Solar power density calculations using two dimensional hermite polynomials



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A problem basic to the tower concept of solar energy collection is the calculation of the power density at the receiver due to flat polygonal reflectors of various orientation and distance. A statistical method involving a two dimensional gaussian approximation utilizing Hermite polynomials is investigated and results are compared with an analytic integration of the solar intensity at specific lattice points on an image plane. Various measures of error between the two methods are monitored as functions of distance and orientation and a comparison of receiver flux distributions is given. The sixth order results of this statistical method compare favorably with those of the analytic integration and require approximately one-fifth the computer time for the formation of receiver power densities.