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8СОЛНЕЧНАЯ ЭНЕРГЕТИКА SOLAR ENERGY
THE SIMPLE CLEAR SKIES MODEL FOR THE LUMINOUS EFFICACY OF DIFFUSE SOLAR RADIATION ON INCLINED SURFACES AT QUETTA, PAKISTAN
Syed Zafar Ilyas, T. N. Veziroglu* , S. M. Nasir, S. M. Raza
Honorable Editor-in-Chief
Group of Renewable Energy Department of Physics, University Of Balochistan,Quetta, Pakistan
* Clean Energy Institute Department of Mechanical Engineering, University of Miami, USA E-mail: szilyas@yahoo.com; szilyas@hotmail.com
In the present work we study the luminous efficacy of diffuse solar radiation incident on vertical surfaces for a clear sky, mean hourly values of diffuse irradiance and diffuse illuminance. We develop a model easy to use, similar to a model previously obtained for horizontal surfaces. To develop the present model for vertical surfaces we assume that the slope of the surfaces influences diffuse illuminance and diffuse irradiance in the same way. As a consequence of this hypothesis, the luminous efficacy of diffuse solar radiation is found to be the same for both horizontal and inclined surfaces.
Introduction
The luminous efficacy of solar radiation is defined as the ratio between illuminance and irra-diance. Thus, if irradiance measurements are available it is possible to estimate illuminance values using a luminous efficacy model. There are a number of studies on the luminous efficacy of solar radiation on horizontal surfaces, among them those published by the authours [1-6]. However, there are only a few work on the luminous efficacy on inclined surfaces, among them [7-9].
In the present work we have modeled the luminous efficacy of diffuse solar radiation for clear skies and vertical surfaces facing North, East, South, West. In [3], a model for the luminous efficacy of diffuse solar radiation on a horizontal surface was developed for clear sky that is cloudless, rather clean skies, considering exclusively a dependence on solar altitude. The diffuse efficacy model was obtained by dividing the corresponding illuminance and irradiance models, both developed from experimental data. The proposed model for the diffuse luminous efficacy on a horizontal surface Kdh was given by the following equation:
Kdh = A (sina where A and B are empirical constants, and a the solar altitude.
To obtain the model for the luminous efficacy of diffuse solar radiation on vertical surfaces we assume that, at least qualitatively, the surface slope affects both the diffuse irradiance and the diffuse illuminance in the same way. We can check that this is a good hypothesis by observing the graphs for diffuse illuminance Ld and diffuse irradiance Ed, versus a, shown in Fig. 1(a) and (b), respec-
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Fig. 1
North
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20
40
60
80
100
North
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10 20 30 40 50 60 70 80 90 b
Solar altitude (degrees)
Статья поступила в редакцию 05.07.2005. The article has entered in publishing office 05.07.2005.
tively, for the North facing vertical surface. Similar plots were obtained for a horizontal surface [3]. As a consequence, the model given by Equation (1) for the ratio between diffuse illuminance and diffuse irradiance will also be valid for the luminous efficacy of diffuse solar radiation on vertical surfaces Kdv.
Experimental data and sky characterisation
The clearness index C and the brightness index A defined in [10] have been used for sky type characterization. These indexes are defined as follows:
North
_ _[(Ed +1 )\Ed + KZ3 ] 1 + kZ3
(2)
250 200 150 100 50 0
0 'ff
10 20 30 40 50 60 70 80 90
East
A = Edm/10, (3)
where Ed is the diffuse horizontal irradiance, I the direct normal irradiance, Z the solar zenith angle, k a constant equal to 1.041 for Z in radians, m the optical air mass, and I0 the extraterrestrial irradiance. We consider clear skies when C > 6.0 and A <0.15 as evaluated from solar radiation data [11].
The experimental data used are mean hourly values of global and diffuse illuminance and irra-diance on horizontal surfaces, and global illuminance and irradiance on vertical surfaces facing North, East, South and West. Measurements were performed at the flat unobsructed roof of the Faculty of Physical Sciences at Quetta (40.40 N, 3.70 W). Irradiance values were obtained with Kipp and Zonen CM6B pyranometers that were recalibrated after each year of use by the Meteorological office Quetta. LICOR sensors were used for illuminance measurements, and were recalibrated every six months by the manufacturer's representative following the approved procedure. Furthermore, the calibration of the illuminance sensors was tested against a reference standard circulated by the Commission Internationale de 1, Eclairage (CIE) through European stations. The shadow band correction method given in [12] was used for diffuse irradiance and illuminance data. Direct illuminance and irradiance are obtained for horizontal surfaces from global and diffuse illuminance and irradiance on these surfaces. Direct illuminance and irradiance on vertical surfaces are obtained from direct illuminance and irradiance on horizontal surfaces using a geometrical factor. Diffuse illuminance and irradiance on vertical surfaces are obtained from global and direct illuminance on these surfaces. The data were obtained for the period January 1998 - December 2003. The data corresponding to the period June-May have been used to develop all the models, and those corresponding to the period June 1995 -November 1995 for their statistical assessment.
The accuracy of the model was determined using as statistical estimators: the absolute value of the square root of the determination coefficient,
80 90
West
250 200 -150 '100 50
□
♦ Series 1
West: Kdv = 117.54(sina)
-0.163
0 10 20 30 40 50 60 70 80 90 d
Fig. 2. Solar altitude (degrees)
the mean bias error, MBE, and the rood mean square error, RMSE.
Models of the luminous efficacy of diffuse solar radiation for clear skies and vertical surfaces
diffuse illuminance and irradiance four vertical surfaces facing N, E,
In Fig. 2 (a)-(d) one can see the Kdv values obtained from i values for the
S and W. If, Kdv values are fitted versus sina using Eq. (1),
North: Kdv = :
the following models are obtained: 110.01(sina)-0 201, r = 0.542, (4) East: Kdv = 122.03(sina)-0152, r = 0.365, (5) South: Kdv = 198.21(sina)-0 097, r = 0.679, (6)
r = 0.423. (7)
It can be observed that the value of r is the highest for the South facing surface, lowest for the East facing surface, and intermediate for the
С. 3. Илиас, Т. Н. Везироглу, С. М. Назир, С. М. Раза Простая модель безоблачного неба для расчета силы света диффузного солнечного излучения на наклонных поверхностях сооружений в г. Кветта, Пакистан
North and West facing surfaces. This is related to the degree of dependence of Kdv on sina as given by Eqs. (4)-(7) or as observed in fig. 2(a)-(d) for Kdv versus a. One can also associate this dependence of the luminous efficacy with solar altitude, different for each surface orientation, with the physical difference between these orientations. The main difference between the four planes lies in the amount of direct radiation on them. As we are dealing exclusively with clear skies, we are not obviously speaking of the state of the sky, whether cloudless overcast or intermediate. We mean that, when clear skies data are considered for the whole period, the possibility of receiving direct radiation is different for each of the four mentioned surfaces For example, the surface facing North has a smaller possibility of receiving direct radiation that the surface facing South. To give more consistences to this commentary we can pay attention to one of the planes receiving an intermediate amount of direct radiation over the whole period of measurements, such as the East-facing plane. In Fig. 3(a) and (b) Kdv has been plotted versus a dividing of the clear sky data for this surface into two sets. For the first set, Fig. 3(a), the surface 'sees' the solar disk or a part of it, and for the second set, Fig. 3(b), the surface does not receive direct solar radiation. One can observe in Fig. 3(a) and (b) that Kdv decreases with increasing solar altitude, but in
East
luminous efficacy (lm/W) О Ol О Ol О О О О О О VU % ♦ ♦ ♦ "Ч ♦ ? i а ♦ ♦ ♦ ♦ ♦ * *4 * .4
Diffuse 5 о о ♦ Series 1
10 20
30 40 a
50 60 70 80 90
> 300 г
J 250 |„200
It 150 £ =
§~ 100
0)
x □
£ □
50 0
10 20
30 40 b
50 60 70 80 90
Fig. 3. Solar altitude (degrees): a — surface "Sun's disk"; b — surface not "Sun's disk"
a more evident way when the surface does not 'see' the solar disk. That is to say, the absence of direct solar radiation results in a faster decrease of Kdv with a than if direct solar radiation is received on the surface. This explains that the dependence of Kdv on a is more pronounced for the surface facing North than for the rest of the orientations, and that for the South facing surface, receiving a large amount of direct solar radiation, the dependence of Kdv on a is almost not noticeable. This apparently previously unnoticed effect, may be related to the anisotropic character of diffuse radiation, as one difference between the four surfaces is that they receive a different amount of circumsolar radiation. When there is no circumsolar contribution for a surface, the most important anisotropic effect is that of multiple Rayleigh scattering and retroscattering near the horizon. In a study of the luminous efficacy of diffuse solar radiation for horizontal surfaces the authors comment that clear sky diffuse luminous efficacy increases with decreasing solar altitude because of increased contribution, on the horizontal, of multiple Rayleigh scattering [10]. This could explain that the variation of Kdv with a is more important for planes receiving little circumsolar radiation.
Statistical assessment of models
When equations (4)-(7) are used to estimate the diffuse illuminance from the corresponding diffuse irradiance values, the statistical results given in Table 1 are obtained.
In Table we can appreciate clear differences in the statistical results obtained for the four orientations that can be explained by the reasons given in the preceding section. So, one can see that the best statistical performance corresponds to the North facing surface with an RMSE lower than 10 % and an MBE of -3.3 %, while for the South facing surface a RMSE of 22.6 % and a MBE of 10.0 % are obtained. This is in coincidence with smaller amount of direct radiation incident on the surface facing North. The MBE and RMSE values for East and West facing surfaces are higher than those for the North facing surface and lower than those for the South facing surface, as expected from the intermediate amount of direct radiation received.
Conclusions
We infer, from the present study, the following conclusions:
Relative RMSE and MBE in diffuse illuminance predicted
PLANE RMSE (%) MBA (%) Mean Ld (klx) Mean Kd (lm/W)
North 21.7 -3.3 6.40 110.65
East 17.3 -2.0 8.07 117.65
South 07.9 10.0 11.80 156.31
West 15.5 -4.6 7.48 126.15
1. A very simple model is developed for the diffuse luminous efficacy for vertical surfaces facing North, East, South and West. The model has the same mathematical form for the four surfaces, with the two empirical coefficients being different for each of them.
2. The model works better when the amount of direct radiation incident on the surface is smaller. For the surface facing North the model offers an excellent performance.
3. If one compares the present statistics with those obtained for complex models developed to predict diffuse illuminance on vertical surfaces [10, 13, 14], the present results for the East and West facing planes are rather acceptable taking into account the simplicity of the model used.
Acknowledgement
I am very much indebted to Clean Energy Research Institute at the University of Miami, USA for providing me research facilities and expertise. Moreover, I am also thankful to Higher Education Commission for sponsoring my visit to USA.
References
1. Robledo L., Soler A. Luminous efficacy of direct solar radiation for clear skies // Energy. 2000. Vol. 25. P. 689-701.
2. Robledo L., Soler A. Luminous efficacy of direct solar radiation for all sky types // Energy. 2001 (in press).
3. Robledo L., Soler A. On the luminous efficacy of diffuse solar radiation // Energy convers manag. 2001. Vol. 42. P. 181-190.
4. Robledo L., Soler A. Luminous efficacy of global solar radiation for clear skies // Energy Convers Manag. 2000. Vol. 41. P. 1769-179.
5. Robledo L., Soler A., Ruiz E. Luminous efficacy of global solar radiation on a horizontal surface for overcast and intermediate skies // Theor. Appl. Clim. 2001. Vol. 69. P. 123-134.
6. Ruiz E., Solar A., Robledo L. Assessment of Munee's luminous efficacy models in Madrid and a proposal for new moidels based on his approach // J. Sol. Energy. Eng. (ASME). 2001 (in press).
7. Littlefair P. J. Measurements of the luminous efficacy of daylight // Lighting Res. Tech-nol. 1988. Vol. 20. P. 177-188.
8. Ullah M. B. International daylight measurement programme — Singapore data II: luminous efficacy for the tropics // Lighting Res. Technol. 1996. Vol. 28. P. 75-82.
9. Soler A., Robledo L. Global luminous efficacies on vertical surfaces for all sky types // Renewable Energy. 2000. Vol. 19. P. 61-64.
10. Perez R., Ineichen P., Seals R., Michalsky J., Stewart R. Modelling daylight availability and irra-diance components from direct and global irradiance // Sol. Energy. 1990. Vol. 44. P. 271-289.
11. Raja I. A. PhD. Thesis, University of Strathelyde, Glasgow, UK.
12. Batlles F. J., Alados Arboledas L., Olmoi F. J. A study of shadow band correctiion methods for diffuse irradiance measurements // Sol. Energy. 1995. Vol. 54. P. 105-114.
13. Robledo L., Soler A. Point source simplified Perez illuminous model for vertical surfaces at Madrid: dependance of model coefficients on surface orientation / / Lighting Res. Technol. 1996. Vol. 28. P. 141-148.
14. Robledo L., Soler A. Dependence on surface orientatiion of coefficients in the circumsolar simplified Perez illuminous model for vertical planes at Madrid // Energy Convers Manag. 1998. Vol. 39. P. 1585-1595.
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Ученые из GE Global Research (Централизованного научного центра компании «General Electric») сообщили об успехе. В прошлом году центр анонсировал свое новое перспективное детище - диоды на мономолекулярных углеродных нанотрубках. Сегодня перспектива стала реальностью - ученые доказали, что применение таких диодов в качестве фотогальванических элементов сильно увеличит эффективность солнечных батарей.
— Открытие фотогальванического эффекта в нашем нанотрубочном устройстве может привести к революционным достижениям в солнечной энергетике. Она станет более эффективна и рентабельна, — делится с журналистами научный руководитель из GE Global Research Маргарет Блом (Margaret Blohm).
Поскорее бы это произошло — очень хочется дешевой энергии.
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