Normal-transformation-based probabilistic load flow with correlated wind and load forecast errors

Abstract

With aggressive government policies driving the electric power systems around the globe towards high renewable energy penetration, methodologies for considering forecast uncertainties in power system analysis and planning are gaining relevance. Probabilistic load flow (PLF) is a useful tool to carry out risk-based power system analysis and planning. This article discusses the need and philosophy of Normal-transformations, elaborating on Nataf transformation and polynomial normal transformation (PNT), to solve PLF and presents a unified approach for representation. Through detailed statistical modeling, the Gaussian mixture (GM) model is found to fit the historical wind and load power forecast error data better compared to widely used parametric models. Sampling of correlated marginal distributions, for scenario generation in PLF, requires the quantile function of the GM distribution, which is not available in a closed expression. A strategy, using quantile functions of Gaussian component sampling and interpolation, to approximate the GM’s quantile function is presented. The presented approximation enables the use of GM for solving PLF with correlated marginals, which is not addressed in the literature. This work also contributes to prevailing research questions by two new performance comparisons: between various higher-order PNT embedded to point estimate methods (PEMs) for PLF, and between PEM and Quasi-Monte Carlo (QMC) methods for PLF analysis. When PEMs are employed for PLF, there is no improvement observed in going for higher than third order PNT (3PNT). Results show that estimating the first four moments of the output variables through QMC-PLF is more accurate compared to PEM-PLF. Formulae useful for implementation of various higher-order PNT, for QMC and PEM, are derived and presented for direct use. Finally, the impact of correlated non-normal modeling of inputs on PLF output variables’ distribution is demonstrated.