Available online at www.sciencedirect.com
APCBEE Procedia 5 (2013) 208 – 220
ICESD 2013: January 19-20, Dubai, UAE
Correlation for the Average Daily Diffuse Fraction with Clearness Index and Estimation of Beam Solar Radiation and Possible Sunshine Hours Fraction in Sabha, Ghdames and Tripoli - Libya F.Ahwidea, A.Spenab and A. El-Kafrawyc b
a Omar Al-Mukhtar University -Darnah-Libya-Faculty of Engineering, Mechanical Dep. Università di Roma Tor Vergata c Al-Baha University-Faculty of Engineering-Mechanical Engineering Dept., KSA Port-Said University-Faculty of Engineering-Production Engineering and Machine Design Dept.
Abstract The daily global solar radiation data obtained from three Libyan locations, region,(Sabha- desert region), (Ghdames- middle region) and (Tripoli- Mediterranean region) were used to establish a relationship between daily diffuse fraction and daily clearness index KT. This relationship was compared with that established by Liu & Jordan, Stanhill, Choudhury, Erbs, and used to derive a correlation for the average daily diffuse fraction. Solar radiation and sunshine duration are intimately related phenomena, which was used to study the equation related of average daily radiation to the extraterrestrial radiation for location and average fraction of possible sunshine hours. Moreover the daily clearness index were calculated and the daily clearness index was used to estimate the frequency of occurrence of days with different values of KT and the cumulative frequency of occurrence of those days. Finally, the relationships for estimating the beam and diffuse components of daily global radiation were obtained using the
© 2013 2013The Published ElsevierbyB.V. Selection © Authors.by Published Elsevier B.V. and/or peer review under responsibility of Asia-Pacific Chemical, Biological & Environmental Engineering Society Selection and peer review under responsibility of Asia-Pacific Chemical, Biological & Environmental Engineering Society Keyword: Solar Radiation, Clearness Index, Daily Diffuse Fraction, Sunshine Hours, Libya..
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2212-6708 © 2013 The Authors. Published by Elsevier B.V. Selection and peer review under responsibility of Asia-Pacific Chemical, Biological & Environmental Engineering Society doi:10.1016/j.apcbee.2013.05.037
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1. Introduction Solar radiation incident on buildings or collection surfaces must be known in order to perform thermal analyses. In general, only measurements of the total horizontal (global) radiation are available. As most surfaces of interest are inclined, it is necessary to estimate the radiation on a tilted surface from measurements of global radiation. Estimation procedures usually require the beam and diffuse components of global radiation. The beam and diffuse components of global radiation can be estimated from empirical relationships. Existing relationships correlate the fraction of the global radiation which is beam or diffuse to an index of atmospheric clarity. Correlations of this type have been developed for use with daily average values of global radiation. 2. The Data Base The data used to develop the correlations presented here are thought to be among the best data available at this time. The measurements data that including horizontal global daily solar radiation and sunshine duration for 9 years from 1982 to 1988 in different stations in Libya [1, 2]. The direct and diffuse daily radiation were estimated. In general, the abundance of solar energy in Libya is evident from the annual daily average of global solar irradiance, which ranges between 5 and 7 kWh/m2.day on horizontal surfaces. This corresponds to a total annual value of 1600 - 2300 kWh/m2.y, as shown in Fig. 1. In this study we concentrated on three different stations, which acquired from observed mean values on meteorological stations . In Figure 2 show the maximum value of sunshine duration in stations selected occurs in June & July and the least in December(mean value is 12, 10 and 8 hr, e.g. respectively).
Fig. 1. Average global daily solar radiation in Sabha, Ghadames and Tripoli
3. Estimation of Average Solar Radiation
uncertain effects in the atmosphere. After the entrance of solar radiation into the troposphere various losses appear due to either absorption, reflection or filtering effects. These local phenomena occur due to the existence of dust, moisture, cloud cover and thickness, aerosols and temperature differences in the lower
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atmosphere. Moreover, records on the earth surface include uncertainty due to measurement errors. Since solar irradiation is correlated with sunshine duration, many researchers starting with Angstrom (1924) have tried to base its estimation on the easily and more economically measurable sunshine duration records. Angstrom has standardized solar radiation with cloudless global irradiation and sunshine duration with astronomical day length. Angstrom suggested a linear relationship in order to estimate the global solar radiation, H, from comparatively simple measurements of sunshine duration, n, according to:
H Ho
a b
n N
(1)
Where H is the average daily global radiation received on a horizontal surface at ground level, H0 is the extraterrestrial radiation for the location, averaged over the time period in question, (H/H0) is termed the average daily clearness index, (n/N) the fraction of daily possible sunshine hours, N is the average daily of the maximum possible daily hours of bright sunshine which it's estimated and n, is the average daily hours of bright sunshine (sunshine duration is measured), i.e. a and b are model parameters, (constants depending on location), these parameters have been estimated so far in the literature by regression techniques. The average day length (number of daylight hours), N can be calculated from Equation [3]:
N Where s
2 15 s
(2)
s
is the sunset hourly angle, descending by:
cos 1 (-tan
(3)
tan ) is solar declension.
Where
23.45 sin (360
to calculate
284 i ) 365
(4)
Values of H0 can be calculated from the following equation :
Ho
24 * 3600 G sc
(1 0.033 cos
360 i )x(cos cos sin 365
Where Gsc is solar constant, equal to 1367 W/m2., i
s
s
180
sin sin )
(5)
s day [3].
The ratios on both sides of the Eqn. 1 are very between zero and one. This linear relationship has been used frequently all over the world in order to estimate the global irradiation at locations where sunshine duration measurement are available.. Many researchers (Solar, 1960; Gopinathan, 1988; Rietveld, 1978; Sabbagh et al., 1977; Swartman and Ogunland, 1967; Dogniaux and Lemonie, 1983) have considered additional meteorological factors to Eqn.1 for the purpose of increasing the accuracy in the coefficients estimate. Although each one of these researchers refined the coefficient estimates, they considered only the average parameter values that are obtained by the least squares method. In some studies, the use of sunshine duration standard deviation is also advised for a better estimation of the model parameters a and b (Ogelman et al., 1984; Gueymard et al., 1995. Additionally, there are some other implied assumptions in all these formulations, as follows. (1) In many applications without considering the scatter diagram of H versus n, automatically a linear regression line is fitted to data at hand according to eqn. (1), in order to determine a and b coefficients. In fact, these coefficients depend vaguely on the variations in the sunshine duration. hence, it is the main purpos of
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this paper to provide a simple technique whereby uncertainties in the process of solar radiation and sunshine duration measurements are treated linguistically by means of fuzzy sets. (2) Most of the formulations relate the global irradiation to the sunshine duration by ignoring some of the meteorological factors such as the relative humidity, maximum temperature, air quality, latitude, elevation above mean sea level, etc. in fact, each one of these factors contributes to the relationship between H and n and their neglect introduces some errors into the predictions. For instance, the model in Eqn. (1), assumes that if all of the other meteorological factors are constant then the global horizontal radiation is proportional to the sunshine duration only. The effects of other meteorological variables appear as deviations from the straight line fit on a scatter diagram, [4]. 4. Relationship Between Solar Radiation and Sunshine Duration In general, it is known that there is relationship between solar radiation and sunshine duration during any period. For the application of the regression technique Angstrom has assumed a linear relationship as in Eqn. (1). However, herein the relationship between these two variables will be deduced from the measurements linguistically. However , monthly radiation and sunshine duration values are adopted for application in this paper. hence, regression lines according to Angstrom in figure 2 provide models for the radiation estimation provided that H, n are calculated and n is observed for a particular duration (Lewis 1989).
Fig. 2. Measured average sunshine duration data in Sabha, Ghadames and Tripoli
In practice, there are always sources of uncertainty of different types such as vagueness and ambiguities and or errors attached to the measurements of sunshine duration.
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Fig. 3. Scatter diagrams and fitted Angstrom models at different locations.
On the other hand, without dividing by H and n the salient features of the H and n scatter diagram are plotted in figure. 4 for the purpose of fuzzy radiation estimation. To this end , the global solar radiation, H,
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and sunshine duration are first fuzzed into fuzzy subsets so as to cover the whole range of changes [4].
Fig. 4 Scatter diagrams for Measurement daily radiation (Hmeas ) versus Sunshine duration ,(n.
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Fig. 5. Frequency of occurrence of days with various clearness index and cumulate of occurrence of those days.
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5. Distribution of clear and cloudy days and hours The frequency of occurrence of periods of various radiation levels , for example, of good and bad days, is of interest in information on the frequency distribution is the link between two kinds of correlations, that of the daily fraction of diffuse whit daily radiation and that of the monthly average fraction of diffuse with monthly average radiation. [3,5] 5.1. Daily clearness index (K KT ) The daily clearness index, KT is the ratio of a particular days radiation to the extraterrestrial radiation for the day. In equation form,
KT
H Ho
(6)
The frequency of occurrence of days with various values of KT is plotted as a function of KT , the resulting distribution could appear like the solid curve of Figure 5. The shape of this curve depends on the average clearness index KT. For intermediate KT values, day with very low KT or very high KT occur relatively infrequently, and most of the days have KT values intermediate between the extremes. The result, shown that the value of KT that occurs more frequently is more or less the same and near 0.75 in desert towns like Sabha and Ghadames, slightly low in the case of Tripoli, situated on coastal zone. Cumulative frequency highlights that for Sabha and Ghadames the majority of KT assume values higher than 0.5, instead for Tripoli this lower limit is lower and near 0.3 [5]. 6. Beam and Diffuse Components of Daily Radiation Studies of available daily radiation data have shown that the average fraction which is diffuse , Hd/H , is a function of KT, the days clearness index. The original correlation of Liu and Jordan (1960) is shown in figure 6; the data were for Blue Hill, Massachusetts. Also shown on the graphs are plots of data for Canadian stations from Ruth and Chant (1976), for New Delhi from Choudhury (1963), Stanhill (1966) and Erbs et al. (1982) have used data from four U. S. and one Australian station, for three different stations in Libya , Sabha, Ghdames and Tripoli from F. Ahwide (2011) [3,5] . there is some disagreement, with difference probably due in part to instrumental difficulties such as shading ring corrections and possibly in part due to air mass and/or seasonal effects. A seasonal dependence is shown; the spring, summer and fall data are essentially the same , while the winter data shows somewhat lower diffuse fractions for high values of K T, [6] . The seasonal is indicated by the sunset hour angle . Equations representing this set of correlations are as follows [4,5]: For
s
Hd H For
s
Hd H
< 81.4°
1.0 0.2727 K T
2.4495 K T2 11.9514 K 3T
0.143
9.3879 K T4 per K T per K T
0.715 0.715
(7)
81.4°
1.0 0.2832 K T 0.175
2.5557 K T2
0.8448 K 3T per K T per K T
0.722 0.722
(8)
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Fig. 6. Correlation of daily total diffuse fraction f , (Hd/H) with daily clearness index, (K KT).
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Fig. 7. Beam and Diffuse components of total daily radiation.
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In Fig. 6 the obtained correlation between Hd/H and KT for Sabha, Tripoli and Ghdames was compared with correlations that available in Liu's and Jordan's , Choudhury's, Erbs's and Stanhill's correlations. The photographs show that the our correlation Besides, as shown in the figure, we can see that the result for Sabha and Ghadames are better than Tripoli. In xceeding to 50% and 60% respectively, while Tripoli can be get to 90%. The percentages of diffuse radiation are corresponding to minimum value of KT equal to 0.5, 0.45 and 0.25 for the three localities.
Fig. 8. Average daily clearness index with fraction of daily possible sunshine hours.
7. Analysis of Resulting and Conclusions For daily global solar radiation data for different cities of Libya, we carried to derive the direct and diffuse components of daily radiation which were obtained. First, we analyzed the daily clearness index and relationship between these indices then the fraction of daily diffuse radiation. The graphs on the frequency and cumulative frequency of KT shown that the maximum value was in Sabha ,which is about 0.75. The frequently of KT values for Sabha and Ghadames were between 0.6 and 0.8. while Tripoli between 0.4 and 0.7(see Fig. 5). they were also shown that there is a close relationship between the fraction of daily diffuse radiation and clearness index. The Fig. 6 shown the correlation of daily total diffuse fraction, (H d/H) with daily clearness index, (KT). We obtained that the good approximation of our approach is sensitive to the curves proposed by Erbs. We have obtained encouraging results for Sabha and Ghadames, the direct component were 67% and 65% respectively and was in the medium for Tripoli 54%, from daily global radiation. Beam and Diffuse components of total daily radiation shows in Fig. 7, for Sabha, Ghadames and Tripoli. Tripoli is unfavorable case because the component of diffuse radiation is higher than direct radiation for the more days of year (normally the end of autumn and winter). The situation for Sabha and Ghadames are certainly better since they have a larger bell of global daily radiation, and the direct components result have been higher than the diffuse.
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Fig. 9. Relationship between Global and diffuse solar radiation with latitude angle
Fig. 10. Relationship between fraction of daily possible sunshine hours with latitude angle.
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Looking at Fig. 4 & 8, we can observe that the Tripoli curve is exception because of its location. For the middle and desert towns, there are a substantial independence of fraction H/H0 from the index n/N as demonstration that in desert occur more frequently a serene sky during the day respect other zones due to the n fact, the values of H/H0 for Sabha and Ghdames are bigger than 0.6 and correspondent to index n/N values respectively equal to 0,73, 0.67. A little higher is the slope of curve about Tripoli because of its location. In these zones there is Mediterranean climate who is responsible of that typically performance of the curve. The relationship between fraction of daily possible sunshine hours with latitude angle were studded (see Fig. 9). Also as shown in Fig. 10, the performance of clearness index for different stations in Libya, Al Kofra, Sabha and Ghdames with additions of Rome and London which is associated with latitude angle. The correlations value depend quite strongly by relative latitude . Acknowledgements The authors wish to thank those who have contributed to this scientific work, A. Thanks also are due to Eng. Hassan. M. Elkmeshy and Eng. Abdulmonim H. Layas for their help to get some data used in this work. References [1] Center of Solar Energy Studies in Libya, Tripoli. [2] Libyan Meteorological Department, Tripoli. [3] John - Interscience publication. TJ810.D8 1991 [4] Zekai r Estimation of Solar Irradiation from Sunshine No. 1. pp.3949,1998. [5] F. Ahwide , Ph.D. Engineering of Energy Sourses of Enhancement of Energy production in Libya, by means of Efficiency and Renewabl roma Tor Vergata, Italy, 2010/2011. [6] Erbs D. G., Klein S. A. , Duffie J. A. , Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation.
