ABSTRACT This paper has been made to estimate the solar radiation on horizontal and inclined surfaces in Sfax, Tunisia. The model developed in this communication can be used to estimate the hourly global, diffuse and direct solar radiations for horizontal surfaces and the total daily solar radiation on inclined and vertical surfaces in the region of Sfax. Moreover, the method presented here can be used to evaluate the energy production in Sfax of photovoltaic projects like water pumping solar, on-grid applications and off-grid applications. The estimation method of the hourly and daily solar radiations used the Liu and Jordon model. In addition, the values of monthly of average daily solar radiation on a horizontal surface are taken from NASA, Surface meteorology and Solar Energy. The mounting position of solar panel is assumed to be facing towards the south of Sfax. The present results are comparable with results of the PVGIS (Photovoltaic Geographical Information System).
Index Terms— Solar Energy, Hourly Solar Radiation, Daily solar radiation, Tilt angle, City: Sfax, TUNISIA.
1. INTRODUCTION The sun is the primary source of energy for the earth's climate system and it releases an enormous amount of radiant energy into the solar system. The radiation from the sun moves in the space as electromagnetic wave. The solar radiation is attenuated, when it goes through the earth’s atmosphere. The attenuation of solar radiation is due to scattering and absorption by air molecules, dust particles and aerosols in the atmosphere. The radiation received by the earth varies according to time of year. It is then partially reflected and absorbed by the atmosphere, so that the sun lights received on the ground have some direct and some diffused. Besides, the solar radiation incident on the surface of the earth is based on many aspects such as climatology, hydrology, biology, and architecture. Then, the solar energy incident on a solar collector in various time scales is a complex function of many factors like the local radiation climatology, the orientation, the tilt of the panel and the ground reflection properties. In addition, sometimes the design of solar energy systems needs the knowledge of the availability of solar radiation data at the location. Therefore, several of models and algorithms have been developed to calculate the solar radiation. In practice, Meteorological measurements of irradiance are usually registered for the horizontal plane by solarimeters as the pyranometer which measures the overall direct and diffuse solar radiation and the pyrheliometer, which measures only the direct radiation. The hourly solar radiation data required for solar energy system design evaluation and performance studies are
generally not available for a number of sites especially in remote locations.
2. Meteorological Data
The Meteorological Data correspond at the location of Sfax such as (latitude: 34.44˚ N, longitude: 10.46˚ E, elevation: 41 m above the sea level, heating design temperature: 8.96 and cooling design temperature: 31.96). These results have been collected from NASA, Surface meteorology and Solar Energy.
3. Basics of solar radiation
First of all, it must be need to know many variables that
will be used in several parts of the model. In the rest of this section, the equations come from a standard textbook on the subject (Solar Engineering of Thermal Processes), by Duffie and Beckman (1991).
3.1. Declination The declination is the angular position of the sun at solar noon, with respect to the plan of the equator. An approximate formula for the declination [1] of the sun is given by Cooper’s equation as follows: 23.45 2 (1)
Where n is the nth day of the year.
2012 First International Conference on Renewable Energies and Vehicular Technology
3.2. Solar hour angle The solar hour angle is the angular dthe sun east or west of the local meridiapositive in the morning and negative in the solar hour angle is equal to zero at solar mhour angle is obtained as follows: 15 12 3.3. Sunset hour angle
The sunset hour angle is the socorresponding to the time when the sun calculated by the following equation:
Where is the latitude of the site andeclination of the sun. 3.4. Extraterrestrial radiation Solar radiation incident outsideatmosphere is called extraterrestrial rextraterrestrial radiation H0 is given as follo 1 0.033 2
Where is the solar constant equal to 1all other variables have the same meaning a 3.5. Clearness index The clearness index is the ratio ofat the surface of the earth to extraterresTherefore, the monthly clearness index is g[3]:
Where: : is the monthly average daily solar
horizontal surface. : is the monthly of the extraterrestr
radiation. 3.6. Mathematical formulation The technique used for determining of the solar day uses the analysis of the moJordan (1996). This theoretical model is detail as follows.
3.6.1. Method
In the beginning of the algorithm, aftsuch as the monthly average daily solar horizontal plan , the inclination angle ,
displacement of an. It becomes afternoon. The
midday of solar
(2)
olar hour angle sets [2]. It is
(3)
nd it is the
e the earth’s radiation. The ows [3]:
(4)
1367 Wm-2 and as before.
f solar radiation strial radiation.
given as follows
(5)
radiation on a
rial daily solar
the distribution odel of Liu and
developed in
ter reading data radiation on a
, the latitude φ,
the longitude L, and the albedo ρ, wthe declination δ, the sunset extraterrestrial radiation H0 and tAfter doing this calculation, wedata by specifying the day of the cosecond step, we calculate the monthsolar radiation from the monthly oa horizontal surface . Then, we calto determine the hourly global horizthe coefficient rd to calculate the hHd. The direct or beam irradiance Hhourly irradiances H and Hd. In the the global hourly irradiance on tiltedof the considered day. This calculatisunrise to the sunset of the day, tchange in the value of the angle ω hoThe total daily solar radiation is ovalues of Ht.
Figure 1.Algorithm of the nu
3.6.2. Calculation of Hourly diffuse i
The actual amount of solar raparticular location on the earth is addition, the regular daily variatiomotion are due to the sun and also that are caused by local atmospheclouds. All these factors can influensunshine daily. In particularity, these direct and diffuse components of so
we proceed to calculate hour angle , the
he clearness index . e go to initialize the onsidered month. In the hly average daily diffuse of the solar radiation on lculate the coefficient rt zontal irradiance H and
hourly diffuse irradiance Hb is calculated from the
third step, we calculate d surface Ht for all hours ion is repeated from the taking into account the
ourly throughout the day. obtained by summing all
umerical method
irradiance
adiation that reaches a extremely variable. In
n and annual apparent the irregular variations
eric conditions such as ce of the distribution of reasons influence in the
lar radiation. The direct
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normal radiation or the beam radiation is the part of the sunlight that directly reaches the earth’s surface. The scattered radiation reaching the earth’s surface is called diffuse radiation. Then a component of the solar radiation is reflected by the earth’s surface, and which is called albedo. The algorithm requires the knowledge of beam and diffuse radiation for every hour of an average day. The algorithm described in the last paragraph shows that the monthly average daily diffuse radiation is calculated from the monthly average daily global horizontal radiation and is determined by Erbs and al [3]. , is calculated by the following equation: 1.391 3.560 4.189 2.137 (6)
When the sunset hour angle is less than 81.4º, and: 1,311 3 ,022 3 ,427 1,821 (7)
When the sunset hour angle is greater than 81.4º, in addition, the ratio of hourly total to daily total diffuse radiation is given as the following equation:
(8)
For each hour of the average day, the diffuse part is calculated with [4]:
(9)
3.6.3. Calculation of Hourly Horizontal irradiance
The global hourly irradiance is a measure of the total hourly solar energy rate incoming in the Earth surface. The Numerical model for predicting the global hourly irradiance has been presented in these equations [5]:
(10)
Where: 0 ,409 0 ,5016 (11)
And: 0 ,6609 0 ,4767 (12)
The equation presented here is a simple approach for the calculation the global hourly irradiance daily distribution based on the formula from Collares-Pereira and Rabl for global irradiance [6]:
(13)
3.6.4. Calculation of Hourly direct or beam irradiance
The hourly direct irradiance Hb is the incident solar radiation that reaches the earth’s surface without being
significantly scattered and coming from the direction of the sun. So, Hb is given as follows [7]:
(14) 3.6.5. Calculation of Hourly irradiance in the tilt surface
The methods to estimate the ratio of diffuse solar radiation on a tilted surface to that of a horizontal are classified as isotropic and anisotropic models [8]. In addition, the isotropic models assume that the intensity of diffuse sky radiation is uniform over the sky dome. Moreover, the analytical expressions of isotopic models are defined as follows:
The Liu and Jordan model [4]:
(15)
The Badescu model [9]:
(16)
The Koronakis model [10]:
(17)
The Tian et al. model [11]: 1 (18)
Where, is the tilt angle?
The correlation procedures that are proposed by Liu and Jordon [1960], Collares-Pereira and Rabl [1979] to obtain the hourly irradiance values on the inclined panel surface are determined as the following ([6], [12] and [13]):
(19)
Where, represents the diffuse reflectance of the ground and represents the ratio of an average day of the beam
radiation on a tilted surface to that on a horizontal surface, which can be expressed as [6]: (20)
Where, is the inclination angle, φ is the latitude and is the declination.
3.6.6. Calculation of Daily tilted irradiance
The daily total is obtained by summing individual hours. The expression formula for the daily irradiance is given as the following [14]:
∑ ; (t = hour) (21)
Where, is the time of rise of the sun and is the
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time of set of the sun. Also, both are dthese equations: 12
And 12 Where, L is the longitude and is the eqso, an approximate formula for the equatminutes is given as follows: .
Where, j is the day of the considered month
4. Results and discussion
Using equations (1) to (4) the dailysolar radiation is calculated for each monththe region of Sfax. Using Matlab, we plotting easily the distribution of the dailyradiation. The daily extraterrestrial radiati4800 Wh.m-2.day for the winter seasoWh.m-2.day for the summer months.
Figure 2.Daily extraterrestrial radiation on surface H0.
The values of monthly of averagradiation on a horizontal surface are takeSurface meteorology and Solar Energy fo
Figure 3.Monthly of average daily solar rahorizontal surface The program developed in Matlab u
Wh/
m2 .D
ay
Wh/
m2 .m
onth
etermined with
(22)
(23)
quation of time, tion of time in
(24)
h.
n
y extraterrestrial h of the year for
have allowed y extraterrestrial ion varies from on and 11500
a horizontal
ge daily solar en from NASA, for city of Sfax.
diation on a
using the above
formulas (6) and (7) allows calcuaverage daily direct solar radiatioaverage daily diffuse solar radiasurfaces. The maximum valuaverage daily diffuse solar radiaWh.m-2.month-1 in summer and the mWh.m-2.month-1 for the month of Daverage daily direct radiation is the monthly of average daily solar rsurface and the monthly aradiation . Hence, the value of the month of June and equals to 5250
Figure 4.Monthly of average daily di
Figure 5.Monthly of average daily di
The meteorological data is inand providing the monthly of averag
and the monthly of average dailythe horizontal surfaces. Correlation to obtain solar irradiance values ohorizontal radiation. The hourly irrinclined panel surface is nindividually considering the direct diffuse irradiance and reflecteradiation on a tilted surface. The albeThe following figures illustrate the global irradiance H, the hourly diffuhourly direct or beam irradiance year. According to these resultsdistributions of the hourly irradianceday vary with a sinusoidal fomaximum sunlight is at midday for eis equal to 360 Wh.m-2.hour-1 inWh.m-2.hour-1 in June. Therefore, thirradiances H, and Hb for each mfollowing table (1).
Wh/
m2 .m
onth
W
h/m
2 .m
onth
ulating the monthly of on and monthly of ation on horizontal e of the monthly
ation equals to 2300 minimum value equals to December. The monthly
the difference between radiation on a horizontal average daily diffuse reaches its maximum in
0 Wh.m-2.month-1.
iffuse radiation
irect radiation
ndicated in section two ge daily diffuse radiation y direct radiation on procedures are required
on tilted surfaces from radiance values on the
normally estimated by or beam irradiance ,
ed components of the edo is assumed to be 0.2. variations of the hourly
use irradiance and the for each month of the
, we observe that the s H, and Hb during a
orm. In addition, the ach day of the year, also n December and 820 he values of the hourly
month is obtained in the
134
Table 1.Values of the hourly irradiances
(a) January
(b) February
(c) March
(d) April
(e) May s H, and Hb
135
(f) June
(g) July
(h) August
(i) September
(j) October
(k) November
(l) December
Figure 6.Hourly components of solsurface
Historical studies and the recenground-based measurements of diffuaccurate due to thermodynamic imoperational techniques that are uMoreover, many important errors acloud fraction suggesting changes iFor this reason, several correlationsused to estimate the diffuse radiatiMatlab program for plotting thprovide the results of the monthradiation for tilt angles (0° to 90°) dTherefore, the values of the monthisotopic models for each month are otable (2).
r
r
lar radiation on a tilted
nt research indicate that use radiation site are less mbalances within some used in these studies. appear to be based on n the daily uncertainty. of isotopic models are ion. We have used the he equations (15) to (18) hly variation of diffuse
described in this figures. hly diffuse irradiance of obtained in the following
136
137
Table 2.Values of the diffuse irradiancmodels
Figure 7.Monthly diffuse irradiance on thsurface with Liu and Jordon model
Figure 8.Monthly diffuse irradiance on thsurface with Badescu model
Figure 9.Monthly diffuse irradiance on thsurface with Koronakis model
ce of isotopic
he each inclined
e each inclined
e each inclined
Figure 10.Monthly diffuse irradiancsurface with Tian model
The figure 11 shows the resultstotal radiation on an inclined plan witfor the region of Sfax. Accordingobserved that the importance of solarthe solar panel in the summer monthof direct irradiance. Also, the amouproduced by a solar panel attached due to the effect of diffuse irradiancthat the maximum average annual totto the angle of inclination that estimated annual electricity producpower equals to 1 kWp, which coroptimum angle for the city of Sfax thTherefore, the values of the monthlyeach inclined surface with Liu aobtained in the following table (3).
Table 2.Values of the monthly total i
ce on the each inclined
s of the monthly average th Liu and Jordon model
g to these results, it is r energy flux received by hs is related to the effect unt of the solar energy to a vertical position is
ce. In addition, we show tal radiation corresponds
equals to 30°. The tion for a photovoltaic rresponds to the annual hat equals to 1868 kWh. y total irradiance on the and Jordon model are
rradiance
138
Figure 11.Monthly total irradiance on the each inclined surface with Liu and Jordon model
The Figure 12 shows the tilt angles for each month of the year when the solar panel is fixed at the optimum angle for the region of Sfax. Moreover, we show that the yearly average tilt is found to be 31° and this result in a fixed tilt throughout the year. The seasonal average is calculated by finding the average value of the tilt angle for each season and this procedure requires that the tilt angle of the collector to be changed four times a year. Hence, the optimum angle of the solar panel in winter is 50° and the total seasonal of the average solar irradiation falling on the collector surface at this tilt is 4197.46 Wh.m-2.season-1. The optimum tilt angle then decreases during the spring months and equals to 20° which collects 5893.33 Wh.m-2.season-1 of solar energy. Also, the optimum tilt angle in summer equals to 5° and the total seasonal of the average solar radiation at this angle is 7236.66 Wh.m-2.season-1. In autumn, the optimum angle should correspond to 40° and the total seasonal of the average solar irradiation collected reaches 5230 Wh.m-2.season-1. The benefit of this procedure that the total annual of the average solar radiation increases of 5305 Wh.m-2.year-1 with β equals to 31° to 5639.36 Wh.m-2.year-1 for the seasonal tilt angle.
Figure 12.Tilt angles for each month of the year
5. Validation
In this section, ours results for each tilt angle which correspond to the total seasonal and annual solar radiation are comparable with the results of the PVGIS (Photovoltaic Geographical Information System). We observe that the difference between these results is referred to the values of the monthly of average daily
solar radiation on a horizontal surface are taken from the NASA, Surface meteorology and Solar Energy and they are not exactly similar with the values of of PVGIS. Also, a part of this difference is due to the estimation algorithm of the incident hourly irradiance values on tilted surface Ht. The results of comparison are presented in the following figures. We show that the difference between ours results and PVGIS results equals to 3%.
Figure 13.Total irradiance for the tilt angle equals to 5°
Figure 14.Total irradiance for the tilt angle equals to 20°
Figure 15.Total irradiance for the annual optimum tilt angle
010002000300040005000600070008000
1 2 3 4 5 6 7 8 9 10 11 12
Our resultsPVGIS results
Ht (Wh.m-2.month-1)
010002000300040005000600070008000
1 2 3 4 5 6 7 8 9 10 11 12
Our resultsPVGIS results
Ht (Wh.m-2.month-1)
010002000300040005000600070008000
1 2 3 4 5 6 7 8 9 10 11 12
Our resultsPVGIS results
Ht (Wh.m-2.month-1)
Month
Month
Month
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Figure 16.Total irradiance for the tilt angle equals to 40°
Figure 17.Total irradiance for the tilt angle equals to 50°
6. Conclusion Today, the high energy use engenders an insufficiency in the recovery of the energy current for the human needs. However, facing economic problems due to large increases in fuel prices, the world has moved gradually towards to the exploitation of new and renewable energies. It is in this context, that we started our work to estimate the hourly global irradiance H, the hourly diffuse irradiance and the hourly direct irradiance for each month of the year for the region of Sfax. We also calculated the monthly diffuse irradiance of isotopic models for each month. Then, we found the values of the monthly total irradiance on the each inclined surface with Liu and Jordon model for the seasonal and annual tilt angles and they are validated with the PVGIS results. Specifically, we have considered the model of Liu and Jordon to determine the distribution of the solar radiation for each month of the year and to take data as the monthly average daily solar radiation on a horizontal plan , the tilt angle β, the latitude φ, the longitude L and the albedo ρ for the location of Sfax. In perspectives, we propose to continue this work with the development of a numerical interface with the Matlab software to determine the estimations of the solar radiations for all regions of Tunisia. In addition, it uses in practical applications such as water pumping solar, on-grid applications and off-grid applications.
7. References
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[2] Duffie, J. A. and W. A. Beckman, 1991: Solar Engineering of Thermal Processes, Second Edition, John Wiley & Sons, Inc., New York.
[3] Erbs, D. G., S. A. Klein, and J. A. Duffie, 1982: Estimation of the Diffuse Radiation Fraction for Hourly, Daily and Monthly average Global Radiation. Solar Energy, Vol. 28, No. 4, pp. 293-302.
[4] Bugler J. The determination of hourly isolation on a tilted plane using a diffuse irradiance model based on hourly measured global horizontal isolation, solar energy 1977, 19.
[5] Vignola, F. and D. K. Mc Daniels, 1984: Diffuse-Global Correlations: Seasonal Variations, solar energy, Vol. 33, No. 5, pp. 397-402.
[6] Collares-Pereira, M. and A. Rabl, 1979: The Average Distribution of Solar Radiation- Correlations between Diffuse and Hemispherical and Between Daily and Hourly Isolation Values. Solar Energy, Vol. 22, No. 1, pp. 155-164.
[7] Liu, B. Y. H. and R. C. Jordan, 1960: The Interrelationship and Characteristic Distribution of Direct, Diffuse, and Total solar radiation, solar energy, Vol. 4, No. 3, pp. 1-19.
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[10] Koronakis PS, on the choice of the angle of tilt for south facing solar collectors in the Athens basin area, Solar Energy 1986; 36:217.
[11] Tian YQ, Davies-Colley RJ, Gong P, Thorold BW. Estimating solar radiation on slopes of arbitrary aspect. Agric Forest Meteorology 2001; 109:67–77.
[12] Liu B, Jordan R. Daily isolation on surfaces tilted towards the equator. Trans ASHRAE 1962, 67. [13] Perez R, Ineichen P, Seals R, Michal sky J, Stewart R. Modeling daylight availability and irradiance components from direct and global irradiance, Solar Energy 1990; 44.
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