البيانات باستخدام تقنيات التعلم العميق
علي محمد رجه أنعام محمد عايد
جامعة الأنبار جامعة الأنبار
مركز دراسات الصحراء مركز دراسات الصحراء
الخلاصة
أصبحت نماذج السلاسل الزمنية مثل الشبكات العصبية المتكررة شائعة للتنبؤ بالإشعاع الشمسي نظرًا لقدرتها القوية على التنبؤ. طور هذا البحث طريقة تعتمد على الذاكرة طويلة المدى (LSTM) للتنبؤ بالإشعاع الأفقي العالمي (كل من حالة الطقس والسماء الصافية). تم اختبار النموذج باستخدام 10 عينات تم اختيارها عشوائيا داخل محافظة الأنبار ، العراق. تم الحصول على البيانات من معلومات الإشعاع الشمسي Helioclim-3 (الإصدار 5) التي تم توفيرها عبر الإنترنت مجانًا للفترة من 1-2-2004 إلى 31-12-2006. بالنسبة لنموذج LSTM ، استخدمنا آخر خمس ساعات من المعلومات حول الإشعاع الشمسي ومعلمات الأرصاد الجوية (درجة الحرارة والرطوبة النسبية وسرعة الرياح واتجاه الرياح وهطول الأمطار) للتنبؤ قبل ساعة واحدة. أظهرت النتائج أن أداء شبكة LSTM المقترحة جيدة بالنظر إلى مواقع العينات ومسارات المناطق المقترحة,لجميع أحوال الطقس . وجد أن الحد الأدنى من RMSE في بيانات الاختبار هو 133.833 وأعلى R2 كان 0.806. بالنسبة لظروف السماء الصافية ، أظهر نموذج LSTM أداءً أفضل من RMSE وبحد أدنى كان 131.048 وأعلى R2 كان 0.825. لذلك ، يمكن أن يكون نموذج LSTM المقترح مفيدًا لأبحاث الطاقة الشمسية وتطبيقاتها في منطقة الدراسة أو أجزاء أخرى من البلدان النامية. يُقترح إجراء مزيد من البحوث لتحسين أداء النموذج في السيناريوهات ومجموعات البيانات الأخرى.
الكلمات المفتاحية: الطاقة الشمسية ، الإشعاع الشمسي ، الشبكة العصبية المتكررة ، الأنبار
Hourly solar radiation prediction based on meteorological
data using deep learning techniques
Ali Muhammad Raja
Anam Muhammad Ayed
Desert Studies Center
Anbar University
Introduction
Solar energy is an important source of renewable energy since it is not immediately exposed to seasonal changes in weather conditions. As solar technologies become advanced and accessible, they are easy to use anywhere around the globe. Solar energy is essential for sustainable development and carbon dioxide reduction. Solar photovoltaic and solar thermal systems develop solar energy for multiple applications. Photovoltaic technology, providing clean and renewable energy, can convert solar radiation into electricity. Recent years have shown increased investment in solar energy. Due to places in high-solar radiation areas, it is particularly useful for developing countries. However, to effectively manage photovoltaic system development, spatial and temporal analysis of solar irradiation and its suitability for renewable energy becomes a popular research area. It helps better manage these systems ‘ effects on the landscape, land use, and biodiversity. Tools such as geographic information systems (GIS), remote sensing, and machine learning offer the possibility to efficiently manage the photovoltaic system by providing observational data or forecasting solar irradiation.
In solar energy research, global horizontal irradiance (GHI) is a significant parameter and can be measured on the top of the atmosphere and the earth’s surface. In specific, the development of solar energy-related research is influenced by high resolution, both temporal and spatial GHI information. This parameter can be acquired via terrestrial measurements or satellite data analysis. The ground measures of GHI in both time and space are precise and high-resolution. In many locations, however, pyranometer maintenance costs are therefore high. Satellite measurements of GHI, on the other hand, are affordable and are thus used to cover ground measurement data scarcity. Examples of low-cost satellite images that provide GHI measurements include Meteosat First Generation (MFG) and Meteosat Second Generation (MSG)/Spinning Enhanced Visible and Infrared Imager (SEVIRI), The Japanese Geostationary Meteorological Satellite (GMS), and the Geostationary Operational Environmental Satellite System (GOES).
The fundamental concept of estimating GHI from satellite data is to discover the connection with statistical or physical methods between satellite products and ground measurements. The common Heliosat-1 and Heliostat-2 (H2) techniques can be implemented using large time-series meteorological satellite data. As the cloud pixel is high in the visible band, the H2 method tests the reflectance difference between the cloud pixel and the clear-sky pixel, also known as the cloud index. In addition to this information, the Linke turbidity factor is used to estimate GHI.
Several time-series techniques have been developed over the past decades to forecast solar irradiance. Statistical methods are popular for forecasting GHI (Verbois et al., 2018). Exponential smoothing by decompositions is applied by many researchers to forecast solar irradiance (Taylor and Snyder, 2012; Yang et al., 2015). For the same purpose, piecewise-linear regression was used by Huang and Davy (2016). Machine learning is also widely applied to GHI forecasting (Huertas-Tato et al., 2018). For example, nearest neighbour ( NN) was used for intra-hour solar irradiance from local telemetry and sky imaging (Pedro and Coimbra, 2015). Model trees were also implemented to make predictions on GHI (McCandless et al., 2015). In another study, a technique for 1-hour-ahead prediction of GHI was proposed based on support vector machines (Feng et al., 2017; Jiang and Dong, 2017). Neural networks (NN) are also applied to forecast GHI (Shaddel et al., 2016; Gutierrez-Corea et al., 2016; Crisosto et al., 2018; Ameen et al., 2019; Pereira et al., 2019). Neural networks and evolutionary optimization methods were combined in Jiang (2017) to perform GHI forecasting. And in Jadidi et al. (2018), neural networks were integrated with a genetic algorithm. Chen (2017) combined NN and NN in a single model for short-term GHI forecasting based on meteorological data. More recently, Benali et al. (2019) combined neural networks with random forests for solar radiation forecasting. There are several other machine learning-based methods developed for GHI forecasting under different time intervals. Examples include the Gaussian process (Zemouri et al., 2017), quantile gradient boosting (Verbois et al., 2018), and wrapper mutual information (Bouzgou and Gueymard, 2019), naïve Bayes (Kwon et al., 2019). Ensemble of various models also has been applied to GHI forecasting (Liu et al., 2016; Jiang et al., 2017).
Deep learning is also among the most commonly used methods for solar irradiance forecasting (Alzahrani et al., 2017). Srivastava and Lessmann (2018) showed that recurrent neural networks, particularly, LSTM methods outperform a large number of alternative forecasting techniques. Qing and Niu (2018) applied LSTM models for hourly day-ahead solar irradiance prediction using weather information. Unlike normal feedforward NN models, LSTM provides parameter sharing in the hidden units across time indexes which enables them to effectively handle time-series datasets.
This research develops deep learning methods for temporal forecasting of GHI based on previous GHI and meteorological data. The method developed is based on recurrent neural networks which are best suitable for time series data analysis and modelling. This paper presents the algorithm and its validation on 10 randomly selected samples within Al-Anbar Province, Iraq. The historical GHI and meteorological data are based on Helioclim-3 Archives available for free online from 2004-02-01 up to Dec. 2006.
research importance:
The importance of research lies in the possibility of investing solar energy and horizontal solar radiation in places of high solar radiation, especially in developing countries, to develop the photovoltaic system and take advantage of solar radiation as renewable energy.
research aims :
The research aims to make time-series to predict hourly solar radiation (temperature, humidity, wind speed and precipitation) based on ground monitoring data and satellites using the LSTM model.
search limits:
The research area is Al-Anbar Province which is Iraq’s largest county by area (Figure 1). It covers a large part of the country’s western territory, sharing boundaries with Syria, Jordan, and Saudi Arabia. Its area is 138,501 km² and is located at 33° latitude and 42° longitude and it is situated at an average elevation of 300 meters above sea level. Ramadi is the provincial capital; Fallujah and Haditha are other major towns. Al-Anbar is regarded as part of the Arabian Peninsula with an estimated population of 1.8 million as of 2017. The geography of the area combines the Euphrates river and steppe around the desert. It is characterized by a desert climate, low precipitation, and a large temperature variation between day and night. The temperature is up to 42 °C in summer, while the average winter temperatures are down to allow of 9 °C. The winds are sometimes up to a maximum of 21 m/s in the northwest and southwest. The average precipitation is 115 mm in winter. The primary types of land cover are barren land (sparsely vegetated), shrubland, grassland, crop/irrigated crop, water, and urban/built up. The geomorphology of the area is mostly flat with a minimum elevation of 50 m and some parts, in particular, the west, reaching 960 m.
Figure 1. The geographic location of the study area (Al-Anbar).
Research Hypotheses:
The research assumes that the use of deep learning techniques and the use of the LSTM model can predict the hourly solar radiation and the possibility of using it as renewable energy.
Search tools:
A group of tools were used in the research, the most important of which are :
- LSTM program for the prediction of hourly solar radiation.
- Data of climate elements for 10 selected sites within the study area.
- Horizontal solar radiation data for the period 2004-2006.
- GPS device.
Research Methodology:
This research develops deep learning methods for GHI temporal prediction based on previous GHI data and meteorological data. The method developed is based on recurrent neural networks which are best suited for analyzing and modelling time-series data. This paper presents the algorithm and its validation on 10 randomly selected samples in Anbar Governorate, Iraq. GHI data and historical meteorological data are based on the Helioclim-3 archive available freely online from 2004-02-01 through December 2006
Datasets:
This research uses the freely accessible Helioclim-3 solar irradiation information (version 5) archival, accessible through the SoDa Service (http:/www.soda-pro.com). It offers information on surface solar irradiation several times (1 minute–monthly), calculated by processing images from the geostationary meteorological Meteosat satellites using climatological data sets of the atmospheric Linke turbidity factor (Espinar et al., 2012). A correlation coefficient higher than 0.9 and a relative mean square error of about 20 per cent of the measured average radiance is found in the validation with hourly ground measures. For our research, hourly data are included, for example, global horizontal radiance, temperature, relative humidity, pressure, wind speed, wind direction and others (MERRA-2 and GFS) (all weather conditions, clear sky, and at the top of the atmosphere). For the 2004-02-01 to 2006-12-31 period. Data were gathered for randomly chosen ten sample points in Al-Anbar (Figure 2).
The collected data are prepared and managed in GIS on a local machine. The data was prepared as shapefiles (locations and attributes) and a second copy of the data was made as excel sheets (.csv). The observations were indexed by date and the attributes were named properly. Features (see Table 1) and the target (solar irradiance) that we are interested to predict are also separated by a special prefix. The CSV files are then read by Pandas and preprocessed. Preprocessing of data included removing No Data observations and outliers. Also, data normalization by the min-max function. Finally, the data was reshaped into proper dimensions as LSTM models require (observations, 1, features). The preprocessed data are then divided into training (50%) and the remaining 50% were kept for validation.
Figure 2. Location of the samples selected to test our method for hourly GHI prediction.
Recurrent Neural Networks
Neural networks are powerful universal function approximators. They heavily depend on large training datasets (pairs of features and ground truth labels). Several types of neural networks have been developed for a wide range of applications. For time-series applications, a particular neural network called recurrent is favourable. This is because such models allow the parameters of the hidden units to be shared across time indexes. This effectively helps the network to build a memory of long sequences which helps recognize and predict sequences. Therefore, this research uses a type of recurrent network namely long short term memory or LSTM (Hochreiter and Schmidhuber, 1997) for solar irradiance forecasting. Instead of traditional recurrent networks, LSTM units help to avoid vanishing gradient or exploding gradient problems.
Figure 3 shows a typical LSTM cell. The hidden units are replaced by memory blocks. Each block contains one or more self-connected memory cells and three multiplicative units known as input, output, and forget gates. These gates allow for write, read, and reset operations within the memory block. In other words, they control the behaviour of the memory block. For an LSTM cell, is the sum of inputs at the time step and its previous time step activations, LSTM updates for the time step gave inputs, and are (Donahue et al., 2015):
where is an element-wise non-linearity such as a sigmoid or Tanh function, is the weight matrix, is the input at the time tep, is the hidden state vector of the previous time step and denotes the input bias vector.
Figure 3. A typical LSTM cell in RNN models.
Proposed Network Architecture
Our proposed LSTM model consists of two LSTM layers with 25 and 10 hidden units, respectively (Figure 4). We use dropout with a 0.5 elimination fraction after the two LSTM layers to regularize the network and avoid overfitting the training data. A dense layer is then used to make a prediction using the features learned by the two LSTM layers. Finally, we use the linear activation layer to produce an output. The inputs and outputs are normalized using mean and standard deviation. After prediction, they are inversed and transformed to the original scale. These parameters and the layers structure are found empirically in our research using a subset of 20% of the data. Details of the input (predictors) and output (target) are given in Table 1.
Figure 4. The proposed LSTM based prediction model for solar irradiation in Al-Anbar Province, Iraq. is the lookback parameter or the sequence length used to make the next hour prediction.
Table 1. Prediction and target variables are used in our LSTM model for solar irradiation prediction.
| Name | Short Name | Units | Used as | Source | ||
| 1 | Irradiation (all weather) | Irradiation | Wh/m2 | Target | HelioClim-3v5 | |
| 2 | Irradiation (clear sky) | Clear-Sky | Wh/m3 | Target | HelioClim-3v5 | |
| 3 | Irradiation over the period at the top of the atmosphere | Top of Atmosphere | Wh/m4 | Target | HelioClim-3v5 | |
| 4 | Temperature at 2 m above ground | Temperature | K | Predictor | MERRA-2 | |
| 5 | Relative humidity at 2 m above ground | Relative humidity | % | Predictor | MERRA-2 | |
| 6 | Pressure at ground level | Pressure | hPa | Predictor | MERRA-2 | |
| 7 | Wind speed at 10 m above ground | Wind speed | m/s | Predictor | MERRA-2 | |
| 8 | Wind direction at 10 m above ground (0 means from North) | Wind direction | Decimal degree | Predictor | MERRA-2 | |
| 9 | Rain depth in mm | Rainfall | kg/m2 | Predictor | MERRA-2 |
Training Methodology
Neural networks are commonly trained with stochastic gradient descent (SGD) by backpropagation. These techniques use easy mathematical tricks like differentiation and chain rules to efficiently minimize a differentiable objective function concerning the model’s parameters. Based on the original SGD, several improved versions of the algorithm are currently existing and are used to train deep learning models that are based on neural networks. The most commonly used optimization method is known as Adam (adaptive moment estimation). It computes adaptive learning rates for each parameter of a network model (Kingma and Ba 2014). In this research, the Adam optimizer was used to minimize the loss function which is the mean square error (Equation 7). All the weights are initialized using a zero-mean Gaussian distribution with a standard deviation of 0.01, and the biases are initialized with a constant of 1. The following parameters were found best in our implementation. A batch size of 512, learning rate = 0.0001, epochs = 500 iterations with early termination by monitoring validation loss for 50 iterations.
where and are the actual and predicted values for a sample and is the total number of training samples.
Accuracy Assessment
The proposed models were evaluated based on two popular metrics known as root mean square error (RMSE) and coefficient of determination (R2). These metrics are widely used for regression problems and in solar energy research. Both are quantitative measures based on the difference between the measured and simulated/predicted values. For a set of measured values ( ) and simulated values ( ) for a sample and the number of samples ( ), RMSE and R2 are calculated using:
where is the number of data; is the actual data and is the predicted data.
Results and Discussions
This section explains the main findings of this research which was conducted to evaluate LSTM based techniques for global horizontal irradiance forecasting at several locations in Al-Anbar Province, West Iraq. The models were designed and implemented in Python using open source libraries such as sci-kit-learn and Keras. All the experiments were tested with a PC with a single GPU operating on Windows 10. The maps were produced in ArcGIS Pro 2.4.
Hourly Global Horizontal Irradiance
Our proposed LSTM network was used to predict hourly GHI (all-weather condition) given the last 5 hours of meteorological data and historical GHI information. The evaluation of the model was performed in 10 different locations. The results are summarized in Table 2. We can see that the model on average predicts the hourly GHI with 135.86±3.71 RMSE and 0.801±0.005 R2 for the training dataset and 140.44±3.67 RMSE and 0.796±0.007 R2 for the testing dataset. These consisted prediction accuracies suggest that the proposed model can be helpful in forecasting GHI values when ground measurements are not available. The models almost performed equally in all the sample locations with location #8 having the lowest testing RMSE of 133.833. The highest R2 (0.806) on the test data was found for location #6. In addition, the scatter plots between the measured and predicted GHI values are shown in Figure 5. The results show that the GHI values predicted by the LSTM model are comparable to those acquired from the HelioClim-3v5 database. This indicates that these models may be reliable in solar energy applications that require solar irradiance values, particularly, when access to ground measurements is expensive or not practical.
Table 2. Error estimates for GHI prediction with LSTM (both training and testing).
| # Location | Training (50%) | Testing (50%) | ||
| RMSE | R2 | RMSE | R2 | |
| 1 | 134.086 | 0.798 | 140.653 | 0.792 |
| 2 | 139.411 | 0.793 | 141.130 | 0.796 |
| 3 | 135.418 | 0.808 | 141.840 | 0.802 |
| 4 | 140.135 | 0.795 | 144.626 | 0.793 |
| 5 | 130.608 | 0.797 | 136.044 | 0.780 |
| 6 | 136.771 | 0.809 | 140.312 | 0.806 |
| 7 | 137.860 | 0.801 | 142.021 | 0.798 |
| 8 | 129.219 | 0.803 | 133.833 | 0.795 |
| 9 | 139.539 | 0.802 | 145.916 | 0.796 |
| 10 | 135.583 | 0.804 | 137.977 | 0.804 |
| 135.86±3.71 | 0.801±0.005 | 140.44±3.67 | 0.796±0.007 |
Figure 5. Scatter plots of the measured and predicted GHI (all-weather condition) at different locations within Al-Anbar.
Hourly Global Horizontal Irradiance (Clear Sky)
Table 3 summarizes the error estimates for the LSTM model applied to GHI prediction with a clear sky using both training and testing datasets. The results suggest that the LSTM model could predict the GHI values of the next hour given the last five hours of information with 138.03±3.86 RMSE and 0.820±0.007 R2 for the training dataset and 143.98±3.39 RMSE and 0.815±0.007 R2 for the testing dataset. Compared to the results obtained for the GHI (all-weather condition), the LSTM model performs slightly better for forecasting GHI clear sky information. On the test dataset, the lowest RMSE (131.048) was found at location #8 and the highest R2 (0.825) at location #9. The scatter plots as shown in Figure 6 also confirm that the LSTM model performs well in predicting GHI clear sky values with the last five hours’ information.
Table 3. Error estimates for GHI prediction with LSTM (both training and testing).
| # Location | Training (50%) | Testing (50%) | ||
| RMSE | R2 | RMSE | R2 | |
| 1 | 139.635 | 0.812 | 145.189 | 0.807 |
| 2 | 140.612 | 0.814 | 145.141 | 0.813 |
| 3 | 140.468 | 0.820 | 144.473 | 0.822 |
| 4 | 141.422 | 0.814 | 147.415 | 0.809 |
| 5 | 131.711 | 0.819 | 138.751 | 0.809 |
| 6 | 140.402 | 0.822 | 147.471 | 0.816 |
| 7 | 137.829 | 0.827 | 144.254 | 0.820 |
| 8 | 131.048 | 0.830 | 137.863 | 0.821 |
| 9 | 136.040 | 0.831 | 142.294 | 0.825 |
| 10 | 141.101 | 0.811 | 146.959 | 0.804 |
| 138.03±3.86 | 0.820±0.007 | 143.98±3.39 | 0.815±0.007 |
Figure 6. Scatter plots of the measured and predicted GHI (clear sky) at different locations within Al-Anbar.
Spatial Distribution of Irradiance
Figure 7 shows the map products for the measured and predicted GHI values for the two cases (all-weather conditions and clear sky). The maps show the spatial distribution of the GHI values (both measured and predicted) in Wh/m2. The measured GHI (all-weather condition) ranges from 932.98 to 985.92. The predicted GHI ranges from 861.72 to 969.30. The maps show that the highest values are concentrated in the southeast part of the area while the northwest parts had the lowest values in both the measured and predicted maps. For the clear sky case, the measured values show that the GHI in the Al-Anbar area ranges from 944.04 to 983.94 with the highest values in the southeast parts. The agreement between the measured and the predicted values also seems to be high with slight differences in the GHI values (minimum and maximum).
Figure 7. Measured and predicted global horizontal irradiance at Al-Anbar Province, Iraq using the LSTM method with the all-weather condition and clear sky. (a) the measured all-weather condition GHI, (b) the predicted all-weather condition GHI, (c) the measured clear sky GHI, and (d) the predicted clear sky GHI.
Conclusions
Solar energy is an alternative energy source that offers sustainability in development, particularly for developing countries. GIS and remote sensing technologies provide tools to estimate solar irradiance from satellite and forecast them to the near future, allowing improved solar energy studies. In this research, we developed a forecasting model based on the LSTM technique for hourly global horizontal irradiance for both all-weather and clear sky conditions. The training and validation data were obtained from the HelioClim-3v5 database for 10 samples within Al-Anbar Province, Iraq. Our results showed that these models can predict hourly GHI values in both all-weather and clear sky conditions given the last five hours of information about the solar irradiance and meteorology such as temperature, relative humidity, wind speed and direction, and rainfall.
The applications of the LSTM model can be expanded to other research fields related to solar energy. Prediction of longer sequences of GHI values with the different input information. These possibilities all can contribute to making solar energy technologies favourable in developing countries. However, future research should evaluate these models on different scenarios and climate patterns. Comparing LSTM predictions with ground measurements at local monitoring stations is also important to be considered in future works.
References
Alzahrani, A., Shamsi, P., Dagli, C., & Ferdowsi, M. (2017). Solar irradiance forecasting using deep neural networks. Procedia computer science, 114, 304-313.
Ameen, B., Balzter, H., Jarvis, C., & Wheeler, J. (2019). Modelling Hourly Global Horizontal Irradiance from Satellite-Derived Datasets and Climate Variables as New Inputs with Artificial Neural Networks. Energies, 12(1), 148.
Benali, L., Notton, G., Fouilloy, A., Voyant, C., & Dizene, R. (2019). Solar radiation forecasting using artificial neural network and random forest methods: Application to normal beam, horizontal diffuse and global components. Renewable energy, 132, 871-884.
Bouzgou, H., & Gueymard, C. A. (2019). Fast short-term global solar irradiance forecasting with wrapper mutual information. Renewable energy, 133, 1055-1065.
Chen, C. R. (2017). k-Nearest Neighbor Neural Network Models for Very Short-Term Global Solar Irradiance Forecasting Based on Meteorological Data. Energies, 10(2), 186.
Crisosto, C., Hofmann, M., Mubarak, R., & Seckmeyer, G. (2018). One-hour prediction of the global solar irradiance from all-sky images using artificial neural networks. Energies, 11(11), 2906.
Espinar, B., Blanc, P., Wald, L., Gschwind, B., Ménard, L., Wey, E., … & Saboret, L. (2012, May). HelioClim-3: a near-real-time and long-term surface solar irradiance database.
Feng, C., Cui, M., Lee, M., Zhang, J., Hodge, B. M., Lu, S., & Hamann, H. F. (2017, July). Short-term global horizontal irradiance forecasting based on sky imaging and pattern recognition. In 2017 IEEE Power & Energy Society General Meeting (pp. 1-5). IEEE.
Gutierrez-Corea, F. V., Manso-Callejo, M. A., Moreno-Regidor, M. P., & Manrique-Sancho, M. T. (2016). Forecasting short-term solar irradiance based on artificial neural networks and data from neighbouring meteorological stations. Solar Energy, 134, 119-131.
Huang, J., & Davy, R. J. (2016). Predicting intra-hour variability of solar irradiance using hourly local weather forecasts. Solar Energy, 139, 633-639.
Huertas-Tato, J., Aler, R., Rodríguez-Benítez, F. J., Arbizu-Barrena, C., Pozo-Vázquez, D., & Galván, I. M. (2018, June). Predicting Global Irradiance Combining Forecasting Models Through Machine Learning. In International Conference on Hybrid Artificial Intelligence Systems (pp. 622-633). Springer, Cham.
Jadidi, A., Menezes, R., de Souza, N., & de Castro Lima, A. (2018). A hybrid ga–mlpnn model for one-hour-ahead forecasting of the global horizontal irradiance in Elizabeth City, North Carolina. Energies, 11(10), 2641.
Jiang, H. (2017). A novel approach for forecasting global horizontal irradiance based on a sparse quadratic RBF neural network. Energy conversion and management, 152, 266-280.
Jiang, H., & Dong, Y. (2017). Forecast of hourly global horizontal irradiance based on structured Kernel Support Vector Machine: A case study of Tibet area in China. Energy Conversion and Management, 142, 307-321.
Jiang, H., Dong, Y., & Xiao, L. (2017). A multi-stage intelligent approach based on an ensemble of two-way interaction models for forecasting the global horizontal radiation of India. Energy Conversion and Management, 137, 142-154.
Kwon, Y., Kwasinski, A., & Kwasinski, A. (2019). Solar Irradiance Forecast Using Naïve Bayes Classifier Based on Publicly Available Weather Forecasting Variables. Energies, 12(8), 1529.
Liu, Y., Shimada, S., Yoshino, J., Kobayashi, T., Miwa, Y., & Furuta, K. (2016). Ensemble forecasting of solar irradiance by applying a mesoscale meteorological model. Solar Energy, 136, 597-605.
McCandless, T. C., Haupt, S. E., & Young, G. S. (2015). A model tree approach to forecasting solar irradiance variability. Solar Energy, 120, 514-524.
Pedro, H. T., & Coimbra, C. F. (2015). Nearest-neighbour methodology for prediction of intra-hour global horizontal and direct normal irradiances. Renewable Energy, 80, 770-782.
Pereira, S., Canhoto, P., Salgado, R., & Costa, M. J. (2019). Development of an ANN-based corrective algorithm of the operational ECMWF global horizontal irradiation forecasts. Solar Energy, 185, 387-405.
Qing, X., & Niu, Y. (2018). Hourly day-ahead solar irradiance prediction using weather forecasts by LSTM. Energy, 148, 461-468.
Shaddel, M., Javan, D. S., & Baghernia, P. (2016). Estimation of hourly global solar irradiation on tilted absorbers from horizontal one using artificial neural network for a case study of Mashhad. Renewable and Sustainable Energy Reviews, 53, 59-67.
Srivastava, S., & Lessmann, S. (2018). A comparative study of LSTM neural networks in forecasting day-ahead global horizontal irradiance with satellite data. Solar Energy, 162, 232-247.
Taylor, J. W., & Snyder, R. D. (2012). Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing. Omega, 40(6), 748-757.
Verbois, H., Huva, R., Rusydi, A., & Walsh, W. (2018). Solar irradiance forecasting in the tropics using numerical weather prediction and statistical learning. Solar Energy, 162, 265-277.
Verbois, H., Rusydi, A., & Thiery, A. (2018). Probabilistic forecasting of day-ahead solar irradiance using quantile gradient boosting. Solar Energy, 173, 313-327.
Yang, D., Sharma, V., Ye, Z., Lim, L. I., Zhao, L., & Aryaputera, A. W. (2015). Forecasting of global horizontal irradiance by exponential smoothing, using decompositions. Energy, 81, 111-119.
Zemouri, N., Bouzgou, H., & Gueymard, C. A. (2017, October). The Gaussian process with linear discriminant analysis for predicting hourly global horizontal irradiance in Tamanrasset, Algeria. In 2017 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B) (pp. 1-5). IEEE
