Representation of non-Gaussian probability distributions in stochastic load-flow studies by the method of Gaussian sum approximations

Abstract

The stochastic load flow (SLF) is extended to include non-Gaussian ‘long-term’ nodal probability-density-function (PDF) data by replacing each non-Gaussian PDF with a ‘Gaussian sum’ approximation. A series of SLFs (stochastic load flows) are then performed and the results recombined, with the correct weightings, to generate non-Gaussian PDF profiles for busbars and lines of interest. Generally less than half of the most likely convolution components need evaluating. P – ø, Q – V decomposition and nodal dependence is easily incorporated in the study and moment matching can be used to determine the ‘best’ lower order Gaussian sum approximation. Long-term network topological impedance changes can also be included in the proposed method.