Optimum distance of solar energy system support structures

Photovoltaic and solar thermal systems are often installed on the ground or on flat roofs. Support racks are used to mount the solar energy systems. Usually these are tilted to get higher annual irradiances, as explained in the section on irradiance on tilted surfaces (see p60).

Furthermore, horizontally installed solar energy systems have relatively high losses due to soiling, for example, through deposition of air pollutants, bird excrement or other dirt deposits on the surface of the collector. Rain or snow can clean tilted surface more easily. As a general rule, the lower the tilt angle the lower is the cleaning effect of rain and snow. In central European climates, average soiling losses in the range of 2-10 per cent can be expected for surfaces tilted at 30° if these are never cleaned manually. These losses can increase significantly for lower surface tilt angles. In other climatic regions with long periods without rain these losses can also increase significantly.

The disadvantage of rows of support structures is that they can cause self-shading. Optimization of the distance between the rows can decrease the shading losses. A way to estimate the optimum distance and tilt angle is described as follows.

The distance d between the rows and the length l of the solar energy system as shown in Figure 2.24 define the degree of ground utilization:

Shading will affect different positions on the tilted solar energy system surface differently. Shading has the highest occurrence at point P0. If the utilization u increases, the shading losses will also rise.

Figure 2.25 Shading Angle a as a Function of the Degree of Ground Utilization u and the Surface Tilt Angle yt

The shading angle

is a function of the ground utilization u and the surface tilt angle yt (see Figure 2.25). If the sun is directly in front of the solar energy system and the sun height is below the shading angle a, self-shading will occur.

With rising shading angles the irradiance losses increase. However, shading losses must be calculated individually for every location. The following calculations are made for Berlin but can easily be transferred to other locations with latitudes around 50° and with a central European climate. Locations at lower latitudes will have significantly reduced shading losses that often can be neglected.

Figure 2.26 shows the relative shading losses s at the point P0 as a function of the shading angle a and the tilt angle yt. The annual irradiation HG tik on tilted but unshaded solar energy systems and the same annual irradiation HG,tilt,red, reduced as a result of self-shading, define the relative shading losses:

It is apparent that solar energy systems are more sensitive to shading losses with higher surface tilt angles.

Since photovoltaic systems are very sensitive to shading, the irradiance at point P0 could be used as a reference for the whole photovoltaic system. Table 2.13 shows the shading angle a and the resulting shading losses s for different degrees of surface utilization for tilt angles between 10° and 30°.

Tilt Angles And Shading
Figure 2.26 Relative Shading Losses s as a Function of the Shading Angle a and Surface Tilt Angle yt in Berlin (52.5°N)

The gain factor g considers the irradiation gains due to the surface tilt angle (see also section on irradiance gain due to surface tilt or tracking, p64). The factor g is the ratio of the annual global irradiation HG,tilt on the tilted surface and the global irradiation HG,hor on a horizontal surface:

The overall correction factor c considers the tilt gains and the shading losses. It is the ratio of the irradiation at point P0 to that on a horizontal surface:

Table 2.13 Shading losses s, Gain Factor g and Overall Correction Factor c for Point P0 at Different Ground Utilizations and Tilt Angles Calculated for

Table 2.13 Shading losses s, Gain Factor g and Overall Correction Factor c for Point P0 at Different Ground Utilizations and Tilt Angles Calculated for

Yt =

SC0

Yt =

1C

u

a

s

g

c

a

s

g

c

1

1.5

38.8°

0.246

1.193

0.900

18.6°

0.048

1.088

1.036

1

2.0

23.8°

0.116

1.193

1.055

9.7°

0.015

1.088

1.072

1

2.5

17.0°

0.074

1.193

1.105

6.5°

0.009

1.088

1.078

1

3.0

13.2°

0.048

1.193

1.136

4.9°

0.006

1.088

1.081

1

3.5

10.7°

0.035

1.193

1.151

3.9°

0.004

1.088

1.084

1

4.0

9.1°

0.029

1.193

1.158

3.3°

0.004

1.088

1.084

Table 2.14 Average Relative Shading Losses s and Overall Correction Factor c for Points P0, P1 and P2 at Different Ground Utilizations and Tilt Angles Calculated for Berlin (52.5°N)

Yt = 30°

Yt = 10°

u

s

g

c

s

g

c

1

1.5

0.098

1.193

1.076

0.018

1.088

1.068

1

2.0

0.048

1.193

1.136

0.006

1.088

1.081

1

2.5

0.032

1.193

1.155

0.004

1.088

1.084

1

3.0

0.021

1.193

1.168

0.003

1.088

1.085

1

3.5

0.016

1.193

1.174

0.002

1.088

1.086

1

4.0

0.013

1.193

1.177

0.002

1.088

1.086

The reduction of the ground utilization u below 0.33 (that is a ratio of the length of the solar energy system rows to the distance of the rows of 1:3) does not result in a significant reduction of the shading factor. Ground utilization higher than 0.4 (1:2.5) may be favoured by lower tilt angles. Considering the 5 per cent higher losses that result from soiling at a tilt angle of 10° instead of 30°, lower tilt angles are recommended for ground utilization values above 0.5 (1:2).

Solar thermal systems are less sensitive to shading than photovoltaic systems. Here, the average irradiance can be used for the estimation of the output of solar thermal systems. This is done by calculating the average shading losses at the points P0, P1 and P2 shown in Figure 2.24. The losses at point P0 have already been estimated. Point P1 will never be shaded. For point P2, the shading angle a. = anLiaii

in the centre of the tilted surface is relevant. Table 2.14 shows the average relative shading losses s as well as the overall correction factor c for the three points P0, P1 and P2. Compared to point P0, the shading losses are much lower. No significant improvements are possible for ground utilization u < 0.4 (1:2.5). Lower tilt angles are generally not recommended.

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