A Theory of Concentrators of Solar Energy on a Central Receiver for Electric Power Generation

The modeling of the performance of large-area solar concentrators for central receiver power plants is formulated using a continuum field representation of ideal heliostat arrays that accounts for two governing factors: the law of reflection of light rays imposes steering constraints on mirror orientations; the proximity of mirrors creates shadow effects by blocking the incident and/or reflected solar radiation. The results of a steering analysis which develops the space-time characteristics of heliostats and of a shadow analysis which determines the local effectiveness of mirrors in reflecting solar energy to a central point are combined to obtain in closed analytical form the global characteristics of circular concentrators. These characteristics which appear as time profiles for mirror orientations, for effective concentration areas (i.e., reflected solar flux), and for concentration ratios, establish theoretical limits of performance against which actual or realistic solar power systems can be compared and assessed.