Fast computation of yearly averages of useful quantities for solar engineering

In solar engineering, many simulations require the computation of averages over a year of quantities such as the efficiency of solar plants. In the case of stationary quantities, i.e., that do not depend on the past history but only on the present conditions, time averages can be replaced by averages over the solar position, which are much faster to compute. Through a suitable choice of coordinates for the Sun position, namely, the hour angle and a declination-equivalent coordinate, the problem can be rewritten as a comparatively simple expression involving the sum of two double integrals; the solution can then be obtained numerically via suitable fast quadrature methods. The average over a year can be computed by transforming the dependence on irradiation, cloudiness, temperature or other instantaneous parameters into two dependences on Sun position – one for winter-spring (ascending declination) and one for summer-winter (descending declination). The proposed method is substantially faster than usual time integration over a year: the speedup factor ranges from 18 to almost 700 in the considered examples. It is especially well-suited to computations that require many yearly averages and could even be unfeasible otherwise. Examples of such applications include multi-parameter optimisations of the configuration of a power plant with the goal of maximizing the overall year production.