EuroSun2008-2

Model Description

In order to evaluate of the performance of the small mirror array, the MMA geometry and movement characteristics were implemented in a raytracing tool. The model includes a complete physical repre­sentation of the coupled movement of the facets of the array. For the simulation, a huge number of rays is generated and their paths are then traced (usually 108 rays). The effects considered in the model are:

• reflection off the glass cover, depending on the incidence angle and on the characteristics of the coat­ing (if applicable)

• absorption in the glass cover

• interaction of MMA components: moving mirror facets, sidewalls and back wall, specular reflection, at the mirror facets, mirror slope errors or facet tracking errors

• A further consideration of the model is the limitation of the angular movement of the MMA mirror facets due to mechanical constraints (e. g. facets hitting the sidewall).

• Instantaneous performance calculations are carried out based on a given direct normal insolation. Annual performance calculations are done by randomly distributing the generated rays over the time period of one year. Each ray has a specific energy according to the actual time and date, based on the instantaneous insolation and the total number of rays used. Integration over the year is then simply ob­tained by summing up the ray energies of each specific event. This is the preferred method since it is exact in principle, with accuracy limited only by the number of rays selected. Other options, such as the weighted summation of a limited number of selected times (e. g. one day per month with a given time period), require approximations to calculate the annual performance and are therefore less accu­rate. More information on the raytracing tool can be found in [4].

4.2. Assumptions

For the evaluation of the MMA performance, the following assumptions were made:

Mini-mirror array:

• box dimensions: (2 x 1)m (Ah = 2m2)

• reflectivity of the mirror facets: 94%

• glass cover: with antireflective coating (“ARC”) and without antireflective coating (“noARC”)

• number of facets: 5 x 10 (50 in total)

• facet dimensions: ideal: (0.2 x 0.2)m; no gap between facets, no movement limitations (“ideal”)

• facet dimensions: realistic: (0.18 x 0.185)m; gap between facets: 2mm, movement limitation by hit­ting sidewalls (“real”)

• no slope or tracking errors

In the ideal case, the possibility of facets touching each other or the sidewalls whenever they are not positioned parallel to the box cover is disregarded. This case defines an upper performance limit. In reality, the dimensions of the mirror facets and the gaps were selected to avoid the angular movement of the facets exceeding the angular movement limits given by geometric considerations. For the realis­tic geometry, the angle limit for the elevation axis is taken to be ± 25°. For the azimuth direction, the limiting angle is ± 48°. These angles are slightly larger than the angles that occur during the operation of the heliostat at this specific location. These angles may vary for other field locations or sites.

The antireflective coating of the glass has a solar-weighted transmittance of 97.3% at perpendicular incidence angles. This model is based on measurements of antireflective coated glazing.

Reference heliostat:

• two-axis tracking (azimuth/elevation)

• mirror dimensions: (2 x 1)m (Ah = 2m2)

• reflectivity of the mirror facets: 92%

• no slope or tracking errors

The reflectivity of the mirrors for the reference heliostat was selected to be 2% lower than that of the mini-mirror array, since the latter is installed in a closed box allowing the use of better and more sensi­tive materials.

Common Data:

• site location: 37.2° northern latitude (Seville, Spain)

• tower height: 100m

In both configurations, clean glass or mirrors were assumed. It is expected that dust will affect per­formance of both configurations in a similar way, so the trends will remain the same.