Analysis of probabilistic load flow using point estimation method to evaluate the quantiles of electrical networks state variables

Abstract

The objective of the paper is to provide a clear and comprehensive analysis of probabilistic load flow using Point Estimation Method, and its accuracy in the evaluation of the quantiles of the state variables of real electrical distribution networks. Three Points Estimation Method (TPEM) has been implemented to evaluate the first four moments of output variables (voltages, currents and active power flows), and several methods to reconstruct the probability density function from moments and calculate the quantiles have been compared, including Generalized Lambda Distribution and Gram-Charlier Development. Monte-Carlo PLF has been taken as reference to evaluate the accuracy of aforementioned TPEM results and the scope of application of the method in a real electrical distribution system.

Joined Probabilistic Load Flow and Sensitivity Analysis of Distribution Networks Based on Polynomial Chaos Method

“…As an example, for a Gaussian-distributed variable ξ r and expansion order β = 3, the β + 1 = 4 quadrature nodes are given by respectively. In general, the number (β + 1) l of nodes in the multi-dimensional grid is greater than the number N b of basis functions defined in (10). A subset of quadrature nodes can thus be selected as testing points to form systems (15) or (16).…”

“…Efficient analytical/approximate stochastic techniques have been recently investigated in the field of power systems [9]- [13]. Among them, the point estimate method [9], [10] provides approximations of the raw statistical moments of some observation variables, while the cumulant method [11], [12] works for linear (or almost linear) problems. In this paper, instead, we will focus on the category of Polynomial Chaos (PC) methods [13] since such techniques work for nonlinear problems and provide the detailed Probability Density Function (PDF) of the desired observation variables.…”

Data-driven uncertainty analysis of distribution networks including photovoltaic generation

“…For what concerns probabilistic analysis, the basic and reference method still remains Monte Carlo simulation [7], [12]. However, due to the heavy computational times it can require, several approximate probabilistic analysis techniques have also been proposed in the literature [13], [14], [15], which includes Point Estimate, Cumulant methods and Surface Response Method [16,17,18,19,20]. Among existing techniques, Cumulant method works well for linear (or almost linear) problems and its application to the nonlinear probabilistic power flow relies on approximate linearizations.…”

Probabilistic Power Flow Analysis Based on Point-Estimate Method for High Penetration of Photovoltaic Generation in Electrical Distribution Systems

“…This approximate method is a strong technique that accurately approximates the expected value and variance of a variable, furthermore, the computational burden is reduced (Plattner, Farah Semlali and Kong, 2017).…”