Network-induced multistability through lossy coupling and exotic solitary states

Abstract

The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. In the latter case, the ongoing transition to distributed renewable energy sources is leading to a proliferation of dynamical actors. The desynchronization of a few or even one of those would likely result in a substantial blackout. Thus the dynamical stability of the synchronous state has become a focus of power grid research in recent years.In this letter we uncover that the non-linear stability against large perturbations is dominated and threatened by the presence of solitary states in which individual actors desynchronise. Remarkably, when taking physical losses in the network into account, the back-reaction of the network induces new exotic solitary states in the individual actors, and the stability characteristics of the synchronous state are dramatically altered. These novel effects will have to be explicitly taken into account in the design of future power grids, and their existence poses a challenge for control.While this letter focuses on power grids, the form of the coupling we explore here is generic, and the presence of new states is very robust. We thus strongly expect the results presented here to transfer to other systems of coupled heterogeneous Newtonian oscillators.

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

“…Solitary states are described as states for which only one single element behaves differently compared with the behavior of the background group, i.e., the neighboring elements. These kinds of states have been observed in generalized Kuramoto-Sakaguchi models [MAI14a, WU18a, TEI19, CHE19b], the Kuramoto model with inertia [JAR15, JAR18], models of power grids [TAH19,HEL20], the Stuart-Landau model [SAT19], the FitzHugh-Nagumo model [RYB19a,SCH19a], systems of excitable units [ZAK16b] as well as in Lozi maps [RYB17] and even in experimental setups of coupled pendula [KAP14]. Solitary states are considered as important states in the transition from coherent to incoherent dynamics [JAR15,SEM15b,MIK18].…”

Dynamic control of intermittent renewableenergy fluctuations in two-layer power grids

“…The investigation of the self-emerging control dynamics following perturbations has highlighted the role played by some specific nodes: dead-ends and dead-trees result to be always problematic, in agreement with recent work [Menck et al, 2014;Auer et al, 2017] where it has been demonstrated that the cost-minimizing creation of deadend or dead-tree structures increases the vulnerability of the power grid to large perturbations. The role of solitary nodes has recently been emphasized [Taher et al, 2019;Hellmann et al, 2020;Berner et al, 2021]. Moreover, it turns out that the Italian power grid can be divided in two specific parts: the northern, continental part, with a higher average connectivity, which is more resilient to perturbations, and the southern, peninsular part, characterized by a low average connectivity.…”

Optimising power system frequency stability using virtual inertia from inverter‐based renewable energy generation

“…The rotation speed (), is the power system frequency in radians per second (rad/s). The damping coefficient ( D ) characterises the power response to the system frequency and is mostly determined by the governor droop control parameter [46]. It can also represent a variety of damping sources, such as control loops and frequency‐depended loads.…”