Building integrated concentrating solar systems - Solar Energy Sciences and Engineering Applications - page 561

Rabl (1976b) and Smith (1976) state that this type of concentrator has a maxi-
mum concentration ratio of [sin( θ max / 2)] − 1 , where θ max = φ r . However, (Mills and

Giutronich, 1978) have shown that the maximum concentration ratio for a parabolic
asymmetric concentrator is

φ l +

cos φ r [ cos( φ r −

sin φ r
tan ( θ max / 2) −

1 +

ω ) − 1 ] C PA max = (17.2.5)

and the minimum concentration ratio is

cos φ l

sin φ l
tan( θ max / 2) −

1 +

C PA min = (17.2.6)

where

sin θ max − cos φ r + cos φ l

cos ω =

2 √ (1

(17.2.7)

− cos φ l cos φ r )

Truncation of the reflectors of an ACPC reduces the size and cost of a system but
results in a loss of concentration. The degree of truncation for a given ACPC can be
determined in terms of the coordinates of a full ACPC. As Figure 17.2.4 illustrates, the
left half of the ACPC is terminated at the point ( y ), instead of the end point ( x L , y L )

of the full ACPC. The right half of the ACPC, is of course, truncated in an analogous
manner. Truncation does not change the absorber area. The width ( l ), height ( h ), and
the position coordinates (

x , ¯ ¯

x ) of the truncated ACPC are (Rabl, 1976b) ¯

x 2

¯

l

cos 2 θ )

= 2 x cos θ − ¯

sin θ ) sin θ +

s (sin θ − (17.2.8)

s (1 +

x 2 cos θ
2 s (1

¯ s

2 cos θ (1

h

=¯ x sin θ +

sin θ ) −

+ sin θ ) (17.2.9)

+

and

⎡
⎣ −

2 ⎤
⎦

1

h cot 2 θ

s (1

1

h

+ sin θ )

cos θ

x ¯ = sin θ + + (17.2.10)

17.2.3 Building integrated concentrating photovoltaics
The following is an analysis of the suitability for architectural integration of the
principle types of existing concentrators, categorized by concentration factor.

17.2.3.1 High concentration systems (C > 100X)

High concentration systems require two-axis tracking with high precision (tolerances
below 0.2 ◦ ). The integrability of such a system will be highly compromised by the
fact that it is mobile and by its size and dimensions which, even when minimized, are
considerable. Incorporation is best achieved on the roof of the building (particularly