Collective nonlinear dynamics and self-organization in decentralized power grids

Abstract

The ongoing transition to renewable energy supply comes with a restructuring of power grids, changing their effective interaction topologies, more and more strongly decentralizing them and substantially modifying their input, output, and response characteristics. All of these changes imply that power grids become increasingly affected by collective, nonlinear dynamic phenomena, structurally and dynamically more distributed and less predictable in space and time, more heterogeneous in its building blocks, and as a consequence less centrally controllable. Here cornerstone aspects of datadriven and mathematical modeling of collective dynamical phenomena emerging in real and model power grid networks by combining theories from nonlinear dynamics, stochastic processes and statistical physics, anomalous statistics, optimization, and graph theory are reviewed. The mathematical background required for adequate modeling and analysis approaches is introduced, an overview of power system models is given, and a range of collective dynamical phenomena are focused on, including synchronization and phase locking, flow (re)routing, Braess's paradox, geometric frustration, and spreading and localization of perturbations and cascading failures, as well as the nonequilibrium dynamics of power grids, where fluctuations play a pivotal role.

Lower bound for entropy production rate in stochastic systems far from equilibrium

“…Schnakenberg [19] proposed a network representation of the master equation, importing results from graph theory [28][29][30] to nonequilibrium thermodynamics. We explore this idea by considering the network representation of the vertices s for a given matching {(s, m(s))|s ∈ S }, where m(m(s)) = 1.…”

Predicting basin stability of power grids using graph neural networks

“…In line with the literature on power grids and as is common in natural science we therefore assume a simplified model of power grids to understand the behavior of simpler models as a proxy to the complex ones. The procedure for simplifications corresponds with the state-of-the-art in the current research landscape for complex power grids Witthaut et al [2022].…”

“…The study of non-linear self-organizing processes in power grids, specifically the interplay of synchrony and active powerflows has been an active topic in the research of complex power grids Witthaut et al [2022]. Depending on the task, different modeling strategies and timescales are used.…”

Collective effects and synchronization of demand in real-time demand response

“…However, system integration of renewable power sources remains a challenge as generation fluctuate on multiple time scales [4][5][6][7]. Hence, methods of statistical physics and complexity science are becoming essential to understand the dynamics and operation of future energy systems [8][9][10].…”