Optimal solar field design of stationary collectors

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 infield 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.