Global, direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah, Saudi Arabia

Applied Energy 87 (2010) 568–576

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Global, direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah, Saudi Arabia A.A. El-Sebaii *, F.S. Al-Hazmi, A.A. Al-Ghamdi, S.J. Yaghmour Physics Department, Faculty of Science, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

a r t i c l e

i n f o

Article history: Received 14 January 2009 Received in revised form 13 June 2009 Accepted 22 June 2009 Available online 29 July 2009 Keywords: Solar radiation Sunshine hours Meteorological parameters Regression analysis Tilted surfaces

a b s t r a c t The measured data of global and diffuse solar radiation on a horizontal surface, the number of bright sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover for Jeddah (lat. 21°420 3700 N, long. 39°110 120 0 E), Saudi Arabia, during the period (1996–2007) are analyzed. The monthly averages of daily values for these meteorological variables have been calculated. The data are then divided into two sets. The sub-data set I (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H0) and the various weather parameters. The sub-data set II (2005–2007) are then used to evaluate the derived correlations. Furthermore, the total solar radiation on horizontal surfaces is separated into the beam and diffuses components. Empirical correlations for estimating the diffuse solar radiation incident on horizontal surfaces have been proposed. The total solar radiation incident on a tilted surface facing south Ht with different tilt angles is then calculated using both Liu and Jordan isotropic model and Klucher’s anisotropic model. It is inferred that the isotropic model is able to estimate Ht more accurate than the anisotropic one. At the optimum tilt angle, the maximum value of Ht is obtained as 36 (MJ/m2 day) during January. Comparisons with 22 years average data of NASA SSE Model showed that the proposed correlations are able to predict the total annual energy on horizontal and tilted surfaces in Jeddah with a reasonable accuracy. It is also found that at Jeddah, the solar energy devices have to be tilted to face south with a tilt angle equals the latitude of the place in order to achieve the best performance all year round. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Solar radiation data are a fundamental input for solar energy applications such as photovoltaic, solar–thermal systems and passive solar design. The data should be reliable and readily available for design, optimization and performance evaluation of solar technologies for any particular location. Unfortunately, for many developing countries, solar radiation measurements are not easily available because of not being able to afford the measuring equipments and techniques involved. Therefore, it is necessary to develop methods to estimate the solar radiation on the basis of the more readily available meteorological data. Many models have been developed to estimate the amount of global solar radiation on horizontal surfaces using various climatic parameters, such as sunshine duration, cloud cover, humidity, maximum and minimum ambient temperatures, wind speed, etc. [1–7]. Wu et al. [8] used the metrological data from 1994 to

* Corresponding author. Permanent address: Department of Physics, Faculty of Science, Tanta University, Tanta, Egypt. Tel.: +20 96505604537; fax: +20 96266951106. E-mail address: [email protected] (A.A. El-Sebaii). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.06.032

2005 of Nanchang station (China) to predict daily global solar radiation from sunshine hours, air temperature, total precipitation and dew point. Sen [9] proposed a nonlinear model for the estimation of global solar radiation from available sunshine duration data. This model is an Angström type model with a third parameter appears as the power of the sunshine duration ratio that gives the nonlinear effects in solar radiation and sunshine duration relationship. A simple model for estimation of monthly average of daily global solar radiation data on horizontal surfaces was recently proposed by Bulut and Büyükalaca [10]. The model was based on a trigonometric function, which has only one independent parameter, namely the day of the year. It was found that the model can be used for estimating monthly average of daily global radiation for 68 provinces of Turkey with a high accuracy. Janjai et al. [11] proposed a model for calculating the monthly average hourly global radiation in the tropics with high aerosol load using satellite data. This model was employed to generate hourly solar radiation maps in Thailand. It is rather important to determine the beam and diffuse components of total radiation incident on a horizontal surface. Once these components are determined, they can be transposed over tilted surfaces, and hence, the short as well as the long term

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569

Nomenclature d H Ho Hb Hd Hd,m Hd,c Hi,c, Hi,m Ht Ht,b Ht,d Ht,gr Kt

day of the year monthly average of daily global radiation on horizontal surface (W/m2 day) monthly average of daily extraterrestrial radiation on horizontal surface (W/m2 day) monthly average of daily beam radiation on horizontal surface (W/m2 day) monthly average of daily diffuse radiation on horizontal surface (W/m2 day) monthly average of daily measured diffuse radiation on horizontal surface (W/m2 day) monthly average of daily calculated diffuse radiation on horizontal surface (W/m2 day) the ith calculated and measured values of H (W/m2 day) monthly average of daily total radiation on tilted surface (W/m2 day) monthly average of daily beam radiation on tilted surface (W/m2 day) monthly average of daily diffuse radiation on tilted surface (W/m2 day) monthly average of daily ground reflected radiation on tilted surface (W/m2 day) monthly average of daily clearness index

performances of tilted flat plate collectors, photovoltaic modules and other solar devices can be estimated. Many authors have presented empirical correlations to estimate the monthly average daily diffuse radiation on a horizontal surface [12–16] where the diffuse fraction Hd/H is either correlated to the monthly average daily clearness index Kt [12–14] or to the fraction of possible number of bright sunshine hours s/s0 [15,16]. Gopinathan [17] proposed empirical correlations of Hd/H with Kt, s/s0 and a combination of them. El-Sebaii and Trabea [18] proposed correlations for estimating horizontal diffuse radiation in Egypt by correlating Hd/H and Hd /H0 with Kt and s/s0. Recently, the neural-network technique was used to estimate hourly values of diffuse radiation on horizontal surfaces at Sa˘o Paulo city (Brazil) using the global radiation and other meteorological parameters [19]. Models were also proposed for estimating daily diffuse radiation using sunshine fraction, clearness index and cloudiness factor [20]. It was found that the models employing clearness index and cloudiness factor were optimum choice for estimating daily diffuse radiation. On the other hand as far as the authors know, few correlations have appeared concerning estimation of direct solar radiation on horizontal surfaces; because it is usually estimated by subtracting diffuse radiation from global radiation. In most cases, the method of subtracting the diffuse radiation from the total radiation does not give accurate results. Therefore, it has become increasingly important to accurately estimate the amount of monthly average of daily direct solar radiation Hb available in a given region of the world for feasibility study and successful implementation of concentrating solar energy systems. Recently, Solanki and Sangani [21] proposed a new method which may be used for estimating Hb on the basis of calculation of the elevation angle constant (e) for a given location and time. Artificial neural-network using satellite data were also used to estimate monthly mean daily average of horizontal direct and diffuse radiation in different cities of Turkey [22]; where diffuse and direct radiation were calculated as functions of optical air mass, turbidity factor and Rayleigh optical thickness for clear-sky. Furthermore, meteorological stations usually measure solar global and diffuse radiation intensities on horizontal surfaces. Mea-

beam radiation conversion factor ground reflected radiation conversion factor total radiation conversion factor regression coefficient monthly average of daily bright sunshine hours (h) monthly average of maximum possible number of sunshine hours (h) T ambient temperature (°C) maximum ambient temperature (°C) Tmax minimum ambient temperature (°C) Tmin amount of cloud cover (octas) Cw relative humidity (%) Rh a, b, c, I1, I2 empirical constants a hourly altitude angle of the sun with respect to horizontal surface (deg) e elevation angle constant b tilt angle with horizontal (deg) h incident angle of beam radiation on tilted surface (deg) incident angle of beam radiation on horizontal surface hz or zenith angle (deg) u latitude (deg) d solar declination angle (deg) xs sunset hour angle (deg) Rb Rr Rt r2 s s0

sured solar radiation data on tilted surfaces are rarely available. Consequently, the solar radiation incident on a tilted surface must be determined by converting the solar radiation intensities measured on a horizontal surface to that incident on the tilted surface of interest in order to design the system size and estimate its long term performance. Total radiation incident on a tilted surface consists of three components: beam radiation, diffuse radiation and ground reflected radiation. The beam radiation on a tilted surface can be computed by the relatively simple geometrical relationship between the horizontal and tilted surfaces. The ground reflected radiation can be estimated with good accuracy with the aid of an isotropic model using a simple algorithm. This is not the case regarding the diffuse component, since diffuse radiation has no define or (singular) angle of incidence on a horizontal surface. There exist a relatively large number of models that attempt to correlate the diffuse radiation on a tilted surface to that measured on a horizontal surface. Generally, these models may be classified as isotropic and anisotropic models. The most common isotropic model is that developed by Liu and Jordan [23] using the simplifying assumption of isotropic distribution of diffuse radiation which is independent of zenith and azimuth angles. On the other hand, the anisotropic models assume the sky as anisotropic source of diffuse radiation. Many investigators [24–26] have used the isotropic and anisotropic models for estimating the total solar radiation incident on tilted surfaces. Noorian et al. [27] recently performed an evaluation of 12 isotropic and anisotropic models to estimate hourly diffuse radiation on inclined surfaces in Iran. Some papers have appeared concerning estimation of solar radiation over Saudi Arabia. Sabbagh et al. [28] estimated the daily global solar radiation for various places in Egypt, Kuwait, Lebanon, Sudan and Saudi Arabia. Al-Ayed et al. [29] proposed empirical correlations for calculating the monthly average of daily global, direct and diffuse solar radiation on horizontal surfaces in Riyadh using the data of 1 year (1986). Multiple correlations between different solar parameters have been proposed by Benghanem and Joraid [30] for estimation of the monthly average of global and diffuse so-

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lar radiation in Medina. Empirical correlations between Hd/H and first, second and third orders of s/s0 have been proposed. Simulation and modeling of hourly total solar radiation on tilted surfaces with different orientations for different climatic zones in Saudi Arabia have been performed by Zuhairy and Sayigh [31]. Also, estimation of monthly average daily and hourly data of solar radiation on a tilted surface and comparison with measured data for Dhahran (Saudi Arabia) is conducted [32,33]. It has been concluded that for hot-arid areas, the isotropic model is more accurate for tilt angle values around the latitude of the location [32]. It is worth mentioning that all the proposed models contain empirical constants, which depend on the season and the geographical location of the place [18,34,35]. However, suggesting models for calculating different components of solar radiation incident on horizontal and tilted surfaces in different places of Saudi Arabia is still of considerable interest. The main objectives of this paper are: (i) to develop empirical correlations to estimate the monthly average daily global solar radiation on horizontal surfaces in Jeddah using the available meteorological data. (ii) To propose empirical correlations for estimating diffuse radiation on horizontal surfaces. (iii) To calculate the total solar radiation incident on tilted surfaces facing south in Jeddah (as a representative for the warm-humid zone in Saudi Arabia) using both isotropic and anisotropic models. These data are not available for most of Saudi cities. 2. Methodology 2.1. Total solar radiation on horizontal surfaces In the present work, data of the monthly average of: daily global solar radiation H on a horizontal surface, number of bright sunshine hours s, ambient temperature T, cloud cover cw, relative humidity Rh and maximum Tmax and minimum Tmin ambient temperatures for Jeddah for the period 1996–2007 were taken from Saudi Ministry of Defense and Aviation, Meteorology and Environmental protection Administration, Jeddah. The data were averaged to obtain the monthly mean daily values by taking the data for the average day of the month. The mean daily values for each month were then averaged over the past 12 years (1996–2007). The obtained average values were divided into two sub-data sets, one of which from 1996–2004 was used for calibrating and developing models, and another for the years 2005–2007 for evaluating models. The correlations to which the measured data were fitted are as follows:

H=H0 ¼ a þ bðs=s0 Þ

standard procedure [35]. H0 and s0 for the average day of each month were calculated using the equations given in the Appendix. As a next step, the computer programs were used to calculate the empirical constants of Eqs. (1)–(8) with the aid of measured values of H and other meteorological parameters. Values of the empirical constants a, b and c are summarized in Table 1. The obtained correlations were then employed to estimate the global radiation H for the considered location (Jeddah) for the period 1996–2007. The calculated values of H were compared with the measured data. The accuracy of estimation of H was tested by calculating the mean bias error (MBE), root mean square error (RMSE) and the mean percentage error (MPE). Low values of RMSE and MPE are desirable. Positive MBE shows overestimation while negative MBE indicates underestimation. The MBE, RMSE and MPE are defined as in the following equations:

i. n Hi;c  Hi;m nhX  2 io1=2 RMSE ¼ Hi;c  Hi;m =n X   Hi;c  Hi;m  100 n MPE ¼ Hi;m

MBE ¼

h H ¼ I2 þ ðI1  I2 Þ sin

ð2Þ

H=H0 ¼ a þ bðs=s0 Þ þ cRh

ð3Þ

H=H0 ¼ a þ bT þ cRh

ð4Þ

H=H0 ¼ a þ bðT max  T min Þ þ ccw

ð5Þ

H=H0 ¼ a þ bðT max  T min Þ0:5 þ ccw

ð6Þ

H=H0 ¼ a þ bðs=s0 Þ þ ccw H=H0 ¼ a þ bðs=s0 Þc

ð7Þ ð8Þ

where a, b and c are empirical constants and s0 is the maximum possible monthly average daily sunshine duration or the day length. The measured data were used in linear and multiple linear regression analysis to obtain the values of empirical constants in Eqs. (1)–(8). Proper computer programs were written in Pascal language for the regression analysis by writing subroutines for calculating the extraterrestrial radiation values H0 and the day length s0 using the

ð11Þ

p 365

i 1:5 ðd þ 5Þ

ð12Þ

2.2. Beam and diffuse radiation on horizontal surfaces According to the elevation angle method, Hb can be estimated as [21]:

Hb ¼ ðHd  HÞ=e

ð13Þ

where e is the elevation angle constant for a given location and time. e is given as [21]:

ð1aÞ

H=H0 ¼ a þ bðs=s0 Þ þ cT

ð10Þ

For the 1st January d = 1, and for 31st December d = 365. I1 and I2 are empirical constants and they should be determined for each location separately by the method of regression analysis [10]. The data available for Jeddah were used to find the coefficients I1 and I2.

e¼ H=H0 ¼ a þ bðs=s0 Þ þ cðs=s0 Þ

ð9Þ

where Hi,c and Hi,m are the ith calculated and measured values of H and n is the number of observations. The nonlinear model proposed by Sen [9] and the Bulut and Büyükalaca [10] model, which were used to estimate H for different places of Turkey were also employed for estimation of H in Jeddah. Sen model is presented above by Eq. (8). Bulut and Büyükalaca model [10] that was based on a trigonometric function with only one independent variable, namely the day of the year d is given by:

ð1Þ 2

hX 

Psunset

sinðaÞ þ 0:0944 12

sunrise

ð14Þ

for maximum sunshine hours in a representative day of the month 612 and

e¼

Psunset

sunrise sinðaÞ þ 0:0944 day length

ð15Þ

for maximum sunshine hours in a representative day of the month >12.where a is the hourly altitude angle of the sun with respect to a horizontal surface for the given location and for a given hour of the day. Eq. (13) was used for calculation of the monthly average daily beam radiation on a horizontal surface in Jeddah using the measured values of H and Hd during the period (1996–2007). This data has been obtained from King Abdul Aziz City for Science and Technology. In order to develop empirical correlations for calculating the monthly average daily diffuse radiation incident on a horizontal surface, the diffuse fraction (Hd/H) and diffuse transmittance (Hd/ Ho) were correlated to first, second and third order correlations

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A.A. El-Sebaii et al. / Applied Energy 87 (2010) 568–576 Table 1 Derived empirical correlations describing the relation between H/H0 and meteorological variables for Jeddah for the period (1996–2004). Model no.

Regression equation

MBE

RMSE

MPE

r2

(1) (2) (3) (4) (5) (6) (7) (8), [9] (12), [10]

H/H0 = 2.81 + 3.78(s/s0) H/H0 = 1.92 + 2.60(s/s0) + 0.006T H/H0 = 1.62 + 2.24(s/s0) + 0.332Rh H/H0 = 0.139  0.003T + 0.896Rh H/H0 = 0.214 + 0.035(Tmax  Tmin)  0.028cw H/H0 = 0.08 + 0.21(Tmax  Tmin)0.5  0.012cw H/H0 = 2.76 + 3.72(s/s0) + 0.001cw H/H0 = 0.864 + 1.862(s/s0)2.344

 1:5 H ¼ 14:92 þ 9:61 sin p ðd þ 5Þ

0.011 0.007 0.009 0.006 0.033 0.044 0.022 0.014 0.018

0.04 0.02 0.03 0.02 0.11 0.15 0.08 0.05 0.07

0.65 0.01 0.26 0.39 0.56 1.43 1.19 0.72 0.85

0.974 0.985 0.986 0.963 0.980 0.996 0.974 0.975 0.921

365

of the clearness index Kt and the relative number of sunshine hours (s/so). It is found that the second and third order correlations do not improve the accuracy of estimation of Hd. Therefore, the following correlations have been obtained for Jeddah:

Hd =H ¼ 4:618  6:269K t ;

2

Hd =H0 ¼ 2:973  4:037K t ;

ð17Þ ð18Þ

where F = 1  (Hd/H)2. The total radiation incident on a tilted surface may be written as

ð19Þ

H t ¼ Rt H

r2 ¼ 0:961

Hd =H0 ¼ 3:002  3:882K t  0:150ðs=s0 Þ;

r 2 ¼ 0:963 r 2 ¼ 0:965

ð20Þ

ð26Þ

ð27Þ

where Rt is the total radiation conversion factor defined as:

Rt ¼ Ht =H ¼ ½1  ðHd =HÞRb þ ðHd =HÞRd þ qð1  cos bÞ=2

ð28Þ

Numerical calculations were performed for calculation of Ht for different tilt angels of a surface facing south using the measured data on horizontal surfaces for the period (1996–2007). 3. Results and discussion

ð21Þ

Eqs. (16)–(21) were used to calculate Hd and the obtained results were compared with the measured values of Hd. The accuracy of estimating Hd was checked by calculating the MBE, RMSE and the MPE. 2.3. Total radiation on tilted surfaces Estimation of total solar radiation incident on tilted surfaces in Jeddah, as a representative for the warm-humid zone in Saudi Arabia, using Liu and Jordan isotropic model [23] and Klucher’s [36] anisotropic model will be carried out in an attempt to check if either the isotropic or the anisotropic model is suitable for such estimation. Comparisons with the data available for Dhahran (lat. 26°180 N) have been performed. Measured data of the monthly average daily beam Hb and diffuse Hd radiation for the period (1996–2007) were used. The monthly average daily total solar radiation on a tilted surface can be written as

ð22Þ

where q is the ground reflectivity. Rb and Rr are the beam and ground reflected radiation conversion factors, given as for both isotropic and anisotropic models:

ð23Þ

and

Rr ¼ ð1  cos bÞ=2

3

r 2 ¼ 0:908

Hd =H ¼ 4:609  6:318K t þ 0:047ðs=s0 Þ;

Rb ¼ cos h= cos hz

Klucher’s model (anisotropic):

2

Furthermore, Hd/H and Hd/Ho were correlated to first and second order correlations of the Kt and s/so combination. Also, it has been found that the second order correlations between Hd/H or Hd/Ho and Kt and s/so combination do not improve the accuracy of estimation of Hd. The following correlations were found to fit the measured data of Hd:

Ht ¼ Hb Rb þ Hd Rd þ HqRr

ð25Þ

Rd ¼ ½ð1 þ cos bÞ=2½1 þ F sin ðh=2Þ½1 þ F cos2 h cos3 hz 

r ¼ 0:899

Hd =H0 ¼ 3:542  3:664ðs=s0 Þ;

Rd ¼ ð1 þ cos bÞ=2

ð16Þ

r ¼ 0:956

Hd =H ¼ 5:488  5:672ðs=s0 Þ;

Liu and Jordan’s model (isotropic):

ð24Þ

where h and hz are the incident angles for beam radiation on tilted and horizontal surfaces, respectively. b is the surface tilt angle with respect to the horizontal. The only difference between the isotropic and anisotropic models appears in the diffuse radiation conversion factor Rd, and it is given below for each model.

Empirical correlations, for estimation of total solar radiation on horizontal surfaces, in the form of Eqs. (1)–(8) are proposed for Jeddah using the meteorological sub-data set I (1996–2004). From the analysis of the measured and calculated values of H, the regression equations between (H/H0) and meteorological variables along with the values of MBE (MJ/m2 day), RMSE (MJ/m2 day), MPE (%) and the regression coefficient (r2) are summarized in Table 1. From the results of Table 1, it is seen that, the values of r2 are higher than 0.92 and the values of the RMSE are found in the range 0.02–0.15 (MJ/ m2 day) indicating fairly good agreement between measured and calculated values of H. The negative values of the MPE show that, Eqs. (2)–(6) slightly overestimate H; but, Eqs. (1), (7), (8), and (12) slightly underestimate H. In all cases, the absolute values of the MPE never reach 1.5%, indicating very good agreement between the measured and calculated data and a fairly good fitting exists between the monthly average of daily global radiation and the other meteorological parameters. The second order correlation between H/H0 and s/s 0, Eq. (1a), does not improve the accuracy of estimation of H. The values of the regression constants a, b and c for Jeddah using the nonlinear model [9], Eq. (8), are obtained as 0.864, 1.862 and 2.344, respectively. Furthermore, it has been found that the model proposed by Bulut and Büyükalaca [10], Eq. (12), represents the measured data satisfactorily and the model constants I1 and I2 for Jeddah are obtained as 24.536 and 14.924, respectively, with a correlation coefficient of 0.921. The agreement between measured and calculated H was also confirmed for each month by calculating the relative percentage error (RPE) for each month defined as:

RPE ¼

Hi;c  Hi;m  100ð%Þ Hi;m

ð29Þ

Fig. 1A and B shows comparisons of the RPE of measured and calculated H for all models examined. It is obvious from the results

572

A

A.A. El-Sebaii et al. / Applied Energy 87 (2010) 568–576 40

80

Eq. (1) Eq. (2) Eq. (3) Eq. (4)

60

30

2

Hb,c (MJ/m day)

40

RPE (%)

Hb,m vs Hb,c linear fit r2=0.978

20

0

20

10

-20

-40

0

1 Jan.

2

3

4

5

6

7

8

9

10

11

12 Dec.

0

5

10

20

25

30

2

Month

Hb,m(MJ/m day)

B 80

Fig. 2. Comparison between measured and calculated beam radiation on horizontal surface in Jeddah (1996–2007). Eq. (5) Eq. (6) Eq. (7) Eq. (8)

60

40

RPE (%)

15

20

0

-20

-40 1 Jan.

2

3

4

5

6

7

8

9

10

11

12 Dec.

Month Fig. 1. Comparisons of monthly relative percentage error (RPE) of monthly average of daily measured and calculated global solar radiation for Jeddah (1996–2004).

of Fig. 1 that the percentage error for a single month rarely exceeds 15% (in many cases it is much less). The correlations given in Table 1 are also used to calculate the annual average of daily global solar radiation on horizontal surfaces in Jeddah. The annual averages of daily global solar radiation calculated for Jeddah are found in fair agreement with those values reported for some Saudi cities (data for Jeddah are not available) in the first solar radiation atlas for the Arab world [37]. The reported annual averages for Taif, Medina and Riyadh are 19.440, 23.040 and 18.360 (MJ/m2 day). The corresponding annual average for Jeddah is found to be 20.506 (MJ/m2 day). It is indicated that the proposed correlations can be used for estimation of annual average of horizontal global solar radiation for Jeddah with a relative percentage error, Eq. (29), rarely exceeds ±2%. The calculated annual average of daily global solar radiation is also compared with 22 years average data of NASA SSE Model [38]. It is found that the proposed correlations are able to estimate the annual average of horizontal global radiation with a relative percentage difference of ±4.1%. The value reported by NASA SSE Model is 21.348 (MJ/m2 day) compared to 20.506 (MJ/m2 day) obtained using correlations given by Eqs. (1)–(8).

To calculate Hb, it is necessary to find the elevation angle constant e for the given location. Table 2 summarizes the average values of e obtained for each month. Values of e for Jeddah are found in the range 0.43–0.73 in agreement with that reported out by Solanki and Sangani [21]. Comparisons between measured and calculated monthly average of daily beam radiation Hb on a horizontal surface have been performed. Fig. 2 presents comparisons between measured and calculated values of Hb for the period (1996–2007). It is indicated from the results of Fig. 2 that the elevation angle method suggested by Solanki and Sangani [21] can be used for estimating Hb in Jeddah with a reasonable accuracy. Furthermore, the annual average of daily beam radiation on a horizontal surface is found to be 21.132 (MJ/m2 day) compared to 24.588 (MJ/m2 day) which reported in 22 years average NASA SSE Model [38] with a relative percentage difference of ±14.1%. Comparisons between measured Hd,m and calculated Hd,c diffuse radiation along with the values of RMSE, MBE and RPE, are summarized in Table 3. It is seen that the low values of the RMSE for all models indicate fairly good agreement between measured and calculated values of Hd. The negative values of RPE indicate that the proposed correlations slightly overestimate Hd. For all models, the absolute values of the RPE never reach 1%, indicating very good agreement between measured and calculated values of the diffuse fraction Hd/H or the diffuse transmittance Hd/Ho and clearness index Kt, relative number of sunshine hours s/so and the combination of them. The latter results are confirmed for each month. Comparison of the monthly relative percentage error (RPE) of monthly Table 3 Measured Hd,m and calculated Hd,c diffuse radiation (MJ/m2 day) and the values of RMSE (MJ/m2 day), MBE (MJ/m2 day) and RPE (%) for Jeddah. Eq. no.

Hd,m

Hd,c

RMSE

MBE

RPE

(16) (17) (18) (19) (20) (21)

12.748

12.461 12.907 12.812 12.524 12.459 12.510

0.083 0.046 0.019 0.063 0.084 0.069

0.024 0.013 0.005 0.019 0.024 0.020

0.21 0.79 0.33 0.93 0.23 0.67

Table 2 Representative values of elevation angle constant e for Jeddah in Saudi Arabia. Month

January

February

March

April

May

June

July

August

September

October

November

December

e

0.43

0.58

0.64

0.73

0.68

0.69

0.67

0.72

0.67

0.57

0.54

0.49

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A.A. El-Sebaii et al. / Applied Energy 87 (2010) 568–576 2.5 tilt ang.=6.76o tilt ang.=21.76o tilt ang.=36.76o tilt ang.=50o tilt ang.=65o tilt ang.=80o tilt ang.=90o

2.0

1.5

Rt

average daily measured and calculated diffuse radiation on horizontal surface for Jeddah using data set II (2003–2007) is shown in Fig. 3. From the results of Fig. 3 it is seen that the RPE for a single month rarely exceeds ±20% (in many cases it is much less). Therefore, Eqs. (16)–(21) are recommended for estimating the horizontal monthly average diffuse radiation at Jeddah. Figs. 4 and 5 show variations of the monthly average daily beam Rb (Fig. 4) and total Rt (Fig. 5) radiation conversion factors for different tilt angels b of the sloped surface. It is seen that both Rb and Rt decrease with increasing b during the summer months. However during winter months, Rb and Rt are found to increase with increasing b until an optimum value beyond which the behavior is reversed. Therefore, a high tilt is required to meet the energy demand in the winter months when the insolation on a horizontal surface is usually low. The optimum values of b are obtained as 6.76° and 36.76° during the summer and winter months, respectively. Fig. 6 presents variations of monthly average daily extraterrestrial Ho and global Hm solar radiation on horizontal surfaces in Jeddah. The monthly average daily values of H0 are calculated for the average day of each month using Eq. (A1). These data are used

1.0

0.5

0.0 1

2

3

4

5

6

7

8

9

10

11

12

Month Fig. 5. Monthly variation of values of Rt for different tilt angles of an inclined surface facing south at Jeddah.

40

Total radiation (MJ/m day)

50

40

RPE (%)

2

20

0

Eq. (16) Eq. (17) Eq. (18) Eq. (19) Eq. (20) Eq. (21)

-20

30

20

H0 Hm Ht, isotropic model Ht, anisotropic model Ht, isotropic model for Dhahran []

-40

10 1

2

3

4

5

6

7

8

9

10

11

12

1

2

3

4

5

Month

6

7

8

9

10

11

12

Month

Fig. 3. Comparisons of monthly average percentage error (RPE) of daily measured and calculated diffuse radiation on horizontal surface for Jeddah using data set II (2003–2007).

Fig. 6. Monthly average of daily total radiation on horizontal and tilted surfaces in Jeddah.

1.6

50 tilt ang.=6.75 o tilt ang.=21.76 o tilt ang.=36.76 o tilt ang. 50 o tilt ang.=65o tilt ang.=80o tilt ang.=90 o

1.4

Ht,b Ht,d (isotropic model) Ht,gr

Ht (MJ/m day)

1.2

Ht

40

Rb

2

1.0

30

0.8 0.6

20

10

0.4 0

0.2 0.0

-10

1

2

3

4

5

6

7

8

9

10

11

12

Month Fig. 4. Monthly variation of values of Rb for different tilt angles of an inclined surface facing south at Jeddah.

1

2

3

4

5

6

7

8

9

10

11

12

Month Fig. 7. Monthly averages of total, direct, diffuse and ground reflected solar radiation on a tilted surface in Jeddah. Tilt angle = u.

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for calculation of total radiation on a tilted surface Ht using the isotropic and anisotropic models when b equals the latitude of Jeddah (21.76°N). Values of Ht calculated using the isotropic model [32] for Dhahran (lat. 26.13°N) are also presented in Fig. 6 for the purpose of comparison. The obtained results are useful for solar engineering

50 6.76o 21.76o 36.76o 50o 65o 80o 90o

30

2

Ht (MJ/m daY)

40

20

10

0 1

2

3

4

5

6

7

8

9

10

11

12

Month Fig. 8. Variations of the monthly average of daily total radiation on a tilted surface facing south with the tilt angle of the surface.

A

design calculations, such as solar collectors and PV modules sloped facing south at a fixed angle. It is shown that, mostly Ht exceeds H as expected. It should be noted that the estimated values are not verified with any measurements due to the inaccessibility of available data. It is also seen from the results of Fig. 6 that, the values of Ht calculated using the anisotropic model sometimes exceeds the values of Ho which is unacceptable. Therefore, it may be concluded that the isotropic model is able to estimates Ht more accurate than the anisotropic model. Furthermore, the values of Ht calculated for Jeddah using the isotropic model are in good agreement with the values of Ht for Dhahran. Fig. 7 presents the monthly average daily beam Ht,b, diffuse Ht,d and ground reflected Ht,gr components of total Ht solar radiation incident on a tilted surface facing south when b equals the latitude of Jeddah. It is obvious that the value of the ground reflected component may be neglected compared to the beam and diffuse components. The maximum value of Ht is obtained as 30 (MJ/m2 day) during March and October. The minimum value of Ht is found to be 23 (MJ/m2 day) during May. To find the optimum tilt angle of the sloped surface, numerical calculations have been performed for different tilt angles. The results are summarized in Figs. 8 and 9. It seen from the results of Figs. 8 and 9 that the optimum tilt angle equals 6.76°, which is (u  15), during the summer months (see Fig. 9B) and equals 36.76°, which is (u + 15°), during the winter months (see Fig. 9A). These results are in good agreement with previous work performed for other locations [35]. At the optimum tilt angles, the maximum

A

11

40

Total annual energy (GJ/m2)

10

30

2

Ht (MJ/m day)

35

25

January February March October November December

20

15

9

8

7

6

5 10

0 0

20

40

60

80

10

20

30

B

6

Total annual energy (GJ/m )

35

5

2

30

Ht (MJ/m2 day)

25

20

15 April May June july August September

10

5

50

60

70

80

90

60

70

80

90

Tilt angle (deg)

Tilt angle (deg)

B

40

100

4

winter monthes summer months

3

2

1

0 0

20

40

60

80

100

Tilt angle (deg) Fig. 9. Dependence of total radiation on a tilted surface facing south on the surface tilt angle during winter (A) and summer (B) months.

0

10

20

30

40

50

Tilt angle (deg) Fig. 10. Variation of total annual energy on a tilted surface facing south with the tilt angle for Jeddah for the whole year (A) and summer and winter months (B).

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A.A. El-Sebaii et al. / Applied Energy 87 (2010) 568–576 Table 4 Comparison of the total annual energy calculated using the isotropic model with that of NASA SSE Model [38] for different tilt angle of a surface facing south. Tilt angle (deg)

6 21 36 90

Total annual energy (GJ/m2) Present

NASA SSE Model

9.792 9.891 9.567 4.982

7.904 8.124 7.915 4.251

RPD (%)

19.3 17.9 17.3 14.5

Acknowledgements Thanks are due to Deanship of Scientific Research, King Abdul Aziz University, Jeddah, Saudi Arabia, for providing financial assistance in the form of Project No. 191/428. We are also thankful to Meteorology and Environmental Protection Administration (Ministry of Defense and Aviation) and King Abdul Aziz City for Science and Technology for providing some solar radiation data. Appendix A

value of Ht is obtained as 36 (MJ/m2 day) during January. Therefore for the best performance of solar energy devices in any location during the winter, the device must oriented to face south with a tilt angle of (u + 15°) to meet the energy demand in the winter months when the insolation on a horizontal surface is usually low. The isotropic model was also used for estimating the total annual energy received as a function of tilt angle for a surface facing south. Fig. 10 shows the total annual energy (Fig. 10A) as well as the total winter and summer energy (Fig. 10B) for Jeddah. It is clear from the results of Fig. 10A that the total annual energy is a maximum for tilt angle equals u (21.76°). However, the slopes corresponding to the maximum estimated winter and summer energies are 36.76° (u + 15) and 6.76° (u  15), respectively. These results are in good agreement with that drawn by Gopinathan [24] and Duffie and Beckman [35]. The obtained values of the total annual energy incident on a tilted surface are compared with those reported in 22 years average data of NASA SSE Model [38]. Table 4 summarizes comparison between the total annual energy obtained for Jeddah using the isotropic model and that of NASA SSE Model for different tilt angles of a surface facing south. From the results of Table 4 it is seen that the isotropic model overestimates the total annual energy with relative percentage differences (RPD) of 19.3%, 17.9%, 17.3% and 14.5% when b equal 6°, 21°, 36° and 90°, respectively. From the above results it can be concluded that the Liu and Jordan isotropic model can be used for calculating total solar radiation incident on tilted surfaces in Jeddah with the aid of the empirical correlations that have been proposed for splitting diffuse and beam components on horizontal surfaces. Moreover, for long term performance of solar energy devices in Jeddah, these devices must be oriented facing south at a tilt angle equals the latitude of the place. 4. Conclusions The main purpose of this paper was calculation of horizontal diffuse and inclined total monthly average daily solar radiation in Jeddah. The measured data were used to develop new correlations that can be used for calculation of diffuse radiation incident on horizontal surfaces. Also, the isotropic and anisotropic models have been used for calculation of total radiation on tilted surfaces in Jeddah. It is concluded that the best performance of solar energy devices under Jeddah prevailing weather conditions, solar collectors or photovoltaic systems, can be achieved when they are oriented to face south with tilt angles equal (u + 15) and (u  15) during the winter and summer seasons, respectively. The tilt angle should be equals the latitude of the place for the long term (annual) performances of these systems. Furthermore, it is advisable to use the correlations which proposed in this work for estimation of monthly average daily diffuse radiation on horizontal surfaces in Jeddah and may be extended to other locations that have similar humid-warm weather. The isotropic models can be used for estimating horizontal diffuse radiation in Jeddah with good accuracy.

Extraterrestrial radiation H0 for the average day of the month on a horizontal surface can be calculated for each month using the following equations [35]:

H0 ¼

24  3600Isc

p

 1 þ 0:033 cos

  360d 365

  2pxs  cos u cos d sin xs þ sin u sin d 360

ðA1Þ

where Isc = 1353 W/m2 is the solar constant and xs is the sunset hour angle given as:

xs ¼  tan u tan d

ðA2Þ

d is the solar declination angle defined as:

  284 þ d d ¼ 23:45 sin 360 365

ðA3Þ

The day length s0 for the average day of the month is calculated using the following formula:

s0 ¼

2 cos1 xs 15

ðA4Þ

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