Spatial correlations for solar PV generation and its tree approximation analysis

Smart grids present interesting challenges as we integrate renewable energy sources such as solar PV cells in residential areas. This paper discusses the spatial modeling for solar irradiation and also deals with the problem of graph representation of the model. For this graph, the Chow-Liu minimum spanning tree algorithm helps us to achieve the optimal tree approximation of the graph by minimizing the Kullback-Leibler divergence which has a more sparse graph representation. We consider normalizing data using the zenith angle and also a standard method by subtracting mean and dividing by deviation (at time interval of day, a year moving average). We compare simulation results for Oahu solar measurement grid (Hawaii) sites and six sites near Denver, Colorado. Simulation results reveal that the KullbackLeibler divergence distance between the graph representation of these sites and their optimal tree approximation is bigger in winter than in summer. Moreover, the position of solar PV cells and their angles have an impact on the connection of the graph during the day and also its optimal tree approximation and the accuracy cost that the tree approximation algorithm pays.