A collection of power-grid-frequency related articles can be found here. We start with the main articles that lead to this power-grid frequency database, as well as a collection of other related research publications and websites, some of which use the data presented here.
Main Publications leading to this database, please include citations when using the data presented here
Open data base analysis of scaling and spatio-temporal properties of power grid frequencies
L. Rydin Gorjão, R. Jumar, H. Maass, V. Hagenmeyer, J. Kruse, M. Timme, C. Beck, D. Witthaut, B. Schäfer
Nature Communications 11, 6362 (2020) [article] [preprint]
Abstract
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. Here, we analyse an open data base of measurements of electric power grid frequencies across 17 locations in 12 synchronous areas on three continents. The power grid frequency is of particular interest, as it indicates the balance of supply and demand and carries information on deterministic, stochastic, and control influences. We perform a broad analysis of the recorded data, compare different synchronous areas and validate a previously conjectured scaling law. Furthermore, we show how fluctuations change from local independent oscillations to a homogeneous bulk behaviour. Overall, the presented open data base and analyses may constitute a step towards more shared, collaborative energy research.
Power grid frequency data base
R. Jumar, H. Maaß, B. Schäfer, L. Rydin Gorjão, V. Hagenmeyer
arXiv:2006.01771, 2020 [preprint]
Abstract
The transformation of the electrical energy system due to the increasing infeed from renewable energy sources has attracted much attention in diverse research communities. Novel approaches for grid control, grid modeling, and grid architectures are widely proposed. However, data from actual power system operation are rarely available but are critically necessary to analyze real-world scenarios or to evaluate models. In the present paper, we introduce a precisely time-stamped data set comprising power grid frequency measurements from twelve independent synchronous areas of different sizes in one-second resolution. Furthermore, the data includes a synchronized measurement of the frequency within the Continental European synchronous area with measurement points in Portugal, Germany, and Turkey, maximizing the geographical span. Finally, we provide excerpts of the underlying raw data. Data were collected using a self-developed Phasor-Measurement-Unit(PMU)-like device, the Electrical Data Recorder (EDR), connected mostly to conventional low-voltage power outlets.
Statistical analysis and modelling of the power-grid frequency
Nonstandard power grid frequency statistics across continents
X Wen, M Anvari, L Rydin Gorjão, GC Yalcin, V Hagenmeyer, B Schäfer Scientific Reports 15 (1), 38470 Link
Abstract
Power-grid frequency reflects the balance between electricity supply and demand in a power system. Measuring the frequency and its variations allows monitoring of the power balance in the system and, thus, frequency grid stability. Gaining insight into the characteristics of frequency variations and defining precise evaluation metrics for these variations enable better assessment of the performance of forecasts and synthetic models of the power-grid frequency. Previous work on the power grid frequency analysis was limited to a few geographical regions and did not quantify the observed effects. In the present contribution, we analyze and quantify the statistical and stochastic properties of self-recorded power-grid frequency data from various synchronous areas in Asia, Australia, and Europe at a sampling resolution of one second. Revealing non-standard statistics of both empirical and synthetic frequency data, we effectively constrain the space of possible (stochastic) power-grid frequency models and share a range of analysis tools to benchmark any model or characterize empirical data. Furthermore, we emphasize the need to analyze data from a large range of synchronous areas to obtain generally applicable models.
Nonlinear Stochastic Modeling of the South Korean Power Grid Frequency Dynamics
U Oberhofer, X Wen, J Lee, H Kim, V Hagenmeyer, B Schäfer 2025 IEEE Kiel PowerTech, 1-6, 2025, Link
Abstract
The mitigation of climate change and the associated restructuring of the energy system is one of the most relevant challenges in society at the moment. A key aspect of the transformation of energy systems is the shift from the use of conventional energy sources to renewable ones. This leads to a more economical use of fossil resources and reduces the environmental impact, but also poses challenges. The increasing amount of renewable energy sources in power grids has a major impact on the grid structure and its stability. Ensuring stability under these changing conditions is a challenge, in particular since power grids and their dynamics differ from region to region. While several studies investigated US or European power grids, Asian grids, such as the South Korean power grid, have been less of a focus. In this article, we analyze in particular the nonlinearity and the bimodality of the frequency time series, and perform a correlation analysis. Further, we use stochastic Fokker-Planck models to create synthetic frequency time series both in a linear and nonlinear manner. We examine the synthetic time series modeled in this way and compare their statistical properties with the empirical data. Thereby, we demonstrate how simple stochastic differential equations can provide a simplified model for the grid frequency, and observe that a model with nonlinear dynamics approximates the empirical data better than a purely linear one.
Non-linear, bivariate stochastic modelling of power-grid frequency applied to islands
U Oberhofer, LR Gorjao, GC Yalcin, O Kamps, V Hagenmeyer, B Schäfer 2023 IEEE Belgrade PowerTech, 2023 Link
Abstract
Mitigating climate change requires a transition away from fossil fuels towards renewable energy. As a result, power generation becomes more volatile and options for microgrids and islanded power-grid operation are being broadly discussed. Therefore, studying the power grids of physical islands, as a model for islanded microgrids, is of particular interest when it comes to enhancing our understanding of power-grid stability. In the present paper, we investigate the statistical properties of the power-grid frequency of three island systems: Iceland, Ireland, and the Balearic Islands. We utilise a Fokker-Planck approach to construct stochastic differential equations that describe market activities, control, and noise acting on power-grid dynamics. Using the obtained parameters we create synthetic time series of the frequency dynamics. Our main contribution is to propose two extensions of stochastic power-grid frequency models and showcase the applicability of these new models to non-Gaussian statistics, as encountered in islands.
Initial analysis of the impact of the Ukrainian power grid synchronization with Continental Europe
PC Böttcher, LR Gorjão, C Beck, R Jumar, H Maass, V Hagenmeyer, B. Schäfer Energy Advances, 2023 Link
Abstract
When Russia invaded Ukraine on the 24th of February 2022, this led to many acts of solidarity with Ukraine, including support for its electricity system. Just 20 days after the invasion started, the Ukrainian and Moldovan power grids were synchronized to the Continental European power grid to provide stability to these grids. Here, we present an initial analysis of how this synchronization affected the statistics of the power grid frequency and cross-border flows of electric power within Continental Europe. We observe faster inter-area oscillations, an increase in fluctuations and changes in the cross-border flows in and out of Ukraine and surrounding countries as an effect of the synchronization with Continental Europe. Overall these changes are small such that the now connected system can be considered as stable as before the synchronization.
Data-Driven Model of the Power-Grid Frequency Dynamics
L. Rydin Gorjão, M. Anvari, H. Kantz, C. Beck, D. Witthaut, M. Timme, B. Schäfer
IEEE Access 8, pp. 43082─43097, 2020, [article] [preprint]
Abstract
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.
Stochastic properties of the frequency dynamics in real and synthetic power grids
M. Anvari, L. Rydin Gorjão, M. Timme, D. Witthaut, B. Schäfer, H. Kantz
Phys. Rev. Research 2, 013339, 2020,
[article]
[preprint]
Abstract
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 analyse 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. Further, 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 analyse in how far dynamically modelled frequency properties match the ones of real trajectories.
Intra-area oscillations
Spectral estimation of low-frequency oscillations in the Nordic grid using ambient synchrophasor data under the presence of forced oscillations.
L. Vanfretti, S. Bengtsson, V. S. Peric, J. O. Gjerde
2013 IEEE Grenoble Conference, pp. 1-6, 2013,
[article]
Abstract
Spectral analysis applied to synchrophasor data can provide valuable information about lightly damped low-frequency modes in power systems. This paper demonstrates application of two non-parametric spectral estimators focusing on mode frequency estimation. The first one is the well-known Welch spectral estimator whereas the application of Multitaper method is proposed here. In addition, the paper discusses mode estimator tuning procedures and the estimators' performances in the presence of “forced” oscillations. The validity of the proposed application of the non-parametric estimators and tuning procedures is verified through both simulated data and PMU data originating from the high-voltage grid of the Nordic power system. Special attention is given to the analysis of the behaviour of different low frequency modes present in the Nordic grid, including that of forced oscillations.
Applications in Machine Learning
Probabilistic and Explainable Machine Learning for Tabular Power Grid Data
A Nikoltchovska, S Pütz, X Li, V Hagenmeyer, B Schäfer Proceedings of the 16th ACM International Conference on Future and Sustainable Energy Systems, 2025 Link
Abstract
Modeling power grid frequency stability is becoming increasingly challenging due to the integration of renewable energy sources. Machine learning approaches, such as gradient-boosted trees, have shown promise in analyzing the complex characteristics of power systems. However, these models are inherently deterministic, providing only point estimates. Meanwhile, the task of capturing the underlying uncertainty, particularly through (deep) probabilistic models, is still underexplored, despite its potential to better account for the stochastic nature of power grid dynamics. In this paper, we first compare the performance of TabNet, a deep learning architecture designed for tabular data, to XGBoost for modeling power grid frequency stability. We then present TabNetProba: a probabilistic extension of TabNet, that enables uncertainty-aware estimates comparable to NGBoost. Using these (trained) models, we leverage explainable artificial intelligence (XAI) to analyze the drivers influencing grid stability and identify sources of uncertainty in two major European synchronous areas: Continental Europe and the Nordic region. Our results demonstrate that TabNetProba achieves competitive performance with state-of-the-art methods while providing reliable uncertainty estimates. We find that load and conventional generation ramps, as well as forecast errors, are the key quantities for modeling and explaining mean stability indicators in both synchronous areas. In Continental Europe, renewable generation emerges as a key factor in explaining model uncertainty, while in the Nordic region, load and generation features dominate uncertainty estimation, allowing for more reliable and interpretable stability estimates for modern power systems.
Physics-informed machine learning for power grid frequency modeling
J Kruse, E Cramer, B Schäfer, D Witthaut PRX energy 2 (4), 043003, 2023 Link
Abstract
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.
Forecasting power grid frequency trajectories with structured state space models
S Pütz, B Schäfer Companion Proceedings of the 14th ACM International Conference on Future and Sustainable Energy Systems, 2023 Link
Abstract
Improving our ability to model, predict, and understand power system dynamics is becoming increasingly important as we face the challenges of transitioning to a carbon-neutral energy system. The power grid frequency is central to power system control as it is the primary observable for balancing generation and demand on short time scales. By facilitating frequency control actions, accurate prediction of grid frequency can improve system stability. In recent years, promising new deep learning techniques for time series forecasting tasks have emerged. Here, we explore the application of structured state space models (S4) to high-resolution power system frequency time series. S4 models have previously demonstrated good performance for long-term dependence tasks, but how useful are they for high-resolution energy time series?
Predicting the power grid frequency of European islands
T Lund Onsaker, HS Nygård, D Gomila, P Colet, R Mikut, R Jumar, H Maass, U Kühnapfel, V hagenmeyer, B Schäfer Journal of Physics: Complexity 4 (1), 015012, 2023 Link
Abstract
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.
Predictability of Power Grid Frequency
J. Kruse, B. Schäfer, D. Witthaut
arXiv:2004.09259, 2020 [preprint]
Abstract
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-neighbor (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 neighbors, 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.
Estimation of Electromechanical Oscillations
Application of Ambient Analysis Techniques for the Estimation of Electromechanical Oscillations from Measured PMU Data in Four Different Power Systems
L. Vanfretti, L. Dosiek, J. W. Pierre, D. Trudnowski, J. H. Chow, R. García-Valle, U. Aliyu
European Transactions on Electrical Power, 21(4), 1640–1656, 2010 [article]
Abstract
The application of advanced signal processing techniques to power system measurement data for the estimation of dynamic properties has been a research subject for over two decades. Several techniques have been applied to transient (or ringdown) data, ambient data, and to probing data. Some of these methodologies have been included in off-line analysis software, and are now being incorporated into software tools used in control rooms for monitoring the near real-time behavior of power system dynamics. In this paper we illustrate the practical application of some ambient analysis methods for electromechanical mode estimation in different power systems. We apply these techniques to phasor measurement unit (PMU) data from stored archives of several hours originating from the US Eastern Interconnection, the Western Electricity Coordinating Council, the Nordic Power System, and time-synchronized Frequency Disturbance Recorder (FDR) data from Nigeria. It is shown that available signal processing tools are readily applicable for analysis of different power systems, regardless of their specific dynamic characteristics. The discussions and results in this paper are of value to power system operators and planners as they provide information of the applicability of these techniques via readily available signal processing tools, and in addition, it is shown how to critically analyze the results obtained with these methods.