Related papers: Newtonian Mechanics Based Transient Stability PART…
In this paper, we derive a number of inequalities which express power-efficiency trade-offs that hold generally for thermodynamic machines operating in non-equilibrium stationary states. One of these inequalities concerns the output power,…
Both relativistic mechanics and Newtonian mechanics are based on principles that have ontological implications. We propose a series of formalisms that rigorously define the ontology underlying mechanical theories, in order to clarify and…
As the proportion of converter-interfaced renewable energy resources in the power system is increasing, the strength of the power grid at the connection point of wind turbine generators (WTGs) is gradually weakening. Existing research has…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability…
Power system stability indices are used as measures to evaluate and quantify the response of the system to external large disturbances. This paper provides a comparative analysis of established transient stability indices. The indices…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
We establish a correspondence between two very general paradigms for systems that persist away from thermal equilibrium. In the first paradigm, a nonequilibrium steady state (NESS) is maintained by applying fixed thermodynamic forces that…
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…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
Transition probabilities for stochastic systems can be expressed in terms of a functional integral over paths taken by the system. Evaluating the integral by the saddle point method in the weak-noise limit leads to a remarkable mapping…
This paper presents a library of second-order models for synchronous machines that can be utilized in power system dynamic performance analysis and control design tasks. The models have a similar structure to the classical model in that…
Multiple types of Nyquist-like impedance-based criteria are utilized for the small-signal stability analysis of converter-based AC systems. It is usually considered that the determinant-based criterion can determine the overall stability of…
The aim of this paper is twofold: First, we give a formal introduction to the basics of the mathematical framework of classical mechanics. Along the way, we prove a Hamiltonian and a Lagrangian version of Noether's Theorem, an important…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
A first-principles description of nuclear systems along the drip lines presents a substantial theoretical and computational challenge. In this paper, we discuss the nuclear theory roadmap, some of the key theoretical approaches, and present…
Transient stability prediction is critically essential to the fast online assessment and maintaining the stable operation in power systems. The wide deployment of phasor measurement units (PMUs) promotes the development of data-driven…
Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…