# A Simplified Modeling Approach of Floating Offshore Wind Turbines for Dynamic Simulations

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## Abstract

**:**

## 1. Introduction

## 2. Case Study

## 3. Modeling Approach

#### 3.1. Aerodynamics

#### 3.2. Structural Dynamics

#### 3.3. Hydrodynamics

#### 3.4. Mooring Dynamics

#### 3.5. Modeling of Wind and Wave Resource

## 4. Model Validation

#### 4.1. Load Case 1

#### 4.2. Load Case 2

#### 4.3. Load Case 3

#### 4.4. Load Case 4

#### 4.5. Load Case 5

#### 4.6. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**OC3 Hywind Spar buoy illustration [21].

**Figure 5.**Decay test response comparison. (

**Top left**), surge. (

**Top right**), pitch. (

**Bottom left**), heave. (

**Bottom right**), fore–aft.

**Figure 6.**Response Amplitude Operators (RAOs): (

**Top left**), surge. (

**Top right**), heave. (

**Bottom left**), pitch. (

**Bottom right**), fore–aft.

**Figure 7.**System response to irregular waves. Left time series, right PSDs of surge, heave, pitch, and fore–aft (

**top**to

**bottom**, respectively).

**Figure 8.**System response to turbulent wind (8 m/s) and still water. Time series of surge, pitch, and fore–aft (

**top**to

**bottom**, respectively).

**Figure 9.**System response to irregular waves and turbulent wind. Left time series, right PSDs of surge, pitch, and fore–aft (

**top**to

**bottom**, respectively).

**Table 1.**OC3 Hywind platform properties [21].

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

Depth to platform base below SWL (Draft) | 120 | m |

Elevation to platform top above SWL | 10 | m |

Taper top depth below SWL | 4 | m |

Taper bottom depth below SWL | 12 | m |

Platform diameter above the taper | 6.5 | m |

Platform diameter below the taper | 9.4 | m |

Platform mass | 7,466,330.0 | kg |

Platform center mass (CM) below SWL | 89.9155 | m |

Platform pitch inertia about CM | 4,229,230,000 | kg m^{2} |

Additional linear damping (${B}_{11}^{linear}$) | 100,000 | N s m^{−1} |

Additional linear damping (${B}_{33}^{linear}$) | 130,000 | N s m^{−1} |

**Table 2.**OC3 Hywind wind turbine properties [22].

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

Rated power | 5 | MW |

Rotor diameter | 126 | m |

Hub height | 90 | m |

Rotor mass | 110,000 | kg |

Rotor inertia | 35,444,067 | kg m^{2} |

Generator inertia | 534.116 | kg m^{2} |

Generator friction | 16.5489 | N s/m |

Gearbox ratio (high-speed to low-speed) | 97 | - |

Nacelle mass | 240,000 | kg |

Nacelle CM above tower top | 1.96 | m |

Tower mass | 347,460 | kg |

**Table 3.**OC3 Hywind mooring system properties [21].

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

Unstretched mooring line length | 902.2 | m |

Mooring line diameter | 0.09 | m |

Equivalent mooring line mass density | 77.7066 | kg/m |

Equivalent mooring line weight in water | 698.094 | N/m |

Equivalent mooring line extensional stiffness (EA) | 384,243,000 | N |

Load Case | Models | Wind | Waves | Analysis |
---|---|---|---|---|

1 | OpenFAST Reduced Model | None | None | Eigenanalysis Decay Tests |

2 | OpenFAST Reduced Model | None | Regular | RAOs |

3 | OpenFAST Reduced Model | None | Irregular JONSWAP spectrum $\begin{array}{c}{H}_{s}=6\mathrm{m}\\ {T}_{p}=10\mathrm{s}\end{array}$ | Time series PSDs |

4 | OpenFAST Reduced Model | Turbulent: Kaimal spectrum ${V}_{w}=8\mathrm{m}/\mathrm{s}$ | None | Time series Statistics |

5 | OpenFAST Reduced Model | Turbulent: Kaimal spectrum ${V}_{w}=18\mathrm{m}/\mathrm{s}$ | Irregular: JONSWAP spectrum $\begin{array}{c}{H}_{s}=6\mathrm{m}\\ {T}_{p}=10\mathrm{s}\end{array}$ | Time series PSDs Statistics |

Degree of Freedom | Frequencies (Hz) | Periods (s) | ||
---|---|---|---|---|

Reduced Model | OpenFAST | Reduced Model | OpenFAST | |

Surge | 0.008 | 0.008 | 125.53 | 125.00 |

Heave | 0.032 | 0.032 | 31.10 | 31.25 |

Pitch | 0.034 | 0.034 | 29.63 | 29.41 |

1st tower fore–aft mode | 0.498 | 0.472 | 2.01 | 2.12 |

DOF | Reduced Model | OpenFAST | Error (%) |
---|---|---|---|

Surge (m) | 12.70 | 12.40 | −2.41 |

Pitch (deg) | 2.63 | 2.51 | −4.78 |

Fore–aft (m) | 0.23 | 0.22 | −4.54 |

DOF | Reduced Model | OpenFAST | Error (%) |
---|---|---|---|

Surge (m) | 1.571 | 1.613 | 2.48 |

Pitch (deg) | 0.358 | 0.336 | −5.88 |

Fore–aft (m) | 0.023 | 0.024 | −3.10 |

DOF | Reduced Model | OpenFAST | Error (%) |
---|---|---|---|

Surge (m) | 10.648 | 10.516 | −1.255 |

Pitch (deg) | 2.185 | 2.149 | −1.675 |

Fore–aft (m) | 0.201 | 0.191 | −5.235 |

DOF | Reduced Model | OpenFAST | Error (%) |
---|---|---|---|

Surge (m) | 1.638 | 1.762 | 7.037 |

Pitch (deg) | 0.837 | 0.830 | −0.843 |

Fore–aft (m) | 0.124 | 0.131 | 5.343 |

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**MDPI and ACS Style**

López-Queija, J.; Robles, E.; Llorente, J.I.; Touzon, I.; López-Mendia, J.
A Simplified Modeling Approach of Floating Offshore Wind Turbines for Dynamic Simulations. *Energies* **2022**, *15*, 2228.
https://doi.org/10.3390/en15062228

**AMA Style**

López-Queija J, Robles E, Llorente JI, Touzon I, López-Mendia J.
A Simplified Modeling Approach of Floating Offshore Wind Turbines for Dynamic Simulations. *Energies*. 2022; 15(6):2228.
https://doi.org/10.3390/en15062228

**Chicago/Turabian Style**

López-Queija, Javier, Eider Robles, Jose Ignacio Llorente, Imanol Touzon, and Joseba López-Mendia.
2022. "A Simplified Modeling Approach of Floating Offshore Wind Turbines for Dynamic Simulations" *Energies* 15, no. 6: 2228.
https://doi.org/10.3390/en15062228