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.

在太阳能工程中，许多模拟都需要计算一年中的平均值，例如太阳能发电站的效率。在固定数量的情况下，即不取决于过去的历史，而仅取决于当前条件，可以用太阳位置的平均值代替时间平均值，这可以更快地进行计算。通过对太阳的位置坐标的适当选择，即，小时角和磁偏角相当于坐标，这个问题可以被改写为涉及两个二重积分的总和比较简单的表达; 然后可以通过适当的快速正交方法以数值方式获得该解。可以通过转换对辐照，浑浊，温度或其他瞬时参数取决于太阳位置，这两个因素取决于太阳的位置-一个对于冬春季节（上升磁偏角），另一个对于夏冬季节（下降磁偏角）。所提出的方法比一年中的常规时间积分快得多：在所考虑的示例中，加速因子从18到几乎700。它特别适合需要很多年均值的计算，否则可能不可行。此类应用的示例包括电厂配置的多参数优化，目的是使全年总产量最大化。在所考虑的示例中，加速因子的范围从18到几乎700。它特别适合需要很多年均值的计算，否则可能不可行。此类应用的示例包括电厂配置的多参数优化，目的是使全年总产量最大化。在所考虑的示例中，加速因子的范围从18到几乎700。它特别适合需要很多年均值的计算，否则可能不可行。此类应用的示例包括电厂配置的多参数优化，目的是使全年总产量最大化。