This paper presents an optimization algorithm for designing linear concentrating solar collectors using stochastic programming. A Monte Carlo technique is used to quantify the performance of the collector design in terms of an objective function, which is then minimized using a modified Kiefer–Wolfowitz algorithm that uses sample size and step size controls. This process is more efficient than traditional “trial-and-error” methods and can be applied more generally than techniques based on geometric optics. The method is validated through application to the design of three different configurations of linear concentrating collector.

1.
Rabl
,
A.
, 1994, “
Edge-Ray Method for Analysis of Radiation Transfer Among Specular Reflectors
,”
Appl. Opt.
0003-6935,
33
, pp.
1248
1259
.
2.
Haeberle
,
A.
,
Berger
,
M.
,
Luginsland
,
F.
,
Zahler
,
C.
,
Baitsch
,
M.
,
Henning
,
H. -M.
,
Rommel
,
M.
, 2007, “
Linear Concentrating Fresnel Collector for Process Heat Applications
,”
Proceedings of the Local Renewables
, Freiburg, Germany, Jun. 13–15.
3.
2008, OPTICAD: Product Homepage, Viewed 20 April, 2009, http://www.opticad.com/http://www.opticad.com/
4.
Muschaweck
,
J.
,
Spirkl
,
W.
,
Timinger
,
A.
,
Benz
,
N.
,
Dörfler
,
M.
,
Gut
,
M.
, and
Kose
,
E.
, 2000, “
Optimized Reflectors for Non-Tracking Solar Collectors With Tubular Absorbers
,”
Sol. Energy
0038-092X,
68
, pp.
151
159
.
5.
Ashdown
,
I.
, 1994, “
Non-Imaging Optics Design Using Genetic Algorithms
,”
J. IESNA
0099-4480,
23
, pp.
12
21
.
6.
Holland
,
J. H.
, 1992,
Adaptation in Natural and Artificial Systems
, 2nd ed.,
MIT
,
Cambridge, MA
.
7.
Daun
,
K.
,
Morton
,
D. P.
, and
Howell
,
J. R.
, 2003, “
Geometric Optimization of Radiant Enclosures Containing Specular Surfaces
,”
ASME J. Heat Transfer
0022-1481,
125
, pp.
845
851
.
8.
Kiefer
,
J.
, and
Wolfowitz
,
J. R.
, 1952, “
Stochastic Estimation of the Maximum of a Regression Function
,”
Ann. Math. Stat.
0003-4851,
23
, pp.
462
466
.
9.
Bertsekas
,
D. P.
, 1999,
Nonlinear Programming
, 2nd ed.,
Athena Scientific
,
Belmont, MA
, pp.
723
728
.
10.
Robbins
,
H.
, and
Monro
,
S.
, 1951, “
A Stochastic Approximation Method
,”
Ann. Math. Stat.
0003-4851,
22
, pp.
400
407
.
11.
Siegel
,
R.
, and
Howell
,
J. R.
, 2002,
Thermal Radiation Heat Transfer
, 4th ed.,
Taylor & Francis
,
New York
, Chap. 10.
12.
Hammersley
,
J. M.
, and
Handscomb
,
D. C.
, 1975,
Monte Carlo Methods
,
Fletcher & Son Ltd.
,
Norwich, UK
, p.
52
.
13.
Kersch
,
A.
,
Morokoff
,
W.
, and
Schuster
,
A.
, 1994, “
Radiative Heat Transfer With Quasi-Monte Carlo Methods
,”
Transp. Theory Stat. Phys.
0041-1450,
23
, pp.
1001
1021
.
14.
Kline
,
S. J.
, and
McClintock
,
F. A.
, 1953, “
Describing Uncertainties in Single-Sample Experiments
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
75
, pp.
3
12
.
15.
Pflug
,
G. C.
, 1996,
Optimization of Stochastic Models: The Interface between Simulation and Optimization
,
Kluwer
,
Boston, MA
, pp.
286
288
.
16.
Dupuis
,
P.
, and
Simha
,
R.
, 1991, “
On Sampling-Controlled Stochastic Approximation
,”
IEEE Trans. Autom. Control
0018-9286,
36
, pp.
915
924
.
17.
Simha
,
R.
, 2003, “
An Algorithm for Gradient-Free Simulation Optimization Using Sampling Control
,”
Int. J. Model. Simulat.
0228-6203,
23
, pp.
197
204
.
18.
Toth
,
D. L.
, 1985, “
On Ray Tracing Parametric Surfaces
,”
SIGGRAPH ’85 Conference Proceedings
, Vol.
19
, pp.
171
179
.
19.
Belegundu
,
A. D.
, and
Chandrupatla
,
T. R.
, 1999,
Optimization Concepts and Applications in Engineering
, 2nd ed.,
Pearson Education
,
Singapore
, pp.
28
29
.
20.
Tesfamichael
,
T.
, and
Wäckelgård
,
E.
, 1999, “
Angular Solar Absorptance of Absorbers Used in Solar Thermal Collectors
,”
Appl. Opt.
0003-6935,
38
, pp.
4189
4197
.
21.
Adsten
,
M.
,
Helgesson
,
A.
, and
Karlsson
,
B.
, 2005, “
Evaluation of CPC-Collector Designs for Stand-Alone, Roof- or Wall Installation
,”
Sol. Energy
0038-092X,
79
, pp.
638
647
.
You do not currently have access to this content.