradient and exploding gradient. To bypass this limitation, several variants of RNN have been developed including Long Short-Term Memory Networks (LSTM) and gated recurrent unit (GRU) networks. Essentially, compared to a simple RNN model, LSTM and GRU models possess the superior capacity in modeling time-dependent data within a longer time span. In Reference [
4], the LSTM model, which is a powerful tool in modeling time-dependent data, is applied to forecast solar power time series data. In Reference [
34], a GRU network, which is an extended version of the LSTM model, has been applied to forecast short-term PV power. In Reference [
35], at first, an LSTM recurrent neural network (LSTM-RNN) is applied for independent day-ahead PV power forecasting. Then, the forecasting results have been refined using a modification approach that takes into consideration the correlation of diverse PV power patterns. Results showed that the forecasting quality is improved by considering time correlation modification. In Reference [
36], by using the LSTM model, a forecasting framework is introduced for residential load forecasting to address volatility problems, such as variability of resident’s activities and individual residential loads. Results show that the forecasting accuracy could be enhanced by incorporating appliance measurements in the training data. In Reference [
37], a hybrid forecasting approach is introduced by combining a convolutional neural network (CNN) and a salp swarm algorithm (SSA) for PV power output forecasting. After classifying the PV power data and associated weather information in five weather classes: rainy, heavy cloudy, cloudy, light cloudy, and sunny, the CNN is applied to predict the next day’s weather type. To this end, five CNN models are constructed and SSA is applied to optimize each model. However, using several CNN models makes this hybrid approach not suitable for real-time forecasting. In Reference [
38], a method combining deep convolutional neural network and wavelet transform technique is proposed for deterministic PV power forecasting. Then, the PV power uncertainty is quantified using quantile regression. Results demonstrated the deterministic model possesses reasonable forecasting stability and robustness. Of course, deep learning models possess the capacity to efficiently learn nonlinear features and pertinent information in time-series data that should be exploited in a wide range of applications.
This study offers a threefold contribution. Firstly, to the best of our knowledge, this the first study introducing a variational autoencoder (VAE) and Restricted Boltzmann Machine (RBM) methods to forecast PV power. Secondly, this study provides a comparison of forecasting outputs of eight deep learning models, including simple RNN, LSTM, ConvLSTM, Bidirectional LSTM (BiLSTM), GRUs, stacked autoencoders, VAE, and RBM, which takes into account temporal dependencies inherently and nonlinear characteristics. The eight deep learning methods and two commonly used machine learning methods, namely logistic regression (LR) and support vector regression (SVR), were applied to forecast PV power time-series data. Finally, for the guidance of short- and long-term operational strategies for PV systems, both single- and multi-step-ahead forecasting are examined and compared in this paper. Data sets from two grid-connected plants are adopted to assess the outputs of the deep learning-driven forecasting methods.
Section 2 introduces the eight used deep learning methods.
Section 3 describes the deep learning-based PV power forecasting strategy.
Section 4 assesses the forecasting methods and compares their performance using two actual datasets. Finally,
Section 5 concludes this study and sheds light on potential future research lines.
3. Deep Learning-Based PV Power Forecasting
The input data consists of PV power output that variates between 0 and the rated output power. Thus, when handling some large-value data with the RNN model, a gradient explosion can be occurred and negatively affects the performance of the RNN. Furthermore, the learning effectiveness of RNN will be reduced. To remedy this issue, the input data is normalized via min-max normalization within the interval
$[0,\phantom{\rule{3.33333pt}{0ex}}1]$, and then used for constructing the deep learning models. The normalization of the original measurements,
$\mathbf{y}$ is defined as:
where
${y}_{min}$ and
${y}_{max}$ refer to the minimum and maximum of the raw PV power data, respectively. After getting forecasting outputs, we applied a reverse operation to ensure that the forecasted data match to the original PV power time-series data.
As discussed above, the generated PV power shows a high level of variability and volatility because of its high correlation with the weather conditions. Hence, for mitigating the influence of uncertainty on the accuracy of the PV power forecasting this work presents a deep-learning framework to forecast PV power output time-series. Essentially, deep learning models are an efficient tool to learn relevant features and process nonlinearity from complex datasets. In this study, a set of eight deep learning models have been investigated and compared for one-step and multiple steps ahead forecasting of solar PV power. The overall structure of the proposed forecasting procedures is depicted in
Figure 3. As shown in
Figure 3, solar PV power forecasting is accomplished in two phases: training and testing. The original PV power data is split into a training sub-data and a testing sub-data. At first, the raw data is normalized to build deep learning models. Adam optimizer is used to select the values of parameters of each model by minimizing the loss function based on training data. Once the models are constructed, they are exploited for PV power output forecasting. The quality of models are quantified using several statistical indexes including the Coefficient of determination (
${R}^{2}$), explained variance (EV), mean absolute error (MAE), Root Mean Square Error (RMSE), and normalized RMSE (NRMSE).
Essentially, the deep learning-driven forecasting methods learn the temporal correlation hidden on the PV power output data and expected to uncover and captures the sequential features in the PV power time series. The main objective of this study is to investigate the capability of learning models namely RNN, LSTM, BiLSTM, ConvLSTM, GRU, RBM, SAE, and VAE for one-step and multiple-steps ahead solar PV power forecasting.
3.1. Training Procedure
The eight models investigated in this study can be categorized into two classes: autoencoders and recurrent neural networks. The autoencoders represented include RBM, VAE, and SAEs while the RNN-based models contain RNN, LSTM, GRU, BiLSTM, and ConvLSTM. The dataset used for training and testing are normalized first, and more data preprocessing is needed for the autoencoder models. For instance, data reshaping is needed to transform the univariate PV power time-series data to a two-dimension matrix to be used as input for the autoencoders including the SAE, VAE, and RBM. The main difference between the two classes in the training phase is the learning way, the RNNs are entirely supervised trained while the auto-encoders are first pre-trained in an unsupervised manner and then the training is completed based on supervised learning. Specifically, RNNs models are trained in a supervised way by using a subset of training as input sequence (
$\mathcal{X}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{x}_{1},\dots ,{x}_{k}$) and an output variable
$\mathcal{Y}={x}_{k+1}$. The sequence length
l, called the lag, is a crucial parameter used in the data preparation phase. The mapping sequence to the next value is constructed using a window sliding algorithm. The value of
l is determined using the Grid Search approach [
51]. Here, the value of
l is chosen 6, which is the lowest value that maximizes the overall performance of the proposed approach.
RNN—based models are trained to learn the mapping function from the input to the output. After that, these trained models are used to forecast new data that complete the sequence. On the other hand, the greedy layer-wise unsupervised plus fine-tuning were applied to RBM, VAE, and SAES. It should be noted that PV power output forecasting based on autoencoder is accomplished as a dimensionality reduction. That is these models do not have the possibility to discover time dependencies or model time series data. Hinton [
44] shows that a greedy layerwise unsupervised learning for each layer followed by a fine-tuning improves the features extraction and learning process of the neural networks dedicated to prediction problems or for dimensionality reduction like autoencoders. The VAE-driven forecasting procedure including the pretreatment step is illustrated in
Figure 4.
3.2. Measurements of Effectiveness
The deep learning-driven forecasting methods will be evaluated using the following metrics:
${R}^{2}$, RMSE, MAE, EV, and NRMSE.
where
${y}_{t}$ are the actual values,
${\widehat{y}}_{t}$ are the corresponding estimated values,
$\overline{y}$ is the mean of measured power data points, and
n is the number of measurements. Instead of using RMSE that relies on the range of the measured values, the benefit of using NRMSE as the statistical indicator is that it does not rely on the range of the measured values. NRMSE metric indicates how well the forecasted model response matches the measurement data. A value of 100% for NRMSE denotes perfect forecasting and lower values characterize the poor forecasting performance. Lower RMSE and MAE values and EV and R2 closer to 1 are an indicator of accurate forecasting.
5. Conclusions
PV power output possesses high volatility and intermittency because of its great dependency on environmental factors. Hence, a reliable forecast of solar PV power output is indispensable for efficient operations of energy management systems. This paper compares eight deep learning-driven forecasting methods for solar PV power output modeling and forecasting. The considered models can be categorized into two categories: supervised deep learning methods, including RNN, LSTM, BiLSTM, GRU, and ConvLSTM, and unsupervised methods, including AE, VAE, and RBM. We also compared the performance of the deep learning methods with two baseline machine learning models (i.e., LR and SVR). It is worth highlighting that this study introduced the VAE and RBM methods to forecast PV power. For efficiently managing the PV system, both single- and multi-step-ahead forecasts are considered. The forecasting accuracy of the ten models has been evaluated using two real-world datasets collected from two different PV systems. Results show the domination of the VAE-based forecasting methods due to its ability to learn higher-level features that permit good forecasting accuracy.
To further enhance the forecasting performance, in future study, we plan to consider multivariate forecasting by incorporating weather data. Also, these deep learning models can be applied and compared using data from other renewable energy systems, such as forecasting the power generated by wind turbines. Further, it will be interesting to conduct comparative studies to investigate the impacts of data from different technologies, such as monocrystalline, and polycrystalline.