Wind turbine & farm

rated turbine: ~6 MWrated turbine
peak Cp (81% of Betz): 0.48peak Cp (81% of Betz)
farm AEP vs naive grid: +18%farm AEP vs naive grid
16-turbine farm: 295 GWh/yr16-turbine farm
design notebooks: 9design notebooks
.djl composition: 1.djl composition

From one rotor to a wake-optimised farm.

A multi-megawatt turbine modelled where aerodynamics, drivetrain dynamics and control meet — the Cp(λ) surface, a two-inertia drivetrain, region-2 MPPT and region-3 pitch control, and turbulent loads — then scaled out to a farm where wake interaction is optimised away for 18% more annual energy. The drivetrain also lives as a runnable acausal .djl over a custom rotational domain.

Aerodynamics, control, and a whole farm.

Each subsystem is its own runnable notebook, building from a single rotor's coefficient curve up to a wake-coupled farm layout.

Rotor aerodynamics

The power coefficient Cp(λ, pitch) and the full power curve — peak Cp ≈ 0.48 at a tip-speed ratio of 8.1, 81% of the Betz limit, across cut-in, rated and cut-out.

Drivetrain

A two-inertia drivetrain — rotor, a compliant low-speed shaft, gearbox and generator — spins up under a K-ω² law to 12.3 rpm and re-settles cleanly after a wind step.

MPPT control

A wind-sensorless K-ω² torque law holds the tip-speed ratio around its optimum through varying wind, capturing near-ideal power in region 2.

Pitch control

A PI pitch loop feathers the blades in region 3 to hold rated power through a +5 m/s gust with only 0.4% overspeed.

Turbulent loads

A Dryden-like turbulent wind field (TI ≈ 0.14) drives the rotor to a ~736 kN thrust load, with a low-frequency-dominated load spectrum from the FFT.

Farm & wake

A Jensen wake model with a CMA-ES layout optimiser lifts wind-rose annual energy 18% over a naive 4×4 grid — the optimised 16-turbine farm on a map.

A notebook plot of turbine power in megawatts and effective power coefficient against wind speed, across cut-in, rated and cut-out — The turbine's power curve: zero below cut-in, the cubic climb through region 2 where MPPT maximises capture, the flat rated plateau where pitch control caps power, and the cut-out. The effective Cp (dashed) shows the rotor running at peak efficiency only in the climb.

A notebook plot of the power coefficient Cp as a function of tip-speed ratio for a family of blade-pitch angles — The aerodynamic heart of the machine: Cp(λ) for a family of blade pitches. The peak — Cp ≈ 0.48 at λ ≈ 8.1, zero pitch — is the operating point MPPT chases in region 2; feathering the pitch slides the whole curve down to shed power in region 3.

A drivetrain on a brand-new physical domain.

The two-inertia drivetrain is a runnable acausal .djl — aerodynamic torque into a rotor inertia, through a compliant shaft and a step-up gearbox, into the generator's torque-control brake. It is built on a custom rotational domain (angle as the potential, torque as the flow) that doesn't ship in the block catalog — defined inline in a few lines and solved by the same kernel that handles electrical and mechanical networks, with no engine changes. It spins up from 1.0 to 1.49 rad/s to its region-2 torque balance, about 6 MW. The same acausal kernel models fluid power, rotational mechanics, or any domain you can write a connector for.

A notebook plot of the rotor thrust-load power spectral density against frequency, dominated by low-frequency content — Turbulent loading in the frequency domain: the power spectral density of rotor thrust under a Dryden-like wind field. The low-frequency dominance is what fatigue analysis cares about — the slow, large gusts that the structure feels cycle after cycle.

Every claim is a number you can re-run.

The notebooks are gated on worker-verified results, and the drivetrain .djl is confirmed solving through the production canvas engine.

Result

Peak power coefficient: 0.48
Rated power held through gust: +0.4% overspeed
Turbine annual energy: 20.3 GWh/yr
Farm annual energy: 295 GWh/yr
Wake-optimised AEP gain: +18%

Detail

Peak power coefficient: 81% of Betz
Rated power held through gust: PI pitch
Turbine annual energy: CF 46%
Farm annual energy: CF 42%, 9% wake
Wake-optimised AEP gain: vs 4×4 grid

Design-grade aero, control and wake.

Aerodynamics is a Cp(λ, pitch) coefficient model, not a blade-element-momentum or CFD rotor; the drivetrain is a lumped two-inertia model; the wake is the analytic Jensen model, not a high-fidelity wake simulation. Turbulence is a Dryden-like spectral field. That is the fidelity wind-farm design needs first: sizing the rotor and drivetrain, tuning the torque and pitch controllers, bounding turbulent loads, and laying out the array so wakes cost the least energy — on your own site wind rose, before a CFD campaign or an aeroelastic model.