A second example of the application of the technique is the provision of a uniformly illuminated receiver surface for heliostat field. The major difference between a paraboloidal dish and a heliostat field is that the optical properties of the heliostat field vary with the incidence angle of the solar radiation, because single heliostats track the sun. This is not the case for a paraboloidal dish where the complete system is always orientated to face the sun. Therefore, with a heliostat field the shape of an optimally uniform illuminated surface varies with the incidence angle of the sun.

By example, Fig. 6 shows the north south cross-section of four different surfaces for a single tower plant and the distribution of concentration over the receiver. The heliostat field has ground coverage by the reflectors of 100% when they are stowed parallel to the ground, and the solar zenith angle is varied for a solar azimuth of 0.

For a heliostat field, the angle between the incoming radiation and the normal of the heliostat field and the angle between the outgoing radiation and the field normal are not equal as in the case of the dish. Therefore the area ATower, which is normal to the radiation reflected onto the tower, usually is not equal to the area ASun, which is normal to the incoming solar radiation.

We may define pSun to be the angle between the normal of the heliostat field and the incoming solar radiation while pTower to be the angle between the normal of the field and the radiation reflected onto the tower. If pSun > pTower than AS. un < A^ower and if

Fig. 6: North-South cross-section of a surfaces for uniform illumination in front of the focal point of a Single Solar Tower with a heliostat field of 100% ground coverage for solar positions with Azimuth 0 and different Zenith angles and the distribution of concentration over the receiver surface along the x-axis of the receiver for the same assumptions.

Tower Fig. 7: Shows the same relations as in Fig. 5 but for a heliostat field instead of a dish. For the case pSun > pTower, which is predominantly the case for regions close to the tower or the sun standing low over the horizon no radiation is lost but the same amount of radiation intercepts areas Ajun and A^ower (Schramek and Mills, 2003). Since A^un < A^ower this means the average density of radiation over A^ower is:

в Sun < Slower than AU > ATower. For the case fisun < pTower, which is predominantly the case for regions further away from the tower or the sun standing in the zenith, radiation is lost due to blocking as described by Schramek and Mills (2003). Therefore, the density of radiation passing the area A^ower is E^ower = ESun.

E

1 Tower

A1 Sun — E

A1 /±T

-E

dField(a) — AField(a) dRece iver (a) ARece i ver (a)

C0s( в Sun ) C0s(P Tower )

< E„

E

1 Receiver

(a)

E

— C1 Receiver

(a)

Sun

(Eq. 4)

(Eq. 5)

For the case zenith angle of the sun pSun — 0 as shown in Fig. 6 we have pSun < PTower for the whole heliostat field which means that Elower — ESun. For an assumed flat receiver d2FieU / dReceiver — const. for all a where dFiM is the distance from the focal point to the specific point in the heliostat field. Therefore for the heliostat field, analogously to the dish, we have following equations:

and

CRecever (a) — cos(r(a)) (Eq. 6)

Receiver

Since for a flat receiver d2FieU / dReceiver — const. while cos(y(a)) is decreasing for the outer regions the concentration decreases in the outer regions as well. Therefore, the receiver has to be bent closer to the focal point in the outer regions to achieve uniform illumination. In Fig. 6 it can be seen that this is the case in the optimised result.

If eSun > 0 there is a region close to the tower where pSun > pTower and where therefore Elower is given by Eq.4. Therefore, we may use the following equations:

dField(a) — AField(a) — EReceiver(a) C°s(Psun) — C1 (a) C0S(eSun) (Eq 7)

dRece, ver(a) ARece, ver(a) ELer(a) ESun С0^(в Tower) Rece"er С0^(в Tower) ‘

CRece, ver (a) — C0S(/(a))

dField C0S(PTower ) dReceiver C0S(PSun )

(Eq. 8)

and

CReceiver (a) ^

C0s(7(a)) d 2

2 dField

C0s(Y(a)) d2Field

Receiver C0s(PTower )

Receiver

C0s(eSun )

if в Sun < Grower if P Sun > в Tower

(Eq. 9)

This gives us the generalised equation:

This means that for pSun > 0, for the outer regions where pSun < pTower, the receiver is equal to the receiver for /3Sun — 0 ,while in the inner region the receiver has to be bent closer to the focal point as well. This effect can be seen in Fig. 6 as well.

Fig. 8 shows the surfaces for uniform illumination for an Multi Tower Solar Array (MTSA), (Schramek and Mills, 2003).

Conclusion

Fig. 8: North-South cross-section of a surfaces for uniform illumination in front of the focal point of a Multi Tower Solar Array with a heliostat field of 100% ground coverage for solar positions with Azimuth 0 and different Zenith angles and the distribution of concentration over the receiver surface along the x-axis of the receiver for the same assumptions.

It was shown that for a given concentrator system a receiver surface can be defined which is evenly illuminated.

This approach provides a means of avoiding the use of reflectors and their attendant optical loss and cost while providing acceptable uniformity of illumination over the receiver surface. It allows formation of uniformly illuminated surfaces either between the reflector and the focal point, or on the other side of the focal point.