The optimal design of stationary photovoltaic and thermal collectors in a solar field, taking into account shading and masking effects, may be based on several criteria: maximum incident energy on collector plane from a given field, minimum field area for given incident energy, minimum cost per unit energy, minimum plant cost, maximum energy per unit collector area or other objectives. These design problems may be formulated as optimization problems with objective functions and sets of constraints (equality and inequality) for which mathematical optimization techniques may be applied. This article deals with obtaining the field design parameters (optimal number of rows, distance between collector rows, collector height and collector inclination angle) that produce maximum annual energy from a given field. A second problem is determination of the minimum field area (length and width) and field design parameters that produce a given required annual energy. The third problem is determination of the optimal field design parameters for obtaining maximum energy per unit collector area from a given field. The results of these optimal designs are compared to a recommended approach of the Israeli Institute of Standards (IIS) in which the solar field design result in negligible shading. An increase in energy of about 20% for a fixed field area and a decrease in field area of about 15% for a given annual incident energy, respectively, may be obtained using the approach formulated in the present article compared to the IIS approach.

1.
Coleman, T. F., Branch, M. A., and Grace, A., 1999, Optimization Toolbox for Use with Matlab, The Math Works, Inc.
2.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1987, Numerical Recipes, Cambridge University.
3.
Wilde, D. J., and Beightler, C. S., 1967, Foundations of Optimization, Prentice-Hall, Inc.
4.
Bany
,
J.
, and
Appelbaum
,
J.
,
1987
, “
The Effect of Shading on the Design of a Field of Solar Collectors
,”
Sol. Cells
,
20
, pp.
201
228
.
5.
Gopinathan
,
K.
,
1991
, “
Optimization of the Angle of Solar Collectors for Maximum Irradiation on Sloping Surfaces
,”
Int. J. Sol. Energy
,
10
, pp.
51
61
.
6.
Barra
,
O.
,
Conti
,
M.
,
Santamata
,
E.
,
Scarmozzino
,
O.
, and
Visentin
,
R.
,
1977
, “
Shadow Effect in Large Solar Collectors in Large Scale Solar Power Plants
,”
Sol. Energy
,
19
, pp.
759
762
.
7.
Appelbaum
,
J.
, and
Bany
,
J.
,
1979
, “
,”
Sol. Energy
,
23
, pp.
497
508
.
8.
Jones
,
R. E.
, and
Burkhart
,
J. F.
,
1981
, “
Shading Effect on Collector Rows Tilted Towards the Equator
,”
Sol. Energy
,
26
, pp.
563
565
.
9.
Budin
,
A.
, and
Budin
,
L.
,
1982
, “
A Mathematical Model for Shading Calculation
,”
Sol. Energy
,
29
, pp.
339
349
.
10.
Groumpos
,
P. P.
, and
Kouzam
,
K. Y.
,
1987
, “
A Generic Approach to the Shadow Effect in Large Solar Power Systems
,”
Sol. Cells
,
22
, pp.
29
46
.
11.
Reise, C., and Kovach, A., 1995, “PV Shading Analysis in Complex Building Geometries,” 13th European Photovoltaic Solar Energy Conference, Nice, France, pp. 2157–2160.
12.
Carlsson, P., Cider, L., and Lindgren, B., 1998, “Yield Losses Due to Shading in a Building-Integrated PV Installation; Evaluation, Simulation and Suggestion for Improvement,” 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, Austria, pp. 2666–2670.
13.
Quaschning, V., and Hanitsch, R., 1998, “Increased Energy Yield of 50% at Flat Roof and Field Installations With Optimized Module Structures,” 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, Austria, pp. 1993–1996.
14.
Weinstock, D., and Appelbaum, J., 2003, “Deployment of Collector in an Optimal Design of Solar Fields,” ISES Solar World Congress 2003, June 14–19, Gothenburg, Sweden.
15.
Erlicki
,
M. S.
, and
Appelbaum
,
J.
,
1970
, “
Solution of Practical Optimization Problems
,”
IEEE Trans. Syst. Sci. Cybern.
,
SSC-6
, pp.
49
52
.
16.
Appelbaum
,
J.
, and
Erlicki
,
M. S.
,
1964
, “
A Problem of Economic Optimization of Electric Equipment Design
,”
IEEE Trans. Commun. Electron.
,
83
, No.
75
, pp.
773
776
.
17.
Shinzinger, R., 1966, “Optimization in Electromagnetic System Design,” In Recent Advances Optimization Techniques, Lavi A. and Vogl T. P. (eds.), Wiley, New York.
18.
Nemhauser, G. L., and Wolsey, L. A., 1988, Integer and Combinatorial Optimization, Wiley.