When to use: Estimating the yearly energy yield of a wind turbine at a given site. The site wind resource is modeled with a Weibull distribution (mean speed + shape factor k), and the turbine response with a power curve (cut-in, rated, cut-out). AEP is the integral of P(v)·f(v) across all wind speeds × 8760 h, reduced by wake and system losses. The capacity factor compares average output to rated power.
This calculator estimates the annual energy production (AEP) of a wind turbine by integrating the turbine power curve against a Weibull-distributed wind speed probability distribution. Engineers use it for wind project feasibility studies, turbine selection, and capacity factor estimation before full microscale wind resource assessments.
AEP is computed as the integral of power output over all wind speeds, weighted by the probability of each wind speed occurring: AEP = 8760 × ∫ P(v) × f(v) dv, where P(v) is the turbine power curve (kW at wind speed v) and f(v) is the Weibull probability density function. The Weibull distribution is the standard model for wind speed frequency at most sites, characterized by two parameters: scale factor c (related to mean wind speed) and shape factor k (describing wind variability).
The turbine power curve defines three operating regions: zero output below cut-in wind speed (typically 3–4 m/s), cubic ramp-up from cut-in to rated wind speed (typically 10–14 m/s), and constant rated power output from rated wind speed to cut-out speed (typically 22–25 m/s), where the turbine shuts down to prevent mechanical overstress. The cubic relationship between power and wind speed means doubling wind speed increases power by 8× — small changes in mean wind speed have large effects on AEP.
Net AEP applies a system and wake loss factor to the gross AEP. Typical losses include wake effects in wind farms (8–15%), electrical transmission losses (1–3%), availability (2–5%), and curtailment (0–5%). A well-designed wind farm achieves 85–90% availability and 5–15% total losses, delivering 85–95% of gross AEP as net generation to the grid.
IEC 61400-1 (Wind Energy Generation Systems — Design Requirements) is the primary standard for wind turbine structural and safety design, specifying wind class definitions (I through III based on mean wind speed and turbulence) and requiring compliance for all grid-connected turbines above 1 kW.
IEC 61400-12 (Wind Energy Generation Systems — Power Performance Measurements of Electricity Producing Wind Turbines) defines the standard method for measuring and reporting power curves, which are the input to AEP calculations. Power curves must be measured with a calibrated anemometer on a met mast positioned one to two rotor diameters upwind of the turbine under defined terrain conditions.
IEEE 1547-2018 governs interconnection requirements for distributed wind generation connected to the grid at distribution voltage levels. Utility-scale wind projects follow NERC reliability standards for bulk power system interconnection. The Betz limit (Cp_max = 16/27 ≈ 0.593) sets the theoretical maximum power extraction coefficient for any wind turbine, establishing the upper bound on aerodynamic efficiency.
Mean wind speed is the most critical site parameter — AEP scales approximately as the cube of mean wind speed. A site with 7 m/s mean wind produces roughly 2.7× more energy than a 5 m/s site with the same turbine (7³/5³ = 2.74). Even a 10% improvement in hub height wind speed (achievable by raising the tower from 80m to 100m) can increase AEP by approximately 30% due to the cubic relationship.
Weibull shape factor k describes wind variability. Sites with k = 2 (Rayleigh distribution) are common for most inland and coastal sites. Higher k (2.5–3.5) indicates steadier winds with less variability, common in trade wind belts and some offshore sites. Lower k (1.5–2.0) indicates more variable winds with more frequent calms and storms. For the same mean wind speed, higher k sites generally produce slightly less AEP because variability is reduced.
Capacity factor (net AEP ÷ (rated power × 8760 hours)) is the standard metric for wind project performance. Onshore wind typically achieves 25–40% capacity factor; offshore wind achieves 35–55%. High-capacity-factor sites (>35%) are generally required for economic viability without production tax credits. Modern turbines with longer blades and lower specific power (W/m²) are optimized for lower wind speed sites and achieve 35–45% capacity factor at Class III sites (7 m/s mean).
Enter the turbine rated power (kW), cut-in wind speed (typically 3–4 m/s), rated wind speed (typically 10–14 m/s), and cut-out wind speed (typically 22–25 m/s) from the manufacturer's power curve data sheet. These define the three regions of the power curve model.
Enter the mean annual wind speed at hub height from a site wind resource assessment (met mast data, reanalysis data from MERRA-2, or NREL's Wind Toolkit). Enter the Weibull shape factor k — use k = 2.0 (Rayleigh) if unknown. Enter total system and wake losses as a percentage.
The calculator numerically integrates P(v) × f(v) from 0 to cut-out in 0.1 m/s steps and multiplies by 8760 hours for gross AEP. Review Net AEP, capacity factor, and Weibull scale factor c. Compare capacity factor against regional benchmarks (25–35% onshore, 35–50% offshore) to validate site suitability.
The Betz limit (16/27 ≈ 59.3%) is the theoretical maximum fraction of kinetic energy that can be extracted from wind by any rotor, derived from momentum theory. No turbine can exceed this — doing so would violate conservation of momentum. Modern large commercial turbines (GE Haliade-X, Vestas V236) achieve power coefficients (Cp) of 0.45–0.50 near rated wind speed, representing 76–84% of the Betz limit and a remarkable engineering achievement.
Onshore wind projects achieving 30–40% capacity factor are generally considered economically competitive with natural gas in most markets. Projects below 25% capacity factor are marginal without strong incentives. Offshore wind achieves 40–55% capacity factor due to stronger, steadier winds. The US average onshore capacity factor has risen from 25% (2010) to 34% (2022) as turbine technology has improved — larger rotors and taller towers access higher-quality wind resources at lower specific power.
Wind speed increases with height following the power law: v(h) = v_ref × (h/h_ref)^α, where α is the shear exponent (typically 0.14 for open terrain, 0.20–0.25 for forested or suburban terrain). For a 80m hub height and surface measurement at 10m with α = 0.14: v(80) = v(10) × (80/10)^0.14 = v(10) × 1.29. A 10m wind of 5 m/s translates to 6.45 m/s at 80m hub height — a 29% increase that more than doubles the AEP.
Wake effect is the reduction in wind speed downstream of a wind turbine, caused by energy extraction from the flow. Turbines in the wake of upstream turbines experience lower wind speeds and higher turbulence, reducing their output by 10–40% depending on spacing, wind direction, and atmospheric stability. Array efficiency for a typical wind farm ranges from 85–95%; the system loss factor in this calculator should include wake losses of 8–15% for farms with tight spacing or complex terrain.
For preliminary feasibility, use NREL Wind Toolkit (windtoolkit.nrel.gov) or Global Wind Atlas (globalwindatlas.info) for mean wind speed at hub height. For bankable energy assessments, a minimum 12-month on-site met mast measurement at or near hub height is required, correlated to long-term reference data (MERRA-2 or ERA5 reanalysis) using MCP (measure-correlate-predict) methods per IEC 61400-12-1 and the IEA Wind Task 32 guidelines.
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