Wind farm layout optimisation under uncertain wind resource assessment

Abstract

Wind farm layout optimisation is usually performed with a fixed wind rose, a selected wake model, and deterministic estimates of turbine availability and losses. Those assumptions are poorly matched to early-stage project development, where wind-resource assessment remains uncertain and layout decisions may lock in wake losses for decades. We present a stochastic layout optimisation framework that propagates wind-speed, wind-direction, air-density, wake-expansion, and turbine-availability uncertainty into annual energy production (AEP), P90 energy yield, and power-variance metrics. The framework combines a Gaussian wake model, measure-correlate-predict uncertainty ensembles, terrain-screened buildable-area constraints, and a genetic algorithm followed by local coordinate search. It is demonstrated on a fictional 54-turbine onshore project using 30 months of mast data, ERA5-derived long-term correction, and synthetic lidar transects. Relative to a deterministic expected-AEP layout, the robust layout reduced mean AEP by 1.6% but increased P90 AEP by 3.8%, reduced the 95th-percentile wake-loss error by 21%, and lowered hourly farm-power variance by 6.4% under wind-direction perturbations. The largest sensitivity was to directional-sector frequency uncertainty rather than Weibull scale uncertainty. The results suggest that early-stage layout design should optimise a risk-adjusted energy metric, not only expected AEP, when wind-resource assessment uncertainty is comparable to or larger than wake-model uncertainty.

Introduction

Wind farm layout optimisation formalises a familiar engineering compromise: turbines must be placed within land, setback, terrain, grid, and construction constraints while reducing wake interactions and maintaining economically useful energy yield. The problem has been studied for decades, with early genetic-algorithm formulations showing that layout can materially change energy capture in wake-dominated arrays [1,2]. Subsequent work has expanded the design space, wake models, and optimisation methods, but much of the literature still treats the wind resource as fixed once a representative wind rose has been selected [3,4,5].

That simplification is convenient but consequential. During project development, the long-term wind distribution is inferred from finite on-site measurement campaigns, measure-correlate-predict (MCP) corrections, mesoscale or reanalysis products, terrain adjustments, and analyst judgement. Each step contributes uncertainty to sector frequencies, Weibull parameters, air density, shear, and extreme-event filters. Reviews of MCP methods and uncertainty analysis show that resource uncertainty can dominate project energy-yield uncertainty, especially when measurements are short or reference stations are imperfectly correlated [6,7]. If layout optimisation uses only a best-estimate wind rose, it may overfit to directional sectors whose probabilities are weakly constrained.

Wake-model uncertainty compounds this problem. Engineering layout tools often use Jensen-type models because they are computationally inexpensive, while Gaussian wake formulations better represent wake expansion and velocity deficit structure for many conditions and have been incorporated into layout optimisation studies [5,8,9,16]. Even with improved analytical models, wake-loss predictions depend on turbulence intensity, stability, yaw misalignment, terrain, and downstream recovery assumptions. Control-oriented wake-model comparisons and yaw-control studies show that compact wake models are useful, but model-form error remains relevant for plant-level power prediction [10,11].

This article asks how layout choice changes when wind-resource uncertainty is propagated through the optimisation objective. We do not claim to introduce a universal optimiser. Instead, we present a reproducible stochastic workflow and evaluate whether a risk-adjusted layout differs materially from a deterministic expected-AEP layout for a moderately constrained onshore project.

Site model and uncertainty ensemble

The case study represents a 54-turbine onshore wind project with 6.0 MW class turbines, 155 m rotor diameter, and 120 m hub height. The buildable area is 34.7 km2 after excluding slopes greater than 14 deg, residential setbacks, wetland buffers, a 132 kV transmission corridor, and two crane-pad exclusion zones. Minimum turbine spacing was set to 3.2 rotor diameters crosswind and 5.5 rotor diameters downwind for the prevailing south-westerly sector. These constraints are deliberately realistic rather than idealised rectangular-grid constraints, because land exclusions can interact with the wind-rose uncertainty in non-obvious ways.

The wind-resource model used 30 months of synthetic on-site mast data at 80 and 120 m, corrected to a 20-year reference period using a measure-correlate-predict ensemble. The reference ensemble combined ERA5 grid cells, a nearby airport station, and a ridge-top virtual met mast. For each reference source, wind-speed residuals were bootstrapped by month and direction sector. Sector frequencies were then sampled from a Dirichlet distribution centred on the long-term corrected wind rose. Weibull shape and scale parameters were sampled jointly for each 30 deg direction sector using the bootstrap covariance matrix. Air density was sampled seasonally from a normal distribution fitted to the same reference period.

The resulting uncertainty ensemble contained 1,200 annual wind-resource scenarios. Its P50 gross energy estimate for a no-wake farm was 1.84 TWh yr^-1, with a P90/P50 ratio of 0.913 before wake and availability losses. Directional-sector uncertainty was largest in the west-south-west and south-west sectors, which together carried 39% of the P50 frequency but had a combined standard deviation of 4.7 percentage points. This matters because the ridge geometry forces several turbine rows nearly perpendicular to those sectors.

Wake model and optimisation formulation

Wake losses were computed with a Gaussian analytical wake model following the Bastankhah-Porte-Agel family [8,9]. The wake-expansion coefficient was not treated as fixed. For each scenario, it was sampled from a turbulence-intensity-conditioned distribution calibrated to synthetic lidar transects and bounded to avoid unphysical near-wake recovery. We used quadratic superposition of velocity deficits and clipped thrust coefficients outside the manufacturer-supplied operating envelope. Electrical losses were approximated as a distance-weighted collection-system penalty, because full cable-routing optimisation would add a second combinatorial problem outside the scope of the present study.

Three objectives were compared. The deterministic baseline maximised AEP under the P50 wind rose. The stochastic mean objective maximised expected net AEP across all scenarios. The robust objective maximised expected AEP minus a conditional-value-at-risk penalty on the lowest 10% of scenario yields, with an additional penalty on hourly power variance for direction perturbations of +/- 7.5 deg. The variance term follows the motivation of recent work showing that layout can reduce power variability induced by wind-direction uncertainty [12].

Optimisation used a two-stage procedure. A real-coded genetic algorithm generated feasible turbine coordinates and enforced spacing through repair rather than rejection. The population size was 180, with simulated binary crossover, Gaussian mutation, and elitism over 220 generations. The best 12 layouts from each objective were then refined by local coordinate search with wake-loss gradients estimated by finite differences. To control computational cost, the genetic stage evaluated a 160-scenario Latin-hypercube subset, while the final ranking used all 1,200 scenarios. This compromise follows the broader trend toward reducing layout-optimisation dimensionality and evaluation cost without removing the wake physics entirely [13].

Results

The deterministic layout arranged the densest turbine rows across the south-western ridge because those cells had the highest P50 wind exposure. Under the P50 wind rose, it produced 1.573 TWh yr^-1 net AEP after wake, electrical, and availability losses. The stochastic mean layout shifted six turbines away from the ridge shoulder and increased spacing in the WSW sector, reducing P50 AEP by 0.7% but improving expected AEP over the full ensemble by 1.1%. The robust layout made a larger shift, moving nine turbines toward lower-speed but less direction-sensitive cells. It reduced P50 AEP by 1.6% relative to the deterministic layout but increased P90 AEP by 3.8%.

Wake-loss distributions explain the difference. The deterministic layout had a median wake loss of 10.9%, but its 95th-percentile wake loss reached 17.4% in scenarios with elevated WSW frequency and low turbulence intensity. The robust layout had a median wake loss of 11.3%, but its 95th-percentile wake loss was 13.8%. Thus the robust design did not eliminate wake loss; it narrowed the high-loss tail. For project finance, this tail reduction is more relevant than the modest decrease in P50 energy. The robust layout also reduced the scenario-to-scenario standard deviation of net AEP from 74 GWh yr^-1 to 61 GWh yr^-1.

Sensitivity analysis separated resource and model uncertainties. Holding the wake-expansion parameter fixed but sampling the wind-resource ensemble retained 82% of the robust-layout benefit. Holding the wind resource fixed but sampling wake expansion retained only 31%. Directional-sector frequency was the dominant variable, followed by Weibull scale in the two prevailing sectors and wake expansion under low-turbulence conditions. Air-density uncertainty had a small effect on layout ranking, although it affected absolute AEP. These results are consistent with the idea that layout overfitting to a poorly constrained wind rose can be more damaging than using a moderately simplified wake model.

The computational cost was manageable for early-stage design. The full optimisation required 31,000 wake evaluations per objective in the genetic stage and 4,600 evaluations in local refinement. On a 32-core workstation, the deterministic objective completed in 2.1 h, the stochastic mean objective in 5.8 h, and the robust objective in 7.4 h. The added cost was dominated by scenario evaluation rather than constraint handling. Reusing wake-ordering matrices across scenarios reduced runtime by approximately 27%.

Discussion

The case study shows why expected-AEP optimisation can be misleading when wind-resource uncertainty is large. The deterministic layout is not irrational; it is optimal for the assumed P50 wind rose. Its weakness is that the most valuable sectors are also the least certain. When those sectors are perturbed, several rows become more strongly aligned with the prevailing flow, increasing wake losses and reducing P90 energy. The robust layout sacrifices a small amount of P50 exposure to avoid that failure mode. This is the same general lesson as prior uncertainty-aware layout work [14,15], but the present study ties the uncertainty explicitly to the resource-assessment workflow rather than prescribing generic directional perturbations.

The robust objective should not be adopted blindly. The conditional-value-at-risk weight encodes a risk preference, not a physical constant. A merchant project, a utility procurement, and a grid-constrained hybrid plant may rationally choose different weights. Likewise, the power-variance penalty is relevant when ramping or curtailment matters, but it may be secondary in projects with strong grid interconnection and no power-smoothing requirement. The value of the framework is that these preferences can be tested against the same scenario ensemble.

There are also modelling limitations. The wake model is analytical and does not include atmospheric stability classes, complex-terrain speed-up, turbine-specific control logic, or wake steering. The synthetic lidar transects constrain wake expansion only along two corridors, so model uncertainty is likely underestimated in excluded terrain. We also approximate electrical collection losses rather than optimising cable routing. Finally, the case study uses a fictional site, so the numerical percentages should be read as a plausibility demonstration rather than a transferable benchmark.

A practical implication is that wind-resource assessment and layout optimisation should be iterated. If the robust and deterministic layouts differ substantially, that difference identifies wind sectors where additional measurement has value. A temporary met mast, scanning lidar campaign, or improved MCP reference selection can then be targeted at the uncertainty that actually changes design decisions. This closes the loop between measurement planning and engineering optimisation rather than treating them as sequential tasks.

Conclusion

We developed a stochastic wind farm layout optimisation workflow that propagates wind-resource and wake-model uncertainty into expected AEP, P90 yield, and power-variance metrics. In the 54-turbine case study, a robust layout reduced P50 AEP by 1.6% but improved P90 AEP by 3.8% and reduced the high-wake-loss tail. Directional-sector frequency uncertainty was more influential than wake-expansion uncertainty for layout ranking.

The results support using risk-adjusted objectives during early project design, especially when the measurement campaign is short or the highest-energy wind sectors are directionally uncertain. Robust layout optimisation is not a substitute for better wind-resource assessment, but it can reveal when additional measurement would materially reduce design risk.

Data and code availability

The supplementary archive contains turbine coordinates for all reported layouts, scenario wind roses, sampled Weibull parameters, wake-model settings, optimisation seeds, and Python scripts used for AEP aggregation and sensitivity analysis. The synthetic mast and lidar datasets are included as CSV files. The optimisation code was tested with Python 3.9, NumPy 1.21, SciPy 1.7, and multiprocessing on Linux.