Page 251 - Design of Solar Thermal Power Plants

234 4. DESIGN OF THE CONCENTRATION SYSTEM

4.2.3 Brief Introduction to the Toroidal Heliostat
A toroid, also known as a toroidal surface, has two symmetric sections
perpendicular to each other, namely the tangential and sagittal sections;
the arcs of these two sections have different curvature radii and therefore
are nonrotational symmetric curved surfaces.
For a fixed incident angle q, the value of the tangential curvature radius
of the toroidal surface is:

R t ¼ 2f t ¼ 2L=cos q 0
and the sagittal curvature radius is:

R s ¼ 2f s ¼ 2L cos q 0
Then according to Eqs. (4.1) and (4.2), the beam spot on a focal plane
with toroidal surface slant distance L has the minimum area, no astigma-
tism, and a diameter of bL, from which the minimum value of the spot size
of the spherical mirror appears when q ¼ 0 , and the toroidal surface can

shift the minimum value of the spot diameter from q ¼ 0 to q ¼ q 0 .
In reality, the surface shape of the heliostat is fixed, whereas the inci-
dent angle q of the solar beam varies over time. Therefore, in order to
determine the surface shape of the toroidal surface, an appropriate q 0
shall be selected, which is referred to as the designed incident angle of the
toroidal surface. Once the slant distance L and designed incident angle q 0
have been determined, the surface shape of the toroidal surface can be
determined accordingly.
R. Zaibel et al. proposed the astigmatic-corrected target-aligned
heliostat with a fixed rotation axis pointing to the target position in
1995, which combines a toroidal surface with a two-axis tracking mode
with a fixed rotation axis pointing to the target position so that during
whole-day sun tracking and solar concentrating by the heliostat, the
incident plane of the solar beam at the mirror surface center (including
normal and incident solar beam at the mirror surface center) always
coincides with the tangential plane of the mirror surface (including the
principal optic axis of the mirror surface and the normal direction of
the mirror surface center). In this case, further optimization design of the
heliostat mirror surface shape is feasible, and the corresponding method
for optimization is also simple, thus making practical application of the
toroidal heliostat feasible. Figs. 4.5 and 4.8 display a two-axis tracking
heliostat with a fixed rotation axis pointing to the target position. The
fixed axis points to the center of the receiver aperture; the slave rotation-
axis is fixed to the heliostat frame and is perpendicular to the fixed axis.
The design method for the surface shape of an astigmatism-corrected
toroidal heliostat uses the variation range of incident angle q of the