Nonlinear System Identification for Model-Based Control of Waked Wind Turbines

TL;DR

This work develops a nonlinear system identification framework to model wind-turbine power extraction in both freestream and waked conditions by representing the power coefficient $C_p$ with compact radial-basis and polynomial basis surrogates. Embedded in a first-order dynamic model and identified in real time via adjoint gradients and ADAM optimization, the approach yields interpretable, adaptive controllers without resorting to black-box learning. Experimental validation in tandem low-turbulence and wind-farm high-turbulence tests demonstrates accurate state prediction and improved model-based control performance over traditional BEM and steady-state methods, including wake mitigation in a downstream turbine. The results highlight robustness and practical applicability for adaptive wind-farm operation, with clear pathways toward integration with MPC and full-scale deployments using lidar data.

Abstract

This work presents a nonlinear system identification framework for modeling the power extraction dynamics of wind turbines, including both freestream and waked conditions. The approach models turbine dynamics using data-driven power coefficient maps expressed as combinations of compact radial basis functions and polynomial bases, parameterized in terms of tip-speed ratio and upstream conditions. These surrogate models are embedded in a first-order dynamic system suitable for model-based control. Experimental validation is carried out in two wind tunnel configurations: a low-turbulence tandem setup and a high-turbulence wind farm scenario. In the tandem case, the identified model is integrated into an adapted Kω^2 controller, resulting in improved tip-speed ratio tracking and power stability compared to BEM-based and steady-state models. In the wind farm scenario, the model captures the statistical behavior of the turbines despite unresolved turbulence. The proposed method enables interpretable, adaptive control across a range of operating conditions without relying on black-box learning strategies.

Figures (14)

• Figure 1: Configuration of interest and relevant variables.
• Figure 2: Experimental setup in the low-turbulence scenario configuration, detailing the measurement of free-stream wind speed $u_1$, rotational speed $\omega_i^*$ of each turbine, and torque actuation via variable resistance $R_{v,i}$ controlled by a 12-bit binary signal $a_{bin,i}$.
• Figure 3: Wind farm configuration in the VKI Wind Engineering Facility L-1B, with the three identified wind turbines highlighted in red.
• Figure 4: Free stream velocity (left) and generator resistance evolution (right) for three representative training episodes (first three rows) and two testing episodes for the low turbulence scenario described in Section \ref{['sec:scenario1']}.
• Figure 5: Left: Time evolution of the hub-height wind velocity of the first turbine ($\hat{u}_1$) and its angular velocity ($\hat{\omega}_1$) for an example test case. Both signals are normalized by mean-centering and min-max scaling. Right: Scatter plot showing the correlation between the two signals. Data are from the "low-turbulence" scenario described in Section \ref{['sec:scenario1']}.