Florian Steinke

Ablation studies regarding the architecture and hyperparameter choices of the conditional generative model and some results not shown in the paper are provided.

With the ongoing implementation of new climate targets, power grids must accommodate a growing number of distributed energy resources (DERs), electric vehicle (EV) home chargers, and heat pumps. To this end, infrastructure upgrades are often necessary, especially at the low-voltage (LV) level. Designing these upgrades may be, however, difficult when lacking a digital and up-todate model of the underlying power grids. This work introduces a novel two-stage Bayesian approach for inferring a probability distribution of power flow-ready grid models for a specified region of interest using available system measurements. The first stage involves integrating power measurements at the secondary substation level to adapt a prior probability distribution of assignments of end-consumers to the secondary substations. In the second stage, available voltage measurements at the end-consumer level are incorporated to estimate the probability distribution of power flow-ready digital models with LV feeders generated using the assignments from the first stage. In a case study investigating a projected scenario of the LV power grid in Schutterwald, Germany, we demonstrate that integrating available system measurements provides conclusive evidence when assessing the voltage criticality of a specified grid segment. Moreover, we show that generated power flow-ready grid models with higher probabilities exhibit similarities to the benchmark grid model from which these measurements originate.

This work examines the value of probabilistic forecasts for optimizing the interaction of local energy systems with electricity markets, namely bid or schedule optimization by the responsible market agent. We aim to understand what type and quality of forecast is needed in the optimization task. First, we theoretically examine typical stochastic programming formulations to find which forecast type, namely expected values, marginal distributions, or joint distributions, is required to achieve the mathematically best possible result. We find that only few specific problem settings require full multivariate joint forecast distributions. In many other common cases, marginal distributions or expected values only are sufficient. Second, we experimentally analyze the influence of forecast errors on the performance of the stochastic program's solution for two important variations of the scheduling problem and compare this to common …

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.

Flexible AC transmission systems (FACTSs) can maximize capacity utilization under time-varying grid usage patterns by actively controlling the power flow of the transmission lines, e.g., with phase-shifting transformers (PST). In this paper, we propose an algorithm to determine the minimum number of PSTs and their location such that the grid can operate robustly for any realization of the (active) power set points from a known, continuous uncertainty set. As we show in our experiments, only considering a few extreme grid scenarios cannot provide this guarantee. The proposed algorithm considers the trade-offs between PST placement and operational decisions, such as PST control and redispatch. By minimizing the worst-case redispatch cost, it yields two affine linear control policies for these as a byproduct. Power flow is modeled as a constrained linear system, and the control design and actuator minimization tasks are formulated as a mixed-integer linear program (MILP). We also design a greedy algorithm, whose optimal value differs less than 20% from the MILP solution while being one to two orders of magnitude faster to compute. The proposed algorithm is evaluated for a small demonstrative 3-bus example and the IEEE 39 bus test system.

Optimization-based design tools for energy systems often require a large set of parameter assumptions, e.g., about technology efficiencies and costs or the temporal availability of variable renewable energies. Understanding the influence of all these parameters on the computed energy system design via direct sensitivity analysis is not easy for human decision-makers, since they may become overloaded by the multitude of possible results. We thus propose transferring an approach from explaining complex neural networks, so-called locally interpretable model-agnostic explanations (LIME), to this related problem. Specifically, we use variations of a small number of interpretable, high-level parameter features and sparse linear regression to obtain the most important local explanations for a selected design quantity. For a small bottom-up optimization model of a grid-connected building with photovoltaics, we derive intuitive explanations for the optimal battery capacity in terms of different cloud characteristics. For a larger application, namely a national model of the German energy transition until 2050, we relate path dependencies of the electrification of the heating and transport sector to the correlation measures between renewables and thermal loads. Compared to direct sensitivity analysis, the derived explanations are more compact and robust and thus more interpretable for human decision-makers.

We consider optimal routing of data packets in communication networks featuring time-variable flow rates and bandwidth limitations. Taking into account recent programmability developments in communication systems, we propose a two-level control scheme: routers with a programmable data plane implement local proportional control policies that forward the incoming data to different available output interfaces at line rate. The local controllers’ parameters are adapted periodically on a slower time scale by a logically centralized (software-defined) network controller running a global coordination algorithm that keeps the routing feasible and optimal with respect to a network metric, such as the average packet delay. A robust optimization approach is selected to handle traffic variations in-between global adaptation steps. The outcome is a non-convex Quadratically Constrained Quadratic Program (QCQP), for which …

The rising penetration of distributed renewable energy sources (RES), electric vehicle (EV) home-chargers, and heat pumps in power distribution systems can lead to violations of the grid operating conditions. To design suitable grid expansion measures for this challenge, grid planners need a good understanding of the existing infrastructure. Trustworthy, readily usable grid models are, however, often not available. This holds especially for distribution grids at the low-voltage level. In this work, a framework is proposed to generate a probability distribution over an ensemble of different, possible grid topologies for a given area of interest. This probabilistic approach allows to explicitly account for the uncertainty implied by the scarcity of the available information. In a case study with EV home-chargers, it is demonstrated how the proposed ensemble-based framework leads to a robust, uncertainty-aware interpretation …

For linear optimization problems with a parametric objective, so-called parametric linear programs (PLP), we show that the optimal decision values are, under few technical restrictions, unimodal functions of the parameter, at least in the two-degrees-of-freedom case. Assuming that the parameter is random and follows a known probability distribution, this allows for an efficient algorithm to determe the quantiles of linear combinations of the optimal decisions. The novel results are demonstrated with probabilistic economic dispatch. For an example setup with uncertain fuel costs, quantiles of the resulting inter-regional power flows are computed. The approach is compared against Monte Carlo and piecewise computation techniques, proving significantly reduced computation times for the novel procedure. This holds especially when the feasible set is complex and/or extreme quantiles are desired. This work is limited to problems with two effective degrees of freedom and a one-dimensional uncertainty. Future extensions to higher dimensions could yield a key tool for the analysis of probabilistic PLPs and, specifically, risk management in energy systems.

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 …

The increasing number of IoT devices in power systems introduces the threat of load altering attacks on power grids using high wattage appliances. Sophisticated adversaries can launch such coordinated attacks by exploiting weaknesses in the IT system used to monitor and control the devices as well as the supply chains of the involved software systems. This paper proposes an ontology-based directed attack graph to model the possible attack paths targeting the devices. Based on this model, we determine the optimal attack strategies of an adversary, assuming that the attacker has complete knowledge of the system and its defenses. We evaluate the resulting attack strategies and quantify the influence of different defense strategies in a case study. The simulation results suggest the high efficiency of the Zero Trust security paradigm, which aims to minimize attack transition probabilities. In our study, this measure …

Linearized power flow with line flow and voltage constraints can be modeled as a system of linear inequalities depending on the power injections. When some injections are controlled by the grid operator while others are determined exogenously, robust control aims at determining grid operator's actions under imperfect system observability such that the grid state is feasible for all possible realizations of the exogenous actions. It was shown how to design and analyze such admissible control policies efficiently for the subclass of affine control laws, but this paper shows that there are important cases that require more general control policies. We show that, for the constrained linear power flow setting, general admissible control policies can always be chosen as piecewise affine (PWA) mappings. The PWA mapping can be explicitly characterized offline or control actions can be computed online by solving an …

A long-lasting, large-scale power blackout has a huge impact on the infrastructure of public life, as well as on critical infrastructure including electricity and water supply. At the same time, it can be observed that the share of renewable energies, and thus the possibility of self-sufficiency, has increased enormously in recent years. This contribution focuses on the question to what extend citizens are willing to share their electricity resources in order to make their city more resilient. In reference to Ostrom's concept of club or common goods, it can be shown if and how the private good of citizen's electricity resources can be transformed into a club or even a common good. Drawing on survey data from the city of Darmstadt we investigated the willingness to share electricity and to participate in participatory formats to enhance urban resilience.

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 …

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 …

In this work, a local multi-modal energy market is introduced to couple district heating and electric systems. In the course of the ongoing decarbonization of energy systems, electric systems have to integrate more and more volatile renewable energies, whereas in thermal systems, the demand for sustainable heat generation is continuously increasing. Market-based coordination of local thermal-electric energy systems can help to alleviate these challenges. In this work, an adequate representation of conversion assets, e.g., heat pumps, is achieved by introducing novel coupling orders in the market. These enable an explicit coupling of heat and electricity, and thus cross-energy load-shifts. In addition, a new type of storage orders is introduced to offer flexibility options by energy storage systems in the local energy system. The benefits of the market scheme are demonstrated for a day ahead cycle of an exemplary …

Water networks as critical infrastructures typically feature emergency electricity generators for bridging short power blackouts. We propose to combine these black start capable generators with available distributed energy resources (DERs) in the power grid, often photovoltaic generation, to jointly restore both the electricity and the water grid in the case of emergencies. This is mutually beneficial for both notworks since common grid-following inverters of DERs cannot supply power without a grid-forming nucleus. We model both grids as a coupled graph and formulate a stochastic mixed-integer linear program to determine optimal switch placement and/or optimal switching sequences jointly for both networks. Limited fuel and power availabilities, grid-forming constraints, storages, and an even distribution of available resources are considered. By minimizing the number of switching devices and switching events we …

This article introduces the problem of performance guarantee design for hybrid power plants (HPPs) with renewable generation. To solve it we propose a novel framework for the determination of performance guarantee levels under weather and load uncertainty. The framework is intended as a decision support tool for HPP solution providers during contract negotiations with owners, where they have to strike a balance between competitive bidding and possible contractual penalties. It is formulated as a stochastic risk-constrained optimization problem, which maximizes guarantee values subject to the risk preferences of the solution provider. HPP performance variability is included into the framework via detailed plant operation simulations. Furthermore, it allows to condition the guarantee levels on the stochastic availability of renewable resources and loads. We demonstrate the application of the framework with the …

A method and device which operates to record and evaluate an output of electrical energy of a hybrid power plant, wherein, in accordance with time and/or load, at least one expected generable and usable energy contribution resulting from the utilization of renewable energy sources and one expected energy contribution resulting from the utilization of convention energy carriers are recorded with different tariffs.

During crises where both communication networks and the electricity grid break down, restoring each individual infrastructure for disaster relief becomes generally infeasible. To tackle this challenge, we propose a disaster management solution using mobile ad-hoc networks (MANETs) formed by unmanned aerial vehicles (UAVs), offering a promising solution for emergency response. Apart from establishing emergency communications for rescue teams, UAV-enabled MANETs can also enable the formation of electrical microgrids based on distributed energy resources (DER) to locally restore the electric power. We determine the optimal locations and the number of UAVs for this purpose, taking the UAVs’ needs for repeated recharging into account. The problem is formulated on a discrete grid of potential places as a mixed-integer linear program (MILP) and solved via an accelerated feasibility query algorithm (FQA …