arXiv subjects

Yannick Werner

Publications and source records attributed to Yannick Werner.

18 recordsLinked to original sources

arXiv2026

Scenario Reduction for Two-Stage Stochastic Mixed-Integer Programs

Two-stage stochastic mixed-integer programs are important tools for decision-making under uncertainty. Representing the uncertainty with many scenarios, however, can make them challenging to solve. Scenario reduction addresses this by finding a distribution supported on fewer scenarios that still yields similar optimal first-stage decisions. In this paper, we revisit the classical scenario reduction theory based on distances between probability distributions and the optimal mass transportation problem. The transportation problem's cost function captures scenario similarity and is central to the effectiveness of scenario reduction. We then review and compare various transportation cost functions from the literature and propose a new one. Using the Forward Selection Algorithm, we prove that our proposed cost function selects the best possible scenario from a given sample on the first draw with respect to the relative approximation error. To reduce the computational cost of evaluating this cost function, we further propose a hybrid algorithm with a scenario pre-selection phase. We assess solution quality and computational complexity on the two-stage stochastic unit commitment problem for small 24-bus and large 300-bus case studies. With only around five scenarios, the proposed cost function approximates the full-distribution optimum to within roughly 2.1% and 0.4% error for the small and large cases, respectively. In contrast, prevalent cost functions often need 25 scenarios or more to achieve that solution quality. The hybrid algorithm achieves similar solution quality while reducing wall-clock time by a factor of 18 and work (per Gurobi solver) by a factor of 66 on the large case study.

math.OC↗

arXiv2026

Towards time-variant scenario reduction for energy system optimization modeling under uncertainty

Stochastic programming has become a popular tool for supporting decision-making under uncertainty in the long-term planning of energy systems. Existing scenario reduction methods, however, are naive about the long-term temporal nature of scenarios, which limits their efficiency in reducing model size. In this paper, we overcome this inefficiency by proposing a novel time-variant scenario reduction framework that explicitly allows for varying scenario aggregations over time. As a result, scenario probabilities become time-variant, enabling not only the accurate capture of scenario realizations but also their probabilities at the time steps that drive investment decisions. This substantially increases flexibility compared to traditional time-invariant methods, which we demonstrate on a two-stage stochastic generation expansion planning problem with uncertain renewable power production.

math.OC↗

arXiv2026

Modelling the Correlation Structure of Uncertain Input Parameters for Energy System Optimization

Statistical dependence among uncertain input parameters in stochastic energy system optimization models is often ignored, even though this can substantially bias outcomes. To address this gap, we are developing a comprehensive framework for characterizing, modelling, and benchmarking statistical dependence. In this work, we present a copula-based workflow to identify, characterize, and model linear and monotonic correlation structures between input parameters, representing the first development step towards this framework. We demonstrate our workflow using solar generation, day-ahead electricity prices, and electricity demand data in Austria between 2019 and 2025. Our results show substantial linear and monotonic dependence between these variables, and that this dependence is well captured by the copula-based approach. Finally, building on this scalable foundation, we highlight key levers for next steps towards the full framework, including time-dependent and higher-dimensional dependence modelling.

math.OC↗

arXiv2026

Temperature-Aware Heat Pump Modeling for Large-Scale Energy System Optimization

Heat pumps are expected to dominate the heating sector, substantially increasing peak electricity demand. At the same time, building thermal inertia enables operational strategies, providing temporal flexibility in heat pump operation and short-term demand response. However, this dynamic behavior is not yet represented in large-scale energy system optimization models. To address this gap, we present an innovative formulation of building thermal inertia. The resulting temperature variable is integrated into a novel conic temperature-aware heat pump efficiency formulation, enabling a more precise emulation of smart control strategies. In a case study of the European energy system, we show that the approach captures operational heating flexibility while remaining computationally efficient. The results indicate substantial untapped flexibility potential, enabling up to a 22% reduction in heating-related electricity costs. This potential can be realized through a suitable energy market design that incentivizes coordinated heat pump control, individually or via aggregators.

eess.SY↗

arXiv2026

Voltage-Aware Grid Aggregation: Expanding the European High-Voltage Network

Energy system optimization models are indispensable for planning the European energy transition. Yet their applicability is constrained by the fundamental trade-off between spatial detail and computational tractability. Modelers often tackle this by spatially aggregating electricity networks. Existing methods, however, neglect differences in voltage levels, reducing them to a single level and thereby overlooking the critical role of transformers in expansion planning. Therefore, we propose a novel voltage-aware network partitioning and aggregation methodology that preserves individual voltage levels and transformers. We demonstrate the effectiveness of this approach and compare it against a voltage-unaware grid aggregation by solving a network expansion problem for a European case study using PyPSA. Our findings show that the proposed methodology preserves up to 70% of the transformer expansion costs in the aggregated model compared to the full grid model, thereby significantly improving the accuracy of investment decisions for transformers in the aggregated grid.

math.OC↗

arXiv2026

NPAP: Network Partitioning and Aggregation Package for Python

NPAP (Network Partitioning and Aggregation Package) is an open-source Python library for reducing the spatial complexity of network graphs. Built on NetworkX, it provides an accessible standalone package designed to be readily integrated with other software and frameworks. Instead of treating the spatial reduction process as a single action, NPAP explicitly splits it into two distinct steps: partitioning, which assigns vertices (nodes) to groups (clusters), and aggregation, which reduces the network based on a given assignment. NPAP's strategy pattern architecture allows users to employ and register custom partitioning and aggregation strategies seamlessly without modifying the core code. Currently, NPAP provides 13 different partitioning strategies and two pre-defined aggregation profiles. Although initially developed with a focus on power systems, its architecture is general-purpose and applicable to any network graph.

cs.SI↗

arXiv2026

QGas: Interactive Gas Infrastructure Toolkit

Gas infrastructure datasets are essential inputs for energy system planning to support strategic decision-making toward decarbonization. However, relevant data are typically scattered across heterogeneous sources, including geospatial datasets, image-based infrastructure plans, and tabular data, making it complex, time-consuming, and error-prone to create topology-consistent network representations with existing tools.This paper presents QGas, an interactive toolkit for visualizing, creating, and collaboratively extending georeferenced gas infrastructure datasets. QGas integrates GIS-based geometry editing with topology-preserving graph operations in a unified web-based environment, enabling users to digitize infrastructure plans, edit network elements, manage attributes, and perform topology-consistent modifications while maintaining a georeferenced representation of the system. The toolkit is implemented using a modular architecture based on Python, JavaScript, and the Leaflet mapping library. An illustrative example demonstrates its application in extending a natural gas dataset to include hydrogen and CO2 infrastructure, highlighting QGas's capability to support the preparation of consistent multi-carrier gas infrastructure datasets for energy system planning.

eess.SY↗

arXiv2026

Simplification Ad Absurdum? Revisiting Gas Flow Modeling for Integrated Energy System Planning

This paper analyzes the implications of simplified pipeline gas flow models for integrated energy system planning. A case study of an integrated power-hydrogen expansion planning problem shows that simplifying pressure-flow relationships and gas dynamics can lead to expansion plans that incur substantial regret when evaluated under a more realistic dynamic gas flow model -- due to suboptimal system expansion, operation, and non-supplied hydrogen. Numerical experiments show that planning under the highly simplified transport and transport-linepack models -- commonly used in expansion studies -- can result in regret exceeding several thousand percent and yield expansion plans that lack robustness across demand levels. Planning under steady-state conditions partially mitigates these effects, but still leaves significant cost-reduction potential untapped compared to dynamic planning due to neglected linepack flexibility. Developing efficient solution algorithms for the dynamic model is a promising direction for future research.

eess.SY↗

arXiv2026

Mapping Austria's Natural Gas and Hydrogen Infrastructure Plans

This paper presents a comprehensive, spatially disaggregated dataset of Austria's natural gas and hydrogen infrastructure towards 2040. The dataset covers the complete gas transmission and distribution networks down to the medium-pressure level and integrates hydrogen expansion plans from the Austrian Gas Grid Management. Transmission infrastructure is reconstructed from ENTSOG maps, converted into a topologically consistent graph representation, and enriched with technical attributes through automated spatial matching with open-source datasets such as OpenStreetMap and Global Energy Monitor. Distribution networks and infrastructure modifications are implemented using QGas, a newly developed GIS-based tool for graph-based infrastructure manipulation. To enable forward-looking energy system analyses, the dataset explicitly represents the stage-wise transition from natural gas to hydrogen infrastructure within a single dataset. Repurposed and newly constructed hydrogen pipelines are integrated within a unified network topology using node splitting and time dependent connector elements, enabling consistent modeling of parallel natural gas and hydrogen operation over time. The resulting dataset provides a detailed representation of Austria's gas and hydrogen infrastructure, including 586 natural gas pipeline segments (5000 km), 113 repurposed segments (1250 km), and 39 newly constructed hydrogen segments (820 km), connecting 720 nodes. Moreover, it includes a comprehensive set of gas demands, biogas production facilities, storage units, electrolyzers, and compressor elements, making it directly applicable for energy system optimization models.

math.OC↗

arXiv2025

Scenario Reduction for the Two-Stage Stochastic Unit Commitment Problem

The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but challenges the solution process. One way to overcome this is by using scenario reduction methods, which aim at finding a distribution supported on fewer scenarios, but leading to similar optimal first-stage decisions. In this paper, we recap the classical scenario reduction theory based on the distance of probability distributions and the optimal mass transportation problem. We then review and compare various formulations of the underlying cost function of the latter used in the literature. Using the Forward Selection Algorithm, we show that a specific formulation of the cost function can be proven to select the best possible scenario from a given sample on the first draw with respect to the Relative Approximation Error. We demonstrate this result and compare the quality of the approximation as well as the computational performance of the different cost functions using a modified version of the IEEE RTS 24-Bus System. In many cases, we find that the optimal solution of the two-stage stochastic unit commitment problem with 200 scenarios can be approximated with around 2% scenarios when using this cost function.

math.OC↗

arXiv2025

On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators

We investigate the capabilities of Quantum Generative Adversarial Networks (QGANs) in image generations tasks. Our analysis centers on fully quantum implementations of both the generator and discriminator. Through extensive numerical testing of current main architectures, we find that QGANs struggle to generalize across datasets, converging on merely the average representation of the training data. When the output of the generator is a pure-state, we analytically derive a lower bound for the discriminator quality given by the fidelity between the pure-state output of the generator and the target data distribution, thereby providing a theoretical explanation for the limitations observed in current models. Our findings reveal fundamental challenges in the generalization capabilities of existing quantum generative models. While our analysis focuses on QGANs, the results carry broader implications for the performance of related quantum generative models.

quant-ph↗

arXiv2025

QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks

Kolmogorov Arnold Networks (KANs), built upon the Kolmogorov Arnold representation theorem (KAR), have demonstrated promising capabilities in expressing complex functions with fewer neurons. This is achieved by implementing learnable parameters on the edges instead of on the nodes, unlike traditional networks such as Multi-Layer Perceptrons (MLPs). However, KANs potential in quantum machine learning has not yet been well explored. In this work, we present an implementation of these KAN architectures in both hybrid and fully quantum forms using a Quantum Circuit Born Machine (QCBM). We adapt the KAN transfer using pre-trained residual functions, thereby exploiting the representational power of parametrized quantum circuits. In the hybrid model we combine classical KAN components with quantum subroutines, while the fully quantum version the entire architecture of the residual function is translated to a quantum model. We demonstrate the feasibility, interpretability and performance of the proposed Quantum KAN (QuKAN) architecture.

quant-ph↗

arXiv2025

Congestion-Sensitive Grid Aggregation for DC Optimal Power Flow

The vast spatial dimension of modern interconnected electricity grids challenges the tractability of the DC optimal power flow problem. Grid aggregation methods try to overcome this challenge by reducing the number of network elements. Many existing methods use Locational Marginal Prices as a distance metric to cluster nodes. In this paper, we show that prevalent methods adopting this distance metric fail to adequately capture the impact of individual lines when there is more than one line congested. This leads to suboptimal outcomes for the optimization of the aggregated model. To overcome those issues, we propose two methods based on the novel Network Congestion Price metric, which preserves the impact of nodal power injections on individual line congestions. The proposed methods are compared to several existing aggregation methods based on Locational Marginal Prices. We demonstrate all methods on adapted versions of the IEEE RTS 24- and 300-Bus systems. We show that the proposed methods outperform existing approaches both in terms of objective function value error and maximum line limit violation, while exhibiting faster node clustering. We conclude that aggregation methods based on the novel Network Congestion Price metric are better at preserving the essential physical characteristics of the network topology in the grid aggregation process than methods based on Locational Marginal Prices.

math.OC↗

arXiv2025

Towards time series aggregation with exact error quantification for optimization of energy systems

Energy system optimization models are becoming increasingly popular for analyzing energy markets, such as the impact of new policies or interactions between energy carriers. One key challenge of these models is the trade-off between modeling accuracy and computational tractability. A recently proposed mathematical framework addresses this challenge by achieving exact time series aggregations merging time periods sharing the same active constraint sets. This aggregation, however, is insufficient when the number of unique active constraints is large. We overcome this issue by aggregating data points from different active constraint sets. While this further reduces model size, it inevitably introduces an error compared to the full model. Yet, we show how this error can be exactly quantified without re-solving the optimization problem, enabling users to trade off computational efficiency and model accuracy proactively. This may be especially useful in energy markets to accommodate varying granularity across short- and long-term time horizons.

math.OC↗

arXiv2024

DisQu: Investigating the Impact of Disorder in Quantum Generative Models

Disordered Quantum many-body Systems (DQS) and Quantum Neural Networks (QNN) have many structural features in common. However, a DQS is essentially an initialized QNN with random weights, often leading to non-random outcomes. In this work, we emphasize the possibilities of random processes being a deceptive quantum-generating model effectively hidden in a QNN. When we choose weights in a QNN randomly the unitarity property of quantum gates is unchanged. As we show, this can lead to memory effects with multiple consequences on the learnability and trainability of QNN one would not expect from a classical neural network with random weights. This phenomenon may lead to a fundamental misunderstanding of the capabilities of common quantum generative models, where the generation of new samples is essentially averaging over random outputs. While we suggest that DQS can be effectively used for tasks like image augmentation, we draw the attention that overly simple datasets are often used to show the generative capabilities of quantum models, potentially leading to overestimation of their effectiveness.

cond-mat.dis-nn↗

arXiv2023

Flexibility of Integrated Power and Gas Systems: Gas Flow Modeling and Solution Choices Matter

Due to their slow gas flow dynamics, natural gas pipelines function as short-term storage, the so-called linepack. By efficiently utilizing linepack, the natural gas system can provide flexibility to the power system through the flexible operation of gas-fired power plants. This requires accurately representing the gas flow physics governed by partial differential equations. Although several modeling and solution choices have been proposed in the literature, their impact on the flexibility provision of gas networks to power systems has not been thoroughly analyzed and compared. This paper bridges this gap by first developing a unified framework. We harmonize existing approaches and demonstrate their derivation from and application to the partial differential equations. Secondly, based on the proposed framework, we numerically analyze the implications of various modeling and solution choices on the flexibility provision from gas networks to power systems. One key conclusion is that relaxation-based approaches allow charging and discharging the linepack at physically infeasible high rates, ultimately overestimating the flexibility.

eess.SY↗

arXiv2023

A Conic Model for Electrolyzer Scheduling

The hydrogen production curve of the electrolyzer describes the non-linear and non-convex relationship between its power consumption and hydrogen production. An accurate representation of this curve is essential for the optimal scheduling of the electrolyzer. The current state-of-the-art approach is based on piece-wise linear approximation, which requires binary variables and does not scale well for large-scale problems. To overcome this barrier, we propose two models, both built upon convex relaxations of the hydrogen production curve. The first one is a linear relaxation of the piece-wise linear approximation, while the second one is a conic relaxation of a quadratic approximation. Both relaxations are exact under prevalent operating conditions. We prove this mathematically for the conic relaxation. Using a realistic case study, we show that the conic model, in comparison to the other models, provides a satisfactory trade-off between computational complexity and solution accuracy for large-scale problems.

math.OC↗

arXiv2022

Modeling Gas Flow Directions as State Variables: Does it Provide More Flexibility to Power Systems?

As a common practice, the direction of natural gas flow in every pipeline is determined ex-ante for simplification purposes, and treated as a given parameter within the scheduling problem. However, in integrated gas and electric power networks with a large share of intermittent renewable power supply, it is no longer straightforward to optimally predetermine the gas flow directions. A wrong predetermination of gas flow directions may result in feasible but not necessarily optimal schedules. We propose a mixed-integer linear optimization model to determine the optimal gas flow directions while scheduling the system. This unlocks additional flexibility to power systems, provided that a tight coordination between power and gas systems exists. The increased flexibility, although it comes at the cost of increased computational complexity, is quantified by comparing the total operational cost of the entire system with bidirectional gas flows as opposed to unidirectional gas flows. We numerically show that modeling gas flow directions as state variables may bring added value not only in the meshed but also in the radial gas networks.

math.OC↗