Improvement of clear sky models for direct solar irradiance considering turbidity factor variable during the day

Abstract

There are several clear sky models used to estimate the amount of received solar energy. Most of them rely on monthly constant turbidity factors which are site dependent. Comparing the results obtained with a clear sky model with data recorded in the period 2013–2016 in the Renewable Energy Systems and Recycling Research Centre in Brasov, Romania, resulted that the model overestimates in the warm season and underestimates in the cold season. To improve the clear sky model, time dependent interpolation polynomials are used instead of constant turbidity factor. Local direct solar irradiance measured each 10 min is used to create daily cubic spline functions using Schoenberg operator. These splines were used to obtain two interpolation polynomials for turbidity factor, for the warm and cold season respectively. The improved clear sky model forms were validated using the direct solar irradiance measured in 2017; the accuracy was improved by reducing the relative error from 8.12% to 4% in warm season and from 5.02% to 4.15% in cold season. As result, a better estimation of the received solar energy, with influence on the system design and financial benefits, is obtained. The methodology can be applied for any location with available measured data.