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We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the…
Nowadays, power system inertia is changing as a consequence of replacing conventional units by renewable energy sources, mainly wind and PV power plants. This fact affects significantly the grid frequency response under power imbalances. As…
The fluctuating dynamics of a network about its stable, noise-free steady state are theoretically investigated. Various causes of non-equilibrium dynamics are identified in terms of the properties and symmetry of the network connections and…
The energy system is rapidly changing to accommodate the increasing number of renewable generators and the general transition towards a more sustainable future. Simultaneously, business models and market designs evolve, affecting power-grid…
In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the…
A challenge for renewable and hybrid power systems is the dynamically stable integration of Renewable Energy Sources (RES). This paper specifically investigates the influence of intermittent RES and measurement delays from power electronic…
Increased share of renewable sources of energy in a power grid leads to larger deviations in grid frequency from the nominal value resulting in more challenging control and its modelling. In this paper we focus on the grid frequency for the…
We study the probability distribution and the escape rate in systems with delayed dissipation that comes from the coupling to a thermal bath. To logarithmic accuracy in the fluctuation intensity, the problem is reduced to a variational…
During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms…
In the electrical grid, the distribution system is themost vulnerable to severe weather events. Well-placed and coordinatedupgrades, such as the combination of microgrids, systemhardening and additional line redundancy, can greatly reduce…
Natural Disasters like hurricanes, floods or earthquakes can damage power grid devices and create cascading blackouts and islands. The nature of failure propagation and extent of damage is dependent on the structural features of the grid,…
Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness…
Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, epidemiology to engineering and robotics. In the presence of noise and uncertainty, inter- actions between the individual components can…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
The increasing global spread of electric vehicles (EVs) has introduced significant interdependence between transportation and power networks. Most of the previous studies on coupled networks focus on the formation of equilibrium states…
Integrating renewable energy production into the electricity grid is an important policy goal to address climate change. However, such an integration faces economic and technological challenges. As power generation by renewable sources…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
With the sharp increase of power demand, large-scale blackouts in power grids occur frequently around the world. Cascading failures are the main causes of network outages. Therefore, revealing the complicated cascade mechanism in grids is…
Given increasing risk from climate-induced natural hazards, there is growing interest in the development of methods that can quantitatively measure resilience in power systems. This work quantifies resilience in electric power transmission…