Validation Methods for Energy Time Series Scenarios From Deep Generative Models

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.Comment: 20 pages, 8 figures, 2 table

Non-standard power grid frequency statistics in Asia, Australia, and Europe

The power-grid frequency reflects the balance between electricity supply and demand. Measuring the frequency and its variations allows monitoring of the power balance in the system and, thus, the grid stability. In addition, gaining insight into the characteristics of frequency variations and defining precise evaluation metrics for these variations enables accurate assessment of the performance of forecasts and synthetic models of the power-grid frequency. Previous work was limited to a few geographical regions and did not quantify the observed effects. In this 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 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.Comment: 7 pages; 7 figure

Understanding power-grid-frequency dynamics with stochastic modelling: The influence of the electricity market

The ongoing energy transition transforms the power system by introducing additional fluctuations via intermittent renewable energy generation To evaluate the various proposed strategies of implementation of renewable energy generation and the impact of market design on the power grid’s stability, a solid understanding of the power grid dynamics, specifically its frequency, is necessary. A pure empirical study on existing power grids is limited due to their small number, limited available data and high costs of implementing control and market schemes in real grids. Our model allows predictions of the frequency statistics for diverse power grids and ultimately enables us to quantify the impact of control proposals and market designs

Rigorous stability criteria on the third‐order model for synchronous generators

Electrical power-grid system stability is essential to provide robust power to allconsumers. The models for electrical-power transmission for synchronous generatorsprovide an exact description of power flow and stability requirements for moretraditional power grids with mechanical generators. Higher-order models can describe thevoltage and rotor-angle with great accuracy, but can only be tackled computationally dueto the dimensionality of the equations and the size of the network. Two main aspects ofemploying there models are the sheer dependency of reductions, as the assumption oflossless lines of the power grid, and the physical existence of generators with inertia. Wehave obtained strict mathematical criteria for the stability of the dynamics of the powergrid in both synchronous machines and inverter-based models, without any assumptionson line losses or the topological structure of the network. These criteria entail a greaterdetail on the fundamental criteria required to safely operate power grids, in particular notdiscarding the influence of dissipative effects, as well as providing a direct correlation ofsystems composed of inverter power systems as well as mechanical generators. Theseresults are particularly important for the ongoing transitions into a more renewable-basedpower system, incorporating a growing number of zero-inertial generators in the powergrid

Stochastic data-driven model of the European power-grid frequency

The energy system is rapidly changing to accommodate the increasing number of renewable generators and the general transition towards a more sustainable future. Simultaneously, new business models and market designs are proposed to stabilise the power grid and its 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. We offer guidelines on how to use the model on any power grid for various mathematical or engineering applications