Broad Ranges of Investment Configurations for Renewable Power Systems, Robust to Cost Uncertainty and Near-Optimality

TL;DR

The paper addresses planning a fully renewable European electricity system under technology-cost uncertainty by combining an $\\epsilon$-constraint near-optimality framework with multi-fidelity Polynomial Chaos surrogate modelling. It solves a large set of investment problems to map the near-optimal space and identifies robust boundary conditions, showing that a broad spectrum of cost-efficient, technologist- and regionally diverse options exists near the cost optimum. The authors deploy 50,000+ low-fidelity and ~1,500 high-fidelity model runs, enabled by Halton sampling and surrogate corrections, to estimate system-costs and capacities across uncertain cost projections. Their results reveal that wind, storage (notably hydrogen), and transmission show distinct cost-sensitivity patterns, and that policy-relevant flexibility can be achieved without compromising near-term cost-efficiency. The methodology provides a practical framework for exploring socially acceptable and robust renewable configurations, with implications for planning under deep cost uncertainty and for communicating viable alternatives to stakeholders.

Abstract

To achieve ambitious greenhouse gas emission reduction targets in time, the planning of future energy systems needs to accommodate societal preferences, e.g. low levels of acceptance for transmission expansion or onshore wind turbines, and must also acknowledge the inherent uncertainties of technology cost projections. To date, however, many capacity expansion models lean heavily towards only minimising system cost and only studying a few cost projections. Here, we address both criticisms in unison. While taking account of technology cost uncertainties, we apply methods from multi-objective optimisation to explore trade-offs in a fully renewable European electricity system between increasing system cost and extremising the use of individual technologies for generating, storing and transmitting electricity to build robust insights about what actions are viable within given cost ranges. We identify boundary conditions that must be met for cost-efficiency regardless of how cost developments will unfold; for instance, that some grid reinforcement and long-term storage alongside a significant amount of wind capacity appear essential. But, foremost, we reveal that near the cost-optimum a broad spectrum of regionally and technologically diverse options exists in any case, which allows policymakers to navigate around public acceptance issues. The analysis requires managing many computationally demanding scenario runs efficiently, for which we leverage multi-fidelity surrogate modelling techniques using sparse polynomial chaos expansions and low-discrepancy sampling.

Figures (6)

• Figure 1: Cross-validation errors by output for varying sample sizes and polynomial orders of least-cost low-fidelity surrogate models.
• Figure 2: Sensitivity of capacities towards their own technology cost. The median (Q50) alongside the 5%, 25%, 75%, and 95% quantiles (Q5--Q95) display the sensitivity subject to the uncertainty induced by other cost parameters.
• Figure 3: Sobol indices. These sensitivity indices attribute output variance to random input variables and reveal which inputs the outputs are most sensitive to. The first-order Sobol indices quantify the share of output variance due to variations in one input parameter alone. The total Sobol indices further include interactions with other input variables. Total Sobol indices can be greater than 100% if the contributions are not purely additive.
• Figure 4: Space of near-optimal solutions by technology under cost uncertainty. For each technology and cost sample, the minimum and maximum capacities obtained for increasing cost penalties $\epsilon$ form a cone, starting from a common least-cost solution. By arguments of convexity, the capacity ranges contained by the cone can be near-optimal and feasible, given a degree of freedom in the other technologies. From optimisation theory, we know that the cones widen up for increased slacks. As we consider technology cost uncertainty, the cone will look slightly different for each sample. The contour lines represent the frequency a solution is inside the near-optimal cone over the whole parameter space. This is calculated from the overlap of many cones, each representing a set of cost assumptions. Due to discrete sampling points in the $\epsilon$-dimension, the plots further apply quadratic interpolation and a Gaussian filter for smoothing.
• Figure 5: Space of near-optimal solutions by selected pairs of technologies under cost uncertainty. Just like in \ref{['fig:fuzzycone']}, the contour lines depict the overlap of the space of near-optimal alternatives across the parameter space. It can be thought of as the cross-section of the probabilistic near-optimal feasible space for a given $\epsilon$ in two technology dimensions and highlights that the extremes of two technologies from \ref{['fig:fuzzycone']} cannot be achieved simultaneously.