Modeling Robust Energy Systems Considering Weather Uncertainty and Nuclear Power Failures: A Case Study in Northern Europe

TL;DR

The paper tackles capacity expansion under two key uncertainties: weather-driven variability in wind/solar and unplanned nuclear outages. It integrates a scenario-based stochastic framework (WU) with a data-driven Adjustable Robust Optimization (ARO) approach (WNU) to capture nuclear failures, applying the method to a seven-node Northern Europe network. The study shows that neglecting nuclear outage uncertainty can leave systems vulnerable to Loss-of-Load, while the WNU approach yields zero LoL under various weather stress tests at a modest cost premium (~0.6%). The results highlight that robust planning rewards additional gas capacity and can sustain higher nuclear capacity with improved resilience, offering a practical methodology for policymakers and system planners facing dual uncertainties. Overall, the work advances robust energy system design by jointly accounting for weather and nuclear outage risks and demonstrates the value of a data-driven robust framework over traditional deterministic or weather-only models.

Abstract

Capacity expansion models used for policy support have increasingly represented both the variability and uncertainty of weather-dependent generation (wind and solar). However, although also uncertain, as demonstrated by the performance of the French nuclear power fleet in 2022, uncertainty arising from nuclear power outages has been largely neglected in the literature. This paper presents the first capacity expansion model that considers uncertainty in nuclear power availability caused by unplanned outages. We propose a mathematical model that combines a scenario-based stochastic optimization approach (to deal with weather-related uncertainties) with a data-driven adjustable robust optimization approach (to deal with nuclear failure-related uncertainties). The robust model represents the bulky behavior of nuclear power plants, with large (1 GW) units that are either on or off, while at the same time letting the model decide on the optimal amount of nuclear capacity. We tested the model in a case for Northern Europe (seven nodes) with a time resolution of 1250 time steps. Our findings show that nuclear power outages do, in fact, impose a vulnerability on the energy system if not considered in the planning phase. Our proposed model performs well and finds solutions that prevent Loss-of-Load (at a price of robustness of 0.6%), even in more extreme weather conditions. Robust solutions are characterized by a higher capacity of gas plants, but, perhaps surprisingly, nuclear power capacity is barely affected.

Figures (14)

• Figure 1: Schematic of interactions in the proposed energy systems.
• Figure 2: Flowchart of the heuristic method used to solve the Weather and Nuclear Uncertainty (WNU) model; F, A, and U represent Favorable, Average, and Unfavorable weather scenarios, respectively.
• Figure 3: Selected regions in the case study, as well as the potential transmission lines among the regions.
• Figure 4: Unplanned nuclear power outages based on 60 separate 12-month samples from six nuclear plants in Sweden. Data source: iaea2023operating.
• Figure 5: Optimal $\text{SC}$ for each year, sorted in ascending order, with the three selected years highlighted to represent the weather scenarios.