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Model Predictive Control of Wind Turbines with Piecewise-Affine Power Coefficient Approximation

Arnold Sterle, Aaron Grapentin, Christian A. Hans, Jörg Raisch

TL;DR

The paper tackles robust wind-turbine control across varying wind regimes by developing an offset-free model predictive controller that unifies pitch and torque control into a single law, eliminating switching. It handles aerodynamic nonlinearity through a piecewise-affine approximation of the power coefficient $C_p(\lambda,u_\theta)$ and a bilinear reformulation to maintain tractable optimization, complemented by wind speed forecasting and a disturbance observer for offset-free operation. The MPC framework explicitly enforces actuator and power constraints while penalizing wear-related variables, and is validated against a state-of-the-art baseline in OpenFAST simulations, showing accurate power tracking and reduced damage-equivalent loads at higher wind speeds. The work demonstrates potential for improved energy capture with lower mechanical wear and provides a foundation for further enhancements like explicit $\Delta d_\omega$ handling and reduced computational complexity for longer horizons.

Abstract

In this paper, an offset-free bilinear model predictive control approach for wind turbines is presented. State-of-the-art controllers employ different control loops for pitch angle and generator torque which switch depending on wind conditions. In contrast, the presented controller is based on one unified control law that works for all wind conditions. The inherent nonlinearity of wind turbines is addressed through a piecewise-affine approximation of the power coefficient, which is modelled in a mixed-integer fashion. The presented controller is compared to a state-of-the-art baseline controller in a numerical case study using OpenFAST. Simulation results show that the presented controller ensures accurate reference power tracking. Additionally, damage equivalent loads are reduced for higher wind speeds.

Model Predictive Control of Wind Turbines with Piecewise-Affine Power Coefficient Approximation

TL;DR

The paper tackles robust wind-turbine control across varying wind regimes by developing an offset-free model predictive controller that unifies pitch and torque control into a single law, eliminating switching. It handles aerodynamic nonlinearity through a piecewise-affine approximation of the power coefficient and a bilinear reformulation to maintain tractable optimization, complemented by wind speed forecasting and a disturbance observer for offset-free operation. The MPC framework explicitly enforces actuator and power constraints while penalizing wear-related variables, and is validated against a state-of-the-art baseline in OpenFAST simulations, showing accurate power tracking and reduced damage-equivalent loads at higher wind speeds. The work demonstrates potential for improved energy capture with lower mechanical wear and provides a foundation for further enhancements like explicit handling and reduced computational complexity for longer horizons.

Abstract

In this paper, an offset-free bilinear model predictive control approach for wind turbines is presented. State-of-the-art controllers employ different control loops for pitch angle and generator torque which switch depending on wind conditions. In contrast, the presented controller is based on one unified control law that works for all wind conditions. The inherent nonlinearity of wind turbines is addressed through a piecewise-affine approximation of the power coefficient, which is modelled in a mixed-integer fashion. The presented controller is compared to a state-of-the-art baseline controller in a numerical case study using OpenFAST. Simulation results show that the presented controller ensures accurate reference power tracking. Additionally, damage equivalent loads are reduced for higher wind speeds.
Paper Structure (16 sections, 32 equations, 7 figures, 1 table)

This paper contains 16 sections, 32 equations, 7 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries
  3. MODEL
  4. Aerodynamic subsystem
  5. Drive train and gearbox subsystem
  6. Generator subsystem
  7. State model
  8. MODEL PREDICTIVE CONTROLLER
  9. Approximation of power coefficient
  10. Wind speed forecast
  11. Bilinear reformulation
  12. Offset-free control
  13. Constraints
  14. Problem formulation
  15. CASE STUDY
  16. ...and 1 more sections

Figures (7)

  • Figure 1: Power coefficient $C_p\left(\lambda,u_\theta\right)$ (data from RWT).
  • Figure 2: Piecewise-affine approximation of $\hat{C}_p$ for $N_R=9$.
  • Figure 3: Power maximization for a 8ms.
  • Figure 4: Power tracking for an average wind speed of 16ms.
  • Figure 5: Controller performance for varying wind speeds.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Remark 1