Related papers: Power Network Dynamics on Graphons
Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks…
Controllability of complex networks arises in many technological problems involving social, financial, road, communication, and smart grid networks. In many practical situations, the underlying topology might change randomly with time, due…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We consider two mathematical dynamical models of gene regulatory networks (GRNs) and obtain results on robust synchronization on these dynamical models based on the existing theoretical results in the coupled cell network formalism. We also…
Power grid operation is becoming increasingly complex due to the rising integration of renewable energy sources and the need for more adaptive control strategies. Reinforcement Learning (RL) has emerged as a promising approach to power…
We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…
Purpose: The computation methods for modeling, controlling and optimizing the transforming grid are evolving rapidly. We review and systemize knowledge for a special class of computation methods that solve large-scale power grid…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
In this contribution we analyze the exponential stability of power networks modeled with the Telegrapher's equations as a system of balance laws on the edges. We show the equivalence of periodic solutions of these Telegrapher's equations…
We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
We study the effects of the allocation of distributed generation on the resilience of power grids. We find that an unconstrained allocation and growth of the distributed generation can drive a power grid beyond its design parameters. In…
To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
With the increased complexity of power systems due to the integration of smart grid technologies and renewable energy resources, more frequent changes have been introduced to system status, and the traditional serial mode of state…
The ongoing energy transition challenges the stability of the electrical power system. Stable operation of the electrical power grid requires both the voltage (amplitude) and the frequency to stay within operational bounds. While much…
We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors…