Data-driven uncertainty analysis of distribution networks including photovoltaic generation

This paper investigates residential distribution networks with uncertain loads and photovoltaic distributed generation. An original probabilistic modeling of consumer demand and photovoltaic generation is presented that is based on the analysis of large set of data measurements. It is shown how photovoltaic generation is described by complex non-standard distributions that can be described only numerically. Probabilistic analysis is performed using an enhanced version of the Polynomial Chaos technique that exploits a proper set of polynomial basis functions. It is described how such functions can be generated from the numerically available data. Compared to other approximate methods for probabilistic analysis, the novel technique has the advantages of modeling accurately truly nonlinear problems and of directly providing the detailed Probability Density Function of relevant observable quantities affecting the quality of service. Compared to standard Monte Carlo method, the proposed technique introduces a simulation speedup that depends on the number of random parameters. Numerical applications to radial and weakly meshed networks are presented where the method is employed to explore overvoltage, unbalance factor and power loss, as a function of photovoltaic penetration and/or network configuration.