# A Methodology for Robust Load Reduction in Wind Turbine Blades Using Flow Control Devices

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## Abstract

**:**

## 1. Introduction

- Modeling the effect of the DBD plasma actuator as a dynamic change in local lift coefficient at the location where the actuator is placed. We refer to this modeling assumption as sectional lift actuation (SLA).
- A control system architecture based on the well-known multi-blade coordinate transformation [6] to reduce dynamic loads of the blade-root flapwise bending moments. This control system, which drives the sectional lift actuators, is coined sectional lift control (SLC).
- A feedback control algorithm designed to achieve load reduction and robustness to both (a) parametric uncertainty in the design model and (b) unmodeled dynamics.

## 2. Turbine Specifications

## 3. Sectional Lift Actuators

## 4. Sectional Lift Control

#### 4.1. SLC Design and Evaluation Criteria

#### 4.2. Multi-Blade Coordinate Transformation

#### 4.3. Design Model via System Identification

`pem`function in MATLAB [40]) is used to identify a state-space model from the simulation data. The 2500-s window of usable data is divided into two sets, a 2000-s long “training” dataset and a 500-s long “validation” dataset. The training dataset is used to obtain models of varying orders, which are evaluated for best fit to the validation dataset. The model mismatch is measured with the normalized root mean square error (NRMSE), defined by

`etfe`command provided by the System Identification Toolbox [40] in MATLAB.

#### 4.4. Variation of Design Model with Wind Speed

#### 4.5. Sectional Lift Control Architecture

#### 4.6. Synthesis of the Control Algorithm

#### Saturation Management

## 5. Loads and Performance Evaluation

#### 5.1. Primary Load

**Lemma**

**1.**

#### 5.2. Secondary Loads

#### 5.3. Turbine Activity

#### 5.4. Scheduling the SLC with Wind Speed

## 6. Conclusions

- The SLC is model-based and can be designed from simple approximate models (physics-based or data) due to the explicit incorporation of a robust stability margin to both parametric uncertainty and unmodeled dynamics.
- The SLC does not interact with the main turbine controller and reduces the controlled loads in below- and above-rated wind conditions, without adverse impacts on turbine power or blade pitch activity.
- The methodology is directly applicable to an actual wind turbine equipped with DBD plasma actuators (or other flow control devices) by using system identification tools to obtain a model from the actuator signals (voltage for DBD plasma actuators) to the controlled moments.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AEP | Annual Energy Production |

DBD | Dielectric Barrier Discharge |

DEL | Damage Equivalent Load |

GF | Gurney Flap |

IPC | Individual Pitch Control |

LCOE | Levelized Cost of Energy |

MBC | Multiblade Coordinate (Transformation) |

MIMO | Multiple-Input, Multiple-Output |

NREL | National Renewable Energy Laboratory |

NRMSE | Normalized Root Mean Square Error |

PRBS | Pseudo-Random Binary Signal |

SISO | Single-Input, Single-Output |

SLC | Sectional Lift Control |

STD | Standard Deviation |

## Appendix A. Details of the Identified Model

**Figure A1.**Pole-zero plots of identified plant model. Zeros beyond 30 rad/s not shown for visualization clarity.

## Appendix B. Proof of Lemma 1

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**Figure 1.**Local loads are controlled on a turbine blade using a DBD plasma actuator [25].

**Figure 4.**Turbine blade with a schematic of the SLA actuator. The signal u denotes the $\Delta {C}_{L}$ command from the controller.

**Figure 9.**Frequency response of transfer function from the input ${u}_{cos}$ to the output ${M}_{cos}$. Yellow line: empirical transfer function, blue line: model transfer function.

**Figure 11.**Singular values ${\sigma}_{1}\left(G\left(j\omega \right)\right)$ and ${\sigma}_{2}\left(G\left(j\omega \right)\right)$ (solid blue) and the norm of the first column of frequency response $\sqrt{|{G}_{11}{\left(j\omega \right)|}^{2}+{\left|{G}_{21}\left(j\omega \right)\right|}^{2}}$ (dashed red).

**Figure 13.**Bode plots of $G\left(j\omega \right)$ in above-rated wind speeds (12, 16, 18, 20 and 24 m/s).

**Figure 14.**Singular values of $G\left(j\omega \right)$ in above-rated wind speeds (12, 16, 18, 20 and 24 m/s).

**Figure 19.**SLC impact on flapwise root bending moment for 18 m/s steady wind with vertical shear exponent $\alpha =0.2$. (

**Top**): time series of actuator command (SLC ON at 400 s), (

**middle**): time series of load (SLC ON at 400 s), (

**bottom**): amplitude spectrum for blade #1; achieved load reduction at 1P is $43\%$ compared with the 46% theoretical upper bound.

**Figure 20.**SLC impact on flapwise root bending moment for 18 m/s turbulent wind with vertical shear exponent $\alpha =0.2$ and turbulence intensity TI $=16\%$. Achieved load reduction at 1P is $32\%$ compared with the $57\%$ theoretical upper bound. Note that the achieved load reduction is smaller than the theoretical upper bound from Equation (19) (which assumes steady wind) due to the presence of turbulence.

**Figure 21.**Variation of blade-root flapwise bending moment DEL with wind speed. (

**Top**): dimensional DEL, (

**bottom**): percentage change.

**Figure 22.**Variation of blade-root edgewise bending moment DEL with wind speed. (

**Top**): dimensional DEL, (

**bottom**): percentage change.

**Figure 23.**Variation of tower fore-aft bending moment DEL with wind speed. (

**Top**): dimensional DEL, (

**bottom**): percentage change.

**Figure 24.**Variation of tower side-side bending moment DEL with wind speed. (

**Top**): dimensional DEL, (

**bottom**): percentage change.

**Figure 25.**Variation of blade tip deflection with wind speed. (

**Left**): mean value, (

**center**): standard deviation, (

**right**): 95th percentile (95% of displacement values below this quantity).

**Figure 26.**Time series of turbine response for 18 m/s wind with vertical shear exponent $\alpha =0.2$. SLC turned on at 400 s.

**Figure 27.**Variation of generator power with wind speed. (

**Top**): mean (

**left**) and STD (

**right**), theoretical values (black dashed line), (

**bottom**): percentage change.

**Figure 28.**Variation of rotor speed with wind speed. (

**Top**): mean (

**left**) and STD (

**right**), (

**bottom**): percentage change.

**Figure 29.**Variation of blade pitch with wind speed. (

**Top**): mean (

**left**) and STD (

**right**), (

**bottom**): percentage change.

**Figure 30.**Variation of blade-root flapwise bending moment DEL with wind speed for various controllers.

Properties | Value | Properties | Value |
---|---|---|---|

Class and category | IEC Class 3A | Rotor orientation | Upwind |

Control | Variable speed, variable pitch | Maximum power coefficient | 0.47 |

Power | $3.4$ MW | Gear ratio | 97 |

Rotor diameter | 130 m | Hub height | 110 m |

Cut-in wind speed | 4 m/s | Minimum rotor speed | $3.8$ rpm |

Rated wind speed | $9.8$ m/s | Rated rotor speed | $11.75$ rpm |

Cut-out wind speed | 25 m/s | Maximum rotor speed | $12.9$ rpm |

Evaluation Criteria | Comments |
---|---|

Loads and Deflections | |

Blade-root flapwise bending moments | Primary load |

Blade-root edgewise bending moments | Secondary load |

Drive train torsion | Secondary load |

Tower fore-aft moment | Secondary load |

Tower side-side moment | Secondary load |

Blade deflection | Secondary metric |

Turbine Performance | |

Power produced | |

Rotor angular speed | |

Collective pitch | Above-rated wind conditions |

Degree of Freedom | Description |
---|---|

FlapDOF1 | First flapwise blade mode DOF |

FlapDOF2 | Second flapwise blade mode DOF |

EdgeDOF | First edgewise blade mode DOF |

DrTrDOF | Drivetrain rotational-flexibility DOF |

GenDOF | Generator DOF |

TwFADOF1 | First fore-aft tower bending-mode DOF |

TwFADOF2 | Second fore-aft tower bending-mode DOF |

TwSSDOF1 | First side-to-side tower bending-mode DOF |

TwSSDOF2 | Second side-to-side tower bending-mode DOF |

Model Order | NRMSE |
---|---|

5 | 0.25 |

6 | 0.18 |

7 | 0.37 |

8 | 0.20 |

Parameter | Value |
---|---|

Actuator Limits | −0.2 to +0.2 |

${K}_{aw}$ | 100 |

${\omega}_{0}$ (rad/s) | 0.37 |

DC-gain $G\left(0\right)$ (kN·m) | $\left(\right)$ |

Robust Controller | I (Identity Matrix) |

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**MDPI and ACS Style**

Gupta, A.; Rotea, M.A.; Chetan, M.; Sakib, M.S.; Griffith, D.T.
A Methodology for Robust Load Reduction in Wind Turbine Blades Using Flow Control Devices. *Energies* **2021**, *14*, 3500.
https://doi.org/10.3390/en14123500

**AMA Style**

Gupta A, Rotea MA, Chetan M, Sakib MS, Griffith DT.
A Methodology for Robust Load Reduction in Wind Turbine Blades Using Flow Control Devices. *Energies*. 2021; 14(12):3500.
https://doi.org/10.3390/en14123500

**Chicago/Turabian Style**

Gupta, Abhineet, Mario A. Rotea, Mayank Chetan, Mohammad S. Sakib, and D. Todd Griffith.
2021. "A Methodology for Robust Load Reduction in Wind Turbine Blades Using Flow Control Devices" *Energies* 14, no. 12: 3500.
https://doi.org/10.3390/en14123500