Power available in the wind is Pwind = ½·ρ·A·v³. A turbine only converts a fraction Cp of it, and Cp itself depends on the tip-speed ratio λ = ωR/v and blade pitch β through the empirical Heier/Slootweg model:
1/λi = 1/(λ+0.08β) − 0.035/(β³+1)
Cp = 0.5176·(116/λi − 0.4β − 5)·exp(−21/λi) + 0.0068·λ
Below rated wind speed the generator tracks λ at its optimum (≈8.1, pitch fixed at 0°) — this is Maximum Power Point Tracking (MPPT), the region-2 control strategy real variable-speed turbines use. Above rated wind speed, rotor speed is held fixed so λ falls as v rises, and the pitch slider now matters: raising β spills lift and drops Cp, which is exactly how real turbines cap mechanical power near the generator's rated capacity without needing a hard clamp. Leave β at 0° above rated speed and the "⚠ overload" badge appears — power is being clipped by the generator limit instead of being shed aerodynamically.
The farm row uses the Jensen/Park wake model: each turbine's thrust coefficient Ct is recovered from its Cp via actuator-disk theory (Cp = 4a(1−a)², Ct = 4a(1−a)), and the velocity deficit behind it decays with downstream distance x as (1−√(1−Ct))·(r₀/(r₀+k·x))². Each turbine 5 rotor-diameters downstream of the last therefore sees a slower, non-uniform inflow — the reason real wind farms space turbines out and why the rearmost machines produce less.
- Power curve — electrical output vs. wind speed for the current D and β; the dot marks turbine 1's live operating point.
- Farm row — blade colour encodes each turbine's local output fraction; the shaded wedge behind each rotor is its wake.