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Effect of load-generation variability on power grid cascading failures
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
R. Rocchetta, E. Patelli, L. Bing, G. Sansavini
Once the uncertainty sources are characterized, a preliminary uncertainty analysis is performed. Monte Carlo method is used to propagate 5e4 samples of the load profile. For each load sample, the cascading failure model is solved 2444 times, one for each contingency listed. The percentile of the demand not served, the average number of failed lines and the line outage frequencies are computed for each load sample as described in Section 3.1. The p95 (DNS) results are summarised in Figure 4. This figure presents a so-called cobweb plot, also known as parallel coordinates plot. It is a simple and effective way of visualising random input and output spaces in high dimensions. The X-axis reports the inputs loads and the percentile of the DNS (on the far right). The Y-axis reports the normalized inputs and output realisations of the Monte Carlo method. Each one of the dark dashed line in the background corresponds to one load profile realisation and corresponding The p95 (DNS) obtained through Nc model evaluations. Red solid lines are conditional samples, which highlight only the load combinations leading to the highest p95 (DNS). It can be observed, later confirmed by Morris’ and Sobols’ analysis, that there is a strong influence of some of the loads (e.g. in nodes 15 and 18) on the extremes of the DNS. In particular, when the power demanded in nodes 15 and 18 is small, the risk of facing severe DNS scenarios increases.
Investigating consumers’ intention of using contactless logistics technology in COVID-19 pandemic: a Copula-Bayesian Network approach
Published in International Journal of Logistics Research and Applications, 2022
Tianyi Chen, Yiik Diew Wong, Xueqin Wang, Duowei Li
In this sub section, cobweb plots are applied to investigate the multivariate distributions for the two intentions. In a cobweb, random variables are presented as vertical lines, while each sample is depicted as a jagged line. The point where a jagged line hits a vertical line denotes the sample value of the random variable in a natural scale. The samples in cobweb plots are generated by Monte Carlo simulation based upon the marginal distribution of each random variable and the correlations between variables as introduced above. Cobweb plots reflect complex interaction between factors by providing a good picture of the joint distribution and dependency relations (Kallen 2002). The cobweb plots corresponding to the Copula-BN for the intention to use contactless is presented in Figure 3. The graphs at the top of the cobweb plots denote the sum densities of the random variables. Since the samples are generated by Monte Carlo simulation, a small number of samples slightly exceed the score range (i.e. as introduced in Section 2.1) on some random variables. Such a small number of samples would not have effects on the following analysis results.