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RESEARCH PAPERS

# Optimization of Economic Solar Field Design of Stationary Thermal Collectors

[+] Author and Article Information
Dan Weinstock

Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

Joseph Appelbaum

Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israelappel@eng.tau.ac.il

J. Sol. Energy Eng 129(4), 363-370 (Apr 28, 2007) (8 pages) doi:10.1115/1.2769690 History: Received August 15, 2006; Revised April 28, 2007

## Abstract

The optimization of solar field designs of stationary thermal collectors, taking into account shading and masking effects, may be based on energy or economic criteria. Obtaining maximum energy from a given field size or determining the required minimum field area that produces a given amount of energy are examples of energy criteria. Designing a solar plant with a minimum cost or a plant that produces minimum cost of unit energy are examples of economic criteria. 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 paper deals with obtaining optimal field and collector design parameters (number of rows, distance between collector rows, collector height, and collector inclination angle) that result in minimum periodic cost of a solar plant producing a given amount of annual energy. A second problem is the determination of optimal field and collector design parameters resulting in minimum cost of unit energy for the solar plant. In both cases, the optimal deployment of the collectors in the solar field as a function of the daily energy demand—cost of land and collector efficiency as parameters—is presented.

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## Figures

Figure 1

Shading by collectors in a solar field

Figure 2

Shadow variation hs=f(ℓs) and shaded area (dark) at 10:00 on January 21

Figure 3

Feasible design region in (K-β) plane in optimization for periodic minimum plant cost. Numbers represent isoperiodic cost lines Cp (in U.S. dollars); heavy lines represent constraints (Eqs. 4,5,6). The optimal solution is marked by a circle and is within the feasible region.

Figure 4

Feasible design region in (W-L) plane in optimization for minimum periodic plant cost. Numbers represent isoperiodic cost lines Cp (in U.S. dollars); heavy lines represent constraints (Eqs. 4,9,10). The optimal solution, marked by a circle, is on the boundary of the feasible region.

Figure 5

Feasible design region in (D-H) plane in optimization for minimum periodic plant cost. Numbers represent isoperiodic cost lines Cp (in U.S. dollars); heavy lines represent constraints (Eqs. 4,5,7). The optimal solution, marked by a circle, is on the boundary of the feasible region.

Figure 6

Periodic plant cost as a function of daily energy demand in optimization for minimum periodic plant cost

Figure 7

Variation of optimal parameters as a function of daily energy demand in optimization for minimum periodic plant cost

Figure 8

Variation of optimal parameters as a function of land cost in optimization for minimum periodic plant cost

Figure 9

Total periodic plant cost as a function of collector efficiency in optimization for minimum periodic plant cost

Figure 10

Variation of optimal parameters as a function of collector efficiency in optimization for minimum periodic plant cost

Figure 11

Cost of unit energy as a function of daily energy demand in optimization for minimum cost of unit energy

Figure 12

Variation of optimal parameters as a function of daily energy demand in optimization for minimum cost of unit energy

Figure 13

Variation of optimal parameters as a function of land cost in optimization for minimum cost of unit energy

Figure 14

Pipe layout in reverse return connection

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