We can choose different shapes for the static concentrators useful surfaces. Using some software which allow the simulation of the light rays way is convenient. For this paper we chose a paraboloidal concentrator.

The rotation paraboloid equation is (Fig.1)

x2 + y2 — 2a2z = 0 (1)

where, a is the radius of the circle obtained by intersecting the paraboloid with the xOy plane at the distance z=1.

In the Fig.2 is being shown the generalized scheme of a concentrator: Ain = Aconc is the area of the light input aperture, Aout = Arec is the area of the exit aperture, 6max, in is the maximum incidence angle, on the entrance aperture, at which it produces the concentration, 6max out is the maximum angle on which the radiation falls on the receptor (PV cell).

The maximum concentration optic factor is [2,8,9]

where, n is the refraction index of the environment in which the cell is immersed (for air n=1). For incidence angles between 0 and 6max, in, the optic concentration factor is equal with the ratio between the radiant flow density on the receiver, Brec, and the radiant flow density on the input aperture, Bconc

b

C = — (3)

optic

conc

The geometric concentration factor is

A

C = — (4)

geom

A out

The concentrator’s performances are determined by the optical efficiency, Ioptic, which is defined as a proportion between the optic concentration factor and the geometric concentration factor

optic

C

The Sun’s declination, 5, at the solar noon in a day of the year, n (n = 1,365), is calculated with the equation

S лі 23,45 • 284 + п

S[rad ] = п———— sin(2n————— ). (6)

180 365

In the equation (6), n is calculated with the equation [10,11,12] n = 30.416(1 -1) + x, (7)

where: 1 is the month (1 = 1,12) and x is the number of the day of the month.

The incidence angle, в, of the radiation on the surface inclined with the 5 angle, orientated with the azimutal angle у is [13,14,15]

cos# = sin8sinфcos5 — sin8cosфsin5cosy + cosScosФcos5cos® +

(8)

+ cos 8 sin ф sin 5 cos Y cos ® + cos 8 sin 5 sin Y sin ® •

where Ф is the latitude of the place.

The hour angle ® is given by the equation

where TS is the solar time (solar hour) and T0 is the solar noon, t0 = 12.

The solar hour is defined as

TS = TL + E — 4Ol — Vl ). (10)

In the (10) equation, (pL is the legal longitude, (pl is the place longitude, TL is the legal hour and E is the time equation,

E = 2.292(0.0075 + 0.1868cos /3 — 3.2077sin /3 — 1.4615cos2^- 4.089sin2^), (11)

where the angle в is

P[rad ] = ^ (n -1). (12)

365

For s=0, we obtain the zenithal distance 0Z,

cos#z = sin8sinф + cos8cosфcosa> (13)

At ground, the solar intensity, B, is

B = S(1 + 0.0034cosn)a• exp(- d/Z0^Q ) (14)

where: S =1353 W/m2, a = 0.88, d = 0.28.

On a surface, A, with random orientation, в, the radiant flow density is

BA = B cos# (15)

If the radiation concentrated from the A] on the A2, the concentrated flow density is

Ba2 = Ba1 • A1/ A2 (16)

The quantity of diurnal solar energy incident on the input aperture of the concentrator has been calculated using the equation:

Qconc =YjnR 2 BconCi АТ i=1

where At is the incrementation step of time, n is the number of temporal sequences with the width At in one day. The quantity of solar energy diurnal incident on the output of the concentrator (photovoltaic cell) has been calculated using the equation:

Qrec =Y. W 2 Breci At (18)

i =1

The efficency of the concentrator has been calculated using the equation:

n = Qrec / Qconc (19)