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Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment is directly connected to the robustness of the operating condition and is evaluated by analyzing proximity to the power flow solution spaces boundary. Calculating location of such a boundary is a computationally challenging task, linked to the power flow equations non-linear nature, presence of technological constraints, and complicated network topology. In this paper we introduce a general framework to characterize points on the power flow solution space boundary in terms of auxiliary variables subject to algebraic constraints. Then we develop an adaptive continuation algorithm to trace 1-dimensional sections of boundary curves which exhibits robust performance and computational tractability. Implementation of the algorithm is described in detail, and its performance is validated on different test networks.
A multivariate density forecast model based on deep learning is designed in this paper to forecast the joint cumulative distribution functions (JCDFs) of multiple security margins in power systems. Differing from existing multivariate density forecas
Riesz potentials are well known objects of study in the theory of singular integrals that have been the subject of recent, increased interest from the numerical analysis community due to their connections with fractional Laplace problems and proposed
A robust and portable power supply has been developed specifically for charging linear transformer drivers, a modern incarnation of fast pulsed power generators. It is capable of generator +100 kV and -100 kV at 1 mA, while withstanding the large vol
This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matern-type Gaussian field priors that enable flexible modeling near the bou
We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank even-order real symmetric tensors. This algorithm applies the tensor power method of Kolda-Mayo to a certain modified tensor, constructed from a matrix flat