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A theoretical upper limit for offshore wind energy extraction
Future energy systems need offshore wind. However, large-scale deployment faces aerodynamic limits that constrain efficiency, energy yield, and grid integration. We present a closed-form analytical model for the theoretical upper limit to offshore wind farm production, expressed through a dimensionless Wind Farm Wind Factor. The model and limit are validated against data from 72 offshore wind farms over 420 cumulative years, demonstrating strong agreement including operational losses. We benchmark national policy targets in Europe and the US, revealing large overestimations of energy production—by nearly 50% in one case—underestimating energy costs, power variability and integration costs, curtailment, and policy risks. The model clarifies the critical design trade-offs between turbine height, specific power, and wind farm density. It provides a rigorous yet simple framework, readily usable by engineers, planners, and policymakers, to forecast wind farm performance, support system planning, and set realistic targets consistent with aerodynamic limits.
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Carlos Simão Ferreira
Delft University of Technology, the Netherlands
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Gunner Chr. Larsen
DTU Wind and Energy Systems, Denmark
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Jens Nørkær Sørensen
DTU Wind and Energy Systems, Denmark
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What inspired you to develop a theoretical upper limit model for offshore wind energy extraction?
Offshore wind is set to play a central role in future energy systems, but as projects scale up, we observed that expectations of energy yield were increasingly drifting away from physical reality. We therefore set out to establish a physically grounded, closed-form analytical model that captures the key aerodynamic processes in the marine atmospheric boundary layer, in particular the role of vertical momentum transport from geostrophic winds several kilometers above the surface. The aim was to develop a rigorous yet simple framework that requires only minimal input and can be used consistently by engineers, planners, policymakers, and system analysts. Rather than replacing detailed simulations, the model provides a transparent benchmark for what is physically achievable at large scales.
Your study mentions a “limit” to how much energy offshore wind farms can produce. What does this mean, and why can’t we just keep building bigger or more turbines?
As wind farms become larger and denser, they no longer behave as collections of isolated turbines, but as large aerodynamic obstacles that modify the entire atmospheric boundary layer. The total energy that can be harvested is fundamentally limited by how efficiently momentum can be transported downward from stronger geostrophic winds aloft to the turbine level. While taller turbines and optimized designs can improve performance, simply adding more turbines does not lead to proportional gains, because vertical momentum replenishment becomes the bottleneck. Our model captures this mechanism and defines a physically grounded upper limit to long-term average production for a given wind climate, turbine design, and wind farm density. Importantly, we also find that efficiency losses saturate at higher densities, implying that very dense wind farms may still be attractive when space use, economics, and environmental constraints are taken into account.
Your findings suggest some national offshore wind targets may overestimate achievable energy production by up to 50%. What are the potential risks of setting such overly optimistic targets?
Energy systems are planned decades in advance and rely on large, long-lived investments in generation assets, grids, storage, and supporting infrastructure. When energy production is systematically overestimated, even if projects are built exactly as planned, the result is a structural electricity shortfall that is difficult and costly to correct. Our benchmarking of policy targets in Europe and the United States shows that some projections implicitly assume capacity factors that exceed aerodynamic limits, in some cases by nearly 50%. Such overestimation hides true system costs; underestimates power variability, integration, and curtailment risks; and can ultimately undermine energy security, investor confidence, and the credibility of national decarbonization strategies.
How can your model support better integration of offshore wind into energy systems, particularly regarding grid stability, storage needs, and investment decisions?
The model provides a clear, physically grounded upper bound on long-term average energy production for large offshore wind developments, expressed through a single dimensionless Wind Farm Wind Factor. This makes it readily usable in energy system scenarios, grid planning studies, and investment analyses, where realistic capacity factors are critical. By constraining expectations early, it helps planners better anticipate storage needs, transmission requirements, curtailment, and complementary generation. Because the framework is simple, transparent, and validated against extensive operational data, it also supports informed dialogue across engineering, economics, and environmental sciences, enabling more robust policy decisions and credible long-term targets.
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Global challenges, equitable solutions
Cell Reports Sustainability is a multidisciplinary, gold open access journal that publishes cutting-edge research across natural, applied, and social sciences that seeks to address the world’s grand challenges.
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