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Abstract

This Focus Issue brings together recent notable advances in the field of dynamical systems and complexity science on the subject of the non-linear collective behavior of power grids and energy systems. Due to the ongoing energy transition, mandated by the epochal challenge that is the decarbonization of human activity, our energy infrastructure is evolving rapidly. This challenges us to understand and rethink current and potential future power grids. In response to this urgent need, the last decade has seen the emergence of a new direction of theoretical research on complex power grids. There is a long tradition of studying models of the complex power grid in the electrical engineering and control theory literature, with the foundational second-order Kuramoto model appearing first in 1981 in the paper by Bergen and Hill,1 leading up to the seminal synchronization results of Dörfler et al.2 and the basin of attraction of the synchronous state of Menck et al.3 The new direction that has been developing using dynamical systems theory complements this by bringing in a new systemic perspective and considering heads on the novel challenge posed by stochastic4 and decentral power generation. This theory- and data-driven research achieved notable insights. A subjective, non-exhaustive list of highlights include (i) the network-wide dynamic response patterns emerging from fluctuating power feed-in;5–7 (ii) time-delayed control mechanisms to reduce grid frequency variation;8 (iii) a deeper understanding of the network structure’s impact on stability;9–13 (iv) new insights into power flows and cascades14,15 and the introduction of dual graphs for new analytic results in this context;16,17 and (v) data-driven and extensive stochastic analysis on renewable energies and power grid frequencies.18–20 The methods and topics in this Focus Issue not only cover further developments in the directions of these highlights but also contribute to a number of new emerging directions that are gaining importance. This includes full range of dynamical systems theory aspects, from delays and control systems, over stochastic systems, and time series analysis to bifurcation theory and multilayer complex networks. We will present the contributions to this Focus Issue grouped according to these themes: multistability and bifurcation structure (Sec. II A), cascades and line failures (Sec. II B), variability and stochastic drivers of power grids (Sec. II C), and control and delays (Sec. II D). Beyond these established areas, we discuss the most important emerging and cross-cutting themes in Sec. III.