Search

Monitoring and modelling the power grid frequency is key to ensuring stability in the electrical power system. Many tools exist to investigate the detailed deterministic dynamics and especially the bulk behaviour of the frequency. However, far less attention has been paid to its stochastic properties, and there is a need for a cohesive framework that couples both short-time scale fluctuations and bulk behaviour. Moreover, commonly assumed uncorrelated stochastic noise is predominantly employed in modelling in energy systems. In this publication, we examine the stochastic properties of the Nordic Grid, focusing on the increments of the frequency recordings. We show that these increments follow non-Gaussian statistics and display spatial and temporal correlations. Furthermore, we report two different physical synchronisation phenomena: a very short timescale phase synchronisation (< 2 s) followed by a slightly larger timescale amplitude synchronisation (2 s–5 s). Overall, these results show that modelling of fluctuations in power systems should not be restricted to Gaussian white noise.

The design and operation of modern energy systems are heavily influenced by time-dependent and uncertain parameters, e.g., renewable electricity generation, load-demand, and electricity prices. These are typically represented by a set of discrete realizations known as scenarios. A popular scenario generation approach uses deep generative models (DGM) that allow scenario generation without prior assumptions about the data distribution. However, the validation of generated scenarios is difficult, and a comprehensive discussion about appropriate validation methods is currently lacking. To start this discussion, we provide a critical assessment of the currently used validation methods in the energy scenario generation literature. In particular, we assess validation methods based on probability density, auto-correlation, and power spectral density. Furthermore, we propose using the multifractal detrended fluctuation analysis (MFDFA) as an additional validation method for non-trivial features like peaks, bursts, and plateaus. As representative examples, we train generative adversarial networks (GANs), Wasserstein GANs (WGANs), and variational autoencoders (VAEs) on two renewable power generation time series (photovoltaic and wind from Germany in 2013 to 2015) and an intra-day electricity price time series form the European Energy Exchange in 2017 to 2019. We apply the four validation methods to both the historical and the generated data and discuss the interpretation of validation results as well as common mistakes, pitfalls, and limitations of the validation methods. Our assessment shows that no single method sufficiently characterizes a scenario but ideally validation should include multiple methods and be interpreted carefully in the context of scenarios over short time periods.

Inferring the network topology from the dynamics of interacting units constitutes a topical challenge that drives research on its theory and applications across physics, mathematics, biology, and engineering. Most current inference methods rely on time series data recorded from all dynamical variables in the system. In applications, often only some of these time series are accessible, while other units or variables of all units are hidden, i.e. inaccessible or unobserved. For instance, in AC power grids, frequency measurements often are easily available whereas determining the phase relations among the oscillatory units requires much more effort. Here, we propose a network inference method that allows to reconstruct the full network topology even if all units exhibit hidden variables. We illustrate the approach in terms of a basic AC power grid model with two variables per node, the local phase angle and the local instantaneous frequency. Based solely on frequency measurements, we infer the underlying network topology as well as the relative phases that are inaccessible to measurement. The presented method may be enhanced to include systems with more complex coupling functions and additional parameters such as losses in power grid models. These results may thus contribute towards developing and applying novel network inference approaches in engineering, biology and beyond.

As in many other nations, the Australian Government implemented monetary and fiscal policies in response to the COVID-19 pandemic to aid economic recovery. Among these policies were specific measures to assist first home buyers (FHBs) in entering the housing market. However, these unprecedented economic policies might have other direct and indirect implications on FHBs, which have yet to be thoroughly explored in the literature. To fill this gap, through a survey, we collected information via public and online mortgage broker platforms from 61 FHBs who successfully entered the housing market or were actively searching during the pandemic. The results found COVID-19 economic responses counterproductive for FHBs, pushing them to a more disadvantaged position due to an overheated property market. In addition, since the onset of the pandemic, property prices have risen significantly, exacerbating housing inequality as FHBs increasingly rely on intergenerational family support, take on more financial risk, and relocate to regional areas due to fear of missing out. The study highlights the need for macroeconomists and housing policymakers to consider these unintended consequences in formulating policies that minimise the adverse effects of economic stimulus measures.

The power grid frequency is the central observable in power system control, as it measures the balance of electrical supply and demand. A reliable frequency forecast can facilitate rapid control actions and may thus greatly improve power system stability. Here, we develop a weighted-nearest-neighbour (WNN) predictor to investigate how predictable the frequency trajectories are. Our forecasts for up to one hour are more precise than averaged daily profiles and could increase the efficiency of frequency control actions. Furthermore, we gain an increased understanding of the specific properties of different synchronous areas by interpreting the optimal prediction parameters (number of nearest neighbours, the prediction horizon, etc.) in terms of the physical system. Finally, prediction errors indicate the occurrence of exceptional external perturbations. Overall, we provide a diagnostics tool and an accurate predictor of the power grid frequency time series, allowing better understanding of the underlying dynamics.

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 operation and power-grid frequency. Problems raised by this ongoing transition are increasingly addressed by transdisciplinary research approaches, ranging from purely mathematical modelling to applied case studies. These approaches require a stochastic description of consumer behaviour, fluctuations by renewables, market rules, and how they influence the stability of the power-grid frequency. Here, we introduce an easy-to-use, data-driven, stochastic model for the power-grid frequency and demonstrate how it reproduces key characteristics of the observed statistics of the Continental European and British power grids. Using data analysis tools and a Fokker-Planck approach, we estimate parameters of our deterministic and stochastic model. We offer executable code and guidelines on how to use the model on any power grid for various mathematical or engineering applications.

Abstract By employing superstatistical methods and machine learning, we analyze time series data of water quality indicators for the River Thames (UK). The indicators analyzed include dissolved oxygen, temperature, electrical conductivity, pH, ammonium, turbidity, and rainfall, with a specific focus on the dynamics of dissolved oxygen. After detrending, the probability density functions of dissolved oxygen fluctuations exhibit heavy tails that are effectively modeled using q-Gaussian distributions. Our findings indicate that the multiplicative Empirical Mode Decomposition method stands out as the most effective detrending technique, yielding the highest log-likelihood in nearly all fittings. We also observe that the optimally fitted width parameter of the q-Gaussian shows a negative correlation with the distance to the sea, highlighting the influence of geographical factors on water quality dynamics. In the context of same-time prediction of dissolved oxygen, regression analysis incorporating various water quality indicators and temporal features identify the Light Gradient Boosting Machine as the best model. SHapley Additive exPlanations reveal that temperature, pH, and time of year play crucial roles in the predictions. Furthermore, we use the Transformer, a state-of-the-art machine learning model, to forecast dissolved oxygen concentrations. For long-term forecasting, the Informer model consistently delivers superior performance, achieving the lowest Mean Absolute Error (0.15) and Symmetric Mean Absolute Percentage Error (21.96%) with the 192 historical time steps that we used. This performance is attributed to the Informer’s ProbSparse self-attention mechanism, which allows it to capture long-range dependencies in time-series data more effectively than other machine learning models. It effectively recognizes the half-life cycle of dissolved oxygen, with particular attention to critical periods such as morning to early afternoon, late evening to early morning, and key intervals between the 16th and 26th quarter-hours of the previous half-day. Our findings provide valuable insights for policymakers involved in ecological health assessments, aiding in accurate predictions of river water quality and the maintenance of healthy aquatic ecosystems.

Abstract In the smart grid of the future, accurate load forecasts on the level of individual clients can help to balance supply and demand locally and to prevent grid outages. While the number of monitored clients will increase with the ongoing smart meter rollout, the amount of data per client will always be limited. We evaluate whether a Transformer load forecasting model benefits from a transfer learning strategy, where a global univariate model is trained on the load time series from multiple clients. In experiments with two datasets containing load time series from several hundred clients, we find that the global training strategy is superior to the multivariate and local training strategies used in related work. On average, the global training strategy results in 21.8% and 12.8% lower forecasting errors than the two other strategies, measured across forecasting horizons from one day to one month into the future. A comparison to linear models, multi-layer perceptrons and LSTMs shows that Transformers are effective for load forecasting when they are trained with the global training strategy.

Abstract The transition to renewable energy sources challenges the operation and stability of the electric power system. Wind and solar power generation are volatile and uncertain, and energy sources may be located far away from the centers of the load. High Voltage Direct Current (HVDC) lines enable long-distance power transmission at low losses, both within and between different synchronous power grids. HVDC interconnectors between different synchronous areas can be used to balance volatile generation by leveraging their fast control behavior, but rapid switching may also disturb the power balance. In this article, we analyze the interaction of HVDC interconnector operation and load-frequency control in different European power grids from operational data. We use explainable machine learning to disentangle the various influences affecting the two systems, identify the key influences, and quantify the interrelations in a consistent way. Our results reveal two different types of interaction: Market-based HVDC flows introduce deterministic frequency deviations and thus increase control needs. Control-based HVDC flows mitigate frequency deviations on one side as desired but generally disturb frequency on the other side. The analysis further provides quantitative estimates for the control laws and operation strategies of individual HVDC links, for which there is little public information. Furthermore, we quantify the importance of HVDC links for the frequency dynamics, which is particularly large in the British grid.

Electricity prices in liberalized markets are determined by the supply and demand for electric power, which are in turn driven by various external influences that vary strongly in time. In perfect competition, the merit order principle describes that dispatchable power plants enter the market in the order of their marginal costs to meet the residual load, i.e. the difference of load and renewable generation. Various market models are based on this principle when attempting to predict electricity prices, yet the principle is fraught with assumptions and simplifications and thus is limited in accurately predicting prices. In this article, we present an explainable machine learning model for the electricity prices on the German day-ahead market which foregoes of the aforementioned assumptions of the merit order principle. Our model is designed for an ex-post analysis of prices and builds on various external features. Using SHapley Additive exPlanation (SHAP) values we disentangle the role of the different features and quantify their importance from empiric data, and therein circumvent the limitations inherent to the merit order principle. We show that load, wind and solar generation are the central external features driving prices, as expected, wherein wind generation affects prices more than solar generation. Similarly, fuel prices also highly affect prices, and do so in a nontrivial manner. Moreover, large generation ramps are correlated with high prices due to the limited flexibility of nuclear and lignite plants. Overall, we offer a model that describes the influence of the main drivers of electricity prices in Germany, taking us a step beyond the limited merit order principle in explaining the drivers of electricity prices and their relation to each other.

Abstract Sustainable energy systems are characterised by an increased integration of renewable energy sources, which magnifies the fluctuations in energy supply. Methods to to cope with these magnified fluctuations, such as load shifting, typically require accurate short-term load forecasts. Although numerous machine learning models have been developed to improve short-term load forecasting (STLF), these models often require large amounts of training data. Unfortunately, such data is usually not available, for example, due to new users or privacy concerns. Therefore, obtaining accurate short-term load forecasts with little data is a major challenge. The present paper thus proposes the latent space-based forecast enhancer (LSFE), a method which combines transfer learning and data augmentation to enhance STLF when training data is limited. The LSFE first trains a generative model on source data similar to the target data before using the latent space data representation of the target data to generate seed noise. Finally, we use this seed noise to generate synthetic data, which we combine with real data to enhance STLF. We evaluate the LSFE on real-world electricity data by examining the influence of its components, analysing its influence on obtained forecasts, and comparing its performance to benchmark models. We show that the Latent Space-based Forecast Enhancer is generally capable of improving the forecast accuracy and thus helps to successfully meet the challenge of limited available training data.

Increasing the capacity of existing lines or adding new lines in power grids may, counterintuitively, reduce the system performance and promote blackouts. The authors propose an approach for prediction of edges that lower system performance and defining potential constrains for grid extensions.

In modern power grids, knowing the required electric power demand and its variations is necessary to balance demand and supply. The authors propose a data-driven approach to create high-resolution load profiles and characterize their fluctuations, based on recorded data of electricity consumption.

Abstract Human activities alter river water quality and quantity, with consequences for the ecosystems of urbanised rivers. Quantifying the role of human-induced drivers in controlling spatio-temporal patterns in water quality is critical to develop successful strategies for improving the ecological health of urban rivers. Here, we analyse high-frequency electrical conductivity and temperature data collected from the River Chess in South-East England during a Citizen Science project. Utilizing machine learning, we find that boosted trees outperform GAM and accurately describe water quality dynamics with less than 1% error. SHapley Additive exPlanations reveal the importance of and the (inter)dependencies between the individual variables, such as river level and Wastewater Treatment Works (WWTW) outflow. WWTW outflows give rise to diurnal variations in electrical conductivity, which are detectable throughout the year, and to an increase in average water temperature of 1 $$\rm{^o}C$$ o C in a 2 km reach downstream of the wastewater treatment works during low flows. Overall, we showcase how high-frequency water quality measurements initiated by a Citizen Science project, together with machine learning techniques, can help untangle key drivers of water quality dynamics in an urbanised chalk stream.

Abstract Air pollution is one of the leading causes of death globally, and continues to have a detrimental effect on our health. In light of these impacts, an extensive range of statistical modelling approaches has been devised in order to better understand air pollution statistics. However, the time-varying statistics of different types of air pollutants are far from being fully understood. The observed probability density functions (PDFs) of concentrations depend very much on the spatial location and on the pollutant substance. In this paper, we analyse a large variety of data from 3544 different European monitoring sites and show that the PDFs of nitric oxide (NO), nitrogen dioxide ( $$NO_2$$ N O 2 ) and particulate matter ( $$PM_{10}$$ P M 10 and $$PM_{2.5}$$ P M 2.5 ) concentrations generically exhibit heavy tails and are asymptotically well approximated by q-exponential distributions with a given width parameter $$\lambda$$ λ . We observe that the power-law parameter q and the width parameter $$\lambda$$ λ vary widely for the different spatial locations. For each substance, we find different patterns of parameter clouds in the $$(q, \lambda )$$ ( q , λ ) plane. These depend on the type of pollutants and on the environmental characteristics (urban/suburban/rural/traffic/industrial/background). This means the effective statistical physics description of air pollution exhibits a strong degree of spatial heterogeneity.

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.

Complex systems, such as the power grid, are essential for our daily lives. Many complex systems display multifractal behavior, correlated fluctuations and power laws. Whether the power-grid frequency, an indicator of the balance of supply and demand in the electricity grid, also displays such complexity remains a mostly open question. Within the present article, we utilize highly resolved measurements to quantify the properties of the power-grid frequency, making three key contributions: First, we demonstrate the existence of power laws in power-grid frequency measurements. Second, we show that below one second, the dynamics may fundamentally change, including a suddenly increasing power spectral density, emergence of multifractality and a change of correlation behavior. Third, we provide a simplified stochastic model involving positively correlated noise to reproduce the observed dynamics, possibly linked to frequency-dependent loads. Finally, we stress the need for high-quality measurements and discuss how we obtained the data analyzed here.

The operation of power systems is affected by diverse technical, economic, and social factors. Social behavior determines load patterns, electricity markets regulate the generation, and weather-dependent renewables introduce power fluctuations. Thus, power system dynamics must be regarded as a nonautonomous system whose parameters vary strongly with time. However, the external driving factors are usually only available on coarse scales and the actual dependencies of the dynamic system parameters are generally unknown. Here, we propose a physics-informed machine learning model that bridges the gap between large-scale drivers and short-term dynamics of the power system. Integrating stochastic differential equations and artificial neural networks, we construct a probabilistic model of the power grid frequency dynamics in continental Europe. Its probabilistic prediction outperforms the daily average profile, which is an important benchmark, on a time horizon of 15 min. Using the integrated model, we identify and explain the parameters of the dynamical system from the data, which reveal their strong time-dependence and their relation to external drivers such as wind power feed-in and fast generation ramps. Finally, we generate synthetic time series from the model, which successfully reproduce central characteristics of the grid frequency such as their heavy-tailed distribution. All in all, our work emphasizes the importance of modeling power system dynamics as a stochastic nonautonomous system with both intrinsic dynamics and external drivers.

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.

Abstract The aviation industry is of great importance for a globally connected economy. Customer satisfaction with airlines and airport performance is considerably influenced by how much flights are delayed. But how should the delay be quantified with thousands of flights for each airport and airline? Here, we present a statistical analysis of arrival delays at several UK airports between 2018 and 2020. We establish a procedure to compare both mean delay and extreme events among airlines and airports, identifying a power-law decay of large delays. Furthermore, we note drastic changes in plane delay statistics during the COVID-19 pandemic. Finally, we find that delays are described by a superposition of simple distributions, leading to a superstatistics.

Power grid frequencies mirror the state of the grid. Here, Rydin Gorjão et al. analyse measurements of power grid frequencies across areas and continents and uncover scaling laws of their fluctuations and spatio-temporal dynamics, which could aid the design, operation and control of power systems.

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.

Summary: Superstatistics is a general method from nonequilibrium statistical physics which has been applied to a variety of complex systems, ranging from hydrodynamic turbulence to traffic delays and air pollution dynamics. Here, we investigate water quality time series (such as dissolved oxygen concentrations and electrical conductivity) as measured in rivers and provide evidence that they exhibit superstatistical behavior. Our main example is time series as recorded in the River Chess in South East England. Specifically, we use seasonal detrending and empirical mode decomposition to separate trends from fluctuations for the measured data. With either detrending method, we observe heavy-tailed fluctuation distributions, which are well described by log-normal superstatistics for dissolved oxygen. Contrarily, we find a double peaked non-standard superstatistics for the electrical conductivity data, which we model using two combined χ2-distributions.

Communication networks and power grids may be subject to cascading failures which can lead to outages. Here the authors propose to investigate cascades using dynamical transients of electrical power grids, thereby identifying possible vulnerabilities that might remain undetected with any static approach.

Abstract  Although it is known that long cortical bone structurally alter their area moment of inertia with age related bone loss maintaining their bending strength, the incidence of fragility fractures associated with cortical thinning still prevails. We hypothesize that cortical thinning with aging increases the local buckling susceptibility under abnormal or eccentric loads, and initiates fracture. The paper presents a series of 3D geometrical model derived from CT scans of a human femoral neck used to simulate age-related bone loss. The purpose of the model is to predict the susceptibility of local buckling at the femoral neck in falls by elderly folks. Geometric three-dimensional models of femoral neck cortices were developed from 7 human cadaver femurs (4 female, 3 male, 52–68 years). Three age related femoral neck models were simulated by either reducing (young age-related model) or increasing (old age-related model) the outer cortical surfaces in the radial-direction, by 1-mm. The control model was the middle-age related model. The inner cortex diameter was also adjusted to equilibrate the compressive stresses, based on the load-profile of a single-legged stance. Based on the old age related model, two additional “fragile” models were simulated by reducing the compressive load profile by 10 and 20% changing the inner cortex diameter, respectively. Using these models for each specimen, the consequence of a fall on the greater trochanter was evaluated. The Finite Strip Method (FSM) was used to investigate the association between local buckling at the femoral neck and the load to failure. Under constant loading, buckling progressively reduced the load to failure with aging, as seen in 2/7 of the middle age (by 9–15%) and 5/7 of the old age (by 7–32%) related models. In the fragile models, a 51% reduction in the load to failure was noted. Structural adaptation to age-related bone loss might preserves the bending strength under physiologic loads, but cortical thinning effects the buckling ratio reaching a critical threshold that would make the bone susceptible to local buckling at the femoral neck increasing the risk of fracture in a fall. [ABSTRACT FROM AUTHOR]

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 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.

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.

The capsid proteins (CPs) of geminiviruses combine multiple functions for packaging the single-stranded viral genome, insect transmission and shuttling between the nucleus and the cytoplasm. African cassava mosaic virus (ACMV) CP was expressed in fission yeast, and purified by SDS gel electrophoresis. After tryptic digestion of this protein, mass spectrometry covered 85% of the amino acid sequence and detected three N-terminal phosphorylation sites (threonine 12, serines 25 and 62). Differential centrifugation of cell extracts separated the CP into two fractions, the supernatant and pellet. Upon isopycnic centrifugation of the supernatant, most of the CP accumulated at densities typical for free proteins, whereas the CP in the pellet fraction showed a partial binding to nucleic acids. Size-exclusion chromatography of the supernatant CP indicated high order complexes. In DNA binding assays, supernatant CP accelerated the migration of ssDNA in agarose gels, which is a first hint for particle formation. Correspondingly, CP shifted ssDNA to the expected densities of virus particles upon isopycnic centrifugation. Nevertheless, electron microscopy did not reveal any twin particles, which are characteristic for geminiviruses.

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.