Page 249 - Design of Solar Thermal Power Plants

232 4. DESIGN OF THE CONCENTRATION SYSTEM

4.2.2 Concentration Astigmatism of a Spherical Heliostat
The most common heliostat type, the spherical mirror (Figs. 4.4 and
4.5), has been applied in the Solar One, Solar Two, Dahan, PS10, PS20, and
Gemasolar solar tower power plants. Fig. 4.6 shows the concentrated solar
image of a spherical heliostat at the Dahan power plant. To address the
off-axis astigmatism problem of the spherical heliostat, E. A. Igel and R. L.
Hughes have carried out in-depth theoretical and experimental research
that for the first time has laid a foundation for the subsequent develop-
ment of a series of heliostats with astigmatism-correction curved surfaces.
For a spherical mirror with a spherical radius of R ¼ 2f, in the case of
off-axis incidence of the parallel beam with an incident angle of q, the
tangential and sagittal focal distances of the mirror surface are f t ¼ fcosq
and f s ¼ f/cosq respectively. It is thus clear that only in the case of
incidence of a parallel beam along the axis of a spherical mirror (q ¼ 0 ),

f t ¼ f s ¼ f; namely the tangential and sagittal focal distances are equal to
the axial focal distance f of the spherical mirror.
For the case of a spherical mirror with diameter D on the target plane
with distance L to the mirror surface center, the focal spot’s height in the
tangential direction and width in the sagittal direction are respectively
shown as follows.
D D
h 1 ¼ ðL f cosqÞ and h 2 ¼ ð f L cosqÞ
f f

FIGURE 4.6 Concentrated solar image of a spherical heliostat [20].