On Solving Probabilistic Load Flow for Radial Grids using Polynomial Chaos

The uncertain nature of electric energy production from distributed generation based on renewable resources has to be considered when managing and operating distribution grids. In several cases, this uncertainty can be described using nonGaussian random variables, requiring appropriate probabilistic load flow techniques. The present paper proposes a method that, exploiting Polynomial Chaos Expansion and Galerkin projection, allows a reformulation of the probabilistic load flow for radial grids as an enlarged deterministic problem. For radial grids, the well known Backward-Forward-Sweep method is applicable. This method does not require any model simplification or assumptions on the probability density function of the input random variables, i.e. it is applicable to non-Gaussian uncertainties. We draw upon a real 84-node grid and compare results against those obtained from Monte Carlo simulation.