In the theoretical analysis we suggest that energy of the beam radiation is converted proportional to the illuminated area. That is an idealization. Instead of the changing illuminated area, we can image the constant area and changing proportional to the illuminated area, the instant value of the irradiance G(ra). It means that we consider GTx (ю) being modulated by the position of the sun in the interval raF <ю <raG. From the point-of-view of energy generation, the results are equal. It means that the instant value of the irradiance is additionally modulated (multiplied with the relative share of the illuminated area of the module).

E = J Ac (ю) • GTz(a) = J Ac • GЧ(ю). (3)

Here the symbol GTx*(ra) means the modulated value of the irradiance on the tilted plane (of the deflected module) GTx*(ra) = GTx(ra)-AC(ra)/AC.

Equation (3) shows the theoretical energy produced during the transient shading in the morning.

The process in the evening is equal, but it develops vice versa.

From the 2-D model of the farm we can find

£ =a tan(1/((DR/WC) /(sin(x)-1)) (4)

or otherwise

t= Sin x. (5)

dR — cosx

We can see that the transient shading process (defined in angle units) is a function of two parameters depending on the deflection angle x and the density of the module columns in the row.

To calculate the energy we have to find the moment (solar hour raF) when the illumination starts from the upper edge of the module. The result of the simulation is shown in Fig. 3 for a south­faced farm. The moment of the start depends on the month (due to changing declination 5). It is independent of the latitude. While the shadow is moving over the module, the speed of its movement is important. Growth of the illuminated area of the module depends on the solar azimuth as. Figure 4 shows that in the morning and in the evening the speed of the changes of the solar azimuth (its derivative) is practically constant and nearly independent of the month (declination). While p0= 45°, it has the value das /dra »“0.85”«const and for a simplification may be considered as “1”. This quality allows us to do a rough analysis by substituting the change of the solar azimuth angle for the change of the clock angle. Therefore, the illuminated area AC (ю) is proportional to the current clock angle, i. e. it is increasing (and decreasing) linearly. The duration of the calculated transient shading for an inner module is shown in Fig. 5.