Related papers: Lagrangian Modelling and Motion Stability of Synch…
We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal…
Synchronous generators and inverter-based resources are complex systems with dynamics that cut across multiple intertwined physical domains and control loops. Modeling individual generators and inverters is, in itself, a very involved…
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…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This raises new challenges for power system stability and design. We…
In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating…
In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert…
High performance tracking control can only be achieved if a good model of the dynamics is available. However, such a model is often difficult to obtain from first order physics only. In this paper, we develop a data-driven control law that…
Increasing the inertia is widely considered to be the solution to resolving unstable interactions between coupled oscillators. In power grids, Virtual Synchronous Generators (VSGs) are proposed to compensate the reducing inertia as rotating…
The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…
We consider the problem of synchronizing two electric power generators, one of which (the leader) is serving a time-varying electrical load, so that they can ultimately be connected to form a single power system. Each generator is described…
Using a Lagrangian mechanics approach, we construct a framework to study the dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. We have shown in our previous work that for…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
This paper investigates the transient stability of power systems co-dominated by different types of grid-forming (GFM) devices. Synchronous generators (SGs and VSGs) and droop-controlled inverters are typical GFM devices in modern power…
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…
Even though a variety of methods have been proposed in the literature, efficient and effective latent-space control (i.e., control in a learned low-dimensional space) of physical systems remains an open challenge. We argue that a promising…
Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a…
Large-scale integration of inverter-based resources into power grids worldwide is challenging their stability and security. This paper takes a closer look at synchronous condensers as a solution to mitigate stability challenges caused by…