Probabilistic Load Flow Based on Holomorphic Embedding, Kernel Density Estimator and Saddle Point Approximation Including Correlated Uncertainty Variables

Probabilistic Load Flow (PLF) methods have been extensively regarded due to the growth of uncertainty and renewable energies penetration in power systems. Given that, the current study aims to propose two novel probabilistic load flow methods based on holomorphic embedding method. Holomorphic method, unlike other iterative methods, introduces a nonlinear equation solver in an independent class, recursively. To that end, Kernel Density Estimator (KDE) and Saddle Point Approximation (SPA) methods are used to efficiently estimate probabilistic characteristics of load flow outputs. The correlations between random input variables with non-normal/normal probability distributions have been considered. The proposed algorithms have been examined on the modified IEEE 14- and 118-bus systems. Finally, to consider the uncorrelated and correlated conditions, the researcher compared the simulation results of the two proposed methods with some well-known and published probabilistic iterative load flow methods such as Monte Carlo Simulation (MCS), Parzen Window (PW), Diffusion method, and 2n + 1 Point Estimate Method (PEM). MCS is always a dependable solution but time-consuming that make it useless for large power systems. In the present study, the accurate results obtained from MCS are regarded as a reference. The comparison of results shows high efficiency and low computational burden of proposed methods, and also the accuracy of these methods in density function estimation of output random variables.