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Estimating Global Solar Radiation On Horizontal Surfaces Using Different Correlation Formulas For Baghdad City 

 

Ali.M.AL-Salihi, Kais.J.Al-Jumaily and Osama.T. Al-Taai

Department of Atmospheric Sciences,

College of Scienc, Al-Mustansiriyah University 

Salihi72@yahoo.com 

 

Abstract 

The sun is basic source of energy in this world; therefore it's necessary to study the solar radiation values and models which are important in a lot of solar radiation research fields because of this energy is pollution free with environment. In this study we have been employed global solar radiation measurements on horizontal surface in Baghdad city in order to carry out mathematical models, the statistical tests shows the good predicting ability of global solar radiation in Baghdad city, concerning to the seventh model which depend on solar zenith angle show good prediction ability, finally concerning to the last model which depend on two important parameter (day and sunshine duration) presented excellent ability in mean values of daily global solar radiation for Baghdad city. This study shows that the predicated result was close to the real values of solar radiation measurements.

Introduction

Solar radiation data are important for the development and the applications of solar energy technology. However, measuring and recording equipment for solar radiation are costly. Therefore, numbers of stations in the developing countries, are very limited and insufficient for use to overcome this problem, some mathematical models relating solar radiation have been proposed, the sunshine duration is considered to be a good predictor of global solar radiation. There are many researcher proposed models for estimating global solar radiation from sunshine duration such as Exell and Salicali [1] Kirtikara and Siriprayuk [2]. During the last two decades the environment of Iraq changed as a part of global climate changes. Therefore, the objective of this work ’is to develop a different new models for the estimation of global solar radiation using new data set. Iraq is a high solar energy country. The climate is most favorable of solar energy

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utilization, but the distribution of the solar radiation over the yearly time scale is not well known .the importance of this work lies on the fundamental need of knowledge of the global solar radiation in Iraq.

One of the promising usage of renewable energy technology is the installation of the solar collector systems which has already demonstrated its effectiveness and holds great promise for hot water collectors .the applications of the solar collector system have became more wide spread in both developed and developing countries [3], [4]. Solar radiation records are available horizontal components surfaces which included both direct and diffuse radiation [5]. The researches which interested with solar radiation modeling in Iraq started in late ninety, in this work, study on the estimation of global daily solar radiation on horizontal surface have been achieved and estimation formula which used to model of solar radiation for Baghdad city additionally the monthly average of sun duration for Baghdad city have been predicted. Also the data of solar zenith angle which widely available from more station in many countries are use to create a correlation between solar zenith angle and global solar radiation which achieved reasonable prediction for global solar radiation.

Renewable energy resources and their applications are intimately related to sustainable development. In other wards, the development of renewable energy technology is now widely seen as be important if the world is move toward a sustainable approach to energy generation [6], [7], therefore we present a number of models depends on time of the year and others depend on solar zenith angle and sun shine duration which is available in most meteorological station. Various models have been proposed to estimate solar radiation by [8], [9], [10], [11], several researches [12], [13] and [14], have demonstrated the predictive ability of Angstrom type one parameter equations correlating the global solar radiation to the percentage of bright sun shine in a simple linear regression form [15]. There are different correlation formulae have been presented to estimate the solar radiation employing various meteorological parameters [16], [17] and [18]. The climate of Iraq is well situated for solar energy potential and its potential is about (3316) hour per year with a (501 Watt per square meter) of solar power as daily average [19], in spite of that the employing of solar energy in numerous life sectors are very limited.

Global Solar Radiation Measurements

The global solar radiation and sunshine duration data employed in this paper were supplied by Energy and Environmental Research Center, A radiometric station was established at the Baghdad city in al-Jadiyiyah location (Lat 33.14o N, Long 44.14o E, elevation 34 m above sea level) has automatic weather observation station measuring the global solar radiation on horizontal surfaces, global and direct normal radiation on hourly basis through the year. Measuring for other radiation and meteorological parameters are also monitored. The station was designed for automatic installation, but minor maintenance, adjustment, clearing of the instruments, etc, were made performed daily [20]. During the (36-month) period from January (1999) to December (2001). Measurements including horizontal solar irradiance and sunshine

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duration were made on the rooftop in a position relatively free from any external obstructions, and readily accessible for inspection, general cleaning and maintenance. Data collection started before sunrise and finished after sunset. All measurements were made for hours and decades and finally, the annual quasi global radiation energy, which is the energy received by horizontal plane from the sun in one year, was calculated from the sum of all the energies of all the decades. Reliable solar radiance distribution databases should be based on long-term systematic measurements. For places where solar radiance distributions are not available, an appropriate model for solar radiation and sunshine duration can be used to generate the required data.  

Result and Discussion

Figure (1) shows the daily and seasonally variation of global solar radiation for Baghdad, where the highest intensity values lies in the summer months with the lowest values are in the winter months. The highest intensity value (7.77 kw/m2), lies in early June and July and the lowest intensity values (0.96 kw/m2) lies in late December and early January. As show in figure (1) there is a big range between the maximum intensity of global solar radiation which represented in summer months (7.77 kw/m2) and the values of winter months (0.96 kw/m2).The main reason for this large variation between summer and winter months values due to the high arid in the summer and the mostly cloudy atmospheres in the winter months, shows the global solar radiation data on a horizontal surface and sin wave correlation formula for Baghdad city and neighbor regions. Some scattered points in the actual data were appeared in figure (1) and this due to the cloudy and dusty days of the year, which the global solar radiation value would be extremely affected. The radiation data are the best source of information for estimating the average incident radiation. The shortage of these data from the neighbor cities of same climate it is possible to use the empirical relations to estimate solar radiation on horizontal surface as a function of time.

six correlation formulas with regression coefficients have been gained for predicting the daily global solar radiation for Baghdad city which plotted in figures (1), (2), (3), (4), (5), (6) and all the six models collected in figure (7).

The general formula for the obtained models and the values of their constants are discussed lately with more details. The first correlation formula which used in this paper was sin wave with constant (Y-value) can be represented as:

12s i n ( ) . . . . . . . . . . . . . . (1 )xG c a a

bπ

= + +  

Where (a ۪ ) is the amplitude, (a1) is the face shift, (b) is the wave length and (c) the (Y- intercept). By substituting the obtained values for these constants in equation (1), the correlation formula for global solar radiation for Baghdad city can be represented as:

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25 0 2 8 .9 3 2 4 9 3 .5 2 s in ( 5 .0 4 ) . . . . . . . . . . . ( 2 )3 8 4 .6 8

xG π= + × +

The regression coefficient (R), for the obtained results in equation (2) is (0.948) which is good value. The standard error is (0.577 kw.h/m2.day) which is also acceptable error within the range.

The second formula which been used was Lorentzin correlation formula can be represented as:

21. . . . . . . . . . . . . . . . . . . . . . . . ( 3 )

1 ( )

aG x ab

=−

+

Where (a ۪ ) is the amplitude, (a1) is the center and (b) is the width, then we substituted the values for this constants in equation (3), therefore the correlation formula for global solar radiation representing for Baghdad city can be defined as:

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7 6 2 9 . 8 6 . . . . . . . . . . . . . . . . . . . . . ( 4 )1 3 0 . 21 ( )1 7 1 . 8

G x=−

+

The regression coefficient (R), for the results of the above equation (4) is (0.942) which is also very good value and the standard error is (0.605 kw.h/m2.day) which is also acceptable.

The third formula which used in this study was Gaussian correlation formula which is represented by the form:

21e x p [ 0 .5 * ( ) ] . . . . . . . . . . . . . . ( 5 )x aG ab−

= −

Where (a ۪ ) is the amplitude, (a1) is the center and (b) is the width, by substituting the values for these constants in equation (5), then the correlation formula for global solar radiation for Baghdad city can be written as:

2172.37387.5 exp[ 0.5 * ( ) ]................(6)114.3

xG −= −

The regression coefficient (R), for the data in equation (6) is (0.942) and the standard error is (0.607 kw.h/ m2.day).

The fourth correlation formula used in this work was pseudo-Vogt formula which defined by the form:

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2 2

1[ ( ) ] . . . . . . . . . . . . . . . .( 7 )1 ( ) (1 ) e x p ( )

G a c x x x xcb b

= ×− −

+ + − 

Where (a ۪ ) is the amplitude, (x ۪ ) is the center and band (c) is the correlation constants, by substituting the values of these constants in equation (7) the correlation formula for global solar radiation for Baghdad city can be written as:  

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17536.2 [0.44 ( )].................(8)172.04 172.041 ( ) (1 0.44)exp( )119.12 119.12

G x x= × ×− −

+ + − 

The regression coefficient (R), for the data in equation (8) is (0.944) and the standard error is (0.598 kw.h/ m2.day).

The fifth correlation formula is fourth order correlation formula which is defined as the form:

2 3 41 2 3 4 ..................(9 )G a a x a x a x a x= + + + +  

Where (a ۪ , a1, a2, a3 and a4) are the correlation constants, then after substituting the values of these constants in equation (9) the correlation formula for global solar radiation for Baghdad city can be written as:

2 3 6 43117.6 8.63 0.699 0.00385 5.44 *10 ..........................(10)G x x x x−= − + − +       The regression coefficient (R), for the data in equation (10) is (0.903) and the standard error is (0.574 kw.h/ m2.day). The last general formula which is depend on the day of the year in this work is Weibul correlation formula which can be represented as:

11/ 11 1 1[ ( ) ( ) ] [( ) ( ) ]

1 1exp[ [( ) ( ) ( )]]........................(11)

cc cc

c

x xc c cG x b a A B Sc c b c

x x c cA B Sb c c

−−−− − −

= − × × +

− − −× − + +

 

Where (ABS) is the absolute value, (a, b, c) and (x ۪ ) is the correlation constants and equal (7352.69, 361.98, 3.32) and (173.96) respectively, then the correlation formula can be written in the following expression after substituting the above constants:

1 3.321/3.32 3.32 13.32

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3.32 1 3.32 1 173.96 3.32 1[ 361.98( ) 7352.69 ( ) ] [( ) ( ) ]3.32 3.32 361.98 3.32173.96 3.32 1 3.32 1exp[ [( ) ( ) ( )]]........................................

361.98 3.32 3.32

xG x ABS

xABS

−−− − − −

= − × × × +

− − −× − + + ..............(12)

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The correlation coefficient (R), for the data in equation (12) is (0.944) and the standard error is (0.598 kw.h/ m2.day) which are also acceptable. Figures (1), (2), (3), (4), (5) and (6) represented the six suggested correlation formula which have been mentioned recently with measurements of daily global solar radiation for Baghdad city as a function of time(day of the year).The predicated and measured irradiance value is plotted for each model separately. Most of the predicated results have a good agreement with the corresponding measured results. The solar radiation which is received by the earth surface is controlled by the changes due to the extraterrestrial radiation variation in addition to important phenomena which are the atmospheric scattering by trace gases and air molecules, water and absorption by Oxygen, water, carbon dioxide (CO2). The mean value of solar radiation for Baghdad city is (5160 kw.h/m2.day). Also Baghdad city receives the highest solar energy in June and July (with mean 7267 kw.h/m2.day) and lowest values of solar radiation in December (with mean 2483 kw.h/m2.day).  

Also in this paper we have been employed an important parameter which is highly effect on solar radiation, this parameter is solar zenith angle which used as prediction factor for global solar radiation by illustrating a correlation formula with first order type as show in equation (13):  

.........................(13)y a bx= +  

      Where (a) is the intercept with (y-axis) and (b) is the slope, after substituting the values for these constants in equation (13), the correlation formula for global solar radiation for Baghdad city can be expressed by the following expression.

9 3 7 8 .6 1 1 1 .7 4 .... . . . . . . . . . .(1 4 )G S Z A= − ×   Where: (SZA) is the solar zenith angle, this formula have been achieved (0.846) regression which is considered as a reasonable and the relation between daily global solar radiation and solar zenith angle is shown in figure (8 and 9). As an attempt of including the day of the year and sunshine duration values in additional model in this work we have been used the sunshine duration data for Baghdad city for four years, it's clear that it is very difficult to propose a correlation formula consider sunshine duration from a valuable records and the day of the year , the data has a high scattering values therefore we take the average values of daily sunshine duration for four years and the values of the daily global solar radiation of the same period and the day of the year in order to illustrate equation (15),and the results of this model was shown in figure(10),The correlation for formula between these two parameters is defined as:  

2 2 ...............(15)G G a D b SSH c D d SSH= + × + × + × + ×  

Where (G) is the daily value of global solar radiation, (D) is the day of the year, (SSH) is sunshine duration by hours. (G ۪ , a, b, c) and (d) are the constants which are equal (9986.28, 2085.49, -2487.16, -163.44) and (151.67) respectively. The (3D- parabolic) correlation formula presented (R) is (0.982) with standard error (0.347 kw.hr/m2.day) then after substituting the correlation constants the above formula will be express as: 

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2 29986.28 2085.49 2487.16 163.44 151.67 ...............(16)G D SSH D SSH= + × − × − × + ×  

If we compare the models which represented by equations (14 and 16 ) we can notice that sunshine duration as an input in the last model (equation 16) is effective more than solar zenith angle.

 

Conclusions 

 A statistically – significant virus models were proposed to predict the daily global radiation over Baghdad city based on the data obtained from Energy and Environmental Research Center. All models are adequate to predict daily global radiation over Baghdad city especially the model which represented by equation (16) which achieved the highest correlation coefficient among the proposed models (98%) with lower error of estimation (0.347 kw.hr/m2.day). The mentioned results of the validation and comparative study indicate that the proposed statistical models based estimation technique for global solar radiation on horizontal surface is very suitable for predicting the solar radiation, this conforms the ability of these models to predict solar radiation on values sufficiently accurate for most purposes. The results indicate that the proposed models seems promising for evaluating solar radiation – resources potential at places where there are no solar radiation on measuring equipments.

 

 

   

 

 

 

 

 

 

 

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