Wind Turbine Farm

Each rotor's mechanical power is P = C_p(λ) · ½ρAv³, where λ = ωR/v is the tip-speed ratio. Below rated wind speed the controller tracks the tip-speed ratio that maximizes C_p (maximum power-point tracking). Above rated wind speed, blade pitch trims C_p down so power holds at the turbine's rated value instead of rising with v³. Betz's law caps any rotor's C_p at 16/27 ≈ 0.593; this model's peak C_p sits lower, in the 0.40–0.48 range real utility turbines actually reach once blade-profile losses are included.

Characteristics

• Cut-in wind speed: 3.5 m/s — below this the rotor is parked
• Rated wind speed: 12 m/s — power output plateaus from here
• Cut-out wind speed: 25 m/s — rotor brakes and feathers to protect the drivetrain
• Peak power coefficient: ≈0.48, tracked via optimal tip-speed ratio λ ≈ 8.1
• Power scales with the cube of wind speed while below rated