# A Review of Point Absorber Wave Energy Converters

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## Abstract

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## 1. Introduction

- Wave power is of a higher power intensity than solar and wind power. For instance, the intensities of solar, wind and wave power are 0.17 $\mathrm{kW}/{\mathrm{m}}^{2}$, 0.58 $\mathrm{kW}/{\mathrm{m}}^{2}$ and 8.42 $\mathrm{kW}/{\mathrm{m}}^{2}$, respectively, at a latitude of 15° N within the Northeast Trades [12].
- Wave power has high availability, being available up to 90% of the time, while the availability of solar and wind power ranges from 20% to 30% [13].
- Harvesting wave energy is currently considered environmentally friendly, as several sea trails only showed little impact on the oceanic environment [22,23]. Currently, most WECs are designed and optimised for energetic sites, and the device size should be downscaled accordingly to perform well in low-energy seas [24].

## 2. Point Absorber Prototypes

#### 2.1. Classification of Point Absorbers

#### 2.2. One-Body Point Absorbers

#### 2.2.1. Floating One-Body Point Absorbers

#### 2.2.2. Submerged One-Body Point Absorbers

#### 2.3. Multi-Body Point Absorbers

#### 2.3.1. Self-Reacting Two-Body Point Absorbers

#### 2.3.2. Self-Contained Two-Body Point Absorbers

#### 2.3.3. Multi-Point Absorbers

## 3. Hydrodynamic Modelling

#### 3.1. Computational Fluid Dynamics Methods

#### 3.2. Potential Flow Theory Methods

#### 3.3. Hybrid Modelling Methods

- For the body-exact treatment method, the instantaneous body position is considered in computing the FK, diffraction, radiation and restoring forces in Equations (7)–(10), while the wave is still assumed to be small. When the body size is small, the nonlinearity in diffraction and radiation are neglectable. For a body with a varying horizontal cross-section, the nonlinearity in the hydrostatic force appears obvious. Considering the large body motion, the nonlinearity in the FK force is more critical than the other force and has a significant impact on PA hydrodynamics [146,149,150].
- For the weak scatterer treatment method, the instantaneous free surface is considered in computing the forces in Equations (7)–(10), while the wetted surface is linearised at the equilibrium point. This method linearises the free-surface boundary condition at $z=\eta \left(t\right)$. Thus, the second-order terms of ${\varphi}_{\mathrm{d}}$ and ${\varphi}_{\mathrm{r}}$ can be added to compute the diffraction and radiation forces in Equations (8) and (9). However, the importance of the nonlinear diffraction and radiation terms mainly depends on the body size. For a small body, these nonlinear forces can be neglected [151].
- For the viscosity treatment method, the viscosity is considered by adding a quadratic term to the Cummins’ equation, according to the Morison equation [152]. This method can significantly improve the modelling accuracy with little computing cost when the relative velocity between the body and fluid is large. The viscous coefficient can be determined analytically, numerically or experimentally [134,153,154]. However, a wide range of wave conditions should be tested to obtain a consistent value [155].
- The mixed treatment method has two subclasses: the body-exact viscosity treatment considering both large body motion and fluid viscosity and the weak-scatter viscosity treatment considering both a large wave height and fluid viscosity. In AQWA, the weak-scatter viscosity treatment is realised by computing the nonlinear FK and hydrostatic forces according to instantaneous wave elevation and adding the viscous force according to the Morison equation [156,157]. In general, PAs’ motion is significantly amplified by power maximisation control, and hence, the nonlinearity induced by large body motion is more critical than that induced by a large wave height. Therefore, the body-exact viscosity treatment is broadly used in PA modelling.

#### 3.4. Experimental Modelling Methods

## 4. Power Take-Off Mechanisms

#### 4.1. Hydraulic PTO Mechanisms

#### 4.2. Mechanical PTO Mechanisms

#### 4.3. Direct-Drive PTO Mechanisms

#### 4.4. Novel PTO Mechanisms

## 5. Control Strategies

#### 5.1. Classical Control Strategy

#### 5.2. Modern Control Strategies

## 6. Discussion

#### 6.1. Perspectives on PA Concepts

#### 6.2. Perspectives on PA Hydrodynamics

#### 6.2.1. Nonlinear Hydrodynamics

#### 6.2.2. Extreme Wave Loads

#### 6.2.3. Array Operation

#### 6.3. Perspectives on PA PTOs

#### 6.4. Perspectives on PA Control

#### 6.5. Perspectives on PA Application

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

WEC | Wave energy converter |

PAWEC | Point absorver wave energy converter |

TRL | Technology readiness level |

TPL | Technology performance level |

LCoE | Levelised cost of energy |

PTO | Power take-off |

O&M | Operation and maintenance |

PA | Point absorber |

DoF | Degree of freedom |

R&D | Research and development |

RAO | Response amplitude operator |

EMEC | European Marine Energy Centre |

AWS | Archimedes wave swing |

UPS | Uninterruptible power supply |

FNT | Float-neck-tank |

CFD | Computational fluid dynamics |

PFT | Potential flow theory |

FNPFT | Fully nonlinear potential flow theory |

LPFT | Linear potential flow theory |

FK | Froude–Krylov |

PMLG | Permanent magnet linear generator |

DEG | Dielectric elastomer generator |

TENG | Triboelectric nanogenerator |

RC | Reactive control |

PC | Passive control |

LC | Latching control |

DC | Declutching control |

ACC | Approximate complex conjugate |

AVT | Approximate velocity tracking |

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**Figure 2.**Point absorber wave energy converters can be further classified into subcategories according to the design geometry, manner of installation and operating mode.

**Figure 3.**The working principles of floating and submerged one-body point absorbers are illustrated in (

**a**,

**b**), respectively.

**Figure 6.**The self-reacting, self-contained and multi-point PAs are illustrated in (

**a**–

**c**), respectively.

**Figure 15.**Direct-drive power take-off mechanisms with a schematic plot (

**a**) and a heaving point absorber with a linear generator (

**b**), adapted from [194].

**Figure 16.**The working principle of a dielectric elastomer generator (

**a**) and its application for a heaving point absorber (

**b**), adapted from [198].

**Figure 17.**A triboelectric nanogenerator as a power take-off mechanism with its work principle (

**a**), a torus-shaped PA prototype (

**b**) and an array (

**c**), adapted from [179].

**Figure 18.**(

**a**) Approximate complex conjugate (ACC) and (

**b**) approximate velocity tracking (AVT) control frameworks.

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**MDPI and ACS Style**

Guo, B.; Wang, T.; Jin, S.; Duan, S.; Yang, K.; Zhao, Y.
A Review of Point Absorber Wave Energy Converters. *J. Mar. Sci. Eng.* **2022**, *10*, 1534.
https://doi.org/10.3390/jmse10101534

**AMA Style**

Guo B, Wang T, Jin S, Duan S, Yang K, Zhao Y.
A Review of Point Absorber Wave Energy Converters. *Journal of Marine Science and Engineering*. 2022; 10(10):1534.
https://doi.org/10.3390/jmse10101534

**Chicago/Turabian Style**

Guo, Bingyong, Tianyao Wang, Siya Jin, Shunli Duan, Kunde Yang, and Yaming Zhao.
2022. "A Review of Point Absorber Wave Energy Converters" *Journal of Marine Science and Engineering* 10, no. 10: 1534.
https://doi.org/10.3390/jmse10101534