Global solar radiation on tilted surfaces in Tunisia: Measurement, estimation and gained energy assessments

Othman, A. Ben; Belkilani, K.; Besbes, M. Article Global solar radiation on tilted surfaces in Tunisia: Measurement, estimation and gained energy assessments Energy Reports Provided in Cooperation with: Elsevier Suggested Citation: Othman, A. Ben; Belkilani, K.; Besbes, M. (2018) : Global solar radiation on tilted surfaces in Tunisia: Measurement, estimation and gained energy assessments, Energy Reports, ISSN 2352-4847, Elsevier, Amsterdam, Vol. 4, pp. 101-109, https://doi.org/10.1016/j.egyr.2017.10.003 This Version is available at: https://hdl.handle.net/10419/187898 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Energy Reports 4 (2018) 101–109 Contents lists available at ScienceDirect Energy Reports journal homepage: www.elsevier.com/locate/egyr Global solar radiation on tilted surfaces in Tunisia: Measurement, estimation and gained energy assessments A. Ben Othman a,c, K. Belkilani a,b,*, M. Besbes a,b aRobotics, Informatics and Complexes Systems, Laboratory LR16ES07, (RISC), National School of Engineers of Tunis, University of Tunis El Manar, Tunisia bHigher Institute of Information and Communication Technologies, University of Carthage, Tunisia cNational School of Engineers of Carthage, University of Carthage, Tunisia article info Article history: Received 5 July 2017 Received in revised form 22 September 2017 Accepted 12 October 2017 Keywords: Solar radiation estimation Inclined surface Optimum tilt angle Gained energy abstract A very important factor in the assessment of solar potential for the installation of photovoltaic plants is the availability of global irradiation data measurements. Such data must be collected over a period of time longer than 11 years and must be accurate. In some countries, it is difficult to have databases of these measures. To overcome this problem, we propose, the use of numerical models to estimate the monthly, seasonally and annually solar energy irradiation (global diffuse and direct solar radiation), especially on tilted surface. The results obtained from the numerical models are compared to the data collected from three regions on Tunisia: Bizerte (in the north), Nabeul (near to the north east) and Djerba (in the south). The actual measurements taken from the meteorological stations and the measurements generated by the numerical models are very close. After the validation of the numerical models, we tried to calculate the best tilt angle for each period of the year to position a photovoltaic panel, in a given region, to reach maximum energy recovery. The practical validation, of the optimal tilt angle search and the adequate period, was conducted at the Research and Technology Center of Energy of Borj Cedria. The obtained results are satisfactory and prove the reliability of the constructed numerical models. ©2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction Solar energy resource data is necessary for the evaluation of the profitability of installing photovoltaic plants. However, the real energy produced cannot be predicted because the energy generation process depends on climatic conditions (Tadros, 2000). The total solar radiation data is scarce in some locations, this is due to the absence of meteorological measurement stations and remote data collection networks, whose installation is expensive (Codato et al., 2008). Research and development efforts are required to ameliorate estimation processes to reach accurate predictions (Deshmukh, 2008;Ashraful Islam et al., 2016;Derouich et al., 2014). Total measured solar radiation data are the best source of information for estimating average incident radiation necessary to calculate the productivity of an installed solar energy systems. In order to evaluate the production of a photovoltaic solar power plant, in a given region, measurements must be made over a period of at least 11 years. Generally, these measures are only available in *Corresponding author at: Higher Institute of Information and Communication Technologies, University of Carthage, Tunisia. E-mail address: [email protected] (K. Belkilani). developed countries (Li et al., 2008;Sebaii et al., 2010;ElMghouchi et al., 2014). To trap the maximum amount of solar radiation, it is possible to use photovoltaic panels powered and driven by a sun system tracking. These panels are often expensive and require excessive maintenance. However, a more cost-efficient method would be the implementation of a periodically-changing (either monthly or seasonally) optimum tilt angle. This period can be monthly or seasonally. The value of the tilt angle and position-shifting periods have always been determined by the measurements collected over tens of years. In the absence of these data, it is possible to use numerical models of prediction. The measurement of solar radiation falling on tilt surface is important to estimate solar radiation in locations where there are no facilities to measure any meteorological data (Loutzenhizer et al., 2007). Studies on and measures in this field are rare (Pandey and Katyar, 2009;Miguel et al., 2001;Despotovic and Nedic, 2015). In this case, various radiation models for inclined surfaces have been proposed. Some of they include isotropic models (Liu and Jordan, 1960;Duffie and Bechman, 1991;Farhan et al., 2015) anisotropic models (Perez et al., 1986;Yao et al., 2015) and models for clear sky (Robeldo and Soler, 2002;Badescu, 2002). The total radiation https://doi.org/10.1016/j.egyr.2017.10.003 2352-4847/©2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc- nd/4.0/). 102 A. Ben Othman et al. / Energy Reports 4 (2018) 101–109 Fig. 1. CMP 3 Pyranometers for global irradiance measurements. Source: (a) (kipp_Zonen_booklet _Pyranometers) (b) (National Institute of Meteorology of Tunisia.) Table 1 CMP3 pyranometer specifications. Spectral range (50% points) 300 to 2800 nm Sensitivity 5 to 20_V/W/m2 Impedance 20 to 200_ Maximum operational irradiance 2000 W/m2 Response time (63%) <6 s Response time (95%) <18 s on tilt surface consists of three components: beam, reflected radiation from the ground and diffuse radiation (Noorian et al., 2008; Notton et al., 2006;Maleki et al., 2017). Each one of these models predicts beam and diffuse components and global solar radiation. Hence, the possibility to estimate the incident radiation on tilted surface (Hameed et al., 2017). All meteorological stations, of the National Institute of Meteorology of Tunisia, measure global solar radiation intensities only on horizontal surface (Evseev and Kudish, 2009). The recorded data are only the monthly averages. To overcome the problem of data scarcity, we propose in this paper, a numerical model to calculate the optimal tilt angles and to calculate the duration of holding of each angle in function of the losses to be gained in the energy production. This paper is divided into two parts: In the first part, we discuss in detail the construction of the numerical model. Then we evaluate the validity of the generated results in comparison with the meteorological data received from, three remote stations in different Tunisian cities, Bizerte in the north, Nabeul in the north east and Djerba in the south. The second part is devoted to the evaluation of profit losses, engendered by the installation with fixed inclination of photovoltaic panels. 2. Model synthesis 2.1. Measurement instruments Measurements are made by pyranometers (global solar radiation) (see Fig. 1). They are radiometers designed to measure the global irradiance on a plane surface resulting from radiant fluxes in the wavelength ranging from 300 to 2800 nm. The received radiation is converted into heat by the blackened surface. The temperature variation between the blackened surface and the body of the instrument is proportionate to the irradiance of the global solar radiation, as is measured by several thermocouples (see Table 1). We used the data obtained from the three stations Bizerte, Nabeul and Djerba. Fig. 2 is a photo that shows the meteorological Fig. 2. Meteorological station energy systems of the National Institute of Meteorology of Tunisia. station energy systems of the National Institute of Meteorology in the Tunis DC. The data of global solar radiation measured (in KWh /m2) in the three meteorological stations was collected over the period between January and December of the year 2015. 2.2. Assumptions In this work, we present the basic solar equations in detail and the empirical relations that can be, consequently be utilized to compute global irradiance as a result. We recall the main equations which are detailed in Duffies and Bechman (2006) and Stone (1993). The Solar radiation which reaches the ground is formed by a direct radiation (I∗) and a diffuse radiation (D∗) which together form the global radiation. The sum of these components equates to the total irradiance (G∗). All these are calculated in W/m2. 2.2.1. Solar energy The earth receives daily a large flow of solar energy. The power of this radiation depends on several criteria, meteorological conditions, atmospheric diffusion (phenomena of dispersion, reflection and absorption). The average amount of solar radiation received at any earth’s surface, is about 1367 W/m2(Wong and Chow, 2001). This total radiation energy is called solar constant. The energy received depends on the day of the year and can be calculated using the following formula: Esol =1367 ×(1+0.00334× cos (360 ×(j−2.7206)/365.25)) (1) j: the order number of the day in the year ranging from 1 on January to 365 on 31 December. for example, 1 January =1, 20 February =51, and so on. A. Latitude and longitude Latitude (Lat) is the angle formed by the equatorial plane and the vector ‘‘center of the earth →local point’’. Longitude (Lon) is the angle formed by the meridian of reference (Greenwich meridian) and the meridian of the local point. The angle is negative to the west and positive to the east. As the earth takes 24 h to spin around its axis ( 360◦) each hour represents 15 degrees of longitude deviation and therefore each degree of longitude represents 4 min. B. Declination Declination (Dec) is the angle formed by the vector ‘‘center of the earth →sun’’ and the equatorial plane of the earth. Moreover, the declination is the angular distance from the sun north or south A. Ben Othman et al. / Energy Reports 4 (2018) 101–109 103 Fig. 3. Maximum and minimum value of declination angle (Maleki et al., 2017). of the earth equator. Maximum and minimum declination angle values are illustrated in Fig. 3 According to Cooper (1969), the declination is obtained from the following equation: Dec =sin−1(0.398 ×sin (0.985 ×j−80)) (2) C. Hour angle Hour angle (Ah) measures the movement of the sun with respect to noon, which is the moment when the sun passes to the meridian plane of the place (zenith). This time angle is negative if the solar time is inferior to 12 pm. The concept is used for describing the rotation of the earth around its polar axis which is equivalent to +15◦per hour during the morning and −15◦in the afternoon (Nia et al., 2013). The hour angle is evaluated as follows Ah =180 ×(Tsv/12 −1)(3) Where Tsv is the local solar time. Position of the sun: The position of the sun is defined by two angles that are: The height of the sun (H) and the azimuth (A). (H) is known, also, as altitude, and it is the angle formed by the horizontal plane of the place considered and the vector ‘‘local point →sun’’. The expression is: H=sin−1(sin (Lat)×sin (Dec)+cos (Dec)×cos (Ah))(4) The solar azimuth (A) is the horizontal angle formed by the meridian plane (north–south axis) and the vertical plane of the vector. It is defined as the angular displacement from the south of the beam radiation projection on the horizontal plane. The sign of the azimuth is the same as that of the hour angle. Here the azimuth angle Ais represented by A=sin−1(cos (Dec)×sin (Ah)) /cos (H)(5) Knowing about latitude and declination makes predicting the exact sunrise and sunset times possible (see Fig. 4). Tsunrise =12 −(cos−1(−tan(Lat)×tan (Dec)))/15 (6) Tsunset =12 +(cos−1(−tan (Lat)×tan (Dec)))/15 (7) The duration of sunshine represents the maximum duration of the day: Di =2/15 ×cos−1(−tan (Lat)×tan (Dec)) (8) D. Coefficient of incidence Coefficient of incidence (CI) is the angle formed by the solar radiation with the perpendicular of a surface. This coefficient defined on the one hand by the height of the sun and its azimuth and Fig. 4. Definition of the sun’s Azimuth angle (Maleki et al., 2017). on the other hand by the orientation (O) and the inclination (I) of the receiving plane. Thus, each receiving plane can be defined by a pair of values, (O, I). The orientation is negative towards the east and positive towards the west. It can be indicated by a geographical direction, like for example north-northeast. As for the inclination, it is equal to 0◦for a horizontal plane and 90◦for a vertical plane (Duffie and Beckman, 2006). The coefficient of incidence, CI, is calculated by the formula (9): CI =sin (I)×cos (H)×cos (O−a)+cos (I)×sin (H) (9) 2.2.2. Direct solar flux Direct solar radiation reaches the atmosphere but its intensity undergoes an attenuation. To evaluate this loss of radiation, the approach is as follows: 1- Define the altitude of the local point to know the atmospheric pressure (Patm): Patm =101325 ×(1−2.26 ×10−5×z)5.25 (10) Where zis the altitude in meters 2- Define saturated vapor pressure (Pvs), average relative humidity (RH) and partial pressure of water vapor (Pv): Pvs=2.165 ×(1.098 +T/100)8.02 (11) Hr =50% (12) Pv=Pvs×Hr (13) Where Tis the air temperature in Celsius 3- Define the relative optical mass (M) from which results the optical thickness of Rayleigh (ER), which determines the attenuation due to diffusion: M=Patm/(101325 ×sin (H)+15198.75 × (3.885 +h)−1.253)(14) ER =1/(0.9×M+9.4)(15) 4- Define Linke’s disorder factor: Tl =2.4+14.6×B+0.4×(1+2×B)×ln (Pv)(16) Where Bis the atmospheric disturbance coefficient, which takes a value: B=0.02 for a mountain location =0.05 for a rural location =0.10 for an urban location =0.20 for an industrial site (polluted atmosphere) 104 A. Ben Othman et al. / Energy Reports 4 (2018) 101–109 Table 2 Geographical coordinates of the study locations. City Latitude Longitude Altitude Bizerte 37◦16′27′′ 09◦52′26′′ 05 m Nabeul 36◦27′21′′ 10◦44′15′′ 14 m Djerba 33◦49′00′′ 11◦0′00′′ 51 m The direct solar radiation (W/m2) on a receiving plane normal to this radiation is therefore: I∗=Esol ×EXP (−ER ×M×Tl)(17) Direct solar flux on inclined and oriented surface is calculated by the formula: S∗=I∗×CI (18) S∗is the value of the direct solar radiation on a receiving plane (O, I). 2.2.3. Diffuse solar flux The diffuse solar radiation arrives at the receiving plane after being reflected by clouds, dust, aerosols and soil. It is assumed that the diffuse solar radiation does not have a predominant (therefore isotropic) direction, so the orientation of the receiving plane does not matter. Only its inclination is decisive. Thus, the diffuse flux for inclined receiver D∗in W/m2is calculated by the formula: D∗=125 ×sin (H)0.4×((1+cos (I)) /2)+ 211.86 ×sin (H)1.22 ×((1−cos (I)/2)) (19) The albedo is called the fraction of the solar radiation reflected by a surface (here the ground), this albedo coefficient has been integrated into the formula (19) with an average value of 0.22. This coefficient depends on the nature of the soil, its temperature and its ability to reflect solar radiation. 2.2.4. Global solar flux The total solar energy received on an inclined surface is the sum of beam and diffuse radiations directly incident on a surface and it is expressed as follows: G∗=S∗+D∗(20) The global radiation is the maximum radiation that it is possible to have on a given receiving plane (O, I), such as a solar thermal collector. The conversion of this energy into usable energy relies on the characteristics of the receiving plane. The collected energy is, also, attenuated by the efficiency of the solar cells, i.e. its ability to make use of this energy. For most part of the work, the model includes numerical definitions with numerous coefficients whose values are regularly valid for many areas in the world. In this study, measured data of global solar radiation and isotropic model has been used to estimate total solar radiation on inclined flat surfaces. 1-Solar radiation in horizontal surface The measures were carried out in the year 2015 in the three cited locations. Geographical coordinates are detailed in Table 2. Results generated by numerical model in horizontal surface are close to those provided by the meteorology station as detailed in Tables 3–5. In Fig. 3, we present the global solar irradiation measured for the year 2015 and estimated measures for Nabeul station. A good match was found between the experimental measures and those generated in the case of horizontal surface (see Tables 3–5). Table 3 Values of measured global solar radiation and estimated by the model in horizontal surface, Bizerte Station, 2015. Table 4 Values of measured global solar radiation and those estimated by the model in horizontal surface, Nabeul station, 2015. The monthly irradiation calculated from the meteorology considering the number of days in a month and daily measured irradiation (see Fig. 5). In addition, we cannot have a good approximation on cloudy days. This is shown in the Fig. 5, where we observe a coincidence between estimated and measured data except for the three points when it was cloudy. Therefore, measures should be taken over a period longer than 11 years, to ensure that climatic conditions are favorable. Fig. 5 represents the global solar radiation from January 1 to December 31. We notice that the model gives a good approximation for the whole year. In Nabeul station for July, August, October, November and December the measurement from the meteorology station are taken respectively only in 16, 6, 28, 28, 13 days. This explains the importance of numerical simulation for estimating solar radiation to compensate for the lack of data. 3. Solar radiation on tilted surface We will discuss the effect of tilting photovoltaic panels to maximize the capture of solar rays. The experimental validation of the calculations will be carried out in comparison with the data collected in the Research and Technology Center of Energy of Borj A. Ben Othman et al. / Energy Reports 4 (2018) 101–109 105 Table 5 Values of measured global solar radiation and estimated by the model in horizontal surface, Djerba station, 2015. Months Global solar radiation (Kwh/m2) Number of measured days Model Meteorology Jan. 103 108 31 Feb. 120 115 28 Mar. 170 172 31 Apr. 201 203 30 May. 229 234 31 Jun. 230 233 30 Jul. 229 229 30 Aug. 203 203 30 Sep. 170 171 30 Oct. 134 134 31 Nov. 97 97 30 Dec. 89 89 31 Fig. 5. Comparison of measured global solar radiation and estimated by the model in horizontal surface, Nabeul Station, 2015. Cedria. We will put emphasis on the importance of the inclination of the solar panel to maximize the efficiency of the energy generation process. We note that the proposed model provides a good approximation of the solar flux received on a horizontal plane throughout each day of the year. Our study aims, also, to examine the performance of solar radiation model for estimating the daily global solar radiation on tilt surface at the three different stations. The global irradiance received by a tilted surface (with an angle in respect to the horizontal plane) in the sum of both beam flux and diffuse flux densities. With a numerical simulation, we can evaluate the maximal energy that could be received by choosing an optimal angle of inclination. Many simulations are carried out to investigate the effect of the tilt angle. Results from simulation for Bizerte city are shown in Fig. 6. The daily value of total solar radiation was maximum during the 26th day of July with a peak value equal to 950 W/m2. Table 6 Seasons and optimal tilts angle, case of Bizerte city. Season Optimal tilt angle Winter 67◦ Spring 40◦ Summer 7◦ Autumn 37◦ Table 7 Values of annual global solar radiation of Bizerte city with different tilt angle. Table 8 Optimal tilt angles and latitude. City Annual optimal tilt angle Latitude Bizerte 37◦37◦16′27′′ Nabeul 36,6◦36◦27′21′′ Djerba 33,3◦33◦49′00′′ To find the optimal angle of inclination, we have used a numerical calculation program which varies the inclination angle from 0◦ to 90◦in steps of 10◦for each hour and throughout the whole year. The calculated daily powers are used to calculate the monthly and annual powers for each angle of the interval under consideration (see Figs. 6–8and Tables 7,10) The values of monthly, seasonal and annual optimum tilt angle obtained for Bizerte city are presented in Tables 6 and 11. These are also plotted against the day of the year in Fig. 9. The optimum angle for a given season is calculated by averaging the values of the optimum tilt angle for each month within that specific season (see Table 6). The optimum angle for maximum solar energy radiation capture varies according to the months of the year (see Fig. 8). The optimum tilts angle increase in winter months and decreases to minimum value in summer and autumn months (Jamil et al., 2016). Annual optimum tilt angle was calculated by averaging the value of optimum tilt angles for all months of the year and was found equal to 37◦in Bizerte. This value of optimal tilt angle is adequately close to the latitude of the studied location (see Table 8). Fig. 6. Global solar flux (W/m2) of the July 26th days for different inclination angle in Bizerte station. 106 A. Ben Othman et al. / Energy Reports 4 (2018) 101–109 Table 9 Values of Global solar radiation of Nabeul city with different tilt angles. Fig. 7. Annual global irradiation of 2015 for Bizerte station. It should be noted that the information about the maximum received solar radiation and the tilt angle are useful for sun tracking collectors that are manually or automatically adjusted. The same calculations led to similar results in the cities of Nabeul and Djerba (see Tables 8–10 and 12). The gains calculated for each city are detailed in Table 13. In the case of Bizerte and Nabeul, the expected gains from a monthly change in the angle of inclination of the panels are almost equal to the expected gains of a seasonal variation. They are significantly higher than the expected gains, if the panels have a fixed inclination throughout the year. As the monthly variation of the inclination requires much more effort, it is advisable, in the case of the cities of Bizerte and Nabeul, to change the angle of inclination of the panels each season. The shortfall is not too great. Table 10 Values of Global solar radiation of Djerba city with different tilt angles. Fig. 9. Variation of monthly, seasonal and annual optimum tilt angle in Tunisia. However, in the case of the town of Djerba, the monthly gain is much higher than the seasonal and annual gain. The variation of the inclination, of the panels, must be monthly. If not, the shortfall will be significant and the losses will be considerable (see Table 14). The gain PG(in percentage) in the availability of solar radiation on an inclined surface and it is defined as: PG(%)=(G∗ Iopti/G∗ I=0−1)×100 (21) Where i=month, season or annual. PL(%)=(1−G∗ Ioptj/G∗ Imonthly)×100 (22) Fig. 8. Global solar radiation for Bizerte station in the year 2015 for different inclination angle. A. Ben Othman et al. / Energy Reports 4 (2018) 101–109 107 Table 11 Monthly solar radiation for Bizerte station with different tilts angles. Table 12 Monthly, seasonal and annual optimum tilt angle for south facing surfaces in Bizerte city. Table 13 Monthly, seasonal and annual optimum tilt angles for south facing surfaces in Nabeul city. Where j=seasonal, annual (see Table 15). Experimental Validation In this part, we use the measured data obtained from the Research and Technology Center of Energy of Borj Cedria (see Fig. 10), (Lat 36◦44’ N, Long 10◦21’N). We compare the values of the energy produced in the months of April and May, in the year 2016 with the values of energy estimated by our numerical model. The photovoltaic panels are inclined at an angle of 30◦. Results of simulation are detailed respectively for the month of April and May in Figs. 12 and 13. The estimated energy produced by the model is close to the energy measured using the ups SB2100- TL shown in Fig. 11. This can reinforce the model and render the validity of global solar radiation in tilted surface in any given location more trustworthy. Table 14 Monthly, seasonal and annual optimum tilt angle for south facing surfaces in Djerba city. Fig. 10. Comparison of average maximum total solar radiation for Bizerte station at month, season and annual tilt angles. 4. Conclusion Faced with the gradual disappearance of fossil energy sources, solar energy is undoubtedly becoming the energy of the future. Seeking a new solar photovoltaic or thermal energy sites of high-productivity, has become a strategic priority for many countries. To validate any given site choice, it is necessary to collect measures of radiations over many years. These measures are not often available. In this paper, we proposed the use of numerical models to estimate the energetic potential of a given site. The results generated by the calculation program were validated by the data measured at three sites Bizerte, Nabeul and Djerba. 108 A. Ben Othman et al. / Energy Reports 4 (2018) 101–109 Table 15 Total solar radiation (kWh/m2) for south facing surfaces at monthly, seasonal and annual optimum tilt angles. Month Bizerte Nabeul Djerba G∗ I=0G∗ Iopt monthly G∗ Iopt seasonal G∗ Iopt annual G∗ I=0G∗ Iopt monthly G∗ Iopt seasonal G∗ Iopt annual G∗ I=0G∗ Iopt monthly G∗ Iopt seasonal G∗ Iopt annual Jan. 69.2 137 137 122 80,2 147 147 135 103 182 174 158 Feb. 76.2 140 138 131 96,2 147 144 142 120 181 166 164 Mar. 126.2 193 188 186 158 197 197 197 170 220 209 209 Apr. 182 195 196 184 182 196 191 194 201 214 199 201 May. 220 223 218 200 220,2 225 225 208 229,2 229 222 206 Jun. 248.9 248.9 242 208 228,9 238 238 210 230 241 235 210 Jul. 239.6 253 253 224 231,6 251 251 226 229,6 253 248 225 Aug. 214.9 232 224 219 221 231 223 223 203,5 235 227 222 Sep. 126.4 194 191 190 160 187 188 188 170 203 192 193 Oct. 98.4 184 184 176 130 183 180 180 134 203 179 185 Nov. 79.8 145 144 133 89,1 156 156 145 97,1 181 167 154 Dec. 69 134 135 119 75 145 145 131 89 175 162 144 Average 157 184 184 174 156 191 190 181 164 209 198 189 % Gain – 17.7 17.3 11.0 23.0 22.0 16.3 27.3 20.4 14.9 Fig. 11. Laboratory of photovoltaic, Research and Technology Center of Energy of Borj Cedria. Fig. 12. Comparison of power generated and power estimated in the location of Borj Cedria , March 2016. In the second part of this paper, we emphasized the need to choose an optimal inclination of photovoltaic panels for a predetermined period, which can be monthly, seasonal or annual. The calculation of the optimum angle of inclination and of the fixation period was validated by the data collected at the Research and Technology Center of Energy of Borj Cedria. However, it seems interesting, too, to predict climatic variations that are increasingly intense today. These variations may affect the quality of the predictions. It is necessary to think of integrating the climatic factor in the numerical models to be designed for the determination of an energetic potential of a site. Fig. 13. Comparison of power generated and power estimated in the location of Borj Cedria, May 2016. 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