# Modeling and Simulation of a Wave Energy Converter INWAVE

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Explanation of the Device

## 3. Modeling of the Device’s Dynamics

#### 3.1. Buoy-Counterweight Modeling

#### 3.2. Power Take Off Module Modeling

#### 3.3. Schematization of Ratchet Gears

#### 3.4. JONSWAP Wave Spectrum Model and Capture Width Ratio

## 4. Simulation in the Time Domain

## 5. Characteristics of the INWAVE Device

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Johansson, T.B. Renewable Energy: Sources for Fuels and Electricity; Island Press: Washington, DC, USA, 1993. [Google Scholar]
- Lindroth, S.; Leijon, M. Offshore wave power measurements—A review. Renew. Sustain. Energy Rev.
**2011**, 15, 4274–4285. [Google Scholar] [CrossRef] - Mørk, G.; Barstow, S.; Kabuth, A.; Pontes, M.T. Assessing the global wave energy potential. In Proceedings of the 29th International Conference on Ocean, Offshore and Arctic Engineering, Shanghai, China, 6–11 June 2010.
- Falnes, J. Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction; Cambridge University Press: Cambridge, UK, 2002. [Google Scholar]
- Clément, A.; McCullen, P.; Falcão, A.; Fiorentino, A.; Gardner, F.; Hammarlund, K.; Lemonis, G.; Lewis, T.; Nielsen, K.; Petroncini, S.; et al. Wave energy in Europe: Current status and perspectives. Renew. Sustain. Energy Rev.
**2002**, 6, 405–431. [Google Scholar] [CrossRef] - Nielsen, S.N.; Jørgensen, S.E. Sustainability analysis of a society based on exergy studies—A case study of the island of Samsø (Denmark). J. Clean. Prod.
**2015**, 96, 12–29. [Google Scholar] [CrossRef] - Yong Jun, S. Available online: https://www.youtube.com/watch?v=-vt2PJdBhkU (accessed on 14 October 2016).
- Sjolte, J.; Sandvik, C.M.; Tedeschi, E.; Molinas, M. Exploring the potential for increased production from the wave energy converter lifesaver by reactive control. Energies
**2013**, 6, 3706–3733. [Google Scholar] [CrossRef][Green Version] - Lattanzio, S.; Scruggs, J. Maximum power generation of a wave energy converter in a stochastic environment. In Proceedings of the 2011 IEEE International Conference on Control Applications (CCA), Denver, CO, USA, 28–30 September 2011; IEEE: New York, NY, USA, 2011; pp. 1125–1130. [Google Scholar]
- Cummins, W.E. The Impulse Response Function and Ship Motions; Technical Report, DTIC Document; David Taylor Model Basin: Washington, DC, USA, 1962. [Google Scholar]
- Dean, R.G.; Dalrymple, R.A. Water Wave Mechanics for Engineers and Scientists; World Scientific Publishing Company: Singapore, 1991. [Google Scholar]
- Budar, K.; Falnes, J. A resonant point absorber of ocean-wave power. Nature
**1975**, 256, 478. [Google Scholar] [CrossRef] - Holmes, B. Tank Testing of Wave Energy Conversion Systems: Marine Renewable Energy Guides; European Marine Energy Centre: Orkney, UK, 2009. [Google Scholar]
- Kang, D.H.; Lee, B.G. Evaluation of Wave Characteristics and JONSWAP Spectrum Model in the Northeastern Jeju Island on Fall and Winter. J. Korean Soc. Mar. Environ. Energy
**2014**, 17, 63–69. [Google Scholar] [CrossRef] - Babarit, A. A database of capture width ratio of wave energy converters. Renew. Energy
**2015**, 80, 610–628. [Google Scholar] [CrossRef] - Hasselmann, K.; Barnett, T.; Bouws, E.; Carlson, H.; Cartwright, D.; Enke, K.; Ewing, J.; Gienapp, H.; Hasselmann, D.; Kruseman, P.; et al. Measurements of Wind-Wave Growth and Swell Decay during the Joint North Sea Wave Project (JONSWAP); Technical Report; Deutsches Hydrographisches Institut: Hamburg, Germany, 1973. [Google Scholar]
- Butcher, J.C. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods; Wiley-Interscience: Hoboken, NJ, USA, 1987. [Google Scholar]
- Ansys, A. User Manual v.13.0, 2010; Century Dynamics Ltd.: Horsham, UK, 2010. [Google Scholar]
- Bosma, B.; Zhang, Z.; Brekken, T.K.A.; Özkan-Haller, H.T.; McNatt, C.; Yim, S.C. Wave energy converter modeling in the frequency domain: A design guide. In Proceedings of the 2012 IEEE Energy Conversion Congress and Exposition (ECCE), Raleigh, NC, USA, 15–20 September 2012; IEEE: New York, NY, USA, 2012; pp. 2099–2106. [Google Scholar]
- Mann, L.; Burns, A.; Ottaviano, M. CETO, a carbon free wave power energy provider of the future. In Proceedings of the 7th European Wave and Tidal Energy Conference (EWTEC), Porto, Portugal, 11–13 September 2007.
- Leijon, M.; Boström, C.; Danielsson, O.; Gustafsson, S.; Haikonen, K.; Langhamer, O.; Strömstedt, E.; Stålberg, M.; Sundberg, J.; Svensson, O.; et al. Wave energy from the North Sea: Experiences from the Lysekil research site. Surv. Geophys.
**2008**, 29, 221–240. [Google Scholar] [CrossRef]

**Figure 2.**INWAVE prototype installed in the northern port of Jeju Island: (

**a**) panorama of the device; (

**b**) buoys; (

**c**) counterweights; and (

**d**) electric generator [7].

**Figure 4.**Power take off (PTO) module consisting of counterweights, pulleys, including ratchet gears, and the generator.

**Figure 12.**Simulation result of the INWAVE device under the JONWSAPwave model with ${H}_{s}=1$ m and ${T}_{p}=4.5$ s when ${b}_{g}=5$ Nm s/rad: (

**a**) wave elevation; (

**b**) buoy’s posture; (

**c**) pulley’s angular speed; (

**d**) rope tension; (

**e**) power from the generator.

**Figure 13.**Graph of ${\overline{P}}_{g}^{*}$ with varying ${b}_{g}$ when ${T}_{p}=4.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$.

Parameter | Value | Unit |
---|---|---|

${\mathsf{\rho}}_{w}$ | 1025 | $\mathrm{kg}/{\mathrm{m}}^{3}$ |

R | 2.5 | $\mathrm{m}$ |

r | 1.5 | $\mathrm{m}$ |

h | 5 | $\mathrm{m}$ |

D | 3 | $\mathrm{m}$ |

${m}_{1}$, ${m}_{2}$ | 250 | $\mathrm{kg}$ |

${m}_{b}$ | 2500 | $\mathrm{kg}$ |

${J}_{b}$ | 3906 | $\mathrm{kg}\xb7$m${}^{2}$ |

${r}_{1}$, ${r}_{2}$ | 0.25 | $\mathrm{m}$ |

κ | 35 | - |

${k}_{r}$ | ${10}^{4}$ | $\mathrm{N}/\mathrm{rad}$ |

© 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Song, S.K.; Sung, Y.J.; Park, J.B. Modeling and Simulation of a Wave Energy Converter *INWAVE*. *Appl. Sci.* **2017**, *7*, 99.
https://doi.org/10.3390/app7010099

**AMA Style**

Song SK, Sung YJ, Park JB. Modeling and Simulation of a Wave Energy Converter *INWAVE*. *Applied Sciences*. 2017; 7(1):99.
https://doi.org/10.3390/app7010099

**Chicago/Turabian Style**

Song, Seung Kwan, Yong Jun Sung, and Jin Bae Park. 2017. "Modeling and Simulation of a Wave Energy Converter *INWAVE*" *Applied Sciences* 7, no. 1: 99.
https://doi.org/10.3390/app7010099