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The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
Ensuring reliable operation of large power systems subjected to multiple outages is a challenging task because of the combinatorial nature of the problem. Traditional approaches for security assessment are often limited by their scope…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
Power system robustness against high impact low probability events is becoming a major concern. To depict distinct phases of a system response during these disturbances, an irregular polygon model is derived from the conventional trapezoid…
This article proposes a data-driven framework to verify the distributed conditions that guarantee the system-wide stability for interconnected power systems. To guarantee system wide stability, the dynamics of each bus are required to…
This paper studies the semi-analytic solution (SAS) of a power system's differential-algebraic equation. A SAS is a closed-form function of symbolic variables including time, the initial state and the parameters on system operating…
Harmonic instability occurs frequently in the power electronic converter system. This paper leverages multi-resolution dynamic mode decomposition (MR-DMD) as a data-driven diagnostic tool for the system stability of power electronic…
In this Letter, we investigate the stability of the statistical equilibrium of spherically symmetric collisionless self-gravitating systems. By calculating the second variation of the entropy, we find that perturbations of the relevant…
Here we develop an approach to predict power grid weak points, and specifically to efficiently identify the most probable failure modes in static load distribution for a given power network. This approach is applied to two examples: Guam's…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…
In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…
The dynamic response of power grids to small disturbances influences their overall stability. This paper examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Dynamic security analysis is an important problem of power systems on ensuring safe operation and stable power supply even when certain faults occur. No matter such faults are caused by vulnerabilities of system components, physical…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
Large scale integration of distributed energy resources and electric vehicles in a transactive energy environment present new challenges in terms of voltage stability and fluctuations in a power distribution system. The impact of different…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
In this paper, in an attempt to improve power grid resilience, a machine learning model is proposed to predictively estimate the component states in response to extreme events. The proposed model is based on a multi-dimensional Support…