arXiv subjects

Florian Steinke

Publications and source records attributed to Florian Steinke.

16 recordsLinked to original sources

arXiv2026

Global Optimization of Flexible District Heating Networks

District heating networks are a central tool to achieve low-carbon heat supplies. In this realm, they face the challenge of dealing with increasingly heterogeneous, partially time-varying renewable sources, thermal storage, and meshed topologies. This paper examines global optimization of the operation of such district heating networks over multiple time steps, based on a stationary, yet realistical nonlinear network model. To accelerate the solution performance of a spatial branch-and-bound algorithm for one time step, the following new methodological ingredients are introduced: exclusion of cyclic flow, symmetry exploitation between supply and return networks, reduction of temperature mixing constraints, novel primal heuristics and branching rules. The proposed methods are evaluated on a set of generated and real-world benchmark network instances with cycles and several suppliers. On the generated benchmark instances, using these methods more than doubles the number of solved instances and more than halves the runtime. For the real-world benchmark instances, the resulting algorithm produces solutions with guaranteed quality in reasonable run time. For multiple time steps that are coupled by a storage, a time decomposition approach is investigated. Under assumptions that are reasonable in practice, this approach is shown to yield an optimal solution. On a small example network, this decomposition is able to compute optimal solutions in less than a second, while solving the complete time-coupled problem is not possible within one hour.

math.OC↗

arXiv2026

Defending the power grid by segmenting the EV charging cyber infrastructure

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.

eess.SY↗

arXiv2024

Solving bilevel problems with products of upper- and lower-level variables

Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with linear upper and lower-level problems. This paper addresses a specific type of bilevel programming problem where the upper-level is linear, and the lower level includes bilinear terms involving product of variables from both levels. We propose a new iterative algorithm that addresses this specific class of bilevel problems by penalizing the duality gap and linearizing the bilinear terms. The effectiveness of the algorithm is argued and demonstrated through a numerical example.

math.OC↗

arXiv2024

Predictions and Decision Making for Resilient Intelligent Sustainable Energy Systems

Future energy systems are subject to various uncertain influences. As resilient systems they should maintain a constantly high operational performance whatever happens. We explore different levels and time scales of decision making in energy systems, highlighting different uncertainty sources that are relevant in different domains. We discuss how the uncertainties can be represented and how one can react to them. The article closes by summarizing, which uncertainties are already well examined and which ones still need further scientific inquiry to obtain resilient energy systems.

eess.SY↗

arXiv2024

Efficient Training of Learning-Based Thermal Power Flow for 4th Generation District Heating Grids

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.

cs.LG↗

arXiv2024

Generative machine learning methods for multivariate ensemble post-processing

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.

physics.ao-ph↗

arXiv2023

DER Pricing Power in the Presence of Multi-Location Consumers with Load Migration Capabilities

Renewable distributed energy resources (DERs) have the potential to provide multi-location electricity consumers (MLECs) with electricity at prices lower than those offered by the grid using behind-the-meter advantages. This study examines the pricing power of such DER owners in a local environment with few competitors and how it depends on the MLEC's ability to migrate a portion of the load between locations. We simulate a dynamic game between an MLEC and the local DER owners, where the MLEC is modeled as a cost-minimizer and the DER owners as strategic profit maximizers. We show that, when the MLEC is inflexible, the DER owners' optimal behavior is to offer their electricity close to maximal prices, that is, at the grid price level. However, when the MLEC can migrate a fraction of the load to the other locations, the prices offered by the DER owners quickly decrease to the minimum level, that is, the DERs' grid feed-in tariffs quickly decrease to a lower level, depending on the load migration capability.

cs.GT↗

arXiv2023

Deep Learning-enabled MCMC for Probabilistic State Estimation in District Heating Grids

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.

cs.LG↗

arXiv2022

Bidding and Scheduling in Energy Markets: Which Probabilistic Forecast Do We Need?

Probabilistic forecasting in combination with stochastic programming is a key tool for handling the growing uncertainties in future energy systems. Derived from a general stochastic programming formulation for the optimal scheduling and bidding in energy markets we examine several common special instances containing uncertain loads, energy prices, and variable renewable energies. We analyze for each setup whether only an expected value forecast, marginal or bivariate predictive distributions, or the full joint predictive distribution is required. For market schedule optimization, we find that expected price forecasts are sufficient in almost all cases, while the marginal distributions of renewable energy production and demand are often required. For bidding curve optimization, pairwise or full joint distributions are necessary except for specific cases. This work helps practitioners choose the simplest type of forecast that can still achieve the best theoretically possible result for their problem and researchers to focus on the most relevant instances.

eess.SY↗

arXiv2021

Probabilistic Forecast Combination for Anomaly Detection in Building Heat Load Time Series

We consider the problem of automated anomaly detection for building level heat load time series. An anomaly detection model must be applicable to a diverse group of buildings and provide robust results on heat load time series with low signal-to-noise ratios, several seasonalities, and significant exogenous effects. We propose to employ a probabilistic forecast combination approach based on an ensemble of deterministic forecasts in an anomaly detection scheme that classifies observed values based on their probability under a predictive distribution. We show empirically that forecast based anomaly detection provides improved accuracy when employing a forecast combination approach.

stat.AP↗

arXiv2021

Implicit Generative Copulas

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.

stat.ML↗

arXiv2021

Measuring LTI System Resilience against Adversarial Disturbances based on Efficient Generalized Eigenvalue Computations

Resilient systems are able to recover quickly and easily from disturbed system states that might result from hazardous events or malicious attacks. In this paper a novel resilience metric for linear time invariant systems is proposed: the minimum control energy required to disturb the system is set into relation to the minimum control energy needed to recover. This definition extends known disturbance rejection metrics considering random effects to account for adversarial disturbances. The worst-case disturbance and the related resilience index can be computed efficiently via solving a generalized eigenvalue problem that depends on the controllability Gramians of the control and disturbance inputs. The novel metric allows improving system resilience by optimizing the restorative control structure or by hardening the system against specific attack options. The new approach is demonstrated for a coupled mechanical system.

eess.SY↗

arXiv2020

Probabilistic multivariate electricity price forecasting using implicit generative ensemble post-processing

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.

stat.AP↗

arXiv2020

On the minimal set of controllers and sensors for linear power flow

We consider a linear power flow model with interval-bounded nodal power injections and limited line power flows. We determine the minimal number of power injections to control based on a minimal set of measurements, such that the overall system is feasible for all assignments of the non-controlled power injections. For the important case where the possible measurements are the nodal power injections, we show that the problem can be solved efficiently as a mixed-integer linear program (MILP). When also line power flows are considered as potential measurements, we derive an iterative, greedy algorithm that provides a feasible, but potentially conservative solution. We apply the developed algorithms to both a small microgrid and a modified version of the IEEE 118 bus test power system. We show that in both cases a sparse solution in terms of the number of required controllers and measurements can be obtained. Moreover, the number of required measurements can be reduced significantly if line flow measurements are considered additionally to nodal power injections.

eess.SY↗

arXiv2019

Modeling Time-dependent CO$_2$ Intensities in Multi-modal Energy Systems with Storage

CO$_2$ emission reduction and increasing volatile renewable energy generation mandate stronger energy sector coupling and the use of energy storage. In such multi-modal energy systems, it is challenging to determine the effect of an individual player's consumption pattern onto overall CO$_2$ emissions. This, however, is often important to evaluate the suitability of local CO$_2$ reduction measures. Due to renewables' volatility, the traditional approach of using annual average CO$_2$ intensities per energy form is no longer accurate, but the time of consumption should be considered. Moreover, CO$_2$ intensities are highly coupled over time and different energy forms due to sector coupling and energy storage. We introduce and compare two novel methods for computing time-dependent CO$_2$ intensities, that address different objectives: the first method determines CO$_2$ intensities of the energy system as is. The second method analyzes how overall CO$_2$ emissions would change in response to infinitesimal demand changes. Given a digital twin of the energy system in form of a linear program, we show how to compute these sensitivities very efficiently. We present the results of both methods for two simulated test energy systems and discuss their different implications.

eess.SP↗

arXiv2017

Can Distribution Grids Significantly Contribute to Transmission Grids' Voltage Management?

Power generation in Germany is currently transitioning from a system based on large, central, thermal power plants to one that heavily relies on small, decentral, mostly renewable power generators. This development poses the question how transmission grids' reactive power demand for voltage management, covered by central power plants today, can be supplied in the future. In this work, we estimate the future technical potential of such an approach for the whole of Germany. For a 100% renewable electricity scenario we set the possible reactive power supply in comparison with the reactive power requirements that are needed to realize the simulated future transmission grid power flows. Since an exact calculation of distribution grids' reactive power potential is difficult due to the unavailability of detailed grid models on such scale, we optimistically estimate the potential by assuming a scaled, averaged distribution grid model connected to each of the transmission grid nodes. We find that for all except a few transmission grid nodes, the required reactive power can be fully supplied from the modeled distribution grids. This implies that - even if our estimate is overly optimistic - distributed reactive power provisioning will be a technical solution for many future reactive power challenges.

physics.app-ph↗