# The Cosine Factor Effect in the Different Solar-Tracking Systems

A PTC tracks the Sun on azimuth or elevation. The collector can be oriented East- West and track the Sun on elevation, or vice versa. The reflected beam is incident on a tube placed in the focal line of the collector, which moves along with it. Once the horizontal coordinates of the Sun are known, cos(Oi) can be calculated as follows :

• For a collector with axis oriented East-West:

• For a collector with axis oriented North-South:

cos(0i) = ((sin(ф) sin(5s) + cos(ф) cos(8s) cos(&>s))2 + cos2(8s) sin2 («s)) 2

(2.3)

Linear Fresnel collectors are quite similar, except that the receiver, located well above a set of mobile flat mirrors, does not move, so tracking is on one-angle, or single-axis.

In a central receiver system, a heliostat tracks the Sun in such a way that the re­flected rays are incident on a single receiver located on top of a tower. Although this tracking is two-axis, the cosine factor also appears, as the normal to the reflecting surface has an angle of deviation with respect to the Sun position vector.

The following formula can be used to calculate the cosine factor for a given heliostat :

nT ■ H

cos(0i) = (2.4)

llnll ■ IIHII

n = [cos(an) sin (an), – cos(an) cos(an), sin(an)]T

H = [cos(ht) sin(at), – cos(ht) cos(at), sin(ht)]T

S = [cos(hs) sin(as), – cos(hs) cos(as), sin(hs)]T

where hs and as are the solar altitude and azimuth angles, ht and at are the fixed tower vector altitude and azimuth angles shown in Fig. 2.1 and hn and an are the heliostat-normal altitude and azimuth angles, measured in the same way as hs and as.

The most efficient tracking is done by the parabolic dish systems, in which track­ing is two-axis and the parabola faces the Sun directly when in tracking mode, so there is no cosine factor effect. This is possible because the parabola has a single focal point, where the receiver may be placed.