How to Calculate Wind Farm Wake Loss Factor
Wake losses are one of the largest and most uncertain deductions applied to wind farm energy yield assessments. Every turbine extracts momentum from the atmosphere, leaving a slower, more turbulent wake that reduces power production for downwind machines. Developers, lenders, and owners need a transparent wake loss factor so bank models, performance guarantees, and operations dashboards reflect the physics behind array layout choices.
This walkthrough focuses on the Jensen (also called Park) wake model because it offers a balance between aerodynamic fidelity and computational tractability. You will see how to define wake loss factor precisely, catalogue the inputs, derive the equations, implement a deterministic calculation, and validate outputs against supervisory control and data acquisition (SCADA) evidence. We also reference complementary workflows such as the Wind Turbine Capacity Factor Calculator and the flexibility valuation guide to show how wake analysis connects with portfolio revenue planning.
Definition and analytical context
Wake loss factor (sometimes called wake loss percentage) is the fractional reduction in aerodynamic power experienced by a downstream turbine relative to the free-stream wind available before any turbines disturb the flow. Formally, it compares the cube of the wake-affected wind speed to the cube of the undisturbed wind speed because wind turbine power is proportional to the third power of velocity within the operational range. The result is typically expressed as a percentage deficit, where 0% indicates no wake loss and 100% indicates total flow stagnation.
The metric underpins energy production estimates, array optimisation, and availability guarantees. Developers include wake loss factors within pre-construction energy yield assessments presented to investors. After commissioning, asset managers reconcile actual production against wake-adjusted baselines to attribute underperformance to controllable factors. Because wake behaviour depends on turbine spacing, terrain-induced turbulence, and rotor aerodynamics, consistent methodology is essential when benchmarking projects in different regions or when negotiating power purchase agreements that rely on expected net energy.
Variables, symbols, and units
Establishing clear symbols prevents accidental mixing of incompatible datasets when running batch analyses. Throughout this guide we apply SI units and rotor-diameter normalisation conventions commonly used in layout design.
- U0 – Free-stream wind speed upstream of the array (m/s).
- x – Downstream separation distance (m).
- D – Rotor diameter of the turbine creating the wake (m).
- CT – Thrust coefficient (dimensionless) from the turbine power curve at the analysed wind speed.
- k – Wake decay constant (dimensionless) describing how quickly the wake radius expands; ranges from approximately 0.04 offshore to 0.1 onshore.
- U – Wind speed at the downstream rotor centreline (m/s).
- Rw – Wake radius at distance x (m).
- fw – Wake loss factor (unitless), reported as a percentage power deficit.
- ηp – Power retention factor (unitless), equal to 1 − fw.
Converting downstream spacing to rotor diameters (x/D) simplifies comparisons across different turbine models within the same project. When you build portfolio dashboards, store both the dimensional spacing and the diameter-normalised value so layout updates or repowering studies can reuse the inputs without recomputation.
Formulas underpinning the Jensen wake model
The Jensen model assumes a linearly expanding “top-hat” wake where velocity deficit is uniform across the wake diameter. Wake radius grows according to Rw = R + kx, with R = D/2. Mass continuity and momentum theory yield the downstream wind speed:
U = U0 \[1 − (1 − √(1 − CT)) / (1 + 2k x / D)2].
Velocity ratio r = U / U0.
Power retention ηp = r3.
Wake loss factor fw = 1 − ηp.
The thrust coefficient governs how much kinetic energy the upstream turbine extracts. Typical operating values sit between 0.75 and 0.9 within the below-rated wind regime. The wake decay constant represents turbulence-driven mixing with ambient air: higher k values shrink the velocity deficit more quickly. The squared denominator enforces conservation of mass by scaling the expanded wake area. Because r must reside between 0 and 1, clamp intermediate results during implementation to avoid numerical artefacts when inputs fall outside realistic ranges.
Translating the equations into code requires careful rounding so financial models and SCADA reconciliations align. The embedded calculator at the end of this article packages the equations, input validation, and formatting using the same patterns that power our battery arbitrage walkthrough, keeping analytical conventions consistent across technologies.
Step-by-step calculation workflow
Step 1: Establish the reference wind regime
Start with a representative free-stream wind speed. For annual energy assessments use long-term mean wind speeds binned by direction sector. For operational diagnostics, extract 10-minute average wind speeds from an upstream meteorological mast or a turbine positioned on the prevailing windward edge. Ensure the sensor height matches hub height or apply shear corrections; mixing heights will distort thrust coefficients pulled from manufacturer curves.
Step 2: Convert turbine spacing into rotor diameters
Measure the centreline distance between the wake-generating turbine and the turbine under analysis. Divide by rotor diameter to obtain spacing in D units. If the site deploys multiple turbine models, calculate spacing relative to the upstream rotor: mixing diameters inside the same sector can introduce bias because the wake growth rate references the upstream rotor radius. Store these values per wind direction to capture staggered layouts.
Step 3: Retrieve thrust coefficients
Turbine manufacturers publish CT curves alongside power curves. Sample the coefficient at the relevant free-stream wind speed. If you only have power coefficient data, convert using CT = 4a(1 − a) where a is the axial induction factor. For SCADA validation, compute empirical thrust coefficients by rearranging the power equation: use measured electrical power to infer the induction factor, then derive CT. Maintain unit consistency by working with air density-corrected wind speeds.
Step 4: Select the wake decay constant
Choose k based on terrain roughness, ambient turbulence intensity, and atmospheric stability. Offshore arrays with low turbulence typically use 0.04–0.06. Onshore flat terrain might warrant 0.07–0.1, while forested or complex topography can exceed 0.12. Align k with the turbulence assumptions in your energy yield assessment so wake predictions match the environmental conditions used during financing. Document the rationale to simplify audits.
Step 5: Compute velocity ratio and wake loss factor
Substitute inputs into the Jensen equation. Calculate r, raise it to the third power for power retention, and subtract from 1 to obtain the wake loss factor. Express the result as a percentage to aid communication with project stakeholders who track other losses such as electrical collection efficiency or curtailment. When assessing entire rows of turbines, propagate the calculation sequentially from the leading row downstream, updating U0 with the wake-affected speed from the previous turbine.
Data validation and operational monitoring
Validation hinges on comparing modelled wake-adjusted production with SCADA data filtered by wind direction, stability class, and turbine availability. Construct directional bins (e.g., 10° increments) and compute average downstream power when the upstream turbine is online. Apply the theoretical wake loss factor to the upstream turbine’s expected power—via the capacity factor calculator referenced earlier—and verify the downstream turbine matches within tolerance. Deviations signal incorrect thrust coefficients, mischaracterised turbulence, or yaw misalignment.
Incorporate seasonal reviews: cold seasons with higher air density can shift operating points along the CT curve, altering wake magnitude. Likewise, maintenance that changes rotor roughness (such as blade cleaning) modifies turbulence and should be logged alongside wake recalculations. Store historical wake factors in a version-controlled analytics repository so refinements remain auditable for lenders and insurers.
Limitations and edge cases
The Jensen model simplifies reality by assuming uniform velocity deficits and neglecting wake meandering. Arrays in complex terrain or under strong thermal stratification may require more advanced models (e.g., Eddy-Viscosity or Large Eddy Simulation) to capture shear layers and yaw misalignment. Additionally, turbines with active wake steering deliberately skew the wake; the simple top-hat assumption breaks down and you should apply directional correction factors derived from field tests.
When multiple wakes overlap—common in high-density offshore layouts—you must combine deficits before computing power retention. Analysts typically use quadratic superposition (root-sum-square of velocity deficits) or energy-balance methods. This article confines itself to single-wake interactions to keep the walkthrough tractable; extend the workflow within spreadsheet or scripting environments where you can sum contributions from each upstream turbine directionally.
Embed: Wind farm wake loss factor calculator
Use the embedded calculator to run deterministic Jensen-model computations with validated formatting. It enforces unit checks, applies a sensible default for the wake decay constant, and outputs both the wake loss percentage and residual rotor wind speed so you can slot the results directly into energy yield and performance monitoring workbooks.