# The Optimal Configuration of Wave Energy Conversions Respective to the Nearshore Wave Energy Potential

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## Abstract

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## 1. Introduction

_{2}. The total potential wave power resource is estimated to be 2TW. According to the Renewable 2022 World Status Report [1], renewable energy sources account for 19.2% of the global energy consumption, traditional biomass (8.9%), and solar and wind power (10.3%) following fossil fuel usage (78.3%). The gap between the market for renewable energy and the consumption of fossil fuels may soon be closed if we consider recent improvements in the renewable energy sector. The global market for alternative energy sources increased from 85 GW in 2004 to 560 GW in 2013 (excluding hydropower) [2,3,4]. With an increase from 48 to 318 GW, the wind industry took the lead in the sector. A number of variables, such as governmental backing, financial incentives, and falling technological prices that made renewable energy affordable, contributed to the revolution in this renewable industry.

#### Related Works

## 2. Wave Energy Resource and the WEC Mechanism

#### 2.1. Wave Energy Characteristics

#### 2.2. Wave Energy Converter Types

#### 2.2.1. Point Absorbers

#### 2.2.2. Oscillating Water Columns

#### 2.2.3. Attenuators

#### 2.2.4. Terminators

#### 2.3. Power Take-Off Mechanism

#### 2.4. Hydrodynamic Interaction Definition

## 3. Recent Advances in Optimizing the WEC Configuration

#### 3.1. Optimization Approaches

#### 3.1.1. Genetic Algorithm

#### 3.1.2. Evolutionary Multi-and Many-Objective Algorithms

#### 3.2. Layout-PTO-Geometry Optimization

## 4. Future Research Direction

## 5. Conclusions

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- Numerous relevant elements are used in the layout optimization studies to find the best solutions. In order to identify the most consistent, repeatable findings throughout the examined research, two patterns, namely the linear and the arrowhead patterns, are depicted in this study. The performance of the arrangement is directly affected by variables, such as the distance and wave direction. Therefore, we agree on a general statement of how increasing or decreasing these factors affects the arrangement of the array.
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- Recently, it has been established as a reasonable standpoint to use the optimization techniques to increase the control methods and enhance the PTO coefficients. The modern meta-heuristic algorithms have also optimized these coefficients. Recent research shows that the maximum power output at lower frequencies increases with the increasing damping coefficient. Experimental evidence is presented to support this notion. A complete cost-benefit analysis is required for each of the many PTO systems that are categorized in this paper, even if the PTO system setup will enhance the LCoE. Further study on the active control methods for the PTO system of the conversions is needed.
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- According to studies, the WECs’ shape optimization may significantly boost performance. Geometry optimization combined with the PTO control approach may lead to better outcomes. While increasing the WECs’ geometry will boost their profitability, performance should be adjusted in light of the rising prices.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

WEC | Wave energy converter |

EA | Evolutionary algorithm |

GA | Genetic algorithm |

OWSC | Oscillating wave surge converter |

BEM | Boundary element method |

CMA-EA | Covariance matrix adaptation evolutionary algorithm |

CMA-ES | Covariance matrix adaptation evolutionary strategy |

MM | Metamodel algorithm |

PTO | Power take-off |

SWAN | Simulating WAve Nearshore |

DOF | Degrees of freedom |

PA | Point absorber |

RAO | Response amplitude response |

OWC | Oscillating water column |

LCoE | Levelized cost of energy |

WD | Wave dragon |

SSG | Sea slot-cone generator |

PF | Potential flow |

CFD | Computational fluid dynamics |

DNS | Direct numerical simulation |

LES | Large eddy simulation |

RANS | Reynolds average Navier–Stokes |

NSE | Navier–Stokes equation |

GSO | Glowworm swarm optimization |

NM | Nelder–Mead |

ANN | Artificial neural network |

SA | Simulating annealing |

PI | Parabolic intersection |

HGGA | Hidden genes genetic algorithm |

RBFNN | Radial basis function neural network |

COBYLA | Constrained optimization technique by linear approximation |

MOEA | Many-objective evolutionary algorithm |

NSGA | Non-dominated sorting genetic algorithm |

HGA-PSO | Hybrid genetic algorithm-particle swarm optimization |

HPTO | Hydraulic power take-off |

FSPMLG | Flux-switching permanent magnet linear generator |

DE | Differential equation |

ANSO | Adaptive neuro-surrogate model |

HCCA | Hybrid coordination channel access |

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**Figure 7.**Transforming wave energy into electrical power by different means, reprinted from Pecher and Kofoed [97].

Author(s)–Year | WEC Type | WEC No. | Objective Function | Algorithm | Ref. | |||
---|---|---|---|---|---|---|---|---|

PA | OWC | Attenuator | Terminator | |||||

Deandres (2014) | ✓ | 2, 3, 4 | q-factor | GA + Parabolic Intersection | [128] | |||

Baltisky (2014) | ✓ | 2, 3, 4, 5, 6 | Mean AEP | Global Control | [129] | |||

Noad et al. (2015) | ✓ | 3, 5 | Absorbed power | Multi-Dimensional Optimization | [106] | |||

Blanco et al. (2015) | ✓ | 2 | Maximize power | EA | [130] | |||

Sharp & DuPont (2016) | ✓ | 5 | Power and cost | GA | [131] | |||

Wu et al. (2016) | ✓ | 25, 50, 100 | Computational cost | EA and CMA-ES | [54] | |||

Sarkar et al. (2016) | ✓ | 40 | Maximize power | GA and Monte Carlo | [42] | |||

Ruiz et al. (2017) | ✓ | >10 | Maximize power | CMA-ES, GA, GSO | [55] | |||

Ferri (2017) | ✓ | >50 | Computational cost | CMA-ES + MM | [132] | |||

Giassi et al. (2017) | ✓ | 9, 12 | Maximize power | GA | [112] | |||

Blanco et al. (2018) | ✓ | 2 | Maximize power | EA | [119] | |||

Sharp and DuPont (2018) | ✓ | 5 | Power and cost | GA | [113] | |||

Giassi et al. (2018) | ✓ | 4–14 | Maximize power | GA + Multiple Scattering | [56] | |||

Fang et al. (2018) | ✓ | 3, 5, 8 | Maximize power | EA | [133] | |||

Neshat et al. (2018) | ✓ | 4 | Maximize power | Meta-Heuristic Algorithm | [134] | |||

Lyu et al. (2019) | ✓ | 3, 5, 7 | Optimal control | GA | [110] | |||

Vatchavayi (2019) | ✓ | 4–9 | Maximize power | CMA-ES | [107] | |||

Neshat et al. (2019) | ✓ | 16 | Maximize power | Neural Optimization + Analytical | [135] | |||

Faraggiana et al. (2019) | ✓ | 1–3 | Minimize LCoE | PSO and GA | [121] | |||

Neshat et al. (2020) | ✓ | 49, 100 | Maximize power | Multi-Strategy EAs | [136] | |||

Neshat et al. (2020) | ✓ | 4, 16 | Maximize power | Cooperative EAs | [137] | |||

Bosma et al. (2020) | ✓ | 5 | Average power | - | [138] |

Author(s)–Year | WEC Type | Parameters | Objective Function | Algorithm | Ref. | |||
---|---|---|---|---|---|---|---|---|

PA | OWC | Attenuator | Terminator | |||||

Babarit (2006) | ✓ | Length, Beam, Draught | Absorbed power, Cost | GA | [143] | |||

Gomes et al. (2010) | ✓ | Radius, Height, Draught, Submergence | Optimal design values | DE, GA | [146] | |||

Colby et al. (2011) | ✓ | Design of Ballast Chamber Cuts, Weight Distribution | Annual power output | EAs | [147] | |||

Victor et al. (2011) | ✓ | Ramp Angle, Freeboard, Submergence | Optimal design values | Multi-Scatter | [148] | |||

Gomes (2012) | ✓ | Length and Diameters of the Small and Large Thickness Tubes | Energy absorption | COBYLA, DE | [149] | |||

Goggins et al. (2014) | ✓ | Geometric Shape and Radii | Maximizing power, Maximizing Significant velocity (double amplitude motion) | - | [150] | |||

Margherittini et al. (2012) | ✓ | Crest Level, Ramp Angle, Ramp Draught | Maximizing hydraulic efficiency | - | [151] | |||

Noad (2015) | ✓ | Length, Flap Width, Hinge Depth | Capture factor | - | [106] | |||

Silva et al. (2016) | ✓ | Radii, Height, Draught, Submergence | Annual averaged power output | COBYLA + GA | [152] | |||

Tom et al. (2016) | ✓ | Flap Size, Vane Size, Vane Number, submergence | Power absorption | Nonlinear optimization | [153] | |||

Li et al. (2016) | ✓ | Length, Draught, Distance | Power absorption | Two-step optimization | [154] | |||

Mahnamfar et al. (2017) | ✓ | Chamber Size, Orifice Size, Submergence, Front Wall | Maximum power | Nash-Sutcliffe Coefficient of Efficiency | [155] | |||

Sergiienko et al. (2017) | ✓ | Radius, Heights, Cone, Angle, Draught | Performance-optimal control | - | [156] | |||

Renzi et al. (2017) | ✓ | Length, Width, Height, Submergence | Capture factor | GA | [157] | |||

Bouali (2017) | ✓ | Immersion Depth, OWC Width | Hydrodynamic efficiency | Sequential procedure | [158] | |||

Esmaeilzadeh et al. (2019) | ✓ | Elongation Coefficients of the WEC Base Shape | Power output | GA | [45] | |||

Wang et al. (2019) | ✓ | Length of the Fore and Aft Barges | Extracted energy | Exhaustive search method | [159] | |||

Ulazia et al. (2020) | ✓ | Chamber Size, Orifice Size, Submergence | Capture width | Two-value optimization | [160] |

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Shadmani, A.; Nikoo, M.R.; Al-Raoush, R.I.; Alamdari, N.; Gandomi, A.H.
The Optimal Configuration of Wave Energy Conversions Respective to the Nearshore Wave Energy Potential. *Energies* **2022**, *15*, 7734.
https://doi.org/10.3390/en15207734

**AMA Style**

Shadmani A, Nikoo MR, Al-Raoush RI, Alamdari N, Gandomi AH.
The Optimal Configuration of Wave Energy Conversions Respective to the Nearshore Wave Energy Potential. *Energies*. 2022; 15(20):7734.
https://doi.org/10.3390/en15207734

**Chicago/Turabian Style**

Shadmani, Alireza, Mohammad Reza Nikoo, Riyadh I. Al-Raoush, Nasrin Alamdari, and Amir H. Gandomi.
2022. "The Optimal Configuration of Wave Energy Conversions Respective to the Nearshore Wave Energy Potential" *Energies* 15, no. 20: 7734.
https://doi.org/10.3390/en15207734