Prediction improvement of potential PV production pattern, imagery satellite-based

The results obtained by using an existing model to estimate global solar radiation (GHI) in three different locations in Tunisia. These data are compared with GHI meteorological measurements and PV_Gis satellite imagery estimation. Some statistical indicators (R, R2, MPE, AMPE, MBE, AMBE and RMSE) have been used to measure the performance of the used model. Correlation coefficient for the different stations was close to 1.0. The meteorology and satellite determination coefficient (R2) were also near 1.0 except in the case of Nabeul station in which the meteorology measurements (R) were equals to 0.5848 because of the loss of data in this location due to meteorological conditions. This numerical model provides the best performance according to statistical results in different locations; therefore, this model can be used to estimate global solar radiation in Tunisia. The R square values are used as a statistical indicator to demonstrate that the model’s results are compatible with those of meteorology with a percentage of error less than 10%.

Scientific Reports | (2020) 10:19951 | https://doi.org/10.1038/s41598-020-76957-8 www.nature.com/scientificreports/ to estimate the data in all Tunisian locations and yield good results close to those generated by meteorological stations and satellite imagery [33][34][35] . The strength of this study lies in being the first in Tunisia to provide an approach of generating local solar radiation using a numerical model. Thus, its results make a great contribution to the literature, the applications that require solar radiation data and the applications used in solar energy production.

Materials and sources
Instrument of measurement of NIM of Tunisia. The pyranometer is a radiometer designed for measuring the GHI, provides experimental data. The received flux is converted to heat by the blackened surface. The variance of the temperature between the surface and the instrument is in proportion to the irradiance of the GHI. It can be detected by a "Thermopile" that consists of a number of thermocouple junctions, usually joined together in series 36,37 .
In this section of study, we use data for several stations Bizerte, Nabeul and Djerba. In this location kipp_ Zonen pyranometer is used for different measurements. Solar radiation estimates from PV_Gis satellite imagery. We present in this section the results of the prediction of the solar radiation from satellite imagery PV_GIS 38 . PVGIS provide an accurate solar radiation free database for Europe, Africa Mediterranean, and South-West Asia. It provides yearly average irradiation as well as the sum of the average sum of GHI per square meter received by the modules of the system in KWh/ m 2 . Moreover, it must be highlighted that the uncertain of measurement in the spatial interpolation of ground station data in several locations is present. This is caused by the distance between different station and the local climatic conditions (Fig. 1).

Numerical simulation
To validate the result and to achieve closeness between the DNI provided by satellite imagery and meteorology, a numerical model is detailed to predict the global solar radiation.
Global solar radiation estimation. The basic solar radiation equations and the empirical relations are used in this section to give the GHI as a result. The very important equations are detailed in 29,39 . They determine the solar irradiance G i,γ incident on a PV or solar panel array inclined with an angle i and oriented with an angle γ for the south direction. Using the declination δ and the hour angle w we can calculate the sun position: where n is an integer representing the number of the day n ∈ [0, 365] , t s is the Solar time: where A = 2(0.986n + 100) and B = 0.986n−2, where t l is the legal time, N is the time zone,t seas is the seasonal correction, and L being the longitude.
The sun elevation angle α a , its azimuth angle a and the sunlight duration D j satisfy the Eq. (3) where ϕ present the latitude. The solar global irradiance G i,γ incident on a photovoltaic array is composed of the direct irradiance S * i,γ and of the diffuse D * i : The solar direct irradiance S * i,γ is expressed by where I * 0 is the Direct irradiance, (1) ω = t s × 360 24 (2) www.nature.com/scientificreports/ with m being the atmospheric optical distance. m = C sinα a where c = 1-0.1z and α a > 15 • at the z altitude and T L is the Linke turbidity factor. The diffuse irradiance D * i can be given by: with a 1 being the albedo, D * 0 being the atmospherical diffuse irradiance on a horizontal surface, and G * 0 being the global solar irradiance:

Results and discussion
Experimentations were carried out in three different positions in Tunisia. Different results are validated with those given by the meteorological station and the satellite imagery. A good congruence between the experiment, meteorology, and satellite imagery for the GHI is found (See Tables 1, 2 and 3).    Figure 3 represent the GHI for Nabeul station from January, 1 to December, 31 It shows that the numerical model gives a good estimation for the whole year only for July in which the measurement from meteorology station of Nabeul are taken during 16 days and August in which the measurements were taken over 6 days. This explains the role of numerical simulation to correct the messing data and to validate the unavailable data for any location in Tunisia from the year.

The evaluation of the performance
According to Fig. 4 we have in the same diagram curves that represent the measured values given by the NIM of Tunisia and the results estimated by the numerical model and the mean errors between the measured data and those calculated by the model. Error values range between 2 and 10%.
Principally, this incongruity is mostly due, first to the lack of data in case of impossibility for the meteorological pyranometer's failure to provide the right measurement such as in Nabeul station. In July the measurement was received all over 16 days and in August they were taken in 6 days. Second, this is justified by the inaccuracy and errors in the mentioned data of radiation and the temperature degrees from the location.
The performance of the model I evaluated by comparing the calculated global solar radiation with the measured data and those estimated by the satellite imagery.
Several statistical tests were used to control the validation and the goodness of the regression models in terms of the coefficient of determination.

Months
Numerical simulation Satellite imagery Meteorology  www.nature.com/scientificreports/ To check the relation between measured and estimated data, we generally use a statistical method by calculating the coefficient of determination R 2 , which can be expressed by the following equation: where G i,m , G i,c , − G i,m , RMSE are the measured GHI ,the calculated GHI, the average of the measured GHI, and the root mean square error 40,41 .
The root mean square of R 2 , is the correlation coefficient (R) which is a linear correlation coefficient that returns a value of between − 1 and + 1 we can so deduce if a good linear relationship between measured and estimated data exist or not (case of R = 0).
To prove the agreement between the measured and calculated values, we can evaluate the percent error (PE) which is mentioned below. Thus the results of the PE calculations remain between threshold values that indicate the validity of the models. The (MPE) is obtained by the sum of the PE values and the number of observations. The absolute of the MPE value is designated as Mean Absolute Percent Error (MAPE).   Table 4).

Conclusion
The global solar radiation measured by pyranometers must be corrected for the obscured part of the sky and for the technical problem due to the use of electronic sensors. The obtained results through simulation of numerical model give better estimation of global solar radiation. www.nature.com/scientificreports/ We can deduce that with these conditions, errors for predicted GHI did not surpass 10%. For the used model is highly accurate for estimating global solar radiation at all Tunisian sites to help researcher to choose the right location to install more PV system efficient.  www.nature.com/scientificreports/ Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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