Description of Wind Energy Production Calculations

1. Recalculating Wind Speed for Hub Height

Wind speed is adjusted from the measured height (usually 10m or 80m) to the hub height of the turbine using the formula:

v_h = v_r * (h / h_r)^α

Where:

• v_h: wind speed recalculated at hub height (h).
• v_r: wind speed measured at reference height (h_r).
• h: hub height of the turbine (m).
• h_r: reference height (m).
• α: terrain roughness coefficient.

Terrain Roughness Coefficient (α):

• Flat and open terrain: α = 0.1.
• Urban or forested areas: α = 0.25.
• High roughness (mountains): α = 0.4.

2. Air Density

Air density (ρ) is essential for calculating wind energy and is influenced by:

• Temperature (T): Affects air pressure.
• Atmospheric Pressure (P): Decreases with altitude.
• Relative Humidity (RH): Introduces water vapor, which is less dense than dry air.

Air density is calculated using the equation:

ρ = P / (R_d * T) * (1 - 0.378 * RH)

3. Wind Power

The power available in the wind is calculated by:

P_wind = 0.5 * ρ * A * v³

Where:

• ρ: air density (kg/m³).
• A: area swept by the turbine blades (m²).
• v: recalculated wind speed (m/s).

4. Turbine Power

The power converted by the turbine is:

P_turbine = C_p * P_wind

Where:

• C_p: power coefficient (theoretical maximum: 0.59; realistic: 0.3–0.45).
• P_wind: wind power (kW).

5. Energy Production

The energy generated per hour is:

E = P_turbine * t

Where:

• E: energy produced (kWh).
• P_turbine: turbine power (kW).
• t: operating time (hours).

6. Application Functionalities

The application provides the following features:

• Ability to save multiple locations with specific names, coordinates, and turbine configurations.
• Selection and loading of saved locations to retrieve their associated turbine settings and coordinates.
• Dynamic recalculations based on the selected location, ensuring accurate results tailored to specific configurations.
• Visualization of hourly and daily wind energy production through interactive tables and graphs.
• Integration with Google Maps for intuitive location selection and marker updates.
• Detailed configuration options for turbines, including height, power limit, and loss coefficients.
• Automatic persistence of configurations and user settings using localStorage.
• Export options for production data in CSV and Excel formats.

Numerical Example

Inputs:

• Wind speed (v_r): 5 m/s (measured at 10m).
• Hub height: 80 m.
• Roughness (α): 0.14.
• Rotor diameter: 120 m.
• Total efficiency: 35%.
• Temperature: 15 °C, pressure: 101325 Pa, humidity: 50%.

Calculations:

• v_h = 5 * (80 / 10)^0.14 = 6.12 m/s.
• ρ = 1.225 * (1 - 0.378 * 0.5) = 1.176 kg/m³.
• A = π * (120 / 2)² = 11309.73 m².
• P_wind = 0.5 * 1.176 * 11309.73 * 6.12³ = 1557.4 kW.
• P_turbine = 0.35 * 1557.4 = 545.1 kW.
• E = 545.1 * 1 = 545.1 kWh.