arXiv subjects

Dirk Witthaut

Publications and source records attributed to Dirk Witthaut.

At least 19 recordsLinked to original sources

arXiv2026

Symmetry breaking in minimum dissipation networks

Natural and engineered supply networks exhibit universal structural patterns, such as the formation of loops, yet the principles governing optimal structures remain unclear. These patterns can be interpreted as solutions of optimization problems in which dissipation is minimized under a constraint on the available resources. Optimal networks break the symmetry of such a problem in two distinct ways: weakly, where the topology stays symmetric but the edge capacities do not, and strongly, altering the topology itself. Both scenarios are organized by the symmetry group of the optimization problem, which determines the pattern of capacities in the weakly broken state and may constrain the residual symmetry of the strongly broken one. Symmetric structures are favored at intermediate fluctuation levels, i.e., noise both induces and suppresses symmetry breaking. Here, we show that symmetry breaking, influenced by network meshing, resource constraints and fluctuations, is a generic organizing principle of optimal transport networks.

nlin.AO↗

arXiv2026

Low-rank corrections to a shared reference Jacobian for GPU-parallel AC $N\!-\!1$ contingency analysis

Contingency analysis repeatedly solves the power-flow equations under many single-element outages, an increasingly demanding workload as operating margins tighten and renewable variability grows. Graphics processing units (GPUs) are attractive for this task, but a change in topology alters the sparsity pattern of the Jacobian, preventing the uniform batched factorization on which efficient GPU solvers rely. This paper presents a GPU-parallel Newton--Raphson solver for $N\!-\!1$ contingency analysis that separates the change in operating state from the change in topology. A single reference Jacobian is inverted once and reused across all contingencies. Each topology change is expressed as a low-rank Woodbury correction, while the residual state-dependent perturbation is handled by an inner iterative solve, a truncated Neumann series or the biconjugate gradient stabilized method. We analyze the spectral radius and condition number of the resulting iteration matrices and show that the reference Jacobian is an effective preconditioner. On transmission-scale benchmarks, the method attains per-topology solve times competitive with an optimized 80-core central processing unit baseline, with the low-rank correction accounting for approximately 1--2\% of the workload. This makes GPU-parallel $N\!-\!1$ contingency analysis feasible at transmission scale without per-topology refactorization.

eess.SY↗

arXiv2026

Linear Approximations Provide Rigorous Conditions for Phase Locking in Oscillator Networks and Power Grids

Synchronization is a fundamental collective phenomenon in many natural and engineered networks. The stable operation of oscillator networks, such as electric power grids, requires phase locking with phase differences across edges below a given threshold. A central question is whether a given network supports such a state. In this contribution, we extend a convex optimization formulation of the nonlinear fixed point equations of the Kuramoto model, that also describe lossless power grids. Based on this formulation, we derive rigorous and tight bounds on the error introduced by an arbitrary approximation of the original model, in particular linear approximations. The bounds yield edge-wise regions of trust around the approximation, within which the true nonlinear solution must lie. They further provide sufficient and necessary conditions for phase locking under prescribed phase difference limits. Numerical experiments show that the bounds are tight over a broad range of parameters.

nlin.AO↗

arXiv2026

Understanding the European energy crisis through structural causal models

Natural gas supplies in Europe were disrupted and energy prices soared in the context of Russia's invasion of Ukraine. Electricity prices in France experienced the largest relative increase among European countries, even though the share of natural gas in the electricity mix is small compared to its neighbours. In this article, we demonstrate the importance of causal statistical methods and propose causal graphs to investigate the French and Spanish electricity markets and pinpoint key influencing factors on electricity prices and net exports. We demonstrate that a causal approach resolves paradoxical results of simple correlation studies and enables a quantitative analysis of indirect causal effects and what-if scenarios. We introduce a linear structural causal model as well as non-linear tree-based machine learning combined with Shapley Flow values. The models elucidate the interplay of gas prices and the unavailability of nuclear power plants during the energy crisis as the high unavailability made France dependent on imports.

stat.AP↗

arXiv2026

Graph Machine Learning: An Opportunity for Power Systems

Modern power systems face growing operational complexity driven by the integration of renewable energy sources, decentralization, and the need for real-time decision-making across a wide range of timescales. Addressing these challenges traditionally relies on model-based methods that, while accurate, can be too slow for operational demands. Machine learning (ML) has therefore emerged as a faster, data-driven alternative. As grid topology plays a central role in power system operation, graph machine learning (GML) methods offer a natural framework for incorporating topological dependencies as an inductive bias. We survey nearly 800 papers at the intersection of GML and power systems, covering forecasting, state estimation, optimization, control, fault diagnosis, and cybersecurity. Power systems constitute an unusually rich benchmark setting for GML, as they combine hard physical constraints, multi-scale dynamics, safety-critical requirements, and scarce labeled data within a single, well-defined domain. Conversely, power systems can benefit from utilizing GML to complement classical solvers, as GML provide scalable, topology-aware approximations with promising generalization and computational efficiency. We identify open challenges, including limited real-world deployment and the need for interpretable models in safety-critical settings. Despite the rapidly growing number of publications, standardized benchmarks and open datasets remain scarce, leaving many results difficult to reproduce and undermining the long-term scientific credibility of the field. We further derive a structured requirements catalog for ML-ready power grid benchmarks, intended to guide future dataset development and improve reproducibility across studies. We call on the community to prioritize dedicated benchmark studies and the release of open datasets and models.

cs.LG↗

arXiv2026

A graph theoretic view on small signal stability of inverter-based power grids

Dynamic grid stability is traditionally ensured with synchronous generators. Modern grids rely substantially more on inverter-based resources, which require grid-forming control to guarantee adequate system-wide synchronization and stability. Small-signal stability has granted various centralized and decentralized stability certificates - but these have primarily been limited to sufficient criteria only. In this work, we construct a necessary and sufficient small-signal stability criterion for lossless inverter-based power grids with arbitrary topology. We show that asymptotic stability is equivalent to the positive definiteness of a single matrix that combines network topology, operating point, and effective droop gains. We derive graph-theoretic stability criteria based on an augmented cone graph and show that the contribution of graph cycles is typically small, as illustrated for three IEEE test cases. The resulting framework yields decentralized stability criteria, quantifies the conservatism introduced by decentralization, and may support the development of future grid codes.

eess.SY↗

arXiv2026

Transmission Topology Optimization using accelerated MapElites

Transmission Topology Optimization has great potential to improve efficiency and flexibility of grid operations through non-costly switching actions, but previous approaches struggle with runtime performance and scalability. In this work, we present an optimization approach that leverages GPU acceleration to speed up computations. In a genetic algorithm setting, topologies are randomly mutated and evaluated in parallel for multiple optimization criteria. Combined with a fully GPU-native DC loadflow solver, there is no CPU-GPU data transfer required in the DC optimization loop. Using a variant of the illumination algorithm MapElites, we efficiently generate a set of diverse candidate solutions on the pareto front. Together with an importing and AC validation step, we present an end-to-end optimization solution that runs in under 15 minutes. The approach is currently under evaluation by operational planning operators in two European TSOs. We furthermore open-source our code at github.com/eliagroup/ToOp.

eess.SY↗

arXiv2026

Phase locking and multistability in the topological Kuramoto model on cell complexes

Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension within simplicial and cell complexes. We introduce the topological nonlinear Kirchhoff conditions to characterize all phase-locked states of the topological Kuramoto model. These states are organized by winding numbers associated with generalized independent cycles, which quantify how phases wind around these cycles. Using rings, Platonic solids, and regular simplices as illustrative examples, we uncover a universal rule: boundaries must have at least five elements for multistability to arise. We further find that independent winding numbers associated with lower- and higher-dimensional boundaries generate cascades of multistability across dimensions. These results show how the topology and boundary structure of cell complexes influence phase locking and multistability, and provide a general framework for collective dynamics on cell complexes.

nlin.AO↗

arXiv2026

Cascading Failures and Critical Infrastructures in Future Renewable European Power Systems

The world's power systems are undergoing a rapid transformation, shifting away from carbon-intensive power generation to renewable sources. As a result, electricity is being transported over ever longer distances, while the intrinsic system inertia provided by thermal power plants decreases. Together, these developments raise the probability of cascading line failures and reduce the stability of the system after a system split. In this article, we assess the risk of cascading failures and system splits in the European power grid for different carbon reduction scenarios. We analyze the most likely and most dangerous splits, and identify critical transmission infrastructures and we discuss potential countermeasures that can address the problem of cascades. Our results show that while the risks of splits causing power failures rises with decarbonization, it can be mitigated cost efficiently.

physics.soc-ph↗

arXiv2026

Voltage-sensitive distribution factors for contingency analysis and topology optimization

Topology optimization is a promising approach for mitigating congestion and managing changing grid conditions, but it is computationally challenging and requires approximations. Conventional distribution factors like PTDFs and LODFs, based on DC power flow, fail to capture voltage variations, reactive power, and losses, thereby limiting their use in detailed optimization tasks such as busbar splitting. This paper introduces generalized distribution factors derived from a voltage-sensitive linearization of the full AC power flow equations. The proposed formulation accurately reflects reactive power flows, Ohmic losses, and voltage deviations while remaining computationally efficient. We derive and evaluate generalized PTDFs, LODFs, and topology modification factors using matrix identities. We discuss potential applications including voltage-aware N-1 security analysis and topology optimization with a focus on busbar splitting. Numerical experiments demonstrate close agreement with full AC solutions, significantly outperforming the traditional DC approximation.

math.OC↗

arXiv2026

Impact of Market Reforms on Deterministic Frequency Deviations in the European Power Grid

Deterministic frequency deviations (DFDs) are systematic and predictable excursions of grid frequency that arise from synchronized generation ramps induced by electricity market scheduling. In this paper, we analyze the impact of the European day-ahead market reform of 1 October 2025, which replaced hourly trading blocks with quarter-hourly blocks, on DFDs in the Central European synchronous area. Using publicly available frequency measurements, we compare periods before and after the reform based on daily frequency profiles, indicators characterizing frequency deviations, principal component analysis, Fourier-based functional data analysis, and power spectral density analysis. We show that the reform substantially reduces characteristic hourly frequency deviations and suppresses dominant spectral components at hourly and half-hourly time scales, while quarter-hourly structures gain relative importance. While the likelihood of large frequency deviations decreases overall, reductions for extreme events are less clear and depend on the metric used. Our results demonstrate that market design reforms can effectively mitigate systematic frequency deviations, but also highlight that complementary technical and regulatory measures are required to further reduce large frequency excursions in low-inertia power systems.

physics.soc-ph↗

arXiv2025

Towards Quantum Algorithms for the Optimization of Spanning Trees: The Power Distribution Grids Use Case

Optimizing the topology of networks is an important challenge across engineering disciplines. In energy systems, network reconfiguration can substantially reduce losses and costs and thus support the energy transition. Unfortunately, many related optimization problems are NP hard, restricting practical applications. In this article, we address the problem of minimizing losses in radial networks, a problem that routinely arises in distribution grid operation. We show that even the computation of approximate solutions is computationally hard and propose quantum optimization as a promising alternative. We derive two quantum algorithmic primitives based on the Quantum Alternating Operator Ansatz (QAOA) that differ in the sampling of network topologies: a tailored sampling of radial topologies and simple sampling with penalty terms to suppress non-radial topologies. We show how to apply these algorithmic primitives to distribution grid reconfiguration and quantify the necessary quantum resources.

eess.SY↗

arXiv2025

Cyber-Physical Systems on the Megawatt Scale: The impact of battery control on grid frequency stability

Electric power systems are undergoing fundamental change. The shift to inverter-based generation challenges frequency stability, while growing digitalisation heightens vulnerability to errors and attacks. Here we identify an emerging risk at the intersection of cyber-physical coupling and control system design. We show that grid frequency time series worldwide exhibit a persistent one-minute oscillatory pattern, whose origin has remained largely unexplained. We trace this pattern back to the energy management systems of battery electric storage systems and demonstrate that the pattern amplitude has increased substantially in the Nordic and British grids. We argue that this effect is a potential burden for stability in future grids with low inertia and an increasing penetration with batteries and smart devices, though it can be mitigated by a revision of battery control algorithms.

eess.SY↗

arXiv2025

Discontinuous stochastic forcing in Greenland ice core data

Paleoclimate proxy records from Greenland ice cores, archiving e.g. $δ^{18}$O as a proxy for surface temperature, show that sudden climatic shifts called Dansgaard-Oeschger events (DO) occurred repeatedly during the last glacial interval. They comprised substantial warming of the Arctic region from cold to milder conditions. Concomitant abrupt changes in the dust concentrations of the same ice cores suggest that sudden reorganisations of the hemispheric-scale atmospheric circulation have accompanied the warming events. Genuine bistability of the North Atlantic climate system is commonly hypothesised to explain the existence of stadial (cold) and interstadial (milder) periods in Greenland. However, the physical mechanisms that drove abrupt transitions from the stadial to the interstadial state, and more gradual yet still abrupt reverse transitions, remain debated. Here, we conduct a one-dimensional data-driven analysis of the Greenland temperature and atmospheric circulation proxies under the purview of stochastic processes. We take the Kramers-Moyal equation to estimate each proxy's drift and diffusion terms within a Markovian model framework. We then assess noise contributions beyond Gaussian white noise. The resulting stochastic differential equation (SDE) models feature a monostable drift for the Greenland temperature proxy and a bistable one for the atmospheric circulation proxy. Indicators of discontinuity in stochastic processes suggest to include higher-order terms of the Kramers-Moyal equation when modelling the Greenland temperature proxy's evolution. This constitutes a qualitative difference in the characteristics of the two time series, which should be further investigated from the standpoint of climate dynamics.

physics.ao-ph↗

arXiv2025

Accelerated DC loadflow solver for topology optimization

We present a massively parallel solver that accelerates DC loadflow computations for power grid topology optimization tasks. Our approach leverages low-rank updates of the Power Transfer Distribution Factors (PTDFs) to represent substation splits, line outages, and reconfigurations without ever refactorizing the system. Furthermore, we implement the core routines on Graphics Processing Units (GPUs), thereby exploiting their high-throughput architecture for linear algebra. A two-level decomposition separates changes in branch topology from changes in nodal injections, enabling additional speed-ups by an in-the-loop brute force search over injection variations at minimal additional cost. We demonstrate billion-loadflow-per-second performance on power grids of varying sizes in workload settings which are typical for gradient-free topology optimization such as Reinforcement Learning or Quality Diversity methods. While adopting the DC approximation sacrifices some accuracy and prohibits the computation of voltage magnitudes, we show that this sacrifice unlocks new scales of computational feasibility, offering a powerful tool for large-scale grid planning and operational topology optimization.

eess.SY↗

arXiv2024

Unified algebraic deviation of distribution factors in linear power flow

Distribution factors are indispensable tools in the design and analysis of power transmission grids. Recently, they received a renewed interest in the field of topology optimization, leading to the definition of bus merge and bus split distribution factors. In this article, we introduce a unified derivation of the most relevant distribution factors based on matrix algebraic manipulations. This approach facilitates the generalization to more complex grid modification, in particular simultaneous switching events or bus splits.

math.OC↗

arXiv2024

Multivariate Scenario Generation of Day-Ahead Electricity Prices using Normalizing Flows

Trading on the day-ahead electricity markets requires accurate information about the realization of electricity prices and the uncertainty attached to the predictions. Deriving accurate forecasting models presents a difficult task due to the day-ahead price's non-stationarity resulting from changing market conditions, e.g., due to changes resulting from the energy crisis in 2021. We present a probabilistic forecasting approach for day-ahead electricity prices using the fully data-driven deep generative model called normalizing flow. Our modeling approach generates full-day scenarios of day-ahead electricity prices based on conditional features such as residual load forecasts. Furthermore, we propose extended feature sets of prior realizations and a periodic retraining scheme that allows the normalizing flow to adapt to the changing conditions of modern electricity markets. Our results highlight that the normalizing flow generates high-quality scenarios that reproduce the true price distribution and yield accurate forecasts. Additionally, our analysis highlights how our improvements towards adaptations in changing regimes allow the normalizing flow to adapt to changing market conditions and enable continued sampling of high-quality day-ahead price scenarios.

cs.LG↗

arXiv2024

Synchronized states of power grids and oscillator networks by convex optimization

Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of synchronization is of utmost practical importance. In this article, we propose a novel approach to compute and analyze the stable stationary states of a power grid or an oscillator network in terms of a convex optimization problem. This approach allows to systematically compute \emph{all} stable states where the phase difference across an edge does not exceed $π/2$.Furthermore, the optimization formulation allows to rigorously establish certain properties of synchronized states and to bound the error in the widely used linear power flow approximation.

eess.SY↗