Solar Electricity Generation Technical Field

The invention pertains to electricity generation using sunlight, and in particular to light concentrators for solar panels and solar panels incorporating them. Background Art

Solar panel technology involves solar panels designed to convert sunlight into electricity, for instance using photovoltaic material. Solar panels are installed on roofs or at other locations where there is good sunlight, so as to maximise the amount of light reaching the panels and the electricity generated. Photovoltaic material generates most electricity when light reaches it perpendicular to the surface of the panel so the panels are generally oriented to face the noon sun.

The photovoltaic material is usually covered by a protective sheet of transparent plastic or glass. It is possible to incorporate lenses to concentrate the sunlight reaching the photovoltaic material. However, except for large scale installations, this has been found to be of limited effectiveness. This is mainly due to two factors:

The sun moves across the sky during the day and, in order for the lenses to work effectively, either the panels or the lenses, or both, must track the sun. This adds manufacturing complexity and cost to solar panels that are rarely justified from an efficiency and economic viewpoint; except in large installations.

A second problem is that lenses work best with light coming from one direction only. Unfortunately, in practice, natural light does not always come directly from the sun but can be diffused or scattered by the atmosphere, clouds or fog.

Disclosure of the Invention

The invention comprises a concentrator for collecting and guiding sunlight to a transducer that converts it to electricity. The concentrator comprising:

A pair of adjacent solid elongate transparent elements having a refractive index greater than air. Each of the elements has a transparent upper surface, a mirrored lower surface and an output surface that is smaller than the upper surface and substantially perpendicular to it. The arrangement being such that the two output surfaces of the pair of adjacent elements sandwich an optical/electrical transducer between them to deliver concentrated solar radiation to both sides of the transducer.

The photovoltaic layer may be bifacial or may be made of two monofacial 'layers' back to back.

The invention possesses very significant advantages over known ways of generating electricity using solar panels based on photovoltaic effects. In particular, the invention reduces the amount of electricity generating material required per surface area exposed to sunlight. In existing technology the surface area of the electricity generating material is the same as that of the area exposed to sun light. The reason is that there has been no simple, effective and low cost way of collecting and concentrating light from a wide variety of directions and intensities onto a smaller area. The invention addresses this problem.

The upper and lower surfaces are shaped and arranged relative to each other such that some of the sunlight that enters the upper surface is refracted as it passes through it and is then reflected from the lower surface before reaching the output surface. Between being reflected from the lower surface and exiting the output surface a proportion of the sunlight is also totally internally reflected from the upper surface. This proportion of the sunlight may be reflected from the lower surface or the upper surface, or both, more than once before exiting the output surface.

The device can accept incoming rays across its entire upper surface and from all angles. The concentration factors achieved are typically between 3 and 6, without the use of sun tracking equipment. The invention has important applications for solar panel technology, for small and large scale installations.

In one example the concentrator has a flat top with the transparent upper surface of both elements being flat and arranged in the same plane.

In this case the lower mirror surfaces of each element, which are symmetrical, may be shaped with curved part in the centre of the concentrator, the curve being in the general shape of an arc of a circle with a centre offset above the flat top of the other element. This spreads the guided solar rays along the surface of the transducer.

Also, at the outer sides of the elements the mirrored surface may be flat. Further, between the flat part and the circular part there may be another curved part that has the curve in the general shape of a parabola with its focal point above the flat top of the other element. This spreads the guided solar rays along the surface of the transducer. The two focal points may not be co-located but separated from each other.

When the top of the concentrator is not flat, the centres may not be above the elements but inside the other element. With the invention, the surface area for the electricity generating material required is reduced by a factor of 3 to more than 6. This means that for each square meter exposed to sunlight, only 20% or less of a square meter of electricity generating material is required. This is very significant as electricity generating material is costly and contributes significantly to the fact that renewable solar electricity is currently more expensive to produce than electricity generated from traditional coal fired power stations for example.

As the light collecting and guiding elements are simple and can be manufactured at low cost, the invention can make solar electricity significantly more affordable for industrial and home uses. Renewable energy sources, such as the sun, need to play an increasing role in reducing our dependence on oil and coal; therefore the commercial applications of this invention are potentially very significant.

The light collecting and guiding elements can be used in conjunction with a large variety of electricity generating materials.

The main application areas of the invention are solar panels such as those installed on roofs for example and also larger installations where it can be used to replace the light tracking machinery that is needed with traditional lenses to keep the light focused throughout the day on a smaller area of photovoltaic material.

The optical/electrical transducer may be a thin flat layer or may be of a different shape or composition. For instance, the transducer layer may comprise a set of rods or spheres (beads) embedded in the transducer layer. The embedded rods or spheres may be arranged regularly in a line, or pseudo randomly along the line.

In a further aspect the invention is a solar panel comprising plural of the concentrators arranged side by side. In this case each element may be arranged to guide solar light to a transducer sandwiched between it and an adjacent element. The panels may comprise more than one set of plural concentrators arranged side by side. In this case the concentrators of each set may be offset from each other. This may be useful for making the panels self-cleaning.

Heat sink material may also be incorporated into the panels.

Brief Description of the Drawings

Examples of the invention will now be described with reference to the accompanying drawings, in which:

Fig. 1(a) is a diagram of a photovoltaic electricity generating panel made up of components.

Fig. 1(b) is one of the components of Fig. 1(a).

Fig. 2 is a cross-section through one of the components of Fig. 1, showing its internal arrangement.

Fig. 3 is a schematic diagram of the cross-section through one of the components of Fig. 1.

Fig. 4 is a diagram of a cross-section through one of the components of Fig. 1 showing one half of the concentrator and how it guides solar rays received at a first angle onto the target area.

Fig. 5 is a diagram of a cross-section through one of the components of Fig. 1 showing one half of the concentrator and how it guides solar rays received at a second angle onto the target area.

Fig. 6 is a diagram of a cross-section through one of the components of Fig. 1 showing one half of the concentrator and how it guides solar rays received at a particular point over a range of angles onto the target area.

Fig. 7(a) is a diagram of a cross-section through one of the components of Fig. 1 showing an alternative design for the concentrator.

Fig. 7(b) is a diagram of a cross-section through one of the components of Fig. 1 showing another alternative design for the concentrator. Fig. 7(c) is a diagram of a cross-section through one of the components of Fig. 1 showing the tulip shape concentrator of Fig. 3.

Fig. 7(d) is a diagram of a cross-section through one of the components of Fig. 1 showing a further alternative design for the concentrator.

Fig. 8(a) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator shaped to have a wide angle of reception.

Fig. 8(b) is a diagram of the concentrator of Fig. 8(a) marked to help explain how it is designed to operate with total internal reflection.

Fig. 8(c) is a diagram of the concentrator of Fig. 8(a) marked to help explain how it is designed to operate with direct reflection.

Figs. 9 (a) to (f) are diagrams of the concentrator of Figs. 8, showing how incident solar radiation is collected and guided by the concentrator from a wide variety of angles of incidence and two different points of incidence. In Figs. 9(a), (c) and (e) from near the edge, and in Figs. 9 (b), (d) and (f) from near the centre.

Fig. 10(a) is a pictorial view of a solar panel with components arranged in a North-South orientation.

Fig. 10(b) is a pictorial view of a solar panel with components arranged in the East- West orientation.

Fig. 11(a) is a pictorial view of a solar panel with components arranged in a North-South orientation showing the range of sunlight received in the North- South plane during the seasons of the year.

Fig. 11(b) is a pictorial view of a solar panel with components arranged in a North-South orientation showing the range of sunlight received in the East- West plane during each day.

Fig. 12 is a diagram of a cross-section through one of the components of Fig. 1 showing a concentrator shaped intermediate those shown in Figs. 3 and 8.

Fig. 13 is a diagram of a solar panel comprising an arrangement of two banks of the concentrators of Fig. 12.

Fig. 14(a) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a rod-shaped transducer. Fig. 14(b) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a set of rod-shaped transducers arranged regularly.

Fig. 14(c) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a sphere-shaped transducer.

Fig. 14(d) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a set of bead- or rod-shaped transducers arranged randomly. Fig. 15(a) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a tilt corresponding to the latitude.

Fig. 15(b) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a tilt corresponding to the latitude +/- 10 degrees.

Fig. 15(c) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a tilt corresponding to the latitude +1-20 degrees.

Fig. 15(d) is a diagram of a cross-section through one of the components of Fig. 1 showing a flat top concentrator with a tilt corresponding to the latitude +/- 30 degrees.

Best Modes of the Invention

Collecting the Sunlight

Referring first to Fig. 1(a), a panel 10 can be seen to be made up from component modules 12. Fig. 1(b) shows a single component. A rectangular framework 14 holds all the components 12 together in a large flat panel 10. In use the upper surface is exposed to collect sunlight. The number of components inside the frame can vary as can the length and width of each component.

The components 12 will now be described with reference to Fig. 2 which shows a cross- section through a component 12. Along the length of the component is a 'concentrator' 20 which collects and guides the sunlight 22 received through the top face of the component, from above. In this example, the cross-section of the concentrator 20 is tulip-shaped with two symmetrical halves 24 and 26 which are made from a material with a refraction index larger than that of air; typically glass or Perspex. In Fig. 3 the corners of the component 12 have been labelled A, B, C and D, and the apexes of the 'tulip' shape have been labelled with the capital letters A, B, E and F. Using this notation the component and concentrator will be explained:

The dotted line 30 extending from A to B represents the upper face of the panel facing sun light. This face may be covered, for instance by a glass or perspex sheet. However, the dotted line simply shows the 'upper boundary' of the concentrator, which could be open.

The curve A to E, and the curve B to E represent the transparent upper surfaces 32 and 33 of each half of the concentrator 20.

The curve A to F, and B to F represent the mirrored lower surfaces 34 and 35 of each half of the concentrator 20.

The line E to F is the target area 36 to which the concentrator 20 guides the solar rays received by the concentrator. Guiding the Collected Sunlight

Referring now to Fig. 4 sunlight 22 is received at an angle of 20° to the horizontal. One particular solar ray 40 passes through the upper face 30 of component 12 and arrives at point 41 on the transparent upper surface 32 of the left element of concentrator 20. Ray 40 is refracted as it enters the transparent surface of the concentrator at point 41.

Inside the concentrator, ray 40 travels to the mirrored lower surface 34 and arrives at point 42. Here ray 40 is reflected by the mirror.

Ray 40 then travels through the concentrator again and arrives at the transparent upper surface 32 at point 43. Here, ray 40 is again reflected even though the surface 32 is transparent. The shapes of the curves and the angles of the upper and lower surfaces 32 and 34 are designed and arranged to ensure total internal reflection.

Ray 40 travels again to the mirrored lower surface 34 and arrives at point 44. Here ray 40 is again reflected by the mirror.

Finally ray 40 travels to the target area 36 where it arrives at point 45. In this example the target area 36 comprises a sheet of photovoltaic material which absorbs ray 40 and converts it to electrical energy. Table 1 below summarises the interactions of an incoming ray 40

with the concentrator 20:

Fig. 5 shows how an incoming ray 50 close to the vertical interacts with the concentrator 20. In this case ray 50 enters through the upper face 30 of component 12 and arrives at point 51 on the transparent upper surface 32 of the left element of concentrator 20. Ray 50 is refracted as it enters the transparent surface of the concentrator at point 51.

Inside the concentrator, ray 50 travels to the mirrored lower surface 34 and arrives at point 52. Here ray 50 is reflected by the mirror. From the mirror ray 50 travels to the target area 36 where it arrives at point 53.

Fig. 6 shows how a range of incoming rays are collected and guided towards the target area by concentrator 20. All of the rays that enter the collector are refracted as they enter, and all are reflected from the mirrored lower surface 34. Some of the reflected rays go directly to the target area 36; others are totally internally reflected from the transparent upper surface 32 of concentrator on their way.

Rays from any angle bounded by the dotted lines 60 and 62 can enter the top of component 12 and arrive at point 64 on the transparent upper surface 32 of the left element 24 of concentrator 20. Rays from the left at a lower angle than ray 62 may hit the right element 26 of the concentrator (not shown); these rays cannot reach point 64 on the left element 24. It will be appreciated that rays impacting concentrator 20 closer to the upper apex, point A, will be received over a wider range of angles than the angle 60-62. Whereas rays impacting close to the bottom of the trough near point E will only be received over a narrow range of angles. In summary, the concentrator 20 is able to collect rays from nearly 0 to 180 degrees, that is every ray that enters the top of component 12, and guide them onto the target area 36. Of course, the photovoltaic material at the target area 36 may absorb solar radiation on both sides; that is rays that are received from both elements 24 and 26 of the concentrator 20.

Concentration

The concentration factor C of the concentrator (one element) can be calculated by comparison with flat plate systems. With reference to Fig. 3, C is given by:

C = ( A - B ) / ( E - F ) Where A - B represents the upper face 30 of the component, and E - F represents the target area 36. The concentration factor provides a measure of the improvement compared to a flat plate system having an area equal to A - B catching the same amount of light. When both elements 32 and 33 are used light can reach the target area from either element and the amount of light guided to the target area is doubled.

Variants

Although only one form of concentrator 20 (the tulip form) has been described so far, it will be appreciated that other forms will also function effectively:

Fig. 7(a) shows a cross-section where the target area 36 is horizontally arranged at the bottom of the concentrator, the upper transparent surface 32 of the concentrator is straight and the lower mirrored surface 34 comprises a straight side arranged at an angle of slightly greater than 90° to the target area.

Fig. 7(b) shows a cross-section where the upper transparent surface 32 of the concentrator is straight and the lower mirrored surface 34 is curved.

Fig. 7(c) shows a cross-section having the familiar tulip shape.

Fig. 7(d) shows a cross-section where the sides are slightly tapered in towards the bottom. The target area is on the lower half of the outer side of the concentrator; between El and D/Fl, and E2 and C/F2. The upper transparent surface 32 of the concentrator is straight. A first straight mirrored surface 34(a) is arranged on the upper half of the outer sides of the concentrator; between El and A. A second mirrored surface 34(b) extends from D/Fl to G.

Other designs are possible. For example, with reference to Fig. 7(d) the straight transparent surface 32 and the straight mirrored surface 34(a) could be curved as shown in Fig. 7(c). In general, variations of the cross-section of the concentrator can be generated by replacing straight or curved sides with a greater number of straight or curved facets, or a mixture of both. For instance, the design of Fig. 7(b) could be varied to replace the straight upper surface with two straight segments angled differently with respect to the horizontal. The lower surface could also be made in two segments but with a rounded part towards the bottom and either a rounded or sharp transition to a straight segment that extends to meet the upper surface. In another alternative, both surfaces could be continuously curved. When the acceptance angle is made less than 180 degrees (since low elevation incoming rays, say with elevation < 20 degrees, carry less energy), then these shapes may make it possible to have a slightly higher concentration factor and at the same time control the overall thickness of the component, and the amount of material used in the manufacturing process.

In all cases, the principle remains to collect and guide the light onto a smaller target surface using refraction, reflection and total internal reflection. Variant with a Flat Top

Figs. 8 show the cross-section of a concentrator 20 with a flat top. The transparent upper surface 32 and 33 of both elements of the concentrator are flat and arranged in the same horizontal plane. The lower mirror surfaces 34 and 35 are symmetrical and only one side will be described for the sake of simplicity. Lower mirror surface 34 is curved in the region of 34(a) between points G and F in the arc of a circle, and straight 34(b) between points A and G. The target area 36 is arranged vertically, and is sandwiched between the two halves 24 and 26 of the concentrator.

Fig. 8(a) shows a ray 80 arriving at point 81 on upper surface 32 at an angle of 40° from the horizontal. Here it is refracted as it enters the concentrator. It meets the lower mirrored surface 34 at point 82 and is reflected back to the upper surface 32 at point 83 where it undergoes total internal reflection. Finally, it arrives at the target area 36, at point 84. The concentration factors for this variant made from perspex and glass are 2.96 and 3.034 respectively, for rays coming from any direction.

The Condition for Total Internal Reflection

Referring now to Fig. 8(b), to achieve internal reflection, angle E-A-G must be the same as angle G-E-F (the refracted angle for an incident angle of 90 degrees). For perspex this angle (using Snell's law) is 42.507 degrees.

The segment E - G is given by ( E - G ) = ( A - E ) * sin i ₂ Where:

The incident angle (with reference to the vertical) at point 81 is i ₁

Refracted angle at point 81 is i ₂

The coordinates of point G are given by:

Abscissa: ( E - H ) = ( E - G ) * sin i ₂

( E - H ) = ( A - E ) * sin i ₂ * sin i ₂

Ordinate: ( H - G ) = ( E - G ) * cos i ₂

The Condition for Direct Reflection onto the Target Area

Referring to Fig. 8(c), incoming rays hitting point E at incident angles less than 90° are refracted as they enter the concentrator and then reflected on the curved surface G - F. Once reflected, they must hit the target area, below point E, where the photovoltaic material is located. If the curve G - F is a circle arc with centre located at E, then all incoming rays entering at point E are refracted, reflected and then hit the photovoltaic target at point E. This could cause heat problems at this point.

To overcome this issue the curve G - F can be designed so that the incoming rays entering at point E are refracted and reflected on curve G - F to point El. It will be appreciated that other positions for El are possible, for example, or slightly higher or lower or more to the right. This has the effect of distributing the reflected rays over a range of the target area 36 instead of concentrating them on point E, and thus reduces any hot spot problem. This leads to a slight reduction of the concentration factor as the distance - F is slightly greater than the distance E - F.

Concentration factor

The concentration factor for one element of the concentrator 24 or 26 is:

C = ( A - E ) / ( E - F ) = ( A - E ) / ( E - G ) = ¾ / n

Where:

Refraction index of air is n

Refraction index of light guide (glass or perspex for example) is r ₂

For both halves of the concentrator 20: C = ( A - B ) / ( E - G )

This is twice the value for one half of the concentrator.

The concentration factors are directly related to the values of the refraction indices of air and the material the concentrator is made of.

The concentration factors for concentrators made from perspex and glass are 2.96 and 3.034 respectively. In practice the concentration factors are likely to be slightly less.

When the acceptance angle is less than 180 degrees, say from -23.5 degrees to +23.5 degrees as discussed below, then the maximum sin i ₂ can be less and the concentration factor higher.

Figs. 9 (a) to (f) show how incident solar radiation is collected and guided by the concentrator of Figs. 8, from a wide variety of angles of incidence and two different points of incidence. In Figs. 9(a), (c) and (e) from near the edge, and in Figs. 9 (b), (d) and (f) from near the centre.

Optical component orientation (azimuth)

The panels 10 made using the concentrators that have been described are not rotationally symmetrical, and unlike conventional panels their performance can be optimised for different azimuth angles. When the components 12 are arranged in a North-South orientation as in Fig. 10(a) the azimuth is 0 degrees. However, when they are in an East- West orientation as in Fig. 10(b) the azimuth is 90 degrees.

For a panel 10 with an elevation equal to the latitude of its location, the possible angles the incoming rays can take with respect to the perpendicular to the panel, are from -23.5 degrees to +23.5 degrees in the North-South direction as the sun moves in the course of a year; see Fig. 11(a). Also, the possible angles the incoming rays can take with respect to the perpendicular to the panel, are from and -90 degrees to +90 degrees in the East- West direction as the sun moves each day; see Fig. 11(b). The optical component azimuth angle impacts on the incoming angles of the rays received by the components 12. In the case of Fig. 10(a) where azimuth angle = 0 the sun will move, across the cross-section of the concentrator, from -90 to +90 degrees during the course of each day. Whereas, when the azimuth angle is 90 degrees the sun transverses an angle, across the cross-section of the concentrator, of -23.5 to +23.5 degrees each year. This has an impact on the optimal design of the optical concentrator.

For the design shown in Figs. 8 with azimuth = 90 degrees, for maximum incident rays of 23.5 degrees, the concentration factor is ~4.12 for perspex. This is the maximum concentration factor for fixed panels with flat top positioned optimally with elevation equal to the latitude of the panel location.

In another example, the cross-section of the concentrator 20 is as shown in Fig. 12, and the azimuth = 90 degrees with incoming rays from -23.5 to +23.5 from the vertical. The panels and components, as the others, are fixed (no sun tracking apparatus) but could also operate with tracking.

The lower mirrored surface A - F has three sections: parts A - Gl, Gl - G2 and G2 - F. Part A - Gl is a straight line with angle H-A-Gl such that rays entering the segment A - H at an incident angle not greater than 32 degrees (in this example) are refracted, reflected on segment A - Gl, undergo total reflection on segment A - E and then hit the target E - F. Note that, as for other implementations, some rays can be reflected on segment A - Gl and totally reflected on segment A - E more than once. Also rays may reflect on segment H - E or curves Gl - G2 or G2 - F before hitting the target E - F.

Part Gl - G2 is a paraboloid shape with focal point E. All rays entering at maximum angle between H and E are then reflected between Gl and G2 and hit the focal point at E (the rays to consider in calculating the paraboloid shape are the dashed rays).

Part G2 - E is an arc circle with centre at point E, as explained with reference to Fig. 8(c).

This design concentrates many incoming rays at point E and could therefore create a heat problem. To obviate this issue the paraboloid shape Gl - G2 can be designed so that the focal point is at point El instead of E. This has the effect of distributing the rays onto a larger part of the segment E - F.

Similarly the segment G2 - F can be designed with a focal point positioned at E2 instead of E, thus spreading the rays entering at point E onto the segment E - F instead of focusing them on point E. This results in heat being better distributed and a slight reduction in the concentration factor. It will be appreciated that other positions are possible for E2, for example, or slightly higher or lower or more to the right When the concentrator has an angle B-A-E = 23.5 degrees the incident rays will be perpendicular to the upper surface 32, and as a result the angle E-A-G must be 21.25 degrees for total internal reflection on surface A - E. This results in an optical concentration factor of approximately 5.6.

Alternatively, when the angle B-A-E = 32 degrees, the angle E-A-G must be approximately 19 degrees for total internal reflection on surface A - E. This results in an optical concentration factor greater than 6.

Designs for azimuth = 90 degrees can also be built with the upper surface of each part in two sections or with a smooth curve, that is flatter in the bottom of the trough formed between the two parts. The considerations above apply in slightly modified form when the azimuth is not either 0 or 90 degrees but in-between these two values.

For practical reasons, for example to ensure that no dirt accumulates in the trough A-E-B, the components can be covered by a flat sheet of perspex or glass joining the points A and B.

Panel positioning

For panels at an azimuth angle of 90 degrees and no flat cover dust and dirt can accumulate at the bottom part of the trough and decrease the amount of light reaching the photovoltaic material. By positioning the panels at an angle, as shown in Fig. 13, the bottom part of the profile is not horizontal and rain water can flow and take dust and dirt away.

The azimuth angle of each panel in Fig. 13 could also be less than 90 degrees so as to accentuate the effective slope draining the water (each panel then becomes a parallelogram or rhomboid instead of a rectangle).

Heat dissipation

Only a fraction of the light energy is converted into electricity in photovoltaic panels (this fraction is the efficiency of the panel). The rest of absorbed light is converted into heat. This heat tends to warm up the photovoltaic material which in turn affects its efficiency. By concentrating the light onto a smaller area of photovoltaic material, as the designs presented in this description can achieve, the temperature of each cell is likely to increase and this may impact on the efficiency of the cells. To reduce that effect, the light needs to be evenly distributed onto the photovoltaic material or the heat needs to be dissipated, or both. Mechanisms for heat dissipation make use of a heat sink; for instance heat radiating foils could be attached to the photovoltaic material, with a thin electric insulation layer to be used to avoid disrupting the electric circuitry.

The photovoltaic layer

The concentrator as described above comprises an optical/electrical transducer in the target zone between its elements. This transducer may be a thin flat layer or may be of a different shape or composition. Fig 14 shows a sample of different possible cross sections for the photovoltaic layer in a flat top concentrator as illustration. The transducer layer may comprise a rod 30, as shown in Fig. 14(a) or a set of rods 32, as shown in Fig.

14(b), embedded in the target area, or a sphere 34, as shown in Fig. 14(c), or a set of spheres or rods, as shown in Fig. 14(d). The rods or spheres, may be arranged regularly, as shown in Fig. 14(b) or pseudo randomly in the target area, as shown in Fig. 14(d). The rods may have rectangular or circle-like cross-section.

Panel elevation for azimuth = 90 degrees

The preceding section considered panels with azimuth = 90 degrees and elevation (or tilt) equal to the latitude of their location. However, for architectural, aesthetic or other reasons it may not always be possible to have the panels at an elevation equal to their latitude. So as not to loose light during part of the year, the acceptance angle of the concentrator would need to be increased, thus leading to a reduction in the concentration factor.

Alternatively, panels could be produced that are optimised for certain offsets; that is the difference between the panel tilt and the latitude of the location, as illustrated in Figs. 15.

Figs. 15 (a), (b), (c) and (d) shows the cross-section of the concentrator for offsets equal to 0, 10 degrees, 20 degrees and 30 degrees, respectively. The acceptance angle for incoming light is shown above the concentrators, with angle (aa) being equal to 2* 23.5. The straight line represents the most demanding incoming angle for each side of the concentrator (this means that all other rays within the acceptance opening would automatically reach the target photovoltaic material). The most demanding incoming rays determine the opening angle (co) of each concentrating element and hence its concentration factor. It can be seen that the two elements in the concentrator, when an offset is present, are not identical. This results in an asymmetrical concentrator with a concentration factor that increases with the offset angle.

In practice, large offsets may lead to a suboptimal collection of the light and this has to be traded against the possible increase in the concentration factor. Also, in order to streamline production, the acceptance angle may be increased so that a panel may be suitable for a range of offsets (say from +/- 10 degrees to +/- 20 degrees); this would lead to a slight reduction in the concentration factor. The considerations above apply to other concentrator designs, such as those shown in Fig. 7 and 12. and to azimuth not equal to 90 degrees.