arXiv subjects

Thomas Hübner

Publications and source records attributed to Thomas Hübner.

4 recordsLinked to original sources

arXiv2026

Duality Gaps in Partially Nonconvex Optimization

We study duality gaps in separable optimization problems that contain both convex and nonconvex functions. Classical bounds on the duality gap of such partially nonconvex problems depend solely on the nonconvex functions. As a result, a problem with many convex functions has no tighter bound than one with none at all. To understand the impact of convex functions on the duality gap beyond the worst case, we analyze a probabilistic setting in which the convex hulls of the functions' epigraphs are independent and identically distributed. Using the Shapley-Folkman lemma, we derive lower bounds on the distribution of the duality gap that depend on both the number of convex and nonconvex functions. These bounds show that zero or small duality gaps become increasingly likely as convex functions outnumber nonconvex ones. This way, they support the intuition that "nearly convex" problems tend to have smaller duality gaps than "purely nonconvex" ones, an intuition that the classical worst-case bounds do not capture. Finally, we use these results to understand why zero or vanishingly small duality gaps occur so frequently in the welfare maximization problems underlying European electricity auctions, drawing on empirical results spanning 281 days in 2023 across 9 countries. To shed light on the economic reasons behind this, we present alternative proofs that exploit the connection between duality gaps and the existence of Walrasian equilibria.

econ.TH↗

arXiv2026

On the Design of Stochastic Electricity Auctions

Electricity is typically traded in day-ahead auctions because many power system decisions, such as unit commitment, must be made in advance. However, when wind and solar generators sell power one day ahead, they face uncertainty about their actual production. In current day-ahead auctions, this uncertainty cannot be directly communicated, leading to inefficient use of renewable energy and suboptimal system decisions. We show how this problem can be addressed using the concept of equilibrium under uncertainty from microeconomic theory. In particular, we demonstrate that electricity contracts should be conditioned not only on the time and location of delivery, but also on the state of the world (e.g., whether it will be windy or calm). This requires a precise definition of the state of the world. Since there are infinitely many possible definitions, criteria are needed to select among them. We develop such criteria and show that the resulting states correspond to solutions of an optimal partitioning problem. Finally, we illustrate how these states can be computed and interpreted using a case study of offshore wind farms in the European North Sea.

econ.GN↗

arXiv2025

Bidding Aggregated Flexibility in European Electricity Auctions

Bidding flexibility in day-ahead and intraday auctions would enable decentralized flexible resources, such as electric vehicles and heat pumps, to efficiently align their consumption with the intermittent generation of renewable energy. However, because these resources are individually too small to participate in those auctions directly, an aggregator (e.g., a utility) must act on their behalf. This requires aggregating many decentralized resources, which is a computationally challenging task. In this paper, we propose a computationally efficient and highly accurate method that is readily applicable to European day-ahead and intraday auctions. Distinct from existing methods, we aggregate only economically relevant power profiles, identified through price forecasts. The resulting flexibility is then conveyed to the market operator via exclusive groups of block bids. We evaluate our method for a utility serving the Swiss town of Losone, where flexibility from multiple heat pumps distributed across the grid must be aggregated and bid in the Swiss day-ahead auction. Results show that our method aggregates accurately, achieving 98% of the theoretically possible cost savings. This aggregation accuracy remains stable even as the number of heat pumps increases, while computation time grows only linearly, demonstrating strong scalability.

eess.SY↗

arXiv2025

Package Bids in Combinatorial Electricity Auctions: Selection, Welfare Losses, and Alternatives

A key challenge in combinatorial auctions is designing bid formats that accurately capture agents' preferences while remaining computationally feasible. This is especially true for electricity auctions, where complex preferences complicate straightforward solutions. In this context, we examine the XOR package bid, the default choice in combinatorial auctions and adopted in European day-ahead and intraday auctions under the name "exclusive group of block bids". Unlike parametric bid formats often employed in US power auctions, XOR package bids are technology-agnostic, making them particularly suitable for emerging demand-side participants. However, the challenge with package bids is that auctioneers must limit their number to maintain computational feasibility. As a result, agents are constrained in expressing their preferences, potentially lowering their surplus and reducing overall welfare. To address this issue, we propose decision support algorithms that optimize package bid selection, evaluate welfare losses resulting from bid limits, and explore alternative bid formats. In our analysis, we leverage the fact that electricity prices are often fairly predictable and, at least in European auctions, tend to approximate equilibrium prices reasonably well. Our findings offer actionable insights for both auctioneers and bidders.

econ.GN↗