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The ongoing rapid transformation of our energy supply challenges the operation and stability of electric power grids and other supply networks. This focus issue comprises new ideas and concepts in the monitoring and control of complex networks to address these challenges.

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the concepts of local (linear) and global stability. Here, we show how systems displaying Hopf bifurcations show contrarian results for these two aspects of stability: Global stability is large close to the point where the system loses its stability altogether. We demonstrate this effect for an elementary model system, an anharmonic oscillator, and a realistic model of power system dynamics with delayed control. Detailed investigations of the bifurcation explain the seeming paradox in terms of the location of the attractors relative to the equilibrium.

Modelling, forecasting and overall understanding of the dynamics of the power grid and its frequency are essential for the safe operation of existing and future power grids. Much previous research was focused on large continental areas, while small systems, such as islands are less well-studied. These natural island systems are ideal testing environments for microgrid proposals and artificially islanded grid operation. In the present paper, we utilise measurements of the power grid frequency obtained in European islands: the Faroe Islands, Ireland, the Balearic Islands and Iceland and investigate how their frequency can be predicted, compared to the Nordic power system, acting as a reference. The Balearic Islands are found to be particularly deterministic and easy to predict in contrast to hard-to-predict Iceland. Furthermore, we show that typically 2–4 weeks of data are needed to improve prediction performance beyond simple benchmarks.

Power-grid systems constitute one of the most complex man-made spatially extended structures. These operate with strict operational bounds to ensure synchrony across the grid. This is particularly relevant for power-grid frequency, which operates strictly at 50 Hz (60 Hz). Nevertheless, small fluctuations around the mean frequency are present at very short time scales

The frequency constitutes a key state variable of electrical power grids. However, as the frequency is subject to several sources of fluctuations, ranging from renewable volatility to demand fluctuations and dispatch, it is strongly dynamic. Yet, the statistical and stochastic properties of the frequency fluctuation dynamics are far from fully understood. Here we analyze properties of power-grid frequency trajectories recorded from different synchronous regions. We highlight the non-Gaussian and still approximately Markovian nature of the frequency statistics. Furthermore, we find that the frequency displays significant fluctuations exactly at the time intervals of regulation and trading, confirming the need of having a regulatory and market design that respects the technical and dynamical constraints in future highly renewable power grids. Finally, employing a recently proposed synthetic model for the frequency dynamics, we combine our statistical and stochastic analysis and analyze in how far dynamically modeled frequency properties match the ones of real trajectories.

Atomic nuclei appearing in cosmic rays (CRs) are typically classified as primary or secondary. However, a better understanding of their origin and propagation properties is still necessary. We analyse the flux of primary (He, C, O) and secondary nuclei (Li, Be, B) detected with rigidity (momentum/charge) between 2 GV and 3 TV by the alpha magnetic spectrometer on the International Space Station. We show that q -exponential distribution functions, as motivated by generalized versions of statistical mechanics with temperature fluctuations, provide excellent fits for the measured flux of all nuclei considered. Primary and secondary fluxes reveal a universal dependence on kinetic energy per nucleon for which the underlying energy distribution functions are solely distinguished by their effective degrees of freedom. All given spectra are characterized by a universal mean temperature parameter ∼200 MeV which agrees with the Hagedorn temperature. Our analysis suggests that QCD scattering processes together with nonequilibrium temperature fluctuations imprint universally onto the measured CR spectra, and produce a similar shape of energy spectra as high energy collider experiments on the Earth.

Air pollution by nitrogen oxides (NO_{x}) is a major concern in large cities as it has severe adverse health effects. However, the statistical properties of air pollutants are not fully understood. Here, we use methods borrowed from nonequilibrium statistical mechanics to construct suitable superstatistical models for air pollution statistics. In particular, we analyze time series of nitritic oxide (NO) and nitrogen dioxide (NO_{2}) concentrations recorded at several locations throughout Greater London. We find that the probability distributions of concentrations have heavy tails and that the dynamics is well described by χ^{2} superstatistics for NO and inverse-χ^{2} superstatistics for NO_{2}. Our results can be used to give precise risk estimates of high-pollution situations and pave the way to mitigation strategies.

The robust operation of power transmission grids is essential for most of today’s technical infrastructure and our daily life. Adding renewable generation to power grids requires grid extensions and sophisticated control actions on different time scales to cope with short-term fluctuations and long-term power imbalance. Braess’ paradox constitutes a counterintuitive collective phenomenon that occurs if adding new transmission line capacity to a network increases loads on other lines, effectively reducing the system’s performance and potentially even entirely destabilizing its operating state. Combining simple analytical considerations with numerical investigations on a small sample network, we here study dynamical consequences of secondary control in AC power grid models. We demonstrate that sufficiently strong control not only implies dynamical stability of the system but may also cure Braess’ paradox. Our results highlight the importance of demand control in conjunction with the grid topology to ensure stable operation of the grid and reveal a new functional benefit of secondary control.

Stable operation of complex flow and transportation networks requires balanced supply and demand. For the operation of electric power grids—due to their increasing fraction of renewable energy sources—a pressing challenge is to fit the fluctuations in decentralized supply to the distributed and temporally varying demands. To achieve this goal, common smart grid concepts suggest to collect consumer demand data, centrally evaluate them given current supply and send price information back to customers for them to decide about usage. Besides restrictions regarding cyber security, privacy protection and large required investments, it remains unclear how such central smart grid options guarantee overall stability. Here we propose a Decentral Smart Grid Control, where the price is directly linked to the local grid frequency at each customer. The grid frequency provides all necessary information about the current power balance such that it is sufficient to match supply and demand without the need for a centralized IT infrastructure. We analyze the performance and the dynamical stability of the power grid with such a control system. Our results suggest that the proposed Decentral Smart Grid Control is feasible independent of effective measurement delays, if frequencies are averaged over sufficiently large time intervals.