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We propose the application of occupation measure theory to the classical problem of transient stability analysis for power systems. This enables the computation of certified inner and outer approximations for the region of attraction of a nominal operating point. In order to determine whether a post-disturbance point requires corrective actions to ensure stability, one would then simply need to check the sign of a polynomial evaluated at that point. Thus, computationally expensive dynamical simulations are only required for post-disturbance points in the region between the inner and outer approximations. We focus on the nonlinear swing equations but voltage dynamics could also be included. The proposed approach is formulated as a hierarchy of semidefinite programs stemming from an infinite-dimensional linear program in a measure space, with a natural dual sum-of-squares perspective. On the theoretical side, this paper lays the groundwork for exploiting the oscillatory structure of power systems by using Hermitian (instead of real) sums-of-squares and connects the proposed approach to recent results from algebraic geometry.
The goal of motion tomography is to recover a description of a vector flow field using information on the trajectory of a sensing unit. In this paper, we develop a predictor corrector algorithm designed to recover vector flow fields from trajectory d
In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g.,
During the last decades, significant advances have been made in the area of power system stability and control. Nevertheless, when this analysis is carried out by means of decentralized conditions in a general network, it has been based on conservati
In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an
This paper develops computable metrics to assign priorities for information collection on network systems made up by binary components. Components are worth inspecting because their condition state is uncertain and the system functioning depends on i