Momentum theory: the rotor is an actuator disk. With axial induction factor a the speed at the disk is v(1-a) and far downstream v(1-2a). Power P = 1/2 rho A v^3 Cp with Cp = 4a(1-a)^2; setting dCp/da = 0 gives a = 1/3 and the Betz limit Cp = 16/27 = 0.593. Thrust coefficient Ct = 4a(1-a). Mass conservation fixes the streamtube radius: r(x) = R sqrt((1-a)/(u/v)).
Real rotors follow Cp(lambda, beta), lambda = omega R / v. Here the widely used empirical fit Cp = 0.5176 (116/li - 0.4 beta - 5) e^(-21/li) + 0.0068 lambda, 1/li = 1/(lambda+0.08 beta) - 0.035/(beta^3+1). Peak is about 0.48 near lambda 8. Electrical power is the rotor power times a 0.95 drivetrain efficiency.
Operating regions (same as the 3D page): below cut-in 3 m/s nothing; between cut-in and rated 12 m/s the controller holds the chosen lambda; above rated the blades pitch to hold 150 kW (power would otherwise rise as v^3); above 25 m/s the turbine feathers and stops.
Simplifications: no wake rotation, tip losses, tower shadow or dynamic stall; gusts are an Ornstein-Uhlenbeck process; the power trace is low-pass filtered with a 4 s time constant. The streamtube drawing is schematic: its expansion comes from mass conservation, not CFD.