Estimating solar radiation using artificial neural networks: a case study of Fiche, Oromia, Ethiopia

Abstract

The precise assessment and evaluation of global solar radiation (GSR) is crucial for designing effective solar energy systems. However, in developing countries like Ethiopia, the cost and maintenance of measuring devices are inadequate. As a result, researchers have explored alternative methods such as empirical models to estimate GSR. This article proposes using artificial neural networks (ANN) to predict daily and monthly averaged horizontal GSR (HGSR) around Fiche town of Ethiopia, using various network types. The input variables were divided into training (70%) and testing (30%) sets to evaluate the network types, with the sigmoid function used as the activation function at the hidden layer and a linear function for the output layer. The predicted mean daily and monthly HGSR ranges from 3.282 kWh/m²/day to 6.967 kWh/m²/day and 4.628 kWh/m² to 6.613 kWh/m² respectively. The values obtained were compared to those provided by NASA observation data and were found to be within acceptable limits. Statistical metrics of MAPE, MSE, and RMSE show that CFBP, FFBP, LR, and EBP are better network types for estimating mean daily HGSR, while EBP, FFBP, CFBP, and LR are better for estimating mean monthly HGSR. Overall, all network types of ANN accurately predicted the mean daily and monthly HGSR. In general, the findings of this study indicated that the location had promising solar energy for producing electricity and for various uses.

Keywords:

• CEBP
• EBP
• FFBP
• Fiche
• input variable
• LR
• solar energy

1. Introduction

Solar energy is a renewable energy source that has been gaining popularity over the past few decades due to its potential to meet the growing energy demand and reduce greenhouse gas emissions. In order to effectively utilize solar energy, it is important to accurately predict the amount of solar radiation that can be harnessed in a particular location. The prediction of solar radiation is necessary for the design, operation, and optimization of solar energy systems, as well as for agricultural and environmental applications (Bae et al., 2016; SHeng et al., 2022). Due to the limitations of field measurements, the current interest in the utilization of solar energy’s potential has led researchers to continue exploring empirical models to estimate GSR using diverse meteorological and geographic parameters In addition to the need to enhance the usage of alternative energies, particularly solar energy, solar potential data must be made available to society in order for it to plan and evaluate energy system initiatives (Ali & Jamil, 2019; Benchrifa et al., 2019; Markovics & Mayer, 2022).

GSR prediction models rely on readily available meteorological parameters like temperature, humidity, and wind speed. Empirical models are created through correlating climatological variables and using linear and nonlinear regressions of geographic and meteorological data. These models are crucial due to the high cost and maintenance of field measurement devices. The prediction is made using known parameters, such as temperature, humidity, sunshine hours, length of solar brightness, longitude, and latitude, which allow for estimating GSR in different regions (Rodríguez Mejia et al., 2022). Obtaining data on solar radiation and other climatic variables in urban areas is essential to evaluate their solar potential (Ağbulut et al., 2021; Takilalte et al., 2022). Accurately assessing and predicting the amount of GSR across the entire energy production region is crucial for effective planning of investments in solar energy production (Rodríguez Mejia et al., 2022).

Numerous studies have been conducted worldwide to estimate the quantity of solar radiation. The primary meteorological factor used to orient renewable energy devices like PV cells and solar water heaters is GSR (Bakirci, 2021). Jubail Industrial City in Saudi Arabia’s monthly GSR potential was computed, and successful findings were attained for all three basic variables: temperature, sunshine, and relative humidity (Mujabar & Chintaginjala Venkateswara, 2021). In the Castile and León Region of Spain, ANN models were used to accurately estimate the horizontal daily global sun irradiation for use in agricultural sciences and technology (Diez et al., 2020). In (Ojo et al., 2021), a multiple-layer perceptron of ANNs with different algorithms was compared with empirical statistical methods, and the ANN accurately predicted the net radiation over Nigeria. The suggested model proved effective at estimating solar radiation using Levenberg-Marquardt, Bayesian regularization, and scaled conjugate gradient training procedures of the ANN (Choudhary et al., 2020). The six machine-learning algorithms estimated the daily global solar radiation with good accuracy in the case of 27 European countries (Bae et al., 2016; Yacef et al., 2012). recommends that one of the forecasting approaches being followed in recent times is the artificial intelligence technique, or using the algorithms of predictive artificial neural networks to predict GSR.

Ethiopia is situated in the tropical region and benefits from ample sunshine. The average solar radiation in Ethiopia is around 5 to 8 kWh/m²/day (Woldegiyorgis, 2019). Despite this, over 90% of households in Ethiopia still heavily rely on solid fuels, primarily wood, for cooking (Bogale et al., 2017). In southern Ethiopia, this reliance is even higher at 97%. As a result, large amount of premature deaths occur each year due to lung cancer, chronic obstructive pulmonary disease, and pneumonia (Desalegn et al., 2011; World Health Organization, 2009). In Adama, Ethiopia, 75% of the populations also use solid fuel for cooking, leading to early mortality (Balidemaj et al., 2021). To reduce these alarming death rates and improve the quality of life, decreasing the use of solid fuel for cooking is crucial. Although solar radiation has not been explored in detail using artificial neural networks in Ethiopia, a few studies have predicted global solar radiation using sunshine and temperature-based models. For instance, in Lalibela, Ethiopia, a study showed that the sun-based model produced better results than the temperature-based model (Woldegiyorgis, 2020). In their study, Benti et al. (2022) utilized the Glover-McCulloch, Louche, and Angstrom-Prescott models to forecast total solar radiation throughout the whole country. According to their results, the GM model yielded the most accurate predictions across all locations (Benti et al., 2022). Backpropagation of the artificial neural network model was applied for the prediction of GSR in Addis Ababa, Ethiopia, and the obtained results had good agreement with actual data (Worki et al., 2016). In Lalibela, Ethiopia, the sunshine-based and ANN models were compared to estimate the daily averaged GSR, and good results were shown by ANN (Woldegiyorgis et al., 2022).

Endalew et al. (2022) suggested that the Ethiopian government and other relevant organizations ought to prioritize efforts to expand access to clean energy sources in rural areas through electricity provision and raise awareness about the adverse effects of solid fuel usage (Endalew et al., 2022). In the meantime, solar PV system installation and electrification in remote areas of Ethiopia are beneficial and suitable as a long-term investment since energy production from PV is a cost-efficient, clean, and promising option for rural electrification (Woldegiyorgis, 2019). In site selection for PV power plants, solar irradiation of at least 1100 kWh/m² per year is typically mandatory to promise technical and economic viability; however, places with higher solar irradiation are favored (Borunda et al., 2022).

The use of artificial intelligence (AI) has become increasingly prevalent in various engineering applications, including composite materials (NASA, World Surface Metrology, n.d.), manufacturing (A. H. Elsheikh et al., 2022; A. H. Elsheikh, 2023; A. H. Elsheikh, Shehabeldeen, et al., 2021; Khoshaim, Elsheikh, et al., 2021; Moustafa & Elsheikh, 2023), renewable energy, and material processing (A. H. Elsheikh et al., 2023; A. H. Elsheikh, Panchal, et al., 2021; Almodfer et al., 2022; Alsaiari et al., 2023; Khoshaim, Moustafa, et al., 2021; Moustafa et al., 2022). Recent publications have demonstrated the potential of AI in these fields, such as the prediction of residual stresses in turning of pure iron using AI-based methods and the use of machine learning in friction stir welding for joint property prediction and tool failure diagnosis (A. H. Elsheikh et al., 2022; A. H. Elsheikh, 2023; A. H. Elsheikh, Shehabeldeen, et al., 2021; Khoshaim, Elsheikh, et al., 2021; Moustafa & Elsheikh, 2023). In renewable energy, AI has been applied to modeling solar energy systems and improving the performance of solar distillers. For instance, low-cost bilayered structures have been developed to enhance solar stills’ performance, and machine learning algorithms have been used for productivity forecasting of solar distillers (A. H. Elsheikh et al., 2023; A. H. Elsheikh, Panchal, et al., 2021; Almodfer et al., 2022; Alsaiari et al., 2023; Khoshaim, Moustafa, et al., 2021; Moustafa et al., 2022). In this study, we aim to apply AI techniques to predict daily and monthly averaged horizontal global solar radiation in Fiche, Ethiopia.

Accurately predicting Global Solar Radiation (GSR) in a particular location is crucial for the successful installation of solar PV and thermal systems. Hence, the objectives of this study were two-fold: first, to assess and contrast the efficacy of various Artificial Neural Network (ANN) models in forecasting daily and monthly average Horizontal Global Solar Radiation (HGSR); second, to estimate the HGSR levels near Fiche, Ethiopia. The findings of this research are expected to be valuable in addressing the issue of indoor air pollution by installing PV and thermal solar systems, which have been responsible for premature deaths.

2. Materials and methods

2.1. Study area and data

This study was carried out in Oromia’s North Shewa Zone, near Fiche town. The town is around 114 km from Addis Ababa, the country’s capital (Figure 1). The altitude of this location is 2839.61 m above sea level, with latitude and longitude of 9.785 ° north and 38.731 ° east, respectively. The area’s yearly average temperature is 14.3 °C. Fiche has a tropical wet and dry or savanna climate and averages 85.74 millimeters of precipitation and 182.25 rainy days per year.The daily values of data for temperature (maximum and minimum), relative humidity, surface pressure, wind speed, and global solar radiation were taken from NASA for a study period of 2016–2021 (Benti et al., 2023).

Figure 1. Map of the study site.

The study involves the use of meteorological data consisting of various parameters such as latitude, longitude, elevation, and daily readings of maximum and minimum temperature, relative humidity, surface pressure, wind speed, and global solar radiation. The data was collected and pre-processed using the Microsoft spreadsheet. The study was carried out following several steps as detailed below.

Step 1: The pre-preprocessed data is divided into two sets, with 70% of the data assigned to the training data set, and the remaining 30% assigned to the testing data set. This approach is commonly used in machine learning and neural network modeling, where the training data is used to train the model, while the testing data is used to evaluate the model’s predictive capabilities.

Step 2: Input variables were selected for the different types of networks in the ANN model. The choice of input variables is an essential step in the modeling process as it determines the accuracy of the model’s predictions. In this case, the input variables were selected based on their potential impact on the output variable, which is the prediction of daily and monthly averaged HGSR.

Step 3: The architecture of the ANN model was constructed, as shown in Figure 1. The architecture of an ANN model refers to the arrangement and interconnection of the model’s layers and nodes.

Step 4: The predictive ability of the network type of the ANN model was evaluated by comparing the predicted outputs with the NASA observation data using statistical metrics such as root mean square error (RMSE), mean square error (MSE), and mean absolute percentage error (MAPE). These statistical metrics are commonly used to assess the accuracy of predictive models, with a lower value indicating a more accurate model. The general flow chart of the study is illustrated in Figure 2.

Figure 2. Flow chart.

To create, train, and test the models, the Data Manager Tool (nntool), a MATLAB R2016a tool, was utilized. The input layer of the network consisted of eight neurons, while the output layer had only one neuron, which is proportional to the number of inputs. Initially, a limited number of neurons were employed in the ANN, and the number was progressively increased until the prediction accuracy and outcomes were deemed satisfactory. To transform the information in the network layers, the hyperbolic tangent sigmoid math function was utilized. The ANN network was implemented and run within the MATLAB environment.

2.2. Artificial Neural Network (ANN)

Artificial Neural Networks (ANNs) are models that can connect multiple variables in large volumes of nonlinear and unreliable data. They are easy to use and do not require advanced mathematical knowledge for problem-solving purposes. Compared to other methods, ANNs require less computational effort to establish a relationship between input parameters and targets (Benti et al., 2023; Garud et al., 2021; Jaber et al., 2022). ANNs are parallel information processing algorithms that are nonlinear and nonalgorithmic (Hoang et al., 2021; Jaber et al., 2022). The basic unit of an ANN is a stack of neurons arranged in multiple layers. The input layer receives the data, the processing begins in the hidden layer, and the output layer generates the conclusion (Figure 3) (Jaber et al., 2022; Kurniawan & Harumwidiah, 2021). After adding bias, the input is multiplied by a weight. The hidden layer, which contains its activation function, receives the input layer signal. This data is processed by the hidden layer, which then sends it to the output layer for activation. A popular activation function for output neurons is purelin, which has the same output format as input (Jaber et al., 2022; Kurniawan & Harumwidiah, 2021). The neurons receive the independent variables (x₁, x₂, …, x_n) and output Y, and the output is calculated using equation (1)(1) $\mathrm{Y}=\mathrm{f}\left(\mathrm{v}\left(\mathrm{w},\mathrm{x}\right)\right)$(1) (Moreira et al., 2021:

Figure 3. Structure of ANN to predict GSR.

(1) $\mathrm{Y}=\mathrm{f}\left(\mathrm{v}\left(\mathrm{w},\mathrm{x}\right)\right)$(1)

(2) $\mathit{v}\left(\mathit{w},\mathit{x}\right)={\sum }_{k=1}^n{w}_k{x}_k+\mathit{b}=\mathit{W}{ }^{\mathrm{\prime }}+\mathit{B}$(2)

where v- is the function used to represent the weights related to each input, and bias is the sum of w₁, w₂,…, w_n weights related to each connection. The vector representation of weight is given as (W’=w₁, w₂, w_n), the input vector is given by (X = x₁, x₂,… x_n), and “b” represents the bias expressed in equation (2)(2) $\mathit{v}\left(\mathit{w},\mathit{x}\right)={\sum }_{k=1}^n{w}_k{x}_k+\mathit{b}=\mathit{W}{ }^{\mathrm{\prime }}+\mathit{B}$(2) . f- represents the activation function, through which the output is generated from the immediately preceding layer, which is chosen based on the presence of a node in the hidden or output layer and the type of problem stated. The logistic sigmoid function, hyperbolic tangent sigmoid function, Gaussian radial basic function, linear Unipolar step function, bipolar step function, Unipolar linear function, and Bipolar linear function are commonly used activation functions in the literature (Jallal et al., 2021), and their illustrations are given in . The nftool feed-forward neural network with different layers is evaluated, and as the number of layers increases, the complexity of the models increases without increasing their performance; hence, the optimum number of layers was two.

2.3. Statistical performance evaluation of network types

To evaluate the predictive capabilities of different network types within the ANN model for daily and monthly averaged HGSR, statistical measures including mean absolute percentage error (MAPE), root mean square error (RMSE), and mean square error (MSE) were employed to assess their performance (Guermoui et al., 2022).

(3) $\mathit{MAPE}=\frac{1}{N}\left[{\sum }_{i=1}^N\left|\frac{{\mathit{G}}_{\mathit{i},\mathit{N}}-G_{\mathit{i},\mathit{P}}}{G_{\mathit{i},\mathit{N}}}\right|\right]\ast 100\mathrm{\%}$(3)

(4) $\mathit{RMSE}={\left[\frac{1}{N}{\sum }_{i=1}^N{\left({\mathit{G}}_{\mathit{i},\mathit{p}}-G_{\mathit{i},\mathit{N}}\right)}^2\right]}^{1/2}$(4)

(5) $\mathit{MSE}=\frac{1}{N}{\sum }_{i=1}^N{\left({\mathit{G}}_{\mathit{i},\mathit{p}}-G_{\mathit{i},\mathit{N}}\right)}^2$(5)

where G_i,P, G_i,N are the values of i^th predicted and the NASA observation data horizontal GSR respectively (Golam et al., 2021; Husain & Khan, 2022).

3. Results and discussion

Figures 4 and 5 depict the comparison between the NASA observation data and the estimated results of daily and monthly averaged HGSR during the study period from 2016 to 2021. For both the entire days and months, there was a strong agreement between the NASA observation data and estimated HGSR values near Fiche, Ethiopia, as supported by the statistical performance evaluation in Table 1. The daily average HGSR varied from day to day due to the nonlinearity of climate conditions, while the monthly average HGS only slightly varied from month to month, as shown in Figure 5 and Table 2. The monthly averaged values of HGSR predicted by the network types of EBP, FFBP, CFBP, and LR closely overlapped each other, in the order listed in Figure 5 and confirmed by the statistical metrics in Table 2. These results demonstrate that the network types of ANN (EBP, FFBP, CFBP, and LR) yielded favorable outcomes at the study site.

Figure 4a. Prediction of daily averaged Horizontal GSR using ANN network type nearby Fiche, Ethiopia (2016–2021).

Figure 4b. (Continued).

Table 1. Statistical metrics performance of ANN model for daily averaged GSR at Fiche, Ethiopia

		Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
FFBP	MSE	0.026	0.052	0.019	0.068	0.048	0.044	0.159	0.094	0.069	0.034	0.034	0.027
	MAPE(%)	2.104	2.785	1.592	3.272	2.754	3.138	7.027	5.577	4.153	2.450	2.305	2.184
	RMSE	0.161	0.228	0.139	0.262	0.218	0.210	0.399	0.307	0.263	0.186	0.183	0.165
LR	MSE	0.018	0.051	0.021	0.050	0.050	0.043	0.143	0.127	0.085	0.045	0.063	0.017
	MAPE(%)	1.630	2.714	1.703	3.061	2.912	3.023	6.089	6.451	4.389	2.877	3.241	1.554
	RMSE	0.136	0.226	0.145	0.224	0.224	0.208	0.378	0.357	0.292	0.214	0.250	0.134
CFBP	MSE	0.015	0.043	0.026	0.055	0.040	0.053	0.140	0.123	0.071	0.096	0.047	0.016
	MAPE(%)	1.559	2.578	1.757	2.974	2.553	3.541	5.937	6.014	4.092	3.908	2.794	1.558
	RMSE	0.124	0.206	0.161	0.235	0.201	0.230	0.374	0.351	0.267	0.310	0.217	0.127
EBP	MSE	0.015	0.046	0.032	0.061	0.053	0.045	0.157	0.094	0.063	0.062	0.085	0.025
	MAPE(%)	1.724	2.616	2.059	3.204	3.095	3.015	7.343	5.599	4.075	3.182	3.600	2.000
	RMSE	0.140	0.215	0.179	0.247	0.231	0.212	0.397	0.307	0.250	0.248	0.293	0.158

Table 2. Statistical metrics of ANN model for monthly averaged GSR at Fiche, Ethiopia (2016–2021)

ANN network types	MSE	RMSE	MAPE
FFBP	0.0063	0.0795	1.0989
LR	0.0079	0.0893	1.2525
CFBP	0.0079	0.0889	1.2075
EBP	0.0057	0.0757	0.0966

The FFBP network type of ANN was found to be the most suitable for predicting daily averaged HGSR during March, August, October, and November when compared to other network types. However, in the months of January, February, April, and December, the results produced by this network type were less accurate compared to other network types. The LR network type of the ANN was effective in predicting daily averaged horizontal GSR during April and June, while it produced unsatisfactory results in August and September. The CFBP network type accurately predicted daily averaged HGSR during January, February, May, July, and December but had poor results during June and October. In September, the EBP network type performed well, whereas it gave inadequate results during March, May, and November when compared to other network types of ANN. Overall, daily averaged horizontal GSR was better predicted by the CFBP, FFBP, LR, and EBP network types, respectively, at the study site. It is worth noting that EBP gave poor results compared to all network types of ANN near Fiche, Ethiopia. However, as indicated in Table 1 and Figure 3, all types of ANN networks are capable of predicting daily averaged HGSR at the study site.

During the study period (2016–2021), the months of March, January, February, and December had the highest daily averaged horizontal GSR. Specifically, on March 27, 13, and 26, the maximum values of 6.967 kWh/m²/day, 6.961 kWh/m²/day, and 6.930 kWh/m²/day were obtained, respectively. On the other hand, the lowest values of 6.195 kWh/m²/day, 6.273 kWh/m²/day, and 6.312 kWh/m²/day were recorded on March 1, 8, and 5, respectively. In January, the maximum daily averaged horizontal GSR was observed on January 23, 28, and 25, with values of 6.727 kWh/m²/day, 6.694 kWh/m²/day, and 6.686 kWh/m²/day, respectively. The minimum values of 5.894 kWh/m²/day, 6.1222 kWh/m²/day, and 6.157 kWh/m²/day were recorded on January 3, 9, and 12, respectively. In February, the maximum daily averaged horizontal GSR was found on February 12, 9, and 11, with values of 6.717 kWh/m²/day, 6.656 kWh/m²/day, and 6.642 kWh/m²/day, respectively. The minimum values of 6.169 kWh/m²/day, 6.230 kWh/m²/day, and 6.229 kWh/m²/day were observed on February 26, 21, and 23, respectively. Among all the months, July, August, September, and June are the months in which the minimum daily averaged horizontal GSR was received, respectively. The highest daily averaged horizontal GSR was found on July 13 (5.433 kWh/m²/day), July 5 (5.263 kWh/m²/day), and July 3 (5.222 kWh/m²/day). For August, the maximum daily averaged horizontal GSR was received on 29-August (5.289 kWh/m²/day), 31-August (5.148 kWh/m²/day), and 22-August (5.095 kWh/m²/day) in order. In September, the maximum daily averaged horizontal GSR was found on 27-September (5.684 kWh/m²/day), 29-September (5.624 kWh/m²/day), and 30-September (5.618 kWh/m²/day) respectively. Generally, the minimum daily averaged horizontal GSR that was received in the month of March is greater than the maximum daily averaged horizontal GSR in the months of July, August, and September. In Ethiopia, July, August, and September are rainy months. As a result, these months received the lowest daily averaged horizontal GSR of any month. While the maximum daily averaged horizontal GSR was obtained in the months of March, April, and February, which are the dry months in Ethiopia.

Figure 5. Prediction of monthly averaged GSR using ANN network type at Fiche, Ethiopia (2016–2021).

A monthly averaged horizontal GSR near Fiche, Ethiopia, is better estimated by the EBP network type of ANN. The unfit results were obtained from network type LR of ANN in the study period (2016–2021), according to Table 2 and Figure 3. However, in this work, all network types of ANN models estimated the monthly averaged horizontal GSR of Fiche, Ethiopia accurately according to the statistical metrics in Table 2 and as shown in Figure 3. In the months of August (4.589 kWh/m²), July (4.624 kWh/m²), and September (5.391 kWh/m2), the minimum averaged horizontal GSR was gained, respectively. The maximum monthly averaged horizontal GSR was found in the months of March (6.652 kWh/m²), January (6.445 kWh/m²), and February (6.418 kWh/m2), in that order. Finally, the maximum daily and monthly averaged horizontal GSR was obtained in the same months as the minimum daily and monthly averaged horizontal GSR during the study period (2016–2021).

In general, as shown in Figure 4, the monthly average HGSR fluctuated very slightly from month to month; however, the daily average HGSR varied from day to day due to the nonlinear nature of climate conditions. Additionally, as illustrated in Figure 5 and verified by the statistical metrics of Table 2, the monthly averaged values of HGSR predicted by the network types of EBP, FFBP, CFBP, and LR closely coincided with one another. Additionally, the network types that performed better in the prediction of daily averaged HGSR will not be effective for monthly averaged HGSR, as illustrated in Tables 1 and 2.

4. Conclusion

This study aimed to evaluate and compare different types of ANN models for estimating daily and monthly average HGSR using input variables and to determine the resource available at the study site. Statistical error tests were used to compare the outcomes of different network types. The results showed good agreement between NASA observation data and predicted HGSR values in the study site for both daily and monthly averages. The predicted mean daily HGSR ranged between 3.282 kWh/m²/day and 6.967 kWh/m²/day, while the predicted mean monthly HGSR was between 4.628 kWh/m² and 6.613 kWh/m². All network types of ANN models were validated, and their performance was evaluated using statistical metrics, including MAPE, MSE, and RMSE. The statistical evaluations revealed that the CFBP, FFBP, LR, and EBP network types of ANN with 19, 15, 17, and 12 neurons, respectively, were the better options to estimate the mean daily HGSR. For monthly estimates, EBP, FFBP, CFBP, and LR network types were accurate, respectively. The statistical evaluation of these metrics found that the MAPE ranged from 1.554% to 7.343%, the MSE ranged from 0.015 kWh/m²/day to 0.127 kWh/m²/day, and the RMSE ranged from 0.124 kWh/m²/day to 0.399 kWh/m²/day. The study revealed that the study site has high potential (2149.09 kWh/m² per year) for installing solar energy systems. The study might benefit prospective solar power investors and help reduce indoor air pollution in rural areas throughout Ethiopia. The study supports efforts to assess solar energy resources and install solar energy in the country’s rural and remote areas.

Nomenclature

Table

Abbreviation Definition		Abbreviation Definition
ANN AP CFBP	Artificial Neural Network Angstrom-Prescott Cascade Forward Back Propagation	HGSR LR	Horizontal Global Solar Radiation Layer Recurrent
EBP FFBP GM GSR	Elman Back Propagation Feed Forward Back Propagation Glover -McCulloch Global Solar Radiation	MAPE MSE RMSE PV	Mean Absolute Percentage Error Mean Square Error Root Means Square Error Photovoltaic

Authors’ contributions

All authors read and approved the final manuscript

Disclosure statement

The authors affirm that they have no known financial or interpersonal conflicts that would have appeared to have an impact on the article presented in this study.