. Conclusion
The paper has presented a statistical approach to finding a reliable model for statistical characterization of long-term insolation based on analysis of past insolation data and employing normal probability distribution, which is characterized by a high level of confidence and could be utilized for solar system energy production assessment and related profitability calculations. The effectiveness of the proposed methodology has been tested on the insolation data collected over the 10-year span (1994–2003) for the particular geographical area, and for the daily average insolation data sets for all months.
The preliminary data analysis has included simple statistical characterization through evaluation of average (mean) values, standard deviations, overall range (i.e. minimum and maximum values) and skewness and kurtosis testing of considered insolation data sets. The data has subsequently been inspected by means of frequency distribution diagrams (histograms) and normal distribution plots, along with quantitative statistical tests including Shapiro–Wilk (SW), Kolmogorov–Smirnov (KS), Lilliefors, and Chi-square. The aforementioned data testing procedure has indicated that the crude insolation data cannot be readily described by a normal probability distribution. An alternative approach, based on Weibull probability distribution fitting has also resulted in unsatisfactory result in terms of goodness-of-fit tests, whereas particularly noticeable discrepancy between Weibull distribution fit and crude data frequency distributions has been observed for April through September data sets.
In order to overcome these problems and derive a suitable statistical methodology for insolation characterization, data set normalization has been performed herein. The considered insolation data sets have been normalized by means of straightforward analytical data set transformations, and the normal probability distribution hypothesis for the transformed data sets has been quantitatively confirmed by using SW, KS, Lilliefors and Chi-square tests, and qualitatively by means of histograms and normal distribution plots. Finally, the proposed methodology has been validated against real data sets, wherein small values of normal probability distribution model error suggest that the proposed methodology should result in a reliable statistical characterization of insolation based on past data. The final statistical model used for insolation characterization has simple structure, i.e. it implements normal probability distributions, and individual data set transformation functions for each month, which makes it convenient for profitability and payback calculations based on analytical description of insolation statistical properties.
Future research is going to be aimed towards further refinement of presented statistical characterization tools, and the development of an appropriate statistical simulation model which could be used for the optimization of the solar power system design and component sizing aimed at achieving the target profitability margins. Further analysis of the proposed statistical model insolation forecasting ability is also going to be considered in our future work.