Wind turbines remove energy from moving air, creating downstream regions of reduced mean wind speed and altered turbulence known as wakes. When turbines share the same inflow, those wakes affect the energy production and mechanical loading of neighbouring machines.
The gold standard is a model whose physical assumptions, wind conditions, turbine characteristics and wake-loss predictions can be tested against independent measurements. A colourful flow field is not evidence of reliable annual yield unless the model handles direction, stability, control and uncertainty.
eduKateSG · Wind Farm Wake Modelling
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Calculate a simplified wake deficit, examine its consequences for power, then test model suitability against real turbine, wind and lidar data.
Full chapter index · Practice and transfer · Education root · How X Works
Full chapter index
Describe the wake · Chapters 1–2
Calculate deficits · Chapters 3–4
Check model assumptions · Chapters 5–7
Validate real performance · Chapters 8–10
Continue the network · Chapters 11–12
CHAPTER 1 OF 12 · Describe the wake
1. A downstream turbine does not see undisturbed upstream wind
A turbine converts a fraction of the incoming wind’s kinetic energy into useful shaft or electrical power. Its rotor leaves a slower mean-flow region downstream. That speed reduction is accompanied by shear and turbulence that can influence power and fatigue loading.
How the wake develops depends on thrust, rotor diameter, atmospheric stability, ambient turbulence, terrain, wind direction and interaction with other wakes. Two turbines separated by a fixed distance may behave very differently in stable night air and convective daytime mixing.
Define the wind quantity. Hub-height speed is not necessarily the same as rotor-equivalent speed, and a ten-minute average cannot describe every gust that influences loads.
Distinguish gross power in free-stream conditions, wake-affected power and net electricity after electrical or operational losses. A model must identify which boundary its prediction covers.
A basic wake model is a reasoning instrument: it permits transparent calculations but cannot directly certify an actual site’s energy return.
CHAPTER 2 OF 12 · Describe the wake
2. Engineering wake models compress a difficult flow problem
High-fidelity fluid mechanics can represent three-dimensional turbulent flow and turbine interaction, but requires substantial information and computation. Engineering wake models simplify the problem for layout analysis, control and large numbers of wind-condition evaluations.
FLORIS, developed through national-laboratory research and collaborators, is an engineering wake and control simulation framework with multiple model families. Models may represent mean velocity deficits, lateral wake deflection, mixing and superposition.
A simplified Jensen or top-hat-type treatment represents a growing wake region with approximately uniform speed deficit across its cross-section. Gaussian models represent a spatially varying deficit. Neither should be used outside its calibrated assumptions merely because it produces a plausible plot.
Wake superposition is not always the sum of isolated percentage losses: interacting flow, turbulence and control can change effective deficits. Layout predictions must specify how overlapping wakes are combined.
IEA Wind Task 31 established a model intercomparison approach because different prediction tools and validation datasets can lead to different conclusions for the same site. Consistent validation definitions are part of a meaningful comparison.
CHAPTER 3 OF 12 · Calculate deficits
3. Worked example: an idealized Jensen-type velocity deficit
Adopt an invented uniform inflow speed U∞ = 10.0 m/s, thrust coefficient CT = 0.75, wake expansion parameter k = 0.05 and a downstream distance x = 5 rotor diameters D. These are modelling assumptions, not parameters for an identified turbine.
In simple axial momentum theory the induction factor is a = [1 − √(1 − CT)]/2, giving a = [1 − √0.25]/2 = (1 − 0.5)/2 = 0.25.
Use the elementary fully overlapped Jensen-type deficit expression ΔU/U∞ = 2a/[1 + 2kx/D]². At x/D = 5, the denominator is [1 + 2 × 0.05 × 5]² = 1.5² = 2.25.
The fractional mean deficit is 2 × 0.25/2.25 = 0.2222. Estimated downstream speed is U = U∞(1 − 0.2222) ≈ 7.78 m/s under the specified top-hat overlap assumption.
This result has no uncertainty estimate, excludes shear and turbulence structure, and assumes a suitable model regime. It cannot be reported as the actual speed at a particular downstream turbine without site-specific validation.
CHAPTER 4 OF 12 · Calculate deficits
4. Worked example: wake recovery changes potential power
Suppose the same toy model uses a larger wake-expansion parameter k = 0.10 at the same x/D = 5, while maintaining CT = 0.75 and U∞ = 10 m/s. The denominator becomes [1 + 2 × 0.10 × 5]² = 2² = 4.
The model deficit is then 0.5/4 = 0.125 and downstream mean speed is 8.75 m/s. This demonstrates a faster modelled recovery as k increases; it does not establish that actual atmospheric turbulence can be represented by freely choosing k.
For a simple aerodynamic comparison holding rotor area, density and power coefficient constant and avoiding rating or control limits, available power scales with U³. At U = 7.78 m/s relative to U∞ = 10 m/s, the approximate ratio is (7.78/10)³ ≈ 0.471.
Under the faster-recovery example the ratio is (8.75/10)³ ≈ 0.670. The large difference shows why the wake-expansion assumption strongly affects predicted output.
Real turbines have nonconstant power curves, cut-in and rated regimes, yaw controls and rotor-averaging effects. Cubing a single modeled point velocity is not a complete power-performance calculation.
CHAPTER 5 OF 12 · Check model assumptions
5. Spacing, alignment and partial wakes complicate the calculation
A turbine directly in line with an upstream rotor may intercept much of its wake; a lateral offset may cause a partial wake. The rotor averages flow over a swept area, rather than sampling only one hub-height point.
The downstream deficit changes with x/D, where D is rotor diameter, not a fixed distance in metres across all turbine sizes. Comparing two layouts in metres alone hides scale differences.
Real wind directions vary around a sector mean. A small direction error can shift which turbines interact, especially where spacing creates narrow alignments. Direction uncertainty should be measured and propagated into predicted wake losses.
Terrain, coastal transitions, atmospheric stability and shear can alter the expansion rate and wake trajectory. A top-hat deficit calibrated over flat terrain in neutral conditions may overpredict or underpredict another location.
The model should specify turbine identities, rotor diameters, heights, thrust and power curves, wind direction convention and the overlap calculation before generating farm totals.
CHAPTER 6 OF 12 · Check model assumptions
6. Turbulence affects both recovery and mechanical loading
Ambient turbulence transports momentum into a wake and can accelerate its recovery. Turbine-generated turbulence changes the downstream fluctuation field and can influence fatigue loading.
Two models with similar mean downstream speeds may predict different load environments. A wake-energy estimate and an engineering reliability estimate therefore need different observables.
Wake meandering describes changes in the location of the turbulent wake over time. A time-averaged wake deficit does not capture every gust, shear episode or loading cycle experienced by blades and towers.
Numerical approaches such as large-eddy simulation can represent unsteady structures at greater computational cost, while engineering models are suitable for many optimization studies. Model fidelity should be chosen for the intended question.
Validation must examine more than average power when the result is used for structural loading or maintenance decisions.
CHAPTER 7 OF 12 · Check model assumptions
7. Lidar, SCADA and met masts provide complementary checks
Wind lidar can measure line-of-sight velocity patterns that help constrain inflow and wake structure. It does not usually observe an entire three-dimensional vector field without assumptions about scan geometry and wind homogeneity.
Supervisory control and data acquisition (SCADA) records provide operational turbine information such as power, rotor speed and selected wind measurements. Nacelle-mounted anemometers may experience turbine-induced flow distortion and need careful correction.
Meteorological masts, scanning lidar, nacelle lidar and SCADA each sample different volumes and time resolutions. Co-locate, synchronize and process them to compare equivalent quantities.
Exclude or label curtailment, outages, sensor faults, wake steering modes and periods of unsuitable quality. If a model is tuned and evaluated against the same data, the reported fit is not an independent validation.
NREL and IEA Wind Task 31 material emphasizes model comparison against controlled datasets. The important output is reproducible predictive error across stated atmospheric and operational regimes, not a single attractive case study.
CHAPTER 8 OF 12 · Validate real performance
8. Wake steering trades immediate turbine output for a farm objective
Yaw misalignment can deliberately deflect a wake in some control strategies. The upstream turbine may sacrifice some power while a downstream turbine gains from receiving less wake impact.
The farm-wide net change depends on direction, turbulence, yaw control response and the number of affected turbines. A strategy that helps one turbine under one condition can be ineffective or harmful in another.
A robust control evaluation compares a specified baseline with a modified controller using appropriately matched conditions. Randomized or alternating periods may help separate the effect of control from wind variability when operationally appropriate.
Controllers are constrained by turbine safety, load envelopes, communications and approved operating limits. Modelled gains should never be treated as authorization to operate turbines outside certified settings.
Document whether the optimization goal is instantaneous farm power, expected annual energy or combined power–load performance. These goals are not identical.
CHAPTER 9 OF 12 · Validate real performance
9. Worked example: weigh two wind-direction sectors
Consider a stylized downstream turbine with only two types of hour in a calendar year. In 30% of hours it is strongly wake-affected and produces a mean 1.0 MW; in the other 70% it produces a mean 1.6 MW. These are hypothetical already-defined operating-state outputs.
The conditional annual mean is P̄ = 0.30 × 1.0 + 0.70 × 1.6 = 0.30 + 1.12 = 1.42 MW. Multiplying by 8,760 hours in a notional non-leap year gives 12,439.2 MWh.
This is not an estimate of a real wind plant’s annual energy. It assumes these sectors span every hour, outputs include any intended losses consistently, there is no downtime and that the frequencies represent the whole year’s conditions.
A realistic annual-energy study sums power over many wind-speed, direction, stability and operational bins, then adjusts for verified availability and other defined losses.
Changing only the wake model without updating these occurrence and power-response assumptions does not establish a new annual yield. The result must be evaluated over representative atmospheric distributions.
CHAPTER 10 OF 12 · Validate real performance
10. Uncertainty and independent performance matter more than a single best fit
Engineering wake models use simplified parameters governing expansion, deflection, turbulence and overlapping deficits. Several parameter choices can reproduce the same power data under one wind direction yet diverge in another.
Compare predicted and measured velocity or power under withheld cases; evaluate errors by spacing, wind direction, turbulence intensity, stability and speed regime. A single mean absolute error can hide systematically poor extreme conditions.
Use appropriate uncertainty treatment for correlated observations: consecutive ten-minute records and nearby turbines are not independent draws. Randomizing individual rows across training and test sets can leak weather regimes into both.
A physically richer simulation is not automatically more reliable than a simple one if the inflow conditions, turbine response or validation data are uncertain. Model cost and predictive purpose must be evaluated together.
IEA Wind Wakebench’s benchmark framework is valuable because it promotes shared definitions, transparent test cases and traceable model results rather than uncheckable model marketing.
CHAPTER 11 OF 12 · Continue the network
11. Practice, FAQs and transferred model assumptions
Practice A: In the same Jensen-type example with a = 0.25, k = 0.05 and x/D = 10, deficit is 0.5/(1 + 1)² = 0.125. Estimated wake-region speed is 8.75 m/s. Identify at least two reasons why the actual rotor-average speed may differ.
Practice B: If a hypothetical turbine produces 2.0 MW without wake effects and 1.5 MW under a representative wake condition, the relative power loss for that condition is (2 − 1.5)/2 = 25%. Explain why it does not automatically imply a 25% annual-energy loss.
FAQ — Does every downstream machine lose the same power? No. Direction, distance, rotor overlap, operating point and other wakes matter.
FAQ — Is a lidar velocity field direct evidence of electrical yield? No. The turbine power curve, control, availability and losses still intervene.
FAQ — Is the most detailed model always the most accurate? No. Correct inflow, validation and appropriate assumptions can matter more than nominal model complexity.
Transfer the same wake calculation from an ideal offshore row to complex hilly terrain. State which model assumptions and validation observations must change before drawing an engineering or financial conclusion.
The following verified eduKateSG reading routes connect the specialist measurement to broader systems and methods. They are complementary explanations, not replacements for a field calibration or validated model.
- The Gold Standard of Wind Energy — turbine generation and power curves
- The Gold Standard of Wind Lidar — line-of-sight wind measurement and uncertainty
- The Gold Standard of Wind Profiling — vertical structure, shear and atmospheric conditions
- The Gold Standard of Atmospheric Science — turbulence, stability and boundary layers
- The Gold Standard of Weather Forecast Verification — independent prediction assessment
- The Gold Standard of Physics — energy, momentum and flow
- The Gold Standard of Statistics — correlated data and out-of-sample uncertainty
Wind farm wake modelling connects turbine energy extraction, atmospheric dynamics and measured wind signals. A model that answers mean farm output does not automatically answer fatigue loading or long-term site suitability.
The linked roots offer routes from fundamental wind physics through lidar observations to statistically fair model evaluation.
Primary sources and reference guidance for checking the techniques, boundaries and assumptions in this article:
- FLORIS Documentation: Wake Modelling and Controls — engineering wake families and model workflow
- IEA Wind Task 31, Wakebench Framework — shared validation and model comparison
- NREL, Open-Source FLORIS Overview — wind-plant interactions and control purposes
- FLORIS, Empirical Gaussian Wake Model Documentation — wake mixing, deficit and deflection details
The velocity-deficit expression uses a simplified fully overlapped Jensen-style top-hat model; its parameters and constant-power-coefficient calculations are teaching assumptions, not site predictions.
The learning standard connects a clear question, an observable, a worked example, a check and a transfer problem. The immutable Clementi Secondary 1 Mathematics teaching reference shows a comparable educational method, not a scientific reference for Wind Farm Wake Modelling.