The multi-objective optimum design of stationary compound parabolic concentrator (CPC) solar collectors is considered. The clear day solar beam radiation and diffuse radiation at the location of the solar collector are estimated. Three objectives are considered in the optimization problem formulation: maximization of the annual average incident solar energy, maximization of the lowest month incident solar energy and minimization of the cost. A modified game theory (MGT) methodology is used for the solution of the three-objective constrained optimization problems. When compared to the optimum results of flat plate solar collectors, the CPC solar collector could significantly reduce the value of cost per unit energy ratio. Parametric studies are conducted with respect to changes in land price. The present study is expected to help designers in creating optimized solar collectors based on specified requirements.

References

1.
Winston
,
R.
, and
Hinterbergerb
,
H.
,
1975
, “
Principles of Cylindrical Concentrators for Solar Energy
,”
Sol. Energy
,
17
(
4
), pp.
255
258
.10.1016/0038-092X(75)90007-9
2.
Abdul-Jabbar
,
N. K.
, and
Salman
,
S. A.
,
1998
, “
Effect of Two-Axis Sun Tracking on the Performance of Compound Parabolic Concentrators
,”
Energy Convers. Manage.
,
39
(
10
), pp.
1073
1079
.10.1016/S0196-8904(97)10020-6
3.
Kim
,
Y.
,
Han
,
G.
, and
Seo
,
T.
,
2008
, “
An Evaluation on Thermal Performance of CPC Solar Collector
,”
Int. Commun. Heat Mass Transfer
,
35
(
4
), pp.
446
457
.10.1016/j.icheatmasstransfer.2007.09.007
4.
Weinstock
,
D.
, and
Appelbaum
,
J.
,
2007
, “
Optimization of Economic Solar Field Design of Stationary Thermal Collectors
,”
ASME J. Sol. Energy Eng.
,
129
(4), pp.
363
370
.10.1115/1.2769690
5.
Rabl
,
A.
,
1976
, “
Optical and Thermal Properties of Compound Parabolic Concentrators
,”
Sol. Energy
,
18
(
6
), pp.
497
511
.10.1016/0038-092X(76)90069-4
6.
Derrick
,
G. H.
,
Bassett
,
I. M.
, and
Mills
,
D. R.
,
1986
, “
Comparsion of Reflector Design for Stationary Tubular Solar Collector
,”
Sol. Energy
,
37
(
3
), pp.
195
203
.10.1016/0038-092X(86)90076-9
7.
Carvalho
,
J.
,
Collares-Pereira
,
M.
, and
Gordon
,
J. M.
,
1987
, “
Economic Optimization of Stationary Non Evacuated CPC Solar Collectors
,”
ASME J. Sol. Energy
,
109
(
1
), pp.
40
45
.10.1115/1.3268176
8.
Suzuki
,
A.
, and
Kobayashi
,
S.
,
1995
, “
Yearly Distributed Insolation Model and Optimum Design of a Two Dimensional Compound Parabolic Concentrator
,”
Sol. Energy
,
54
(
5
), pp.
327
331
.10.1016/0038-092X(95)00003-A
9.
Mills
,
D. R.
, and
Giutronich
,
J. E.
,
1977
, “
Asymmetrical Non-Imaging Cylindrical Solar Concentrators
,”
Sol. Energy
,
20
(
1
), pp.
45
55
.10.1016/0038-092X(78)90140-8
10.
Tripanagnostopoulos
,
Y.
,
Yianoulis
,
P.
,
Papaefthimiou
,
S.
, and
Zafeiratos
,
S.
,
2000
, “
CPC Collectors With Flat Bifacial Absorbers
,”
Sol. Energy
,
69
(
3
), pp.
191
203
.10.1016/S0038-092X(00)00061-X
11.
Mallick
,
T. K.
,
Eames
,
P. C.
,
Hyde
,
T. J.
, and
Norton
,
B.
,
2004
, “
The Design and Experimental Characterization of an Asymmetric Compound Parabolic Photovoltaic Concentrator for Building Façade Integration in the UK
,”
Sol. Energy
,
77
(
3
), pp.
319
327
.10.1016/j.solener.2004.05.015
12.
Mallick
,
T. K.
,
Eames
,
P. C.
, and
Norton
,
B.
,
2007
, “
Using Air Flow to Alleviate Temperature Elevation in Solar Cells Within Asymmetric Compound Parabolic Concentrator
,”
Sol. Energy
,
81
(
2
), pp.
173
184
.10.1016/j.solener.2006.04.003
13.
Fraidenraich
,
N.
,
Tiba
,
C.
,
Brandão
,
B. B.
, and
Vilela
,
O. C.
,
2008
, “
Analytic Solutions for the Geometric and Optical Properties of Stationary Compound Parabolic Concentrators With Fully Illuminated Inverted V Receiver
,”
Sol. Energy
,
82
(
2
), pp.
132
143
.10.1016/j.solener.2007.06.012
14.
Trupanagnostopolos
,
Y.
, and
Souliotis
,
M.
,
2004
, “
ICS Solar Systems With Horizontal Cylindrical Storage Tank and Reflector of CPC or Involute Geometry
,”
Renewable Energy
,
29
(
1
), pp.
13
38
.10.1016/S0960-1481(03)00139-3
15.
Tripanagnostopoulos
,
Y.
, and
Yianoulis
,
P.
,
1996
, “
CPC Solar Collectors With Multichannel Absorber
,”
Sol. Energy
,
58
(
1–3
), pp.
49
61
.10.1016/0038-092X(96)00055-2
16.
Weinstock
,
D.
, and
Appelbaum
,
J.
,
2004
, “
Optimal Solar Field Design of Stationary Collectors
,”
ASME J. Sol. Energy Eng.
,
126
(
3
), pp.
898
905
.10.1115/1.1756137
17.
Hu
,
Y.
, and
Rao
,
S. S.
,
2009
, “
Game-Theory Approach for Multi-Objective Optimal Design of Stationary Flat-Plate Solar Collectors
,”
Eng. Optim.
,
41
(
11
), pp.
1017
1035
.10.1080/03052150902890064
18.
Rao
,
S. S.
, and
Hu
,
Y.
,
2010
, “
Multi-Objective Optimal Design of Stationary Flat-Plate Solar Collectors Under Probabilistic Uncertainty
,”
ASME J. Mech. Des.
,
132
(
9
), p.
094501
.10.1115/1.4002133
19.
Stadler
,
W.
,
1984
, “
A Survey of Multi-Criteria Optimization for the Vector Maximum Problem, Part I: 1776–1960
,”
J. Optim. Theory Appl.
,
29
(
1
), pp.
1
52
.10.1007/BF00932634
20.
Marler
,
R. T.
, and
Arora
,
J. S.
,
2004
, “
Survey of Multi-Objective Optimization Methods for Engineering
,”
Struct. Multidiscip. Optim.
,
26
(
6
), pp.
369
395
.10.1007/s00158-003-0368-6
21.
Rao
, and
Singiresu
S.
,
2009
,
Engineering Optimization Theory and Practice
, 4th ed.,
Wiley
,
Hoboken
.
22.
Rao
,
S. S.
,
1984
, “
Multiobjective Optimization in Structural Design in the Presence of Uncertain Parameters and Stochastic Process
,”
AIAA J.
,
22
(11), pp.
1670
1678
.10.2514/3.8834
23.
Zeleny
,
M.
,
1984
,
Multiple Criteria Decision Making
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
24.
Koksalan
,
M.
,
Wallenius
,
J.
, and
Zionts
,
S.
,
2011
,
Multiple Criteria Decision Making: Early History to the 21st Century
,
World Scientific
,
Singapore
.
25.
Deb
,
K.
,
2001
,
Multi-Objective Optimization Using Evolutionary Algorithms
,
Wiley
,
Chichester
, UK.
26.
Coello
,
C. A. C.
,
Van Veldhuizen
,
D. A.
, and
Lamont
,
G. B.
,
2002
,
Evolutionary Algorithms for Solving Multi-Objective Problems
,
Kluwer/Plenum
,
New York
.
27.
O'Gallagher
,
J. J.
,
2008
,
Nonimaging Optics in Solar Energy (Synthesis Lectures on Energy and the Environment, Technology, Science, and Society)
Morgan and Claypool Publishers
,
San Rafael, CA
.
28.
Rao
,
S. S.
, and
Hati
,
S. K.
,
1979
, “
Game Theory Approach in Multicriteria Optimization of Function Generating Mechanisms
,”
ASME J. Mech. Des.
,
101
(
3
), pp.
633
639
.10.1115/1.3454113
29.
Rao
,
S. S.
, and
Freiheit
,
T. I.
,
1991
, “
A Modified Game Theory Approach to Multiobjective Optimization
,”
ASME J. Mech. Des.
,
113
(
3
), pp.
286
291
.10.1115/1.2912781
30.
Hottel
,
H. C.
,
1976
, “
Simple Model for Estimating the Transmittance of Direct Solar Radiation Through Clear Atmospheres
,”
Sol. Energy
,
18
(
2
), pp.
129
134
.10.1016/0038-092X(76)90045-1
31.
Liu
,
B. Y. H.
, and
Jordan
,
R. C.
,
1960
, “
Interrelationship and Characteristic Distribution of Direct, Diffuse and Total Solar Radiation
,”
Sol. Energy
,
4
(
3
), pp.
1
19
.10.1016/0038-092X(60)90062-1
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