Academician Dmitrii Strebkov,
post-graduate Pavel Litvinov,
candidate of technical science Eduard Tverjanovich
(All-Russia Scientific Research Institute of Electrification of Agriculture)

Now the cost of modules of solar batteries is high enough. It is possible to lower this cost (in 1,4^1,6 time) using concentration of sunlight and solar cells with two-sided photosensivity. In order to prevent complication of a construction of the photoelectric converter with concentrating modules [1, 2], in the All-Russia Scientific Research Institute of Electrification of Agriculture (ВИЭСХ) the conceptual direction on development of photo­electric modules with concentrators only for stationary installation is accepted (without devices of tracing behind a seen position of the Sun on a firmament).

Fig. 1. Geometry of a profile of the stationary U-shaped concentrator

Principle of functioning stationary U-shaped cylindrical parabolic concentrators with the receiver located in a focal plane the following. Such concentrators assume use of photoelectric converters with a two-sided effective surface and have the big concentration in comparison with compound cylindrical concentrators. The profile of the U-shaped asymmetrical stationary concentrator [3, 4] with a continuous reflecting covering (fig. 1) is formed by two branches of parabola AB and CD, unrolled concerning common focal point F on angles ai and a2 accordingly at an aperture angle of the stationary concentrator (сн+а2) and connected among themselves on circle BC. In such concentrator under condition of |5|<a1, |6|<a2 where 5 — the angle of current declination of the sun, all rays go on receiver OF located below of a focal point of the concentrator.

SHAPE * MERGEFORMAT

Curves AB and CD (fig. 1) are parabolas and are described by the equation y2 = 2 • p • x = 4 • f • x, Where p — key parameter of a parabola, and f — a focal length of a parabola. For convenience of accounts plane OF on fig. 1 is inclined on an angle a1. Then the limiting ray, which else will hit in the concentrator, and will not be shaded by a wall of the concentrator, directed under an angle (a1+a2) in relation to an axis of abscissas x. It is described by the equation y = tg(a1 +a2)■ x + b also it is a tangent to a profile of a parabola of the concentrator in point A (x, y). A solution of a system of these equations is:

x =-

f

tg2(a1 + a2)

y =

2 ■ f tg(a1 + a 2)

Proceeding from this, distance from point A to a focal

plane:

L1 = 2 • f • (

1

— (

tgcq

1

1 — x) • sin 01). (1)

cosa1 • tg(a1 + a 2) tg(a1 + a2) 2 • tg2(a1 + a2) 2 In a similar way, considering curve CD, distance from point D up to a focal plane is obtained:

L2

2 • f • (

1 cosa2 • tg(a1 + a2)

(

tga 2 tg(a1 + a 2)

1 2 • tg2(a1 + a2)

1 ■ sin a 2). (2)

K L L1 +L 2 K r ■= h =_ІГ“

2 • f

1

1

1

h cosa1 • tg(a1 + a 2) cosa1 cosa tga1 • sin a1 + tga2 • sin a2 sin a1 + sin a2 sin a1 + sin a2

-) —

2

(3)

tg(a1 + a 2)

2 • tg2(a1 + a 2)

2

)

In case the stationary concentrator is symmetric a1=a2= a, and the height of the receiver coincides with its focal length (h=f), is obtained:

к г 0 = 4 • (-

1

— (:

tga

1

‘cosa • tg(2 • a) ‘tg(2 • a) 2 • tg2(2 • a) 2 At a=23,5° it is obtained: L=3,5f. In this case: Kr0=3,5.

— ) • sin a).

(4)

Tests of mockups of modules with stationary concentrators have shown, that nonuniformity of light exposure, as it was necessary to expect, is much more strongly expressed for angles of declination of the sun 5=23,5° and for concentrators with a continuous reflecting covering. For functioning of solar cells the preference should be returned planar mirror surfaces from the point of view of the uniform light exposure. The mode of an arrangement of mirrors on a profile (fig. 2) is of interest. The arrangement фацет concerning the receiver and each other may be various: a) an arrangement of planar mirror surfaces on an ideal profile; b) an arrangement of planar mirror surfaces on a tangent to lateral aspect of an ideal profile.

If the concentrator will have a smaller breadth of profile AD the light flux directed to the concentrator, will be used short. If a breadth of a profile to execute more rated then at some angle of rays shading parts of solar rays by walls of the concentrator will be observed. Proceeding from this, the ration of a breadth of the concentrator to the receiver equal:

Fig. 2. An arrangement of planar mirror surfaces on an U-shaped profile (the left half), or on a tangent to an U-shaped profile (the right half)

At the same time, stationary concentrators with planar mirror surfaces as have shown researches, have the major losses of radiation and geometrical concentration, than the stationary concentrator of an ideal profile with a continuous reflecting surface. It is connected, first of all, to partial loss of the radiation overflowing the receiver of sunlight. Besides the major nonuniformity of functioning of the stationary planar mirror concentrator within one year is observed at an arrangement of mirrors on the inner side of a pattern with an ideal rated profile.

The increase of height of the receiver the planar mirror stationary concentrator though allows to use a solar energy more full, however leads to significant decrease of geometrical concentration. Good power parameters are observed at an arrangement of mirrors on a tangent to lateral aspect of a pattern with an ideal profile.

In other important parameter influencing functioning of the stationary U-shaped concentrator, the select of an expansion angle a is. The profile of the concentrator represented on fig. 1, has an aperture angle 2a. At 5<-a, or 5>a the sun within all day remains outside of a visibility range of the concentrator. At — a<5<a, but 5, close to +a the concentrator works short time. An operating time of the concentrator according to the introduced circuit at various angles a at latitude of Moscow is introduced on fig. 3.

Fig. 3. An operating time of the stationary U-shaped symmetric concentrator in the course of year

Thus, the more aperture angle of the concentrator, the is more time of its work in one year. However, at increase of an aperture angle, geometrical concentration Kr0 decreases because of the breadth on midship of the stationary concentrator is reduced. From the graph (fig. 3) it is visible, that the greatest operating time t the U-shaped stationary symmetric concentrator within day is observed in days of the spring and autumn equinox, in the similar image geometrical concentration of Kr0 (3) changes also. A character of association of size of an aperture angle 2a (or an expansion angle a) from an uptime of the concentrator within day t and geometrical concentration of Kr0 is seen.

As a result of computer modelling of functioning of the U-shaped stationary concentrator power performances (fig. 4) were obtained.

The graph (fig. 4) is represented for latitude ф=56.5° (Moscow), however character of associations is fair and for all latitudes. At modelling it was supposed, that the concentrator has optical efficiency t=0.8; it was oriented on latitude of region and worked all-the-year — round. From fig. 4 it is visible, that at annual use of the concentrator in days with 5<-a and 5>a the stationary U-shaped symmetric concentrator generally remains disabled. It is observed under condition of a<23.5°.

Researches of function of capacity of the module by means of the computer have shown, that the stationary concentrator at an expansion angle a =23.5° in days, the close to a summer and winter solstice, has a dip in a power generation. As a result of this it is impossible to consider an expansion angle of the stationary concentrator a=23.5° optimum. The maximum power generation within one year falls at the stationary concentrator with an expansion angle a=27.5°. In this case the power generation is more as contrasted to a power generation the stationary concentrator with an expansion angle a=23.5° on 9%.

The carried out computer simulation of operation of the U-shaped stationary concentrator can be used for a select of such geometrical performances of the stationary concentrator, as an optimum aperture angle, a breadth on a midsection of the concentrator, its depth, etc. Energy performances can be the useful by optimization of the listed above geometrical sizes at a known time in use of the concentrator within day, and also phase of functioning of the concentrator in one year. The time in use of the concentrator within day and phase of functioning within one year is determined in turn by performances of a sink.

The literature

1. Г. Раушенбах. Справочник по проектированию солнечных батарей. М.: Энергоатомиздат, 1983 р. 57-60.

2. J. C. Minano, A. Luque, J. Parada. Recent results of non-tracing photovoltaic concentrators. Invited paper at the Fourth Sunshine Workshop on Crystalline Silicon Solar Cells. Makuhari, Japan, 1992.

3. A Luque ed., Adam Hilger. Solar Cells and Optics for Photovoltaic Concentration. — Bristol, UK, 1989, pp. 381-395.

4. J. C. Minano. Static concentration. International Journal of Solar Energy, №6, 1988, pp. 367-386.