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Hybrid systems combine both discrete and continuous state dynamics. Power electronic inverters are inherently hybrid systems: they are controlled via discrete-valued switching inputs which determine the evolution of the continuous-valued…
We study a type of port-Hamiltonian system, in which the controller or disturbance is not applied to the flow variables, but to the systems power, a scenario that appears in many practical applications. A suitable framework is provided to…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Existing methods to determine the stability of a power system to small perturbations are based on eigenvalue analysis and focus on the asymptotic (long-term) behavior of the power grid. During the preasymptotic (short-term) transient,…
As bulk synchronous generators in the power grid are replaced by distributed generation interfaced through power electronics, inertia is removed from the system, prompting concerns over grid stability. Different metrics are available for…
The objective of this paper is to report some computational results for the theory of DAE stability boundary, with the aim of advancing applications in power system voltage stability studies. Firstly, a new regularization transformation for…
This paper proposes a novel Gronwall inequality-based method for transient stability assessment for power systems. The challenges of applying such methods to power systems are how to construct the differential inequality and how to treat…
We consider the problem of stability analysis for distribution grids with droop-controlled inverters and dynamic distribution power lines. The inverters are modeled as voltage sources with controllable frequency and amplitude. This problem…
This paper studies stability analysis of DC microgrids with uncertain constant power loads (CPLs). It is well known that CPLs have negative impedance effects, which may cause instability in a DC microgrid. Existing works often study the…
To fully learn the latent temporal dependencies from post-disturbance system dynamic trajectories, deep learning is utilized for short-term voltage stability (STVS) assessment of power systems in this paper. First of all, a semi-supervised…
Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…
We present a method to design distributed generation and demand control schemes for primary frequency regulation in power networks that guarantee asymptotic stability and ensure fairness of allocation. We impose a passivity condition on net…
DC grids are prone to small-signal instabilities due to the presence of tightly controlled loads trying to keep the power consumption constant over range of terminal voltage variations. Th, so-called, constant power load (CPL) represents a…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
The energy mix of future power systems will include high shares of wind power and solar PV. These generation facilities are generally connected via power-electronic inverters. While conventional generation responds dynamically to the state…
We study the problem of the stability of a two-component droplet. The standard solution known from the literature is based on a particular form of the mean field energy functional, in particular on distinction of hard mode and soft mode…
Simulating potential cascading failures can be useful for avoiding or mitigating such events. Currently, existing steady-state analysis tools are ill-suited for simulating cascading outages as they do not model frequency dependencies, they…
In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range…
Conventional power system optimization framework is becoming less reliable and efficient due to the stability issues brought by the ever-increasing inverter-interfaced renewable penetration. To ensure system stability during system…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…