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Robust LQ Optimal Control for Wind Turbine Power Tracking Operation

Aaron Grapentin, Christian A. Hans, Jörg Raisch

TL;DR

This work addresses robust active power tracking for wind turbines under wind variability by formulating a multivariable LQ controller synthesized via linear matrix inequalities over multiple equilibria. An augmented state including integral errors for speed and power is paired with an external-input estimator to enable region-wide stability guarantees and accurate trajectory tracking. The control framework designs region-specific LQ regulators for two operating regions and blends them to yield a single, implementable law, with formal stability assurances for all linearized models. In OpenFAST simulations, the proposed method achieves substantially lower power-tracking error with comparable load levels, indicating meaningful practical benefits for wind-turbine operation and grid integration.

Abstract

In this paper, a robust linear quadratic optimal control approach for accurate active power tracking of wind turbines is presented. For control synthesis, linear matrix inequalities are employed using an augmented wind turbine state model with uncertain parameters. The resulting controller ensures robust stability in different operating regions. In a case study, the novel approach is compared to existing controllers from literature. Simulations indicate that the controller improves power tracking accuracy while leading to similar mechanical wear as existing approaches.

Robust LQ Optimal Control for Wind Turbine Power Tracking Operation

TL;DR

This work addresses robust active power tracking for wind turbines under wind variability by formulating a multivariable LQ controller synthesized via linear matrix inequalities over multiple equilibria. An augmented state including integral errors for speed and power is paired with an external-input estimator to enable region-wide stability guarantees and accurate trajectory tracking. The control framework designs region-specific LQ regulators for two operating regions and blends them to yield a single, implementable law, with formal stability assurances for all linearized models. In OpenFAST simulations, the proposed method achieves substantially lower power-tracking error with comparable load levels, indicating meaningful practical benefits for wind-turbine operation and grid integration.

Abstract

In this paper, a robust linear quadratic optimal control approach for accurate active power tracking of wind turbines is presented. For control synthesis, linear matrix inequalities are employed using an augmented wind turbine state model with uncertain parameters. The resulting controller ensures robust stability in different operating regions. In a case study, the novel approach is compared to existing controllers from literature. Simulations indicate that the controller improves power tracking accuracy while leading to similar mechanical wear as existing approaches.
Paper Structure (16 sections, 1 theorem, 38 equations, 6 figures)

This paper contains 16 sections, 1 theorem, 38 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Model
  4. Aerodynamic System
  5. Drive Train and Generator
  6. Tower Dynamics
  7. State Model
  8. Control Approach
  9. State Model Augmentation
  10. Equilibrium Computation
  11. Linearization
  12. Robust Control Design
  13. External Input
  14. Overall Controller
  15. Case Study
  16. ...and 1 more sections

Key Result

Lemma 1

Given a constant external input $w^s=^T$, there exists an equilibrium $(x^s, u^s, w^s)$ with $x^s=^T$ and ${u^s=^T}$, if and only if with $\lambda^s=\frac{r}{N_g}\frac{\omega^{d,s}}{V^s}$, has a solution $\theta^s\in[\underline{\theta}, \overline{\theta}]$, where $\underline{\theta}, \overline{\theta}\in\mathbb{R}$ denote the lower and upper pitch angle bound.

Figures (6)

  • Figure 1: Closed-loop control scheme.
  • Figure 2: Wind turbine operating regions.
  • Figure 3: Wind turbine simulation model.
  • Figure 4: Power tracking comparison.
  • Figure 5: Power tracking comparison.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Lemma 1
  • proof