# An Inter-Comparison of Dynamic, Fully Coupled, Electro-Mechanical, Models of Tidal Turbines

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Models

#### 2.1. BEMT Model

#### 2.2. CFD/BEMT Model

#### 2.3. Electrical System Model

#### 2.4. Coupling of Systems

## 3. Cases Setup

^{−1}, in any relative direction simultaneously.

^{2}to test the performance of the mechanical—electrical coupled system.

## 4. Results and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Togneri, M.; Pinon, G.; Carlier, C.; Bex, C.C.; Masters, I. Comparison of synthetic turbulence approaches for blade element momentum theory prediction of tidal turbine performance and loads. Renew. Energy
**2020**, 145, 408–418. [Google Scholar] [CrossRef] - Ahmadi, M.H.B.; Yang, Z. The evolution of turbulence characteristics in the wake of a horizontal axis tidal stream turbine. Renew. Energy
**2020**, 151, 1008–1015. [Google Scholar] [CrossRef] - Zhou, Z.; Elghali, S.B.; Benbouzid, M.; Amirat, Y.; Elbouchikhi, E.; Feld, G. Tidal stream turbine control: An active disturbance rejection control approach. Ocean Eng.
**2020**, 202, 107190. [Google Scholar] [CrossRef] - Sousounis, M.C.; Shek, J.K.H.; Sellar, B.G. The effect of supercapacitors in a tidal current conversion system using a torque pulsation mitigation strategy. J. Energy Storage
**2019**, 21, 445–459. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Liu, H.; Lin, Y.; Li, W.; Gu, Y. Design and test of a 600-kW horizontal-axis tidal current turbine. Energy
**2019**, 182, 177–186. [Google Scholar] [CrossRef] - Alvarez, E.A.; Rico-Secades, M.; Corominas, E.L.; Huerta-Medina, N.; Guitart, J.S. Design and control strategies for a modular hydroKinetic smart grid. Electr. Power Energy Syst.
**2018**, 95, 137–145. [Google Scholar] [CrossRef] - Vasquez, F.A.M.; Oliveira, T.F.D.; Junior, A.C.P.B. On the electromechanical behavior of hydrokinetic turbines. Energy Convers. Manag.
**2016**, 115, 60–70. [Google Scholar] [CrossRef] - Ortega, A.; Nambiar, A.; Ingram, D.; Sale, D. Torque control of a laboratory scale variable speed hydrokinetic tidal turbine—CFD simulation and validation. In Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering, Virtual Conference, Virtual Conference, Online, 3–7 August 2020. [Google Scholar]
- Sousounis, M.C.; Tomy, J.P.; Paboeuf, S.; Shek, J.K.H. Tide-to-wire model development for realistic tide environments. In Proceedings of the 13th European Wave and Tidal Energy Conference, Naples, Italy, 1–6 September 2019. [Google Scholar]
- Vogel, C.R.; Willden, R.H.J.; Houlsby, G.T. Blade element momentum theory for a tidal turbine. Ocean Eng.
**2018**, 169, 215–226. [Google Scholar] [CrossRef] - RealTide Project Webpage. Deliverable D3.1 Generalised Tide-to-Wire Model. Available online: https://www.realtide.eng.ed.ac.uk (accessed on 27 July 2020).
- Scarlett, G.T.; Viola, I.M. Unsteady hydrodynamics of tidal turbine blades. Renew. Energy
**2020**, 146, 843–855. [Google Scholar] [CrossRef] - Sheng, W.; Galbraith, R.A.M.; Coton, F.N. A Modified Dynamic Stall Model for Low Mach Numbers. J. Sol. Energy Eng.
**2008**, 130, 031013. [Google Scholar] [CrossRef] - Ning, S.A. A simple solution method for the blade element momentum equations with guaranteed convergence. Wind Energy
**2014**, 17, 1327–1345. [Google Scholar] - Bahaj, A.S.; Batten, W.M.J.; McCann, G. Experimental verifications of numerical predictions for the hydrodynamic performance of horizontal axis marine current turbines. Renew. Energy
**2007**, 32, 2479–2490. [Google Scholar] [CrossRef] - Janiszewska, J.M.; Ramsay, R.R.; Hoffmann, M.J.; Gregorek, G.M. Effects of Grit Roughness and Pitch Oscillations on the S814 Airfoil; National Renewable Energy Laboratory—NREL: Golden, CO, USA, 1996. [Google Scholar]
- NREL Webpage (National Renewable Energy Laboratory). Simulator for Wind Farm Applications—SOWFA. Available online: https://www.nrel.gov/wind/data-tools.html (accessed on 27 July 2020).
- FastFlume Webpage. Available online: https://github.com/nnmrec/fastFlume (accessed on 27 July 2020).
- Sale, D.; Aliseda, A. The flow field of a two-blades horizontal axis turbine via comparison of RANS and LES simulations against experimental PIV flume measurements. In Proceedings of the 4th Marine Energy Technology, Washington, DC, USA, 25–27 April 2016. [Google Scholar]
- Sorensen, J.; Shen, W. Numerical Modeling of Wind Turbine Wakes. J. Fluids Eng.
**2002**, 124, 393–399. [Google Scholar] [CrossRef] - The OpenFOAM Foundation Webpage. Available online: https://www.openfoam.org (accessed on 27 July 2020).
- Churchfield, M.; Li, Y.; Moriarty, P. A large-eddy simulation study of wake propagation and power production in an array of tidal-current turbines. Philos. Trans. R. Soc. A
**2013**, 371, 20120421. [Google Scholar] [CrossRef] [PubMed] [Green Version] - LEMOS Webpage. Institute for Modeling and Numerical Simulation at the University of Rostock. Available online: https://github.com/LEMOS-Rostock/LEMOS-2.4.x (accessed on 27 July 2020).
- Martinez, L.; Leonardi, S. Wind Turbine Modeling for Computational Fluid Dynamics; National Renewable Energy Laboratory—NREL: Golden, CO, USA, 2012. [Google Scholar]
- Sousounis, M.C. Electro-Mechanical Modelling of Tidal Arrays. Ph.D. Thesis, The University of Edinburgh, Edinburgh, UK, 2018. [Google Scholar]
- Open Source Modelica Consortium Webpage. Available online: https://openmodelica.org (accessed on 27 July 2020).
- Functional Mock-Up Interface Webpage. Available online: https://fmi-standard.org/ (accessed on 28 September 2020).
- Wu, B.; Lang, Y.; Zargari, N.; Kouro, S. Wind Generators and Modeling. In Power Conversion and Control of Wind Energy Systems; John Wiley & Sons: Hoboken, NJ, USA, 2011; pp. 49–85. [Google Scholar]
- Sousounis, M.C.; Shek, J.K.H.; Crozier, R.C.; Mueller, M.A. Comparison of Permanent Magnet Synchronous and Induction Generator for a Tidal Current Conversion System with Onshore Converters. In Proceedings of the 2015 IEEE International Conference on Industrial Technology, Seville, Spain, 17–19 March 2015. [Google Scholar]
- Wu, B.; Lang, Y.; Zargari, N.; Kouro, S. Variable-Speed Wind Energy Systems With Synchronous Generators. In Power Conversion and Control of Wind Energy Systems; John Wiley & Sons: Hoboken, NJ, USA, 2011; pp. 275–316. [Google Scholar]
- Wu, B.; Lang, Y.; Zargari, N.; Kouro, S. Power Converters in Wind Energy Conversion Systems. In Power Conversion and Control of Wind Energy Systems; John Wiley & Sons: Hoboken, NJ, USA, 2011; pp. 87–152. [Google Scholar]
- Payne, G.S.; Stallard, T.; Martinez, R. Design and manufacture of a bed supported tidal turbine model for blade and shaft load measurement in turbulent flow and waves. Renew. Energy
**2017**, 10, 312–326. [Google Scholar] [CrossRef] - Noble, D.R.; Draycott, S.; Nambiar, A.; Sellar, B.G.; Steynor, J.; Kiprakis, A. Experimental Assessment of Flow, Performance, and Loads for Tidal Turbines in a Closely-Spaced Array. Energies
**2020**, 13, 1977. [Google Scholar] [CrossRef] - Batten, W.M.J.; Bahaj, A.S.; Molland, A.F.; Chaplin, J.R. Experimentally validated numerical method for the hydrodynamic design of horizontal axis tidal turbines. Ocean Eng.
**2007**, 34, 1013–1020. [Google Scholar] [CrossRef]

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**Figure 2.**Block diagram of the electrical model of the tidal system, after [9].

Number of blades | 3 |

Rotor diameter (m) | 1.2 |

Hub diameter (m) | 0.12 |

Hub location over tank bed (m) | 1 |

Rated speed (rad/s) | 15.7 |

Pole pairs | 20 |

Nominal frequency (Hz) | 50 |

Phase resistance (Ω) | 10.5 |

D-axis phase inductance (H) | 0.0785 |

Q-axis phase inductance (H) | 0.0785 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (RPM) | (RPM) | (RPM) | (%) |

0.6 | 79.2 | 73.5 | 5.7 | 7.8 |

1.0 | 132.1 | 121.7 | 10.4 | 8.5 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (Nm) | (Nm) | (Nm) | (%) |

0.6 | 6.8 | 5.8 | 0.9 | 16.0 |

1.0 | 18.8 | 15.9 | 2.9 | 18.3 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (W) | (W) | (W) | (%) |

0.6 | 56.1 | 44.8 | 11.2 | 25.0 |

1.0 | 259.6 | 202.3 | 57.3 | 28.4 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (N) | (N) | (N) | (%) |

0.6 | 145.7 | 170.3 | −24.6 | 14.4 |

1.0 | 404.7 | 467.0 | −62.3 | 13.3 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (Nm) | (Nm) | (Nm) | (%) |

0.6 | 6.8 | 5.8 | 1.0 | 16.5 |

1.0 | 18.8 | 15.8 | 2.9 | 18.5 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (W) | (W) | (W) | (%) |

0.6 | 55.2 | 43.7 | 11.5 | 26.3 |

1.0 | 253.4 | 196.2 | 57.2 | 29.2 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (V) | (V) | (V) | (%) |

0.6 | 114.6 | 106.2 | 8.4 | 7.9 |

1.0 | 190.3 | 176.7 | 13.5 | 7.7 |

Uo | BEMT | CFD/BEMT | Difference | Difference |
---|---|---|---|---|

(m/s) | (A) | (A) | (A) | (%) |

0.6 | 0.161 | 0.170 | −0.009 | 5.338 |

1.0 | 0.448 | 0.425 | 0.023 | 5.491 |

**Table 11.**Standard deviation of the mechanical and electrical variables using the BEMT/CFD approach.

Uo | Rotational | Thrust | Rotor | Rotor | Electrical | Electrical |
---|---|---|---|---|---|---|

Speed | Torque | Power | Torque | Power | ||

(m/s) | (RPM) | (N) | (Nm) | (W) | (Nm) | (W) |

0.6 | 0.6 | 3.9 | 0.2 | 2.0 | 3.4 | 25.7 |

1.0 | 0.8 | 9.7 | 0.7 | 9.0 | 6.5 | 79.9 |

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**MDPI and ACS Style**

Ortega, A.; Tomy, J.P.; Shek, J.; Paboeuf, S.; Ingram, D.
An Inter-Comparison of Dynamic, Fully Coupled, Electro-Mechanical, Models of Tidal Turbines. *Energies* **2020**, *13*, 5389.
https://doi.org/10.3390/en13205389

**AMA Style**

Ortega A, Tomy JP, Shek J, Paboeuf S, Ingram D.
An Inter-Comparison of Dynamic, Fully Coupled, Electro-Mechanical, Models of Tidal Turbines. *Energies*. 2020; 13(20):5389.
https://doi.org/10.3390/en13205389

**Chicago/Turabian Style**

Ortega, Arturo, Joseph Praful Tomy, Jonathan Shek, Stephane Paboeuf, and David Ingram.
2020. "An Inter-Comparison of Dynamic, Fully Coupled, Electro-Mechanical, Models of Tidal Turbines" *Energies* 13, no. 20: 5389.
https://doi.org/10.3390/en13205389