Radiation losses due to collector arrangement

There are two main losses that are needed to be taken into account before dimensioning and calculating any solar installation.

2.2.5.1 Losses due to orientation and tilting

To calculate these losses, it will be necessary to know about the collector: the value of the tilting angle, β, which indicates tilting, and its azimuth angle, γ, which denotes orientation. Figure 2.2.25 shows a short reminder of these angles.

Figure 2.2.25. Orientation and tilting angle of a collector.

Once these values are known, the calculation for tilting limits is as follows:

First, is necessary to decide which the maximum acceptable losses are. For example, in Spanish solar energy regulation DB HE-4, the limits for the losses are show in Table 2.2.2 and depend on the type of installation that is going to be dimensioned; if it is going to be a general case, collector superposition²² or architectonic integration²³.

22 Collector superposition: the collectors are placed along the building’s shape, without double functionality, as in architectonic integration (CTE, 2009).

23 Architectonic integration: collectors involve a double function, energetic and architectonic; further, they substitute conventional constructive elements or are themselves part of architectural composition (CTE, 2009).

Table 2.2.2. Limit energy losses.

Case Orientation and tilting Shadows Total

General 10% 10% 15%

Superposition 20% 15% 30%

Architectonic integration 40% 20% 50%

Then, the acceptable tilting limits will be defined using Figure 2.2.26, where is represented the maximum percentage of available energy depending on the collector disposition, for a latitude of φ = 41º.

The tilting limits are the intersections between the curve that defines the value of the maximum available energy (that is the opposite percentage of the limit energy losses listed on Table 2.2.2), and the azimuth line. The higher value for β correspond the maximum tilting (βmax) and the lower is the minimum tilting (βmin).

Figure 2.2.26. Percentage of available energy, taking into account the losses due to orientation and tilting, for the case of latitude: φ = 41º.

In the case that there is no possible intersection, it implies that the losses are higher that the acceptable, consequently, the installation is outer limits. Otherwise, these values should be corrected for the real latitude where the installation will be placed, φ_r. These corrections are:

• Maximum tilting: βmax = β (φ = 41º) – (41º - φr)

• Minimum tilting: βmin = β (φ = 41º) – (41º - φr)

If it is obtained a negative angle, that means that the minimum theoretic tilting is βmin = 0º.

26 2.2. Theoretical background 2.2.5.2 Losses due to shadows

These kind of solar radiation losses over a surface are caused by the surrounding shadows and, as orientation losses, are expressed as the percentage of solar radiation which reaches the surface if there was no shadow.

For calculate them, the procedure is to compare the profile of obstacles which affect the collecting surface with the sun’s path diagram. An example of this diagram is shown in Figure 2.2.27, valid for the Iberian Peninsula.

Figure 2.2.27. Sun’s path diagram along the year.

It is usually divided in portions, delimited by the solar heights, α_s, and identified by a letter and a number (A1, A2,... D14). Each portion represent the sun’s path during a specific period of time, therefore, it has a particular contribution to the annual global solar irradiation over the surface object of study. Hence, the fact that an obstacle covers one of the portions implies that an amount of radiation is lost, particularly the one which is intercepted by the obstacle.

In the first place, the location of the main obstacles, their azimuth and height coordinates, are needed to be calculated. Then, these coordinates should be represented over the sun’s path diagram. Next, for obtaining the numerical data, a reference table should be selected; choosing the one whose situation is more alike than the one that is going to be studied. These tables vary depending on the tilting angle, β, and the azimuth angle, γ; and are listed in Appendix II: Reference tables for shadow losses. The number in each cell indicates the percentage of solar global radiation that would be lost if the corresponding portion would be intercepted by an obstacle.

The comparison between the profile of obstacles with the sun’s path diagram allow obtaining the shadow losses of the solar global radiation over the surface during the year. Therefore, all the contributions of the portions that are total or partially covered by the obstacle’s profile should be summed. In the case of partial covering, a filling factor²⁴ must be used; a numeric value must be chosen close to the values: 0,25; 0,50; 0,75 or 1.

(CTE, 2009)

And last, but not least, it has to be taken into account the distance between collectors to avoid shadows between them. Figure 2.1.28 represents the geometric coefficients.

24 Filling factor: is the ratio relating the covered fraction of the portion and its totality.

Figure 2.2.28. Distance between collector and possible obstacles.

The minimum distance between collectors, d, measured over the horizontal, between a row of collectors and an obstacle of height, h, which could produce shadows over the installation, must guarantee a minimum of 4 hours of sun light around the winter’s solstice midday (21^st December). Then, this minimum distance between the collectors and/or obstacles is expressed as follows

0 = ℎ

(61º − ) = ℎ · S

Equation 2.2-27

Where k is a dimensionless coefficient dependant on the latitude, φ.

S = 1

(61º − )

Equation 2.2-28

Table 2.2.3 shows significant values of this dimensionless coefficient for latitudes from diverse areas or cities of the countries object of study.

Table 2.2.3. Values of k for different latitudes.

Country City/Area Latitude φ [º] k

Canary Islands 28 -0,013

The distance between the rear part of a row and the beginning of the next one must not be lower than the obtained with Equation 2.2-27, considering h as the height difference between the highest part of a row and the lowest part of the next one, doing the measures according to the plane which contains the collector’s bases.

(IDAE, 2009)