Uncertainty Quantification of the Crosstalk in Multiconductor Transmission Lines via Degree Adaptive Stochastic Response Surface Method

The degree adaptive stochastic response surface method is applied to analyze statistically the crosstalk in multiconductor transmission lines (MTLs). The coefficient of polynomial chaos expansion (PCE) is obtained based on the least angle regression. The truncation degree of PCE is iterated using the degree adaptive truncation algorithm, and the optimal proxy model of the crosstalk of the original MTLs that satisfies the actual error requirements is calculated. The statistical properties of crosstalk in MTLs (such as mean, standard deviation, skewness, kurtosis, and probability density distribution) are obtained. The failure probability of the electromagnetic compatibility in the MTLs system is considered. The global sensitivity indices of crosstalk-related factors are analyzed. Finally, the proposed method is proved to be effective compared with the conventional Monte Carlo method. The uncertainty quantification of crosstalk in MTLs can be calculated efficiently and accurately.

Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis

The present work demonstrates an efficient method for reliability analysis using sequential development of the stochastic response surface. Here, orthogonal Hermite polynomials are used whose unknown coefficients are evaluated using moving least square technique. To do so, collocation points in the conventional stochastic response surface method (SRSM) are replaced by the sparse grid scheme so as to reduce the number of function evaluations. Moreover, the domain is populated sequentially by the sparse grid based on the outcome of the optimization to find out the most probable failure point. Hence, the support points are generated based on a coupled effect of the optimization for failure region and the sub-grids hierarchy. Continuous and differentiable penalty function is imposed to determine multiple failure points, if any, by repeating the optimization. Once the response surface is developed, reliability analysis is carried out using importance sampling. Five different benchmark examples are presented in this study to validate the performance of the proposed modeling. As the accuracy of the method is established, two reliability-based design examples involving nonlinear finite element (FE) analysis of plates are demonstrated. Numerical study shows the efficiency of the proposed sequential SRSM in terms of accuracy and number of time-exhaustive evaluation of the original performance function, as compared to other methods available in the literature. Based on these results, it may be concluded that the proposed method works satisfactorily for a large class of reliability-based design problems.

An Improved Stochastic Response Surface Method Based Probabilistic Load Flow for Studies on Correlated Wind Speeds in the AC/DC Grid

This paper proposed a probabilistic load flow technique of AC/VSC-MTDC (Alternate Current/Voltage Source Control-Multiple Terminal Direct Current) hybrid grids based on an improved stochastic response surface method. The applied traditional stochastic response surface method is inherent with the capability to tackle correlated normal variables; however, the accuracy is poor in the case of correlated diverse distributions. To address this issue, NATAF transformation was adopted to transform the correlated wind speeds and loads following arbitrary distributions into the variables that are subject to standard normal distributions. The collection points could be selected to establish the polynomial relationship among the independent standard normal variables and the output responses. Then, the probability distributions and statistics of the responses could be accurately and efficiently estimated. The modified IEEE 14-bus system, involving an additional VSC-MTDC system, wind speeds following various distributions, and diverse consumer behaviors, was used to demonstrate the validity and capability of the proposed method.