2. Mathematical Modeling

This chapter presents a detailed mathematical analysis of PTCs. It is divided into three sections: tracking of the Sun, optical analysis and thermal analysis. The first section is an overview of equations and relationships used in solar geometry to determine the position of the Sun and, hence, the slope and the angle of incidence that in each instant must be assumed by a PTC to correctly follow the Sun. Since PTCs usually have one degree of freedom, correlations valid for east-west and north-south axis with continuous adjustment are discussed. The optical analysis starts by introducing the concentration ratio and continues presenting a thorough description of the geometry of a PTC. Optical errors and geometrical effects are also presented. Then, the optical analysis is concluded by taking into account the optical properties of the materials generally adopted in PTCs: the mirror, the cover and the absorber. The last section involves the thermal analysis of a PTC, i.e. the energy balance of the receiver. Each heat flux is described in detail, in order to determine the thermal efficiency of a PTC.