Probabilistic Load Flow based on Parameterized Probability-boxes for Systems with Insufficient Information

The increased penetration of intermittent renewable energy sources and random loads has caused many uncertainties in the power system. It is essential to analyze the effect of these uncertain factors on the behavior of the power system. This study presents a new powerful approach called probability-boxes (p-boxes) to consider these uncertainties by combining interval and probability simultaneously. The proposed method is appropriate for problems with insufficient information. In this paper, the uncertainty of distribution functions is modeled according to the influence of natural factors such as light intensity and wind speed. First, the p-boxes load flow problem is studied using an appropriate point estimation method to calculate statistical moments of probabilistic load flow (PLF) outputs. Then, the Cornish–Fisher expansion series is used to obtain the probability bounds. The proposed approach is analyzed on the IEEE 14-bus, and IEEE 118-bus test systems consist of loads, solar farms, and wind farms as p-boxes input variables. The obtained results are compared with the double-loop sampling (DLS) approach to show the proposed method’s precision and efficiency.©2021 The Authors. Published by IEEE. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/This work has been funded by Academy of Finland (Grant Number: Profi4/WP2)fi=vertaisarvioitu|en=peerReviewed

Non-intrusive stochastic analysis with parameterized imprecise probability models: I. Performance estimation

© 2019 Elsevier Ltd Uncertainty propagation through the simulation models is critical for computational mechanics engineering to provide robust and reliable design in the presence of polymorphic uncertainty. This set of companion papers present a general framework, termed as non-intrusive imprecise stochastic simulation, for uncertainty propagation under the background of imprecise probability. This framework is composed of a set of methods developed for meeting different goals. In this paper, the performance estimation is concerned. The local extended Monte Carlo simulation (EMCS) is firstly reviewed, and then the global EMCS is devised to improve the global performance. Secondly, the cut-HDMR (High-Dimensional Model Representation) is introduced for decomposing the probabilistic response functions, and the local EMCS method is used for estimating the cut-HDMR component functions. Thirdly, the RS (Random Sampling)-HDMR is introduced to decompose the probabilistic response functions, and the global EMCS is applied for estimating the RS-HDMR component functions. The statistical errors of all estimators are derived, and the truncation errors are estimated by two global sensitivity indices, which can also be used for identifying the influential HDMR components. In the companion paper, the reliability and rare event analysis are treated. The effectiveness of the proposed methods are demonstrated by numerical and engineering examples

Non-intrusive stochastic analysis with parameterized imprecise probability models: II. Reliability and rare events analysis

© 2019 Elsevier Ltd Structural reliability analysis for rare failure events in the presence of hybrid uncertainties is a challenging task drawing increasing attentions in both academic and engineering fields. Based on the new imprecise stochastic simulation framework developed in the companion paper, this work aims at developing efficient methods to estimate the failure probability functions subjected to rare failure events with the hybrid uncertainties being characterized by imprecise probability models. The imprecise stochastic simulation methods are firstly improved by the active learning procedure so as to reduce the computational costs. For the more challenging rare failure events, two extended subset simulation based sampling methods are proposed to provide better performances in both local and global parameter spaces. The computational costs of both methods are the same with the classical subset simulation method. These two methods are also combined with the active learning procedure so as to further substantially reduce the computational costs. The estimation errors of all the methods are analyzed based on sensitivity indices and statistical properties of the developed estimators. All these new developments enrich the imprecise stochastic simulation framework. The feasibility and efficiency of the proposed methods are demonstrated with numerical and engineering test examples

PSO-embedded adaptive Kriging surrogate model method for structural reliability analysis with small failure probability

In the present study, a novel adaptive surrogate model method is proposed for the analysis of structural reliability with small failure probability. In order to address the problems with conventional adaptive Kriging surrogate model method based on candidate sample pool, the adaptive Kriging surrogate model method which integrates Particle Swarm Optimization algorithm (PSO) is put forward. In the course of implementation, the surrogate model is gradually improved through an iterative process and the high-value samples are selected to update the surrogate model through an optimization solution carried out by using PSO. Numerical examples are used to evaluate the computational performance of the proposed method, and a further discussion is conducted around the revision to the learning function. The results show that the introduction of PSO not only increases the possibility of obtaining high-value samples, but also significantly improves the solution accuracy of the adaptive Kriging surrogate model method for structural reliability analysis. Meanwhile, the proposed method overcomes the problem caused by the conventional candidate pool-based selection method through the optimization algorithm to determine high-value samples, achieving an excellent performance in dealing with the small failure probability. In addition, the proposed method is applicable to achieve a reasonable balance between solution accuracy and efficiency through the revised learning function which takes into account local neighborhood effects