# A New Proposal for the Closed-Loop Orientation Control of a Windfloat Turbine System

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## Abstract

**:**

## 1. Introduction

## 2. Brief Description of the Wind Turbine

## 3. Hydrostatic Equilibrium

- The area under the righting torque curve (ART) at the second intercept must not be less than 30% in excess of the area under the wind heeling torque (AHT) curve at the same limiting angle;
- The first intercept must be less than 15°;
- The righting torque curve must be positive for the entire range of angles, from upright to the second intercept.

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#### Mooring Lines Effect over the Device

## 4. Dynamic Model

- (i)
- The vertical motion of the generator is ignored, because the water ballast is pumped only among the ballast tanks.
- (ii)
- The displacements of the center of gravity are negligible when ballast handling moves water among tanks.
- (iii)
- The added masses of the submerged part are constant, well known, and considered to be lumped.
- (iv)
- Viscous friction is modeled as being constant and is considered to be fully uncoupled.
- (v)
- Restoring effects are computed geometrically.
- (vi)
- Only small angle variations are considered, because the main issue of the proposed controller is to maintain the vertical orientation of the generator.

#### 4.1. Control Torques Produced by Actuators

#### 4.2. Torques Owing to the Loss of Buoyancy

#### 4.3. Torques from Wind

#### 4.4. Rotation Dynamics

#### 4.4.1. Local Inertia Matrix

#### 4.4.2. Computation of the Rotation Kinetic Energy

#### 4.4.3. Computation of the Rotation Potential Energy

#### 4.4.4. Lagrange Formulation

#### 4.4.5. Proposed Dynamic Model

## 5. Proposed Control

- (i)
- An inertial measurement unit (IMU) is required in order to obtain the orientation variables $\mathit{q}\left(\mathrm{t}\right)={\left(\begin{array}{cc}{\mathsf{\phi}}_{\mathrm{x}}\left(\mathrm{t}\right)& {\theta}_{\mathrm{y}}\left(\mathrm{t}\right)\end{array}\right)}^{\mathrm{T}}$ and their time derivatives $\dot{\mathit{q}}\left(\mathrm{t}\right)={\left(\begin{array}{cc}{\dot{\mathsf{\phi}}}_{\mathrm{x}}\left(\mathrm{t}\right)& {\dot{\theta}}_{\mathrm{y}}\left(\mathrm{t}\right)\end{array}\right)}^{\mathrm{T}}$. All the terms of functions $M\left(\mathit{q}\right)$ and $\mathit{V}\left(\mathit{q},\dot{\mathit{q}}\right)$ can be computed from these signals, with the exception of the term ${\mathsf{\tau}}_{w}\left(\mathit{q}\right)$ and;
- (ii)
- The strain gauge load cells located over the bearings of the rotor make it possible to compute ${\mathsf{\tau}}_{w}\left(\mathit{q}\right)$ by measuring the real thrust over the hub of the rotor and applying Equation (25) or;
- (iii)
- By using the information captured by the vane and anemometer located on the gondola and estimating the force of the wind from tables of the known ${\mathrm{C}}_{\mathrm{T}}$ coefficients [24] and Equations (23)–(25).

## 6. Validation Setup

#### 6.1. Orcaflex Model

#### 6.2. Matlab–Orcaflex Integration

## 7. Validation Results

#### 7.1. Validation of System Decoupling

#### 7.2. External Disturbances: Waves and Wind

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

- Stokes, C.; Beaumont, E.; Russell, P.; Greaves, D. Anticipated coastal impacts: What water-users think of marine renewables and why. Ocean Coast. Manag.
**2014**, 99, 63–71. [Google Scholar] [CrossRef] - Dalir, F.; Motlagh, M.S.; Ashrafi, K. A dynamic quasi comprehensive model for determining the carbon footprint of fossil fuel electricity: A case study of Iran. J. Clean. Prod.
**2018**, 188, 362–370. [Google Scholar] [CrossRef] - Alashkar, A.; Gadalla, M. Thermo-economic analysis of an integrated solar power generation system using nanofluids. Appl. Energy
**2017**, 191, 469–491. [Google Scholar] [CrossRef] - Facci, A.L.; Cigolotti, V.; Jannelli, E.; Ubertini, S. Technical and economic assessment of a SOFC-based energy system for combined cooling, heating and power. Appl. Energy
**2017**, 192, 563–574. [Google Scholar] [CrossRef] - Amrollahi, M.H.; Bathaee, S.M.T. Techno-economic optimization of hybrid photovoltaic/wind generation together with energy storage system in a stand-alone micro-grid subjected to demand response. Appl. Energy
**2017**, 202, 66–77. [Google Scholar] [CrossRef] - Younesian, D.; Alam, M.-R. Multi-stable mechanisms for high-efficiency and broadband ocean wave energy harvesting. Appl. Energy
**2017**, 197, 292–302. [Google Scholar] [CrossRef] - A Clean Planet for All a European Strategic Long-Term Vision for a Prosperous, Modern, Competitive and Climate Neutral Economy; European Commission: Brussels, Belgium, 2018.
- Offshore Wind Energy: Action Needed to Deliver on the Energy Policy Objectives for 2020 and Beyond; European Commission: Brussels, Belgium, 2008.
- Mikati, M.; Santos, M.; Armenta, C. Electric grid dependence on the configuration of a small-scale wind and solar power hybrid system. Renew. Energy
**2013**, 57, 587–593. [Google Scholar] [CrossRef] - Leung, D.Y.; Yang, Y. Wind energy development and its environmental impact: A review. Renew. Sustain. Energy Rev.
**2012**, 16, 1031–1039. [Google Scholar] [CrossRef] - Şahin, A.D. Progress and recent trends in wind energy. Prog. Energy Combust. Sci.
**2004**, 30, 501–543. [Google Scholar] [CrossRef] - Wind Energy: A Gender Perspective; International Renewable Energy Agency: Abu Dhabi, UAE, 2020.
- Offshore Wind in Europe Key Trends and Statistics 2019; WindEurope: Brussels, Belgium, 2020.
- Renewables 2019 Global Status Report; REN21: Paris, France, 2019.
- Harrison, J.; Garrad, A.; Warren, T.; Powell, J. Floating Offshore Wind: Installation, Operation & Maintenance Challenges Approval; Revision History Version: A Floating Offshore Wind: Installation Challenges; Blackfish Engineering Design Ltd.: Bristol, UK, 2020. [Google Scholar]
- Hywind | Saipem. Available online: https://www.saipem.com/en/projects/hywind?referral=%2Fen%2Fprojects (accessed on 15 September 2020).
- PELASTAR | Tension Leg Platform. Available online: https://pelastar.com/ (accessed on 15 September 2020).
- Castro-Santos, L.; Filgueira-Vizoso, A.; Carral, L.; Fraguela, F. Economic feasibility of floating offshore wind farms. Energy
**2016**, 112, 868–882. [Google Scholar] [CrossRef] - WindFLoat Atlantic Project | edp.com. Available online: https://www.edp.com/en/innovation/windfloat (accessed on 15 September 2020).
- IEC. Wind Turbines-Part 1: Design Requirements. 2005. Available online: www.iec.ch (accessed on 13 October 2020).
- Antonutti, R.; Peyrard, C.; Johanning, L.; Incecik, A.; Ingram, D. The effects of wind-induced inclination on the dynamics of semi-submersible floating wind turbines in the time domain. Renew. Energy
**2016**, 88, 83–94. [Google Scholar] [CrossRef] [Green Version] - Roddier, D.; Cermelli, C.; Aubault, A.; Weinstein, A. WindFloat: A floating foundation for offshore wind turbines. J. Renew. Sustain. Energy
**2010**, 2, 033104. [Google Scholar] [CrossRef] - DTU 10 MW RWT dtu-10mw-rwt · GitLab. Available online: https://rwt.windenergy.dtu.dk/dtu10mw/dtu-10mw-rwt (accessed on 27 September 2020).
- Bak, C.; Zahle, F.; Bitsche, R.; Kim, T.; Yde, A.; Henriksen, L.C.; Natarajan, A.; Hansen, M. DTU Wind Energy Report-I-0092; DTU Wind Energy: Roskilde, Denmark, 2013. [Google Scholar]
- Bak, C.; Zahle, F.; Bitsche, R.; Kim, T.; Yde, A.; Henriksen, L.C.; Hansen, M.H.; Blasques, J.P.A.A.; Gaunaa, M.; Natarajan, A. Description of the DTU 10 MW Reference Wind Turbine; DTU Wind Energy: Roskilde, Denmark, 2013; p. 138. [Google Scholar]
- Lopez-Pavon, C.; Souto-Iglesias, A. Hydrodynamic coefficients and pressure loads on heave plates for semi-submersible floating offshore wind turbines: A comparative analysis using large scale models. Renew. Energy
**2015**, 81, 864–881. [Google Scholar] [CrossRef] - Lavrov, A.; Soares, C.G. Modeling the Heave Oscillations of Vertical Cylinders with Damping Plates. In Safe Offloading from Floating LNG Platforms View project MARSTRUCT-Network of Excellence on Marine Structures; CORDIS: Luxembourg, 2016. [Google Scholar] [CrossRef]
- Díaz, H.; Rodrigues, J.M.; Soares, C.G.; Díaz, H.; Rodrigues, J.M.; Soares, C.G. Preliminary Cost Assessment of An Offshore Floating Wind Farm Installation on the Galician Coast; Taylor & Francis Group: London, UK, 2016. [Google Scholar]
- Páginas—Estadística Mensual. Available online: http://www.puertos.es/es-es/estadisticas/Paginas/estadistica_mensual.aspx (accessed on 11 May 2018).
- MAXSURF Naval Architecture Software. Available online: https://maxsurf.net/ (accessed on 13 October 2020).
- Stability and Watertight Integrity; DNVGL-OS-C301; DNV GL: Oslo, Norway, 2018.
- Fossen, T.I. Handbook of Marine Craft Hydrodynamics and Motion Control; Wiley: Hoboken, NJ, USA, 2011. [Google Scholar]
- Pérez, R.; López, A.; Núñez, L.R.; Somolinos, J.A. Detail design of a ballast control room for an underwater tidal energy converter. Brodogradnja
**2017**, 69, 39–52. [Google Scholar] [CrossRef] [Green Version] - Siciliano, B.; Lorenzo, S.; Villani, L.; Orilo, G. Robotics: Modelling, Planning and Control, 2nd ed.; Springer: London, UK, 2010. [Google Scholar]
- Weibull, W. A Statistical Distribution Function of Wide Applicability. J. Appl. Mech.
**1951**, 18, 293–297. [Google Scholar] - Espín, M. Modelado Dinámico y Control de Maniobras de Dispositivos Submarinos; UPM (Escuela Técnica Superior de Ingenieros Navales): Madrid, Spain, 2015. [Google Scholar]
- De La Portilla, M.P.; Piñeiro, A.L.; Sánchez, J.A.S.; Morales, R. Modelado Dinámico y Control de un Dispositivo Sumergido Provisto de Actuadores Hidrostáticos. RIAI Rev. Iberoam. Autom. Inform. Ind.
**2018**, 15, 12. [Google Scholar] [CrossRef] [Green Version] - Orcina. 2016. Available online: https://www.orcina.com/SoftwareProducts/OrcaFlex/ (accessed on 25 November 2020).
- MathWorks. 2020. Available online: https://es.mathworks.com/products/matlab/ (accessed on 25 November 2020).
- Sørensen, A.J. Marine Control Systems Propulsion and Motion Control of Ships and Ocean Structures; Norwegian University of Science and Technology: Trondheim, Norway, 2013. [Google Scholar]
- Fernández-Caballero, A.; Belmonte, L.M.; Morales, R.; Somolinos, J.A.; Morales, R. Generalized Proportional Integral Control for an Unmanned Quadrotor System. Int. J. Adv. Robot. Syst.
**2015**, 12, 85. [Google Scholar] [CrossRef] [Green Version] - Morales, R.; Feliu, V.; Sira-Ramirez, H. Nonlinear Control for Magnetic Levitation Systems Based on Fast Online Algebraic Identification of the Input Gain. IEEE Trans. Control Syst. Technol.
**2011**, 19, 757–771. [Google Scholar] [CrossRef]

**Figure 3.**Curve of static stability of the device with respect to the $y$-axis. (

**a**) Curve of static stability for $y$-axis and (

**b**) rotating platform around the $y$-axis (stable range).

**Figure 4.**Curve of static stability of the device with respect to x-axis (stable range). (

**a**) Curve of static stability for the x-axis and (

**b**) rotating platform around the y-axis.

**Figure 12.**Step responses for different gains of the controllers. (

**a**) Step responses for the x-axis rotation. (

**b**) Step responses for the y-axis rotation.

**Figure 13.**Zoom of step responses for different gains of the controllers. (

**a**) Zoom of the ${\phi}_{x}$ responses in the neighborhood of the instant ${t}_{2\theta}=400\mathrm{s}$. (

**b**) Zoom of the ${\theta}_{y}$ responses in the neighborhood of the instant ${t}_{2\phi}=550\mathrm{s}$.

**Figure 15.**Open loop and closed loop time responses under step variations of wind magnitudes. (

**a**) Open loop and closed loop responses for the x-axis rotation. (

**b**) Open loop and closed loop responses for the y-axis rotation.

**Figure 16.**Full simulation of the open loop and closed loop response of the device with real wind and waves data taken from [29]. (

**a**) Open loop and closed loop responses for the x-axis rotation. (

**b**) Open loop and closed loop responses for the y-axis rotation.

**Table 1.**Main dimensions of the floating platform under study (taken from [22]).

Column diameter (m) | 10.7 |

Heave plate diameter (m) | 13.7 |

Horizontal distance among columns (m) | 56.4 |

Pontoon diameter (m) | 1.8 |

Bracing diameter (m) | 1.2 |

Operating draft (m) | 22.9 |

**Table 2.**Main dimensions of the wind turbine (taken from [25]).

Rotor diameter (m) | 178.3 |

Tower height (m) | 115.6 |

Hub height (m) | 119 |

Tower mass (ton) | 605 |

Hub mass (ton) | 105.52 |

Nacelle mass (ton) | 446.04 |

Blade mass (ton) | 41.72 |

Cut-in, Rated (m/s) | 4, 11.4 |

Cut-out wind speed (m/s) | 25 |

Rotor speed range (rpm) | 6–9.6 |

Approximated maximum tower top thrust (kN) | 3242 |

Displacement (ton) | 7995 |

Trim (deg) | 0.02 |

KB (m) | 9.65 |

KG (m) | 23.29 |

KM_T (y) (m) | 28.19 |

KM_L (x) (m) | 28.12 |

Area | $\mathit{x}$-Axis | $\mathit{y}$-Axis |
---|---|---|

ART | $4.66\times {10}^{6}$ | $2.47\times {10}^{6}$ |

AHT | $2.12\times {10}^{6}$ | $1.64\times {10}^{6}$ |

ART/AHT | $2.21>1.30$ | $1.51>1.30$ |

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**MDPI and ACS Style**

Horno, L.D.; Somolinos, J.A.; Segura, E.; Morales, R.
A New Proposal for the Closed-Loop Orientation Control of a Windfloat Turbine System. *J. Mar. Sci. Eng.* **2021**, *9*, 26.
https://doi.org/10.3390/jmse9010026

**AMA Style**

Horno LD, Somolinos JA, Segura E, Morales R.
A New Proposal for the Closed-Loop Orientation Control of a Windfloat Turbine System. *Journal of Marine Science and Engineering*. 2021; 9(1):26.
https://doi.org/10.3390/jmse9010026

**Chicago/Turabian Style**

Horno, Leticia Del, José A. Somolinos, Eva Segura, and Rafael Morales.
2021. "A New Proposal for the Closed-Loop Orientation Control of a Windfloat Turbine System" *Journal of Marine Science and Engineering* 9, no. 1: 26.
https://doi.org/10.3390/jmse9010026