Patterns and correlations in European electricity prices.

Electricity markets are central to the coordination of power generation and demand. The European power system is divided into several bidding zones, each having an individual electricity market price. While individual price time series have been intensively studied in recent years, spatiotemporal aspects have received little attention.

Predicting dynamic stability from static features in power grid models using machine learning.

A reliable supply with electric power is vital for our society. Transmission line failures are among the biggest threats for power grid stability as they may lead to a splitting of the grid into mutual asynchronous fragments. New conceptual methods are needed to assess system stability that complement existing simulation models.

Optimizing the geometry of transportation networks in the presence of congestion.

Urban transport systems are gaining in importance, as an increasing share of the global population lives in cities and mobility-based carbon emissions must be reduced to mitigate climate change and improve air quality and citizens' health. As a result, public transport systems are prone to congestion, raising the question of how to optimize them to cope with this challenge. In this paper, we analyze the optimal design of urban transport networks to minimize the average travel time in monocentric as well as in polycentric cities.

Dual communities in spatial networks.

Both human-made and natural supply systems, such as power grids and leaf venation networks, are built to operate reliably under changing external conditions. Many of these spatial networks exhibit community structures. Here, we show that a relatively strong connectivity between the parts of a network can be used to define a different class of communities: dual communities.

Understanding Braess' Paradox in power grids.

The ongoing energy transition requires power grid extensions to connect renewable generators to consumers and to transfer power among distant areas. The process of grid extension requires a large investment of resources and is supposed to make grid operation more robust. Yet, counter-intuitively, increasing the capacity of existing lines or adding new lines may also reduce the overall system performance and even promote blackouts due to Braess' paradox.

Dynamic stability of electric power grids: Tracking the interplay of the network structure, transmission losses, and voltage dynamics.

Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous machines. The results are based on an extensive linear stability analysis of the third-order model for synchronous machines, comprising the classical power-swing equations and the voltage dynamics.

Revealing drivers and risks for power grid frequency stability with explainable AI.

Stable operation of an electric power system requires strict operational limits for the grid frequency. Fluctuations and external impacts can cause large frequency deviations and increased control efforts. Although these complex interdependencies can be modeled using machine learning algorithms, the black box character of many models limits insights and applicability.

Network isolators inhibit failure spreading in complex networks.

In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after.

Arbitrary-Order Finite-Time Corrections for the Kramers-Moyal Operator.

With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers-Moyal operator via a power-series expansion of the exponential operator. This expansion is necessary for deriving the different terms in a stochastic differential equation. With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers-Moyal coefficients.

Open database analysis of scaling and spatio-temporal properties of power grid frequencies.

The electrical energy system has attracted much attention from an increasingly diverse research community. Many theoretical predictions have been made, from scaling laws of fluctuations to propagation velocities of disturbances. However, to validate any theory, empirical data from large-scale power systems are necessary but are rarely shared openly.

Topological Determinants of Perturbation Spreading in Networks.

Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach that reveals universal features determining the spreading dynamics in diffusively coupled networks and disentangles them from factors that are system specific. In particular, we first analytically identify a purely topological factor encoding the interaction structure and strength, and second, numerically estimate a master function characterizing the universal scaling of the perturbation arrival times across topologically different networks.

Discontinuous transition to loop formation in optimal supply networks.

The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding redundant edges to supply networks is costly, yet beneficial for resilience. Loops typically form when costs for new edges are small or inputs uncertain.

Multistability in lossy power grids and oscillator networks.

Networks of phase oscillators are studied in various contexts, in particular, in the modeling of the electric power grid. A functional grid corresponds to a stable steady state such that any bifurcation can have catastrophic consequences up to a blackout. Also, the existence of multiple steady states is undesirable as it can lead to transitions or circulatory flows.

Wind Power Persistence Characterized by Superstatistics.

Mitigating climate change demands a transition towards renewable electricity generation, with wind power being a particularly promising technology. Long periods either of high or of low wind therefore essentially define the necessary amount of storage to balance the power system. While the general statistics of wind velocities have been studied extensively, persistence (waiting) time statistics of wind is far from well understood.

The winner takes it all-Competitiveness of single nodes in globalized supply networks.

Quantifying the importance and power of individual nodes depending on their position in socio-economic networks constitutes a problem across a variety of applications. Examples include the reach of individuals in (online) social networks, the importance of individual banks or loans in financial networks, the relevance of individual companies in supply networks, and the role of traffic hubs in transport networks. Which features characterize the importance of a node in a trade network during the emergence of a globalized, connected market? Here we analyze a model that maps the evolution of global connectivity in a supply network to a percolation problem.

Fluctuation-induced distributed resonances in oscillatory networks.

Across physics, biology, and engineering, the collective dynamics of oscillatory networks often evolve into self-organized operating states. How such networks respond to external fluctuating signals fundamentally underlies their function, yet is not well understood. Here, we present a theory of dynamic network response patterns and reveal how distributed resonance patterns emerge in oscillatory networks once the dynamics of the oscillatory units become more than one-dimensional.

Author Correction: Dynamically induced cascading failures in power grids.

The original version of this Article omitted the following from the Acknowledgements: 'Finally, we gratefully acknowledge support from the German Science Foundation (DFG) by a grant toward the Cluster of Excellence "Center for Advancing Electronics Dresden" (cfaed)'. This has been corrected in both the PDF and HTML versions of the Article.

Impact of climate change on backup energy and storage needs in wind-dominated power systems in Europe.

The high temporal variability of wind power generation represents a major challenge for the realization of a sustainable energy supply. Large backup and storage facilities are necessary to secure the supply in periods of low renewable generation, especially in countries with a high share of renewables. We show that strong climate change is likely to impede the system integration of intermittent wind energy.

Inferring power-grid topology in the face of uncertainties.

We develop methods to efficiently reconstruct the topology and line parameters of a power grid from the measurement of nodal variables. We propose two compressed sensing algorithms that minimize the amount of necessary measurement resources by exploiting network sparsity, symmetry of connections, and potential prior knowledge about the connectivity. The algorithms are reciprocal to established state estimation methods, where nodal variables are estimated from few measurements given the network structure.

Hysteretic Percolation from Locally Optimal Individual Decisions.

The emergence of large-scale connectivity underlies the proper functioning of many networked systems, ranging from social networks and technological infrastructure to global trade networks. Percolation theory characterizes network formation following stochastic local rules, while optimization models of network formation assume a single controlling authority or one global objective function. In socioeconomic networks, however, network formation is often driven by individual, locally optimal decisions.

Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series.

Wind power generation exhibits a strong temporal variability, which is crucial for system integration in highly renewable power systems. Different methods exist to simulate wind power generation but they often cannot represent the crucial temporal fluctuations properly. We apply the concept of additive binary Markov chains to model a wind generation time series consisting of two states: periods of high and low wind generation.

Dynamically induced cascading failures in power grids.

Reliable functioning of infrastructure networks is essential for our modern society. Cascading failures are the cause of most large-scale network outages. Although cascading failures often exhibit dynamical transients, the modeling of cascades has so far mainly focused on the analysis of sequences of steady states.

Rotor-angle versus voltage instability in the third-order model for synchronous generators.

We investigate the interplay of rotor-angle and voltage stability in electric power systems. To this end, we carry out a local stability analysis of the third-order model which entails the classical power-swing equations and the voltage dynamics. We provide necessary and sufficient stability conditions and investigate different routes to instability.

Natural wind variability triggered drop in German redispatch volume and costs from 2015 to 2016.

Avoiding dangerous climate change necessitates the decarbonization of electricity systems within the next few decades. In Germany, this decarbonization is based on an increased exploitation of variable renewable electricity sources such as wind and solar power. While system security has remained constantly high, the integration of renewables causes additional costs.