A methodology for normal distribution-based statistical characterization of long-term insolation by means of historical data

Abstract

Solar system size and related profitable operation with shortest possible return-of-investment period are key enabling factors for a wider commercial use of solar energy systems and further developments of related technologies. Accordingly, the collection and statistical characterization of long-term solar energy (insolation) data may be regarded as an essential step in solar power system design, which should yield probable safety margins of the solar energy system based on the past (historical) data and their estimated statistical properties. To this end, this paper proposes a statistical approach to long-term solar energy availability characterization based on analysis of historical insolation data, augmented by a normalization procedure implementing straightforward data set transformations. The proposed approach has produced a normalized set of probability distributions for the solar energy data collected for the Zagreb (Republic of Croatia) greater metropolitan area over a 10-year period, which can be used for the assessment of energy availability of a prospective solar power system. The proposed methodology has been validated by means of statistical normality (goodness-of-fit) criteria, such as those included in Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Chi-square tests. These tests have been first used to indicate the discrepancy of the original (crude) insolation data probability distribution with respect to normal distribution. A comparative analysis based on Weibull probability distribution has further confirmed that statistical characterization based on original data set may not be able to provide favorable results. After suitable data set transformations have been applied, the statistical validation tests have confirmed the transformed data set normal probability distribution hypothesis. The normalized model was additionally validated through comparison of probability levels of transformed data with the probability of occurrence of actual (crude set) data points. Thus normalized and validated statistical model might be convenient for straightforward characterization of available insolation for the purpose of profitability calculations, and prospective solar power system sizing studies.