# T2FL: An Efficient Model for Wind Turbine Fatigue Damage Prediction for the Two-Turbine Case

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## Abstract

**:**

## 1. Introduction

## 2. Methodology: Surrogate Model Development

#### 2.1. Selection of Input Variables And Limits

#### 2.1.1. Input Parameters

- Ambient wind speed (${U}_{ambient}$),
- Ambient wind direction ($\varphi $),
- Ambient wind turbulence intensity ($T{I}_{ambient}$).

- Derating percentage of Upstream WT ($DE{R}_{upstream}$),
- Derating percentage of Downstream WT ($DE{R}_{downstream}$).

#### 2.1.2. Input Space

#### 2.2. Definition of Training Set Data and Output

- Blade root flapwise ($BRF$) and edgewise ($BLE$) bending moments
- Tower base fore-aft ($TBFA$) bending moment
- Tower top yaw ($TTY$) moment (nacelle yaw bearing)
- Electrical power (${P}_{el}$)
- Rotor speed ($\omega $)
- Blade pitch angle ($\theta $)

#### 2.3. Simulation Platforms (HAWC2 and DWM)

#### 2.4. Neural Network

## 3. Verification of the Surrogate Model

## 4. Applications

#### 4.1. Power and Fatigue Studies of Two-Turbine Wind Farms

#### 4.1.1. Power Production

#### 4.1.2. Tower Fatigue Damage

#### 4.1.3. Blade Fatigue Damage

#### 4.2. Wind Farm Control: Synthesised Optimum Operation

#### Example

#### 4.3. Wind Farm Layout Optimisation

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the wind farm layout consisting of two turbines with diameter D and interspace l equal to x times the diameter.

**Figure 2.**Illustration of the HAWC2-DWM framework for the prediction of turbine component fatigue damage.

**Figure 3.**Illustration of the Dynamic Wake Meandering (DWM) method. The upfront wakes are superpositioned to the ambient turbulence, including a stochastic meandering process [18].

**Figure 4.**Normalised wind turbine mean electrical power, torque, blade pitch and rotor speed curves as a function of wind speed for different derating percentages.

**Figure 6.**Contours of normalised power output of turbine array. Wind direction is 0, 10 and 22 degrees from left to right. Default wind conditions are mean wind speed of 8 m/s, turbulence intensity of 7%, and wind direction of 0 degrees, in which direction is aligned with turbine array. Turbine interspace is 5D.

**Figure 7.**Contours of normalised power output of turbine array. Ambient turbulence intensity is 7%, 14% and 27% from left to right. Default wind conditions are mean wind speed of 8 m/s, turbulence intensity of 7%, and wind direction of 0 degrees, in which direction is aligned with turbine array. Turbine interspace is 5D.

**Figure 8.**Contours of normalised power output of turbine array. Ambient mean wind speed is 8, 12 and 16 m/s from left to right. Default wind conditions are mean wind speed of 8 m/s, turbulence intensity of 7%, and wind direction of 0 degrees, in which direction is aligned with turbine array. Turbine interspace is 5D.

**Figure 9.**Impact of wind conditions and turbine power set-points on simulated sum TBFA damage equivalent loads of two turbine array. Contour lines show sum TBFA loads normalised by the load of upstream turbine in default wind conditions. Grey dashed lines denote contours of same sum power output of turbine array. Wind direction is 0, 10 and 22 degrees from left to right. Default wind conditions are mean wind speed of 8 m/s, turbulence intensity of 7%, and wind direction of 0 degrees, in which direction is aligned with turbine array. The distance between the turbines is 5D.

**Figure 10.**Impact of wind conditions and turbine power set-points on simulated sum Tower Bottom Fore-Aft (TBFA) damage equivalent loads of two turbine array. Contour lines show sum TBFA fatigue normalised loads. Ambient turbulence intensity is 7%, 14% and 27% from left to right.

**Figure 11.**Impact of wind conditions and turbine power set-points on simulated sum TBFA damage equivalent loads of two turbine array. Contour lines show sum TBFA normalised fatigue loads. Ambient mean wind speed is 8, 12 and 16 m/s from left to right.

**Figure 12.**Impact of wind conditions and turbine power set-points on simulated sum blade root flapwise (BRF) damage equivalent loads of two turbine array. Contour lines show sum BRF fatigue loads normalised by the load of upstream turbine in default wind conditions. Grey dashed lines denote contours of same sum power output of turbine array. Wind direction is 0, 10 and 22 degrees from left to right. Default wind conditions are mean wind speed of 8 m/s, turbulence intensity of 7%, and wind direction of 0 degrees, in which direction is aligned with turbine array.

**Figure 13.**Impact of wind conditions and turbine power set-points on simulated sum BRF damage equivalent loads of two turbine array. Contour lines show sum BRF normalised fatigue loads. Ambient turbulence intensity is 7%, 14% and 27% from left to right.

**Figure 14.**Impact of wind conditions and turbine power set-points on simulated sum BRF damage equivalent loads of two turbine array. Contour lines show sum BRF normalised loads. Ambient mean wind speed is 8, 12 and 16 m/s from left to right.

**Figure 15.**Optimum ratios of turbine power set-points as a function of total power reference for different wind directions and turbine spacing. The ambient wind speed is 8 m/s, turbulence intensity is 7% and turbine spacing is 5D, 7D and 9D from left to right subplots.

**Figure 16.**Optimum ratios of turbine power set-points as a function of total power reference for different turbulence intensity (TI) and turbine spacing. The ambient wind speed is 8 m/s, wind direction is 0 degrees and turbine spacing is 5D, 7D and 9D from left to right subplots.

Variable | Unit | Lower Bound | Upper Bound | Number of Sampling Point |
---|---|---|---|---|

${U}_{ambient}$ | (m/s) | 4 | 24 | 11 |

$\varphi $ | (deg) | 0 | 22 | 9 |

$T{I}_{ambient}$ | (%) | 7 | 27 | 3 |

$DE{R}_{upstream}$ | (%) | 0 | 70 | 8 |

$DE{R}_{downstream}$ | (%) | 0 | 70 | 8 |

l | (D) | 3 | 20 | 5 |

Model | Blade DEL (%) | Tower DEL (%) | El. Power (%) |
---|---|---|---|

BR | 1.145 | 1.253 | 0.029 |

LM | 1.132 | 1.186 | 0.045 |

Ensemble model | 1.054 | 1.118 | 0.028 |

Model | Blade DEL (%) | Tower DEL (%) | El. Power (%) |
---|---|---|---|

BR | 0.753 | 0.829 | 0.015 |

LM | 0.746 | 0.790 | 0.024 |

Ensemble model | 0.680 | 0.732 | 0.015 |

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**MDPI and ACS Style**

Galinos, C.; Kazda, J.; Lio, W.H.; Giebel, G.
T2FL: An Efficient Model for Wind Turbine Fatigue Damage Prediction for the Two-Turbine Case. *Energies* **2020**, *13*, 1306.
https://doi.org/10.3390/en13061306

**AMA Style**

Galinos C, Kazda J, Lio WH, Giebel G.
T2FL: An Efficient Model for Wind Turbine Fatigue Damage Prediction for the Two-Turbine Case. *Energies*. 2020; 13(6):1306.
https://doi.org/10.3390/en13061306

**Chicago/Turabian Style**

Galinos, Christos, Jonas Kazda, Wai Hou Lio, and Gregor Giebel.
2020. "T2FL: An Efficient Model for Wind Turbine Fatigue Damage Prediction for the Two-Turbine Case" *Energies* 13, no. 6: 1306.
https://doi.org/10.3390/en13061306