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A Data-Driven Nonparametric Approach for Probabilistic Load-Margin Assessment Considering Wind Power Penetration
A modern power system is characterized by an increasing penetration of wind power, which results in large uncertainties in its states. These uncertainties must be quantified properly; otherwise, the system security may be threatened. Facing this challenge, here we propose a cost-effective, data-driven approach to assessing a power system's load margin probabilistically. Using actual wind data, a kernel density estimator is applied to infer the nonparametric wind speed distributions, which are further merged into the framework of a vine copula. The latter enables us to simulate complex multivariate and highly dependent model inputs with a variety of bivariate copulae that precisely represent the tail dependence in the correlated samples. Furthermore, to reduce the prohibitive computational time of traditional Monte-Carlo simulations that process a large amount of samples, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model through a Bayesian-learning framework. To accelerate the convergence rate of this Bayesian algorithm, a truncated polynomial chaos surrogate, which serves as a highly efficient, parametric Bayesian prior, is developed. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. Results of simulations that are performed on several test systems reveal the impressive performance of the proposed method in the probabilistic load-margin assessment.
Modeling Spatial Asymmetries in Teleconnected Extreme Temperatures
Abstract Combining strengths from deep learning and extreme value theory can help describe complex relationships between variables where extreme events have significant impacts (e.g., environmental or financial applications). Neural networks learn complicated nonlinear relationships from large datasets under limited parametric assumptions. By definition, the number of occurrences of extreme events is small, which limits the ability of the data-hungry, nonparametric neural network to describe rare events. Inspired by recent extreme cold winter weather events in North America caused by atmospheric blocking, we examine several probabilistic generative models for the entire multivariate probability distribution of daily boreal winter surface air temperature. We propose metrics to measure spatial asymmetries, such as long-range anticorrelated patterns that commonly appear in temperature fields during blocking events. Compared to vine copulas, the statistical standard for multivariate copula modeling, deep learning methods show improved ability to reproduce complicated asymmetries in the spatial distribution of ERA5 temperature reanalysis, including the spatial extent of in-sample extreme events.
Data-driven projection pursuit adaptation of polynomial chaos expansions for dependent high-dimensional parameters
Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in the realms of UQ and inference. Among these, polynomial chaos expansions (PCE), when adapted to low-dimensional quantities of interest (QoI), provide effective yet accurate approximations for these QoI in terms of an adapted orthogonal basis. These adaptation techniques have been cast as projection pursuits in Gaussian Hilbert space in what has been referred to as a projection pursuit adaptation (PPA) by Xiaoshu Zeng and Roger Ghanem (2023). The PPA method efficiently identifies an optimal low-dimensional space for representing the QoI and simultaneously evaluates an optimal PCE within that space. The quality of this approximation clearly depends on the size of the training dataset, which is typically a function of the adapted reduced dimension. Here, the complexity of the problem is thus mediated by the complexity of the low-dimensional quantity of interest and not the complexity of the high-dimensional parameter space.