Wind star: Jensen, layout and net AEP

A wind turbine draws energy from the flow — and in doing so, it creates behind it a slower and more turbulent wind region: the wake (wake). If another wind turbine is installed in that region, it will catch less wind and generate less energy. In parks with tens or hundreds of turbines, the cumulative effect of the wakes can reduce production by 5 to 20% — the difference between raw AEP and net AEP that appears in any resource assessment report.

Understanding the mechanics of the wake is essential for three practical decisions: the layout of the park (positioning of turbines to minimize the mutual impact), the selection of spacing (trade-off between terrain area and wake loss), and the estimation of the wake uncertainty component in the budget that feeds the P90 required by the lender.

What generates the wake: the thrust coefficient Ct

The intensity of the wake depends on how much the turbine slows the wind — quantified by the thrust coefficient Ct The Ct is the relationship between the drag force exerted by the rotor and the kinetic energy available in the free flow:

Ct = T / (½ ρ A V₀²)

T  — rotor thrust force (N)
ρ  — air density (~1.225 kg/m³ at sea level)
A  — rotor swept area = π D²/4
V₀ — free-stream wind speed (m/s)

# The Ct varies with the wind speed:
# V < 5 m/s (before rated): Ct high → 0,75–0,90
# . V . . rated (11–13 m/s): Ct begins to fall
# V > 15 m/s (top rated): Low Ct → 0.20–0.40 (pitch control)

# Theoretical maximum of Betz: Ct = 8/9 - 0.889 at maximum extraction point
# – Real turbines: Ct_max – 0,75–0,88 in range 6–10 m/s

The maximum Ct occurs in the speed range that most contributes to AEP (6–10 m/s for most sites in the Northeast). Therefore, wake losses are more severe precisely when the resource is better — the wake effect has more impact on annual production than the isolated instant Ct curve suggests.

The Jensen model (Park): the geometry of the wake

The Jensen model — published in 1983 and still widely used in software such as WAsP, FLORIS and OpenWind for its analytical simplicity — describes the wake as a linear expansion cone, with uniform speed within the cone (top-hat profile):

# Speed on the wake x distance of the rotor:
V_w / V₀ = 1 − (1 − √(1−Ct)) × (D / (D + 2k×x))²

D   — rotor diameter (m)
k   — wake-decay constant (adimensional)
x   — downwind distance in metres
V₀  — free-stream wind speed (m/s)

# Range radius (linear growth):
r_w(x) = D/2 + k×x

# Speed deficit (fraction):
ΔV/V₀ = 1 − V_w/V₀ = (1 − √(1−Ct)) × (D / (D + 2k×x))²

The parameter • k It controls the rate of expansion of the wake and depends mainly on the roughness of the terrain and the local atmospheric turbulence:

The speed deficit and recovery with distance

2 shows how the speed deficit (ΔV/V0) declines with the distance to the downwind, for three k values and with Ct=0.80 (typical value in the speed range that most contributes to AEP).

Overlay of wakes: parks with multiple turbines

In real parks, a turbine can receive the combined wake of two or more upstream turbines. Jensen's model uses linear overlap: the resulting deficit is calculated as the sum weighted by the area of individual deficits within the downstream rotor:

# Linear deficit overlap (standard Jensen method):
ΔV_total / V₀ = Σᵢ (ΔVᵢ / V₀ × Aᵢ / A_rotor)

A_rotor — total downstream rotor area (m²)
Aᵢ      — overlap area between wake i and the downstream rotor (m²)
ΔVᵢ     — wake-i deficit at the intersection

# Alternative (RSS — root of the sum of the squares):
ΔV_total / V₀ = √(Σᵢ (ΔVᵢ / V₀)²)  — conservative, less commonly used

# net AEP from the park:
AEP_liq = Σⱼ [ P(V_j_eff) × Δt ]    # - sum hour-to-hour with effective V
        ≈ AEP_gross × (1 − η_wake)   # Approach to planning

The total loss of wake at park level (η_wake) depends on three main factors: the spacing between turbines (in multiples of D), the directional distribution of wind (wind rose), and the density of the park (number of turbines per km2). The relationship is not linear — the difference between 4D and 6D of spacing has a much greater impact on wake loss than the difference between 8D and 10D.

Increased turbulence: the second effect of the wake

In addition to the speed deficit, the wake adds turbulence to the flow that reaches the downstream turbines. The increased turbulence intensity (ΔTI) follows the formulation of Frandsen (2005), used by IEC 61400-1 Ed. 4:

TI_efetivo = √(TI_ambiental² + TI_wake²)

TI_wake ≈ 0,9 / (1,5 + 0,3 × x/D × √Ct)   (Frandsen, IEC 61400-1 Ed.4)

# Example: x=5D, Ct=0.80, TI_environmental=7%:
TI_wake = 0.9 / (1.5 + 0.3×5×√0.8) = 0.9 / (1.5 + 1.342) = 0.9/2.842 = 0.317 = 31.7%?

# In practice, TI_wake is added as an independent contribution:
TI_efetivo = √(0.07² + 0.08²) ≈ 10.6%   # Increase from 7→10.6% to 5D

The increase in IT on the wake impacts fatigue loads on the blades and tower of downstream turbines — this is what determines the effective turbulence class of the site. In dense parks, central turbines (internal to the park) can receive effective IT 50–100% higher than ambient IT, which directly affects the IEC class selection (see NT.04). Site classification reports for parks must declare the IT representative by turbine position, not only the IT environment measured at the weather station.

The uncertainty of wake modeling as a component of AEP

The Jensen model overestimates the deficit near the rotor and underestimates the recovery in the intermediate zone (3–6D) compared to LiDAR measurements and CFD results. Most modern models — Gaussian wake (Bastankhah & Porté-Agel, 2014), FLORIS, PyWake — better reproduce the lateral velocity distribution on the wake, but require more calibration parameters and higher computational cost.

For the uncertainty budget of AEP (discussed in NT.06 For wind), wake modeling uncertainty is typically one of the largest components:

σ_wake ≈ 10–30% of estimated wake loss

# Example: Onshore park with estimated η_wake = 8% (AEP_brute = 200 GWh):
Estimated AEP_net = 200 × (1 − 0.08) = 184 GWh
σ_wake = 20% × 8% = 1.6% of AEP → 3.2 GWh of uncertainty (1σ)

# Impact on P90:
# σ_wake contributes as any other component in the total RSS
# Factor: Depends on model approval and quality of input data

The calibration of the wake model with measured data — simultaneous measurement campaigns in two or more turbines, or operational data of SCADA crossed with wind rose — can substantially reduce σ_wake. This is especially relevant in expansions of existing parks (repowering or adding turbines) where historical production data already allow calibrating the model before the investment decision.

AEP gross and net AEP in resource assessment report

The Bankability Resource Assessment Report needs to explicitly report the gross AEP (without wake) and net AEP (with wake applied), with the following minimum structure:

AEP_gross   = Σⱼ P(V_j) × h_j    # Power curve × hours per V bin
AEP_wake    = AEP_gross × η_wake  # Loss of wake (%)
AEP_net = AEP_gross − AEP_wake

# More losses (calculated separately):
AEP_after_electrical = AEP_net × (1 − η_electrical)   # collector, transformer and line losses
AEP_disp     = AEP_after_electrical × availability    # Downtime, maintenance

# P50 final delivered to the network:
AEP_P50 = AEP_disp

The clear decomposition is a requirement of due diligence — and the loss of wake is often the largest component of AEP gross loss to AEP delivered to the network, greater than the combined electrical and availability losses.