Modeling Solar Energy Data using Periodic Regression

Abstract

Solar energy data was collected from two sites in western Michigan, USA that are not homogeneous with respect to location and solar panels used.  Data from one site was collected from August 1, 2009 through July 31, 2019 and the second site from July 12, 2017 through July 31, 2019 and summarized statistically.  The average monthly solar energy was higher during the summer and lower during the winter. The variation is higher during the winter and lower during the summer.  The annual cycle of average monthly solar energy, as well as the variation, was modeled using periodic regression equations comprised of intercept, sine, and cosine terms as well as an additive term for the difference between the two sites.  Model parameters were estimated from all collected data as well as from only the 2017 through 2019 data.  All estimated values are statistically significant and consistent in magnitude and sign between the two energy equations. The adjusted coefficients of estimates exceeded 80%.  It was concluded that the average monthly solar energy pattern at each site was the same but with different magnitudes and not changing in time.  Thus, the model could be applied to all sites in the west Michigan area, now and in the future.  For the variation in average monthly solar energy models, the adjusted coefficient of estimation was slightly above 75%.  While all parameter values were statistically significant, they were different in magnitude and sign indicating the possibility of a change in variation over time.