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This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we have established the stability theory and proposed stability conditions based on the delta dissipativity. In Part…
This paper shows that a necessary and sufficient condition for the small-signal stability of an inverter-integrated power system can be expressed in terms of semidefinite matrix inequalities determined only by the synchronous reactance of…
In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent…
We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary,…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One…
In this paper, a simple algorithm for detailed system-level thermal noise analysis is developed, demonstrated, and verified. This method uses noise-wave theory and noise covariance matrices to cascade noise and scattering parameters of…
The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between…
We have discovered specific conditions for generic scattering systems to act as wave splitters that are robust to any change in relative amplitude or phase of an arbitrary injected waveform. Specifically for complex systems with tunable…
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation $u_{tt}-u_{xx}+V'(u)=0$, where $u$ is a scalar-valued function of $x$ and $t$, and the…
We consider an electrical chain of N nonlinear capacitors coupled by linear inductors assuming that voltage dependence of capacitors represents an even function. We prove that only 5 symmetry determined nonlinear normal modes (NNM) can…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We recently introduced the "Virtual VNA" concept which estimates the $N \times N$ scattering matrix characterizing an arbitrarily complex linear reciprocal system with $N$ monomodal lumped ports by inputting and outputting waves only via…
In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique…
We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems. In particular we show that the structured singular value is always equal to its convex upper bound for nonnegative…
Stability of power electronic converters connected to power grids is commonly assessed by using the impedance criterion. On the contrary, stability of power grids is typically analysed by using network state-space representation and system…
This paper examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal…
The rapid rise in inverter-based renewable resources has heightened concerns over subsynchronous resonance and oscillations, thereby challenging grid stability. This paper reviews approaches to identify and mitigate these issues, focusing…
The wide deployment of renewable generation and the gradual decrease in the overall system inertia make modern power grids more vulnerable to transient instabilities and unacceptable frequency fluctuations. Time-domain simulation-based…
The Phasor measurement unit (PMU) measurements are mandatory to monitor the power system's voltage stability margin in an online manner. Monitoring is key to the secure operation of the grid. Traditionally, online monitoring of voltage…