# Performance of a Direct-Driven Wave Energy Point Absorber with High Inertia Rotatory Power Take-off

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## Abstract

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## 1. Introduction

- An innovative approach using a rotatory generator for wave energy and tuning the natural frequency is discussed in [9], where a pendulum excited by the heave motion of the WEC turns a rotatory generator. The pendulum can be designed, so that it is in resonance at the frequency of the incident wave and so the power absorption is maximised.
- The dynamo presented in [16] converts the bi-directional movement of the buoy into a unidirectional rotation for the generator what might result in similar inertia effects as the PTO presented here. However, the design requires a complex gearbox and a rectifier to make the pulsed output of the WEC grid conforming. The effects of the increased inertia on the power absorption are not investigated.
- Concepts based on flywheels, like in [17] (and similarly in [24,25]) convert the linear bi-directional motion of the buoy into a bi-directional rotation, but the generator connected to a flywheel is run in uni-directional motion. A controllable clutch connects the generator with the buoy shaft whenever it might accelerate the generator shaft. In the meantime the generator is run by the energy stored in the flywheel. As the generator’s angular velocity does not follow the buoy’s velocity, it does not show the high inertia of the alternating generator and is only able to absorb energy while the buoy is moving downwards. The power output is very smooth and may need no or only little smoothing to be grid compatible, and so the peak-to-average power ratio is much lower than in conventional WEC designs.
- A bi-directional winch based design, similar to the concept presented here, but with a gearbox and the PTO placed in the buoy is used in the WEC described in [21]. The generator is a conventional electrical machine used in industrial servo applications. It only produces power while moving upwards and operates in motoring mode during downwards motion.

## 2. Design of the Physical Model PTO

- Viscous dampers create an accurate damping force by forcing a fluid through a small hole. The damping can be changed by varying the hole diameter.
- Eddy-current breaks provide a nearly ideal, contactless velocity proportional force by moving a conductive material through a magnetic field. The damping can be adjusted by varying the magnetic field.
- Small permanent electric generators, like automotive alternators or bicycle hub dynamos are cost effective and provide the absorbed power directly.

#### 2.1. Characteristics

#### 2.2. Influence of Inertia on Absorbed Power

#### 2.3. Differences to Linear Generator

- The damping is increased by factor ${({r}_{d}/{r}_{l})}^{2}$ for the rotational direct-driven generator, less magnets/coils are needed for the same damping.
- If ${r}_{c}>{r}_{l}$, the inertia of the rotatory PTO can be much higher with the same weight. The eigenfrequency decreases with the inertia.
- The stroke length of the rotational PTO is not directly limited by the generator height.
- For a rotatory motor a good bearing (e.g., roller bearing) is much easier to design than for a translatory generator. On the other hand, the force acting on the rotatory bearing is much higher than on a linear generator bearing. Furthermore a winch based rotatory generator has friction due to the rope unwinding.

## 3. Theory of Wave Body Interactions

## 4. Physical Experiments

#### 4.1. Physical Model Set-up

#### 4.2. Wave Tank Tests

## 5. Numerical Simulations

#### 5.1. Numerical Model

#### 5.2. Parameters

## 6. Results and Discussion

#### 6.1. Numerical Simulations

#### 6.2. Numerical Simulations and Physical Tests

#### 6.3. Overall

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

WEC | Wave energy converter |

PTO | Power take-off |

IMU | Inertia measurement unit |

WAMIT | WaveAnalysisMIT; Wave interaction analysing tool |

COAST laboratory | Coastal, ocean and sediment transport laboratory; |

Facility at the University of Plymouth containing the wave tank | |

Q-factor | quality factor |

DDE | Delayed differential equation |

g | gravity acceleration |

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**Figure 1.**Simplified sketch of the PTO with relevant radii. Here ${r}_{d}$ is the distance from the disc’s centre to the magnets, ${r}_{w}$ is the radius of the winch for the line leading to the weight, and ${r}_{l}$ is the radius of the winch of the line leading to the buoys.

**Figure 2.**Processing of the measured data. Here v is the linearised velocity and x the linearised position.

**Figure 3.**Instantaneous damping related to the mean damping, plotted over the disc position. The calculation is based on the disc rotational velocity after reaching constant velocity while a force of $12.5$ N (model scale) is acting on the line. Mean damping is full scale equivalent. Graph shows one test with 2.25 revolutions.

**Figure 4.**Acceleration measured and low pass filtered (orange) in relation to the theoretical acceleration (100%, blue line). The yellow line represents the value the measured acceleration tends to. Values are directly measured from the scale model.

**Figure 5.**Measured damping of the PTO (blue) in relation to the gap width, measured in turns of the vice knob. The dotted line shows the trend of the magnetic flux according to Equation (1). The curve is scaled so that it matches with the measurement for the zero clamp position.

**Figure 6.**(

**a**) Photo of the physical scale model; (

**b**) Schematic of the set-up during the scale model testing in the wave tank.

**Figure 8.**Matrix of power output for two direct-driven PTOs with different inertia, but the same weight, calculated by the numerical simulation and compared to a generator with $M={m}_{w}$, so a linear generator.

**Figure 9.**Position of the translator in the numerical simulation for Ts = 7.5 s and Hs = 0.75 m (

**a**), and Hs = 1.75 m (

**b**). The thin blue curve is from the PTO with low inertia ($45\phantom{\rule{4.pt}{0ex}}\mathrm{t}$), the thick orange curve with high inertia ($120\phantom{\rule{4.pt}{0ex}}\mathrm{t}$). The damping was set to $75\phantom{\rule{4.pt}{0ex}}\mathrm{kNs}/\mathrm{m}$. All values scaled to full scale equivalents.

**Figure 10.**Matrix of generated power (${d}_{PTO}{v}^{2}$) for two direct-driven PTOs with different inertia, but same weight, results of the wave tank test.

**Figure 11.**Position of the translator in the wave tank tests for Ts = 7.5 s and Hs = 0.75 m (

**a**), and Hs = 1.75 m (

**b**). The thin blue curve is from the PTO with low inertia ($53\phantom{\rule{4.pt}{0ex}}\mathrm{t}$), the thick orange curve with high inertia ($101\phantom{\rule{4.pt}{0ex}}\mathrm{t}$). The damping was set to $100\phantom{\rule{4.pt}{0ex}}\mathrm{kNs}/\mathrm{m}$. All values scaled to full scale equivalents.

**Figure 12.**Comparison of the generated power in the physical wave tank tests (

**orange**), the numerical simulation using a medium stiff line with ${c}_{l}=133\phantom{\rule{4.pt}{0ex}}\mathrm{kN}/\mathrm{m}$ and ${d}_{l}=10\phantom{\rule{4.pt}{0ex}}\mathrm{kN}/\mathrm{m}$ (

**grey**) and the numerical simulation using an ideal stiff line with ${c}_{l}=4\phantom{\rule{4.pt}{0ex}}\mathrm{GN}/\mathrm{m}$ and ${d}_{l}=1\phantom{\rule{4.pt}{0ex}}\mathrm{kN}/\mathrm{m}$ (

**blue**). The inertia was set to $M=53\phantom{\rule{4.pt}{0ex}}\mathrm{kg}$.

Parameter | Model Scale Value | Full Scale Value |
---|---|---|

disc radius (${r}_{s}$) | $0.2$ m | 2 m |

attachment radius (${r}_{w}$ and ${r}_{l}$) | 10 mm | $0.1$ m |

Mass weight (${m}_{w}$) | 5 kg | 5000 kg |

Mass buoy (${m}_{b}$) | 5 kg | 5000 kg |

Inertia disc (J) | 48 kg | $\mathrm{48,000}$ kg |

PTO damping (${d}_{PTO}$) | 312 Nm/s | 100 kNm/s |

Sea state duration | $6.5$ min | 20 min |

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## Share and Cite

**MDPI and ACS Style**

Thomas, S.; Giassi, M.; Göteman, M.; Hann, M.; Ransley, E.; Isberg, J.; Engström, J. Performance of a Direct-Driven Wave Energy Point Absorber with High Inertia Rotatory Power Take-off. *Energies* **2018**, *11*, 2332.
https://doi.org/10.3390/en11092332

**AMA Style**

Thomas S, Giassi M, Göteman M, Hann M, Ransley E, Isberg J, Engström J. Performance of a Direct-Driven Wave Energy Point Absorber with High Inertia Rotatory Power Take-off. *Energies*. 2018; 11(9):2332.
https://doi.org/10.3390/en11092332

**Chicago/Turabian Style**

Thomas, Simon, Marianna Giassi, Malin Göteman, Martyn Hann, Edward Ransley, Jan Isberg, and Jens Engström. 2018. "Performance of a Direct-Driven Wave Energy Point Absorber with High Inertia Rotatory Power Take-off" *Energies* 11, no. 9: 2332.
https://doi.org/10.3390/en11092332