DEI Analysis: A = 0.10 (Wider Wakes)

This page documents the Danish Energy Island regret analysis using the TurboGaussian wake model with A=0.10.

See also: A=0.02 Analysis | DEI Case Study | Methodology

Configuration

Parameter	Value
Wake Model	TurboGaussianDeficit
A (expansion)	0.10
ct2a	ct2a_mom1d
ctlim	0.96
Superposition	SquaredSum
Ambient TI	0.06
Optimization	50 starts × 2000 iterations

A=0.10 produces wider wake cones, meaning wakes expand more rapidly and dissipate faster with downstream distance.

Summary Results

Case	Regret (GWh)	Regret (%)	Pareto Points
Farm 1 (SW, 214°)	2.08	0.04%	2
Farm 2 (W, 262°)	0.30	0.01%	2
Farm 3 (NW, 335°)	0.00	0.00%	1
Farm 4 (N, 349°)	0.00	0.00%	1
Farm 5 (NE, 19°)	0.00	0.00%	1
Farm 6 (E, 57°)	0.00	0.00%	1
Farm 7 (SE, 89°)	0.37	0.01%	2
Farm 8 (S, 163°)	15.81	0.28%	3
Farm 9 (SSW, 186°)	0.00	0.00%	1
All 9 combined	9.70	0.18%	4

Key finding: Farm 8 (South) remains the dominant source of regret at 15.81 GWh. With wider wakes (A=0.10), overall regret is reduced compared to A=0.02.

Individual Neighbors Analysis

Pareto frontiers for each of the 9 neighbors. Blue circles = liberal strategy (ignore neighbor), red squares = conservative strategy (consider neighbor). Black outlines indicate Pareto-optimal layouts.

Observations

• Farm 8 (S, 163°): Dominant regret source at 15.81 GWh (0.28%)
• Farm 1 (SW, 214°): Reduced to 2.08 GWh (vs 18.19 GWh at A=0.02)
• Farms 3, 4, 5, 6, 9: Zero regret - no design tradeoff
• Farms 2, 7: Negligible regret (<0.4 GWh)

Wider wakes spread the energy deficit over a larger area, making it easier for layout optimization to mitigate neighbor impacts.

Regret by Direction

Design regret is concentrated at Farm 8 (South, 163°). Wider wakes reduce regret from most directions.

The southern neighbor dominates regret at both A values, but the magnitude is substantially reduced with wider wakes.

All Neighbors Combined

Pareto frontier when all 594 neighbor turbines are present. The combined regret (9.70 GWh) is lower than Farm 8 alone.

Layout	AEP Alone	AEP with All 594	Wake Loss
Liberal-optimal	5731 GWh	5534 GWh	-3.4%
Conservative-optimal	5723 GWh	5543 GWh	-3.1%
Regret		9.70 GWh

The combined case shows 4 Pareto-optimal layouts spanning 9.70 GWh of regret.

Comparison with A=0.02

Metric	A=0.02	A=0.10	Change
Wake cone	Narrow	Wide	-
Target AEP (alone)	5469 GWh	5731 GWh	+4.8%
Farm 8 regret	28.51 GWh	15.81 GWh	-45%
Combined regret	11.52 GWh	9.70 GWh	-16%
Wake loss (combined)	14%	3%	-79%

Key differences: - Higher standalone AEP: Wider wakes = less internal wake loss = higher baseline AEP - Lower regret: Wider wakes are easier to avoid through layout optimization - Much lower wake loss: 3% vs 14% loss when all neighbors present

Physical Interpretation

The A parameter controls wake expansion rate: wake_width = A × downstream_distance.

A Value	Wake Character	Regret Implication
0.02	Narrow, persistent	Concentrated wake deficit harder to avoid
0.10	Wide, dissipating	Distributed deficit easier to mitigate

Narrow wakes create "corridors" of reduced wind that layouts must route around. Wide wakes create a gentler reduction across a broader area that layouts can partially ignore.

Data Files

Results are stored in analysis/dei_A0.10/:

• layouts_farm{1-9}.h5 - Optimized layouts for each neighbor case
• layouts_combined.h5 - Optimized layouts for all-neighbors case
• dei_single_neighbor_turbopark_farm{1-9}.json - Individual farm results
• dei_single_neighbor_turbopark_farm.json - Combined case results

Replication

# Run all farms in parallel batches
for farm in 1 2 3 4 5 6 7 8 9; do
    pixi run python scripts/run_dei_single_neighbor.py \
        --n-starts=50 --max-iter=2000 \
        --A=0.10 --farm=$farm --skip-combined \
        -o analysis/dei_A0.10
done

# Run combined case (memory intensive)
pixi run python scripts/run_dei_single_neighbor.py \
    --n-starts=50 --max-iter=2000 \
    --A=0.10 --only-combined \
    -o analysis/dei_A0.10