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

Data-driven model of the power-grid frequency 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

Open data base 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. Here, we analyse an open database 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 database and analyses constitute a step towards more shared, collaborative energy research

Mechanisms underlying skeletal muscle insulin resistance induced by fatty acids: importance of the mitochondrial function

Insulin resistance condition is associated to the development of several syndromes, such as obesity, type 2 diabetes mellitus and metabolic syndrome. Although the factors linking insulin resistance to these syndromes are not precisely defined yet, evidence suggests that the elevated plasma free fatty acid (FFA) level plays an important role in the development of skeletal muscle insulin resistance. Accordantly, in vivo and in vitro exposure of skeletal muscle and myocytes to physiological concentrations of saturated fatty acids is associated with insulin resistance condition. Several mechanisms have been postulated to account for fatty acids-induced muscle insulin resistance, including Randle cycle, oxidative stress, inflammation and mitochondrial dysfunction. Here we reviewed experimental evidence supporting the involvement of each of these propositions in the development of skeletal muscle insulin resistance induced by saturated fatty acids and propose an integrative model placing mitochondrial dysfunction as an important and common factor to the other mechanisms

Effects of DHA- Rich n-3 Fatty Acid Supplementation on Gene Expression in Blood Mononuclear Leukocytes: The OmegAD Study

Background: Dietary fish oil, rich in n-3 fatty acids (n-3 FAs), e. g. docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), regulate inflammatory reactions by various mechanisms, e. g. gene activation. However, the effects of long-term treatment with DHA and EPA in humans, using genome wide techniques, are poorly described. Hence, our aim was to determine the effects of 6 mo of dietary supplementation with an n-3 FA preparation rich in DHA on global gene expression in peripheral blood mononuclear cells. Methods and Findings: In the present study, blood samples were obtained from a subgroup of 16 patients originating from the randomized double-blind, placebo-controlled OmegAD study, where 174 Alzheimer disease (AD) patients received daily either 1.7 g of DHA and 0.6 g EPA or placebo for 6 months. In blood samples obtained from 11 patients receiving n-3 FA and five placebo, expressions of approximately 8000 genes were assessed by gene array. Significant changes were confirmed by real-time PCR. At 6 months, the n-3 FAs group displayed significant rises of DHA and EPA plasma concentrations, as well as up-and down-regulation of nine and ten genes, respectively, was noticed. Many of these genes are involved in inflammation regulation and neurodegeneration, e. g. CD63, MAN2A1, CASP4, LOC399491, NAIP, and SORL1 and in ubiqutination processes, e. g. ANAPC5 and UBE2V1. Down-regulations of ANAPC5 and RHOB correlated to increases of plasma DHA and EPA levels. Conclusions: We suggest that 6 months of dietary n-3 FA supplementatio