Florian Steinke

Jieyu Chen, Tim Janke, Florian Steinke et al.

Ensemble weather forecasts based on multiple runs of numerical weather prediction models typically show systematic errors and require post-processing to obtain reliable forecasts. Accurately modeling multivariate dependencies is crucial in many practical applications, and various approaches to multivariate post-processing have been proposed where ensemble predictions are first post-processed separately in each margin and multivariate dependencies are then restored via copulas. These two-step methods share common key limitations, in particular the difficulty to include additional predictors in modeling the dependencies. We propose a novel multivariate post-processing method based on generative machine learning to address these challenges. In this new class of nonparametric data-driven distributional regression models, samples from the multivariate forecast distribution are directly obtained as output of a generative neural network. The generative model is trained by optimizing a proper scoring rule which measures the discrepancy between the generated and observed data, conditional on exogenous input variables. Our method does not require parametric assumptions on univariate distributions or multivariate dependencies and allows for incorporating arbitrary predictors. In two case studies on multivariate temperature and wind speed forecasting at weather stations over Germany, our generative model shows significant improvements over state-of-the-art methods and particularly improves the representation of spatial dependencies.

Kirill Kuroptev, Florian Steinke, Efthymios Karangelos

This paper examines defending the power grid against load-altering attacks using electric vehicle charging. It proposes to preventively segment the cyber infrastructure that charging station operators (CSOs) use to communicate with and control their charging stations, thereby limiting the impact of successful cyber-attacks. Using real German charging station data and a reconstructed transmission grid model, a threat analysis shows that without segmentation, the successful hack of just two CSOs can overload two transmission grid branches, exceeding the N-1 security margin and necessitating defense measures. A novel defense design problem is then formulated that minimizes the number of imposed segmentations while bounding the number of branch overloads under worst-case attacks. The resulting IP-MILP bi-level problem can be solved with an exact column and constraint generation algorithm and with heuristics for fast computation on large-scale instances. For the near-real-world Germany case, the applicability of the heuristics is demonstrated and validated under relevant load and dispatch scenarios. It is found that the simple scheme of segmenting CSOs evenly by their installed capacity leads to only 23% more segments compared to the heuristic optimization result, suggesting potential relevance as a regulatory measure.

Andreas Bott, Mario Beykirch, Florian Steinke

Thermal power flow (TPF) is an important task for various control purposes in 4 Th generation district heating grids with multiple decentral heat sources and meshed grid structures. Computing the TPF, i.e., determining the grid state consisting of temperatures, pressures, and mass flows for given supply and demand values, is classically done by solving the nonlinear heat grid equations, but can be sped up by orders of magnitude using learned models such as neural networks. We propose a novel, efficient scheme to generate a sufficiently large training data set covering relevant supply and demand values. Instead of sampling supply and demand values, our approach generates training examples from a proxy distribution over generator and consumer mass flows, omitting the iterations needed for solving the heat grid equations. The exact, but slightly different, training examples can be weighted to represent the original training distribution. We show with simulations for typical grid structures that the new approach can reduce training set generation times by two orders of magnitude compared to sampling supply and demand values directly, without loss of relevance for the training samples. Moreover, learning TPF with a training data set is shown to outperform sample-free, physics-aware training approaches significantly.

Andreas Bott, Tim Janke, Florian Steinke

Flexible district heating grids form an important part of future, low-carbon energy systems. We examine probabilistic state estimation in such grids, i.e., we aim to estimate the posterior probability distribution over all grid state variables such as pressures, temperatures, and mass flows conditional on measurements of a subset of these states. Since the posterior state distribution does not belong to a standard class of probability distributions, we use Markov Chain Monte Carlo (MCMC) sampling in the space of network heat exchanges and evaluate the samples in the grid state space to estimate the posterior. Converting the heat exchange samples into grid states by solving the non-linear grid equations makes this approach computationally burdensome. However, we propose to speed it up by employing a deep neural network that is trained to approximate the solution of the exact but slow non-linear solver. This novel approach is shown to deliver highly accurate posterior distributions both for classic tree-shaped as well as meshed heating grids, at significantly reduced computational costs that are acceptable for online control. Our state estimation approach thus enables tightening the safety margins for temperature and pressure control and thereby a more efficient grid operation.

Tim Janke, Mohamed Ghanmi, Florian Steinke

Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility especially in high dimensions, while commonly used non-parametric methods suffer from the curse of dimensionality. A popular remedy is to construct a tree-based hierarchy of conditional bivariate copulas. In this paper, we propose a flexible, yet conceptually simple alternative based on implicit generative neural networks. The key challenge is to ensure marginal uniformity of the estimated copula distribution. We achieve this by learning a multivariate latent distribution with unspecified marginals but the desired dependency structure. By applying the probability integral transform, we can then obtain samples from the high-dimensional copula distribution without relying on parametric assumptions or the need to find a suitable tree structure. Experiments on synthetic and real data from finance, physics, and image generation demonstrate the performance of this approach.

Tim Janke, Florian Steinke

The reliable estimation of forecast uncertainties is crucial for risk-sensitive optimal decision making. In this paper, we propose implicit generative ensemble post-processing, a novel framework for multivariate probabilistic electricity price forecasting. We use a likelihood-free implicit generative model based on an ensemble of point forecasting models to generate multivariate electricity price scenarios with a coherent dependency structure as a representation of the joint predictive distribution. Our ensemble post-processing method outperforms well-established model combination benchmarks. This is demonstrated on a data set from the German day-ahead market. As our method works on top of an ensemble of domain-specific expert models, it can readily be deployed to other forecasting tasks.