# A Parametric Study of Wave Energy Converter Layouts in Real Wave Models

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## Abstract

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## 1. Introduction

## 2. Numerical Modelling

#### 2.1. Wave Energy Converter

**R**denotes the real part of the equation, ${F}_{x}$ is the excitation vector consists of amplitude and phase of the wave, S is the wave spectrum, $\varphi $ is the stochastic phase angle, ${\eta}_{\tau}$ represents water elevation and ${f}_{e}$ is the element of force vector [48]. The load force of PTO is modeled as a linear spring-damper system.

#### 2.2. Wave Resource

#### 2.3. Array Interaction Criteria

## 3. Layout Assessment Routine

## 4. Results and Discussions

#### 4.1. Sensitivity of Two-Buoy Array Performance to Distance

#### 4.2. Sensitivity of Three-Buoy Array Performance to Distance

#### 4.3. Sensitivity of Four-Buoy Array Performance to Distance

#### 4.4. Sensitivity of Five-Buoy Array Performance to Distance

#### 4.5. Sensitivity Analysis of q-Factor to the Relative Angle of Rotation

#### 4.6. Landscape Analysis

#### 4.7. Interaction Based Layout Selection

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

WEC | Wave Energy Converter |

PTO | Power Take-off |

PSO | Particle Swarm Optimisation |

GA | Genetic Algorithm |

EA | Evolutionary Algorithms |

DE | Differential Evolution |

GWO | Gray Wolf Optimiser |

ML | Machine Learning |

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**Figure 1.**Schematic representation of the CETO6 modelled point absorber wave energy converter (adapted from [60]).

**Figure 3.**Layout Setup of (

**a**) 2 buoys array (linear), (

**b**) 3 buoys array (triangle-shape), (

**c**) 4 buoys array (square-shape) and (

**d**) 5 buoys array (pentagon-shape), with regard to dominant wave direction.

**Figure 8.**q-factor results distribution and mean value per five meters of the Wave Energy Converters (WECs)’ distance over rotation angle due to significant wave direction in the Perth wave model. (Fifty percent of results near the mean value are plotted in a box, the range of other results is shown by a dashed line).

**Figure 9.**The q-factor results distribution and mean value every five meters of WECs’ distance over rotation angle due to the significant wave direction in the Adelaide wave model. (Fifty percent of results near the mean value are plotted in a box, the range of the other results is shown by a dashed line).

**Figure 10.**The q-factor results distribution and mean value per five meters of WECs’ distance over rotation angle due to significant wave direction in Tasmania wave model. (Fifty percent of results near the mean value are plotted in a box, the range of other results are shown by a dashed line).

**Figure 11.**q-factor results distribution and mean value per five meters of WECs’ distance over rotation angle due to significant wave direction in the Sydney wave model. (Fifty percent of results near the mean value are plotted in a box, the range of the other results is shown by a dashed line).

**Figure 12.**Exploited energy distribution of the WECs array over entire area in Sydeny wave scenario.

**Figure 13.**Exploited energy distribution of the WECs array over the entire area in the Perth wave scenario.

**Figure 14.**Exploited energy distribution of the WECs array over the entire area in the Adelaide wave scenario.

**Figure 15.**Exploited energy distribution of the WECs array over the entire area in the Tasmania wave scenario.

**Table 1.**A briefly survey some of the recent literature on the layout, Power Take-Off (PTO) parameters and design optimisation of wave energy converters.

Objective | WECs Type | WECs Number | Method | Year | References |
---|---|---|---|---|---|

Design & PTOs | submerged | 2 | Experimental observations | 2020 | [17] |

Layout & PTOs | fully-submerged | 4, 16 | Cooperative EAs | 2020 | [18] |

Design & PTOs | fully-submerged | 1 | Hybrid EAs | 2020 | [29] |

Layout | fully-submerged | 50, 100 | Multi-strategy EAs | 2020 | [30] |

Design & PTOs | heaving WEC | 1 | Evolutionary and GA | 2020 | [19] |

PTOs | oscillating wave surge converter | 1 | GA | 2020 | [20,31] |

Design | sloped-motion WEC | 1 | Heuristic optimization | 2020 | [32] |

PTOs | oscillating water column-based | 1 | Water cycle algorithm | 2020 | [33] |

PTOs | hinged-type WECs | 1 | Experimental observations | 2020 | [34] |

PTOs | oscillating wave surge converter | 1 | GA and ML | 2020 | [35] |

Layout | submerged | 25 | PSO | 2020 | [36] |

Design | submerged flat plate | 1 | GA | 2019 | [37] |

Design & Layout | cylindrical heaving WECs | 3, 5, 7 | GA | 2019 | [38] |

Design | submerged | 2 | GA | 2019 | [39] |

Layout | fully-submerged | 4, 16 | Smart heuristic | 2019 | [40] |

Layout | fully-submerged | 4, 16 | Nuro-adaptive EA | 2019 | [41] |

PTOs | freely floating | 2 | EAs | 2019 | [42] |

Design | hinge-barge WEC | 2 | gradient-based method | 2019 | [43] |

Design | fully-submerged | 1, 2, 3 | GA, PSO | 2019 | [44] |

Layout & PTOs | fully-submerged | 16 | Hybrid EAs | 2019 | [45] |

Layout & PTOs | fully-submerged | 4, 9 | Heuristics | 2019 | [46] |

Feasibility Study & Design | oscillating wave surge converter | 3 | Numerical and GWO | 2019 | [47] |

Layout | heaving WEC | 1 | GWO | 2019 | [48] |

Layout | heave-constrained cylinder | 5 | improved GA | 2018 | [49] |

Layout | fully-submerged | 4, 16 | Local search | 2018 | [50] |

Layout | oscillating WEC | 3, 5, 8 | improved DE | 2018 | [51] |

Layout & LCoE | fully-submerged | 4, 9, 36 | Multi-objective EAs | 2018 | [52] |

PTOs | submerged | 1 | Hidden GA | 2018 | [53] |

Layout & PTOs | submerged | 4, 7, 9, 14 | hybrid GA | 2018 | [54] |

Layout | semi-submerged | 1000 | approximate analytical method | 2015 | [9] |

Layout | submerged | 32 | randomized geometries | 2013 | [26] |

Layout | floating + partially submerged | 4 | sensitivity analysis | 2014 | [25] |

Design & Layout | submerged | 4 | sensitivity analysis | 2017 | [24] |

Design | point-absorbing WECs | 100 | analytical multiple scattering | 2015 | [55] |

Design & Layout | floating over-topping WECs | 9 | Down-scaling techniques | 2018 | [56] |

Design & PTOs | heaving WEC | 9, 16, 25 | sensitivity analysis | 2012 | [57] |

Parameter | Perth | Adelaide | Sydney | Tasmania |
---|---|---|---|---|

Two-buoy layout maximum q-factor | 1.0091 | 1.0163 | 1.0003 | 1.003 |

$\mathit{\alpha}$_{(degrees)} | 40 | 0.00 | 130 | 80 |

distance_{(meter)} | 160 | 165 | 400 | 160 |

Three-buoy layout maximum q-factor | 1.0026 | 0.9987 | 0.9939 | 0.9976 |

$\mathit{\alpha}$_{(degrees)} | 10 | 10 | 10 | 10 |

distance_{(meter)} | 445 | 445 | 445 | 405 |

Four-buoy layout maximum q-factor | 1.0053 | 1.0046 | 0.9958 | 1.0019 |

$\mathit{\alpha}$_{(degrees)} | 60 | 60 | 60 | 20 |

distance_{(meter)} | 485 | 485 | 485 | 485 |

Five-buoy layout maximum q-factor | 0.9949 | 0.9899 | 0.9849 | 0.9905 |

$\mathit{\alpha}$_{(degrees)} | 18 | 63 | 45 | 18 |

distance_{(meter)} | 250 | 275 | 450 | 250 |

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**MDPI and ACS Style**

Amini, E.; Golbaz, D.; Amini, F.; Majidi Nezhad, M.; Neshat, M.; Astiaso Garcia, D.
A Parametric Study of Wave Energy Converter Layouts in Real Wave Models. *Energies* **2020**, *13*, 6095.
https://doi.org/10.3390/en13226095

**AMA Style**

Amini E, Golbaz D, Amini F, Majidi Nezhad M, Neshat M, Astiaso Garcia D.
A Parametric Study of Wave Energy Converter Layouts in Real Wave Models. *Energies*. 2020; 13(22):6095.
https://doi.org/10.3390/en13226095

**Chicago/Turabian Style**

Amini, Erfan, Danial Golbaz, Fereidoun Amini, Meysam Majidi Nezhad, Mehdi Neshat, and Davide Astiaso Garcia.
2020. "A Parametric Study of Wave Energy Converter Layouts in Real Wave Models" *Energies* 13, no. 22: 6095.
https://doi.org/10.3390/en13226095