WREC 1996

MODELING DAYLIGHT ON INCLINED SURFACES FOR APPLICATIONS TO DAYLIGHT CONSCIOUS ARCHITECTURE

Luis Robledo* and Alfonso Soler**

*Departamento de Sistemas Inteligentes Aplicados, E.U. Informatica, Universidad Polit~cnica de Madrid,

Ctra de Valencia km 7, 28031 Madrid, Spain. **Departamento de Fisica e Instalaciones Aplicadas, E.T.S. de Arquitectura. Universidad Polit~cnica de Madrid,

Avda Juan de Herrera 4, 28040 Madrid, Spain.

ABSTRACT

In the present work the circumsolar and the point source version of the Perez model have been evaluated for South facing vertical surfaces at Madrid. Different data sets have been used. The coefficients Fij in the model have been determined using jointly experimental data obtained for vertical planes facing N, E, S and W, and also with data for just the South vertical planes. Different values of the half angle ~ corresponding to the circumsolar region have been used, and the most simple version of the model is recommended.

KEYWORDS

Daylight conscious architecture;Illuminance on inclined surfaces; Perez model.

INTRODUCTION

One way energy can be saved in buildings is through better use daylight. Design of windows, use of innovative daylighting systems and prediction of the savings from new forms of electric lighting control are important in relation to this aim. However, to quantify the energy effects of daylight or to simply estimate daylight illuminances in different parts of a room, knowledge of illuminances received at external surfaces with different slopes is necessary. One way to estimate these values is converting available or estimated radiation data into external horizontal illuminances using a luminous efficacy model, and then estimating illuminances at inclined surfaces from illuminances at horizontal surfaces. In recent years illuminance measurements have increased world wide, mainly through the International Daylight Measuring Programme (IDMP), launched in 1991 by the Commission Internationale de l'Eclairage (International Energy Agency, 1994). Thus, direct modeling of illuminances on inclined surfaces from illuminances on horizontal surfaces is now becoming a more realistic approach. There are different models to predict the illuminance on an inclined surface. The chosen model must be easy to use and should predict illuminances with the highest possible accuracy. The model proposed by Perez (Perez et al,

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WREC 1996

1986), mostly tested for solar irradiances instead of illuminances, is usually considered as one of the more accurate. However in its original formulation the model is rather complex and difficult to use. A simplified version of the model is available (Perez et al, 1987), which considers the circumsolar region caracterized by a half angle ~ and an infinitesimal horizon band with an elevation of 0 ° . The most easy to use being the point source version, which considers circumsolar radiation as coming from a point at the centre of the sun's disk. To use any of the versions one must know a set of coefficients obtained from illuminance data from horizontal and inclined surfaces.

In the present work we have statistically assessed with different data sets for different values of a the simplified version for vertical South facing surfaces at Madrid, Spain, where continous measurements of illuminances are routinely obtained in a General Class Station in the framework of the IDMP.

MODELS

In general global illuminance on an inclined plane is obtained from its direct and diffuse components. Direct illuminance can be calculated from the difference between global and diffuse illuminance on a horizontal surface or from measurements of direct normal illuminance.

The hourly diffuse illuminance on an inclined surface with a slope @ is obtained in the simplified Perez model from the following equation:

E~= Eh[0.5(I-FI) (l+cos~) + (a/b)Fl+F2sin~] (I)

where Eh is the horizontal illuminance and F 1 and F 2 are coefficients which respectively express the degree of anisotropy of the circumsolar and the horizon regions. These coefficients show a dependence on the parameters that define theh sky conditions : a) The zenithal angle, and the most simple version of the model is recommended. b) The clearness index ~ defined through:

= (Eh + En)/Eh (2)

A modified clearness index, ~', has been proposed in Perez et al (1990):

~,= [(E h + En)/E h + kZ3)]/[l + kZ 3] (3)

E n being the direct normal illuminance.

C) The sky's brightness A defined by:

A = Ehm/E o (4)

where E o is the mean extraterrestial normal illuminance and m the optical air mass.

The model considers a set of categories for ~ or ~' and for each of them

F 1 and F 2 are given as:

F 1 = FII + FI2*A + FI3*Z F2 = F21 + F22,A + F23*Z (5)

The coefficients Fij corresponding to each category can be obtained by fitting the measured data

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WREC 1996

In the point source version (~ = 0 °) a and b are given as

a = max(0,cosO) ; b = max(0.087,cosZ) (6)

8 being the incidence angle of the sun on the surface and Z the zenithal angle.

In the circumsolar version of the simplified Perez model (~ # 0 °) the corresponding expressions for a and b are the same as in first version of the model (Perez et al, 1986). They are more complex than those given in (6) and the utilization of the model results more ardous. There is a general agreement that the circumsolar version is more accurate than the point source version. In the available literature coefficients Fij in (I) are calculated using jointly data for 4 orientations, usually N,E,S and W, and ~ = 90 ° .

In the present work the circumsolar and the point source versions have been evaluated for exclusively South facing vertical surfaces as follows:

MI. Point source version with coefficients obtain by Perez using data for all orientations and some U.S. stations (Perez et al, 1990).

M2. Point source version with coefficients obtained for Madrid with data for all orientations.

M3. Point source version with coefficients developed for Madrid with data for South orientation.

M4. Point source version with two sets of coefficients obtained for Madrid for South orientation, but separating the data for a/b # 0 and the data for a/b = 0. (Corresponding respectively to the vertical plane respectively seeing or not the centre of the sun). A detailed justification of this modification of the point source version is given in Robledo and Soler, 1996.

M5 to M9. Circumsolar simplified Perez model with coefficients obtained for South orientation and ~ taking respectively values 7.5 ° , 15 ° , 20 ° , 25 ° and 35 ° .

MI0. Circumsolar version for ~ = 25 ° with coefficients obtained using jointly data obtained for the four vertical planes facing N,E,S and W.

METHODS

Experimental data consist of mean hourly values of diffuse and global illuminance on a horizontal surface, and global illuminance on vertical surfaces facing N, E, S and W. The data used, obtained in the flat roof of the Escuela T~cnica Superior de Arquitectura in Madrid (40.3°N, 4.4°W), belong to the period August 1992 - September 1993. A complete description of the experiment is given in Robledo and Soler (1996).

To statistically assess model's validity two different estimators have been calculated, the root mean square deviation (RMSD) and the mean bias deviation (MBD).

RESULTS

In Table 1 we give the relatives values MBD and RMSD for M1 to MI0, for global illuminance.

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Table i. Statistical performance of models for the South orientation at Madrid

Global Illuminance

Model M1 M2 M3 M4 M5 M6 M7 M8

RMSD 3.00 3.16 1.85 1.76 1.84 1.73 1.67 1.64

MBD -2.28 1.23 0.05 0.01 0.01 0.01 0.01 0.01

M9 MI0

1.67 2.42

0.01 1.02

Average Global Illuminance 32.44 klux

Relating the RMSD it is clear that the models which predict better are M3 to M9, for which Fij have been calculated using only data for the South facing surface. Of there, M6 to M9 (15°< ~ < 35 ° ) give similar RMSD. However M3 and M4, both point source, (M4 obtained by separating the data for the surface seeing or not the sun), predict almost as well as M6-M9 and are much easier to use. Thus, looking for an equillibrium between prediction accuracy and easy use, the most simple version of the Perez model, the point source, specially M4, can be recommended. It has to be emphasized that both M3 and M4 are developed using only data for the South plane.

CONCLUSIONS

The circumsolar and the point source versions of the Perez model have been tested for Madrid. For the South facing surface, prediction accuracy is similar for both versions when the coefficients Fij used are determined only with data for this orientation. As a consequence, if we look for both prediction accuracy and easy use, the point source version can be recommended.

REFERENCES

International Energy Agency (1994). World Network of Daylight Measuring Stations (IDMP), Report No. IEA-SHCP-17E-2

Perez, R., Stewart, R., Arbogast, C., Seals, R. and Scott, J. (1986). An anisotropic hourly diffuse radiation model for sloping surfaces: Description, performance validation, site dependency evaluation. Solar Energy 36, 487-497.

Perez, R., Seals, R., Ineichen, P., Stewart, R. and Menicucci, D. (1997). A new simplified version of the Perez diffuse irradiance model for tilted surfaces. Solar Energy 39, 221-231.

Perez, R., Ineichen, P., Seals, R., Michalsky, J. and Stewart, R. (1990). Modeling daylight availability and irradiance components from direct and global irradiance, Solar Enerqy 44, 271-289.

Robledo, L. and Soler, A. (1996). Performance assessment of the point source version of the simplified Perez illuminance model for vertical surfaces at Madrid: dependence of model coefficients on surface orientation. International Journal of Lighting Research and Technoloav, accepted for publication.

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