# Wave Resource Assessments: Spatiotemporal Impacts of WEC Size and Wave Spectra on Power Conversion

^{*}

## Abstract

**:**

^{3}kW, respectively.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Traditional Wave Resource Assessment Methods

#### 2.2. WEC Net Power Assessment (NPA)

## 3. Case study WEC, Assessment Locations, and Study Scenarios

## 4. Results

#### 4.1. IEC Assessment

#### 4.2. WEC Net Power Assessment (NPA)

#### 4.2.1. Mean Annual Average Energy Production

#### 4.2.2. Monthly Power and COV

^{5}, 5.5 × 10

^{4}, 3.5 × 10

^{3}, and 440 kW/m

^{3}for the 1, 2, 5, and 10 m devices, respectively. This quick analysis indicates that the WECs with a smaller size generally have better efficiency than the WECs with a larger size at WETS from 2000 to 2010.

#### 4.2.3. Instantaneous Power

## 5. Discussion

## 6. Conclusions

^{3}kW, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Budal diagram for a 5 m WEC. The black star line corresponds to the net power extractable by the device.

**Figure 3.**Recreation of Beatty et al.’s research using RM3 WEC data. The black solid line is the radiation power limit, the dashed red line is Budal’s upper bound for [15] body A, the red crosses are experimental data points that were found by Beatty et al. [15], and the solid green line is the gross incident wave power that interacts with the device. Here, the y-axis describes the wave power normalized by wave amplitude squared (${\eta}^{2}$).

**Figure 5.**Power limit behavior and resulting net power for the hourly spectrum at PacWave for a 10 m WEC.

**Figure 6.**Basic schematic of the heaving spherical WEC used in this study. The device captures energy by oscillating vertically (heaving) in the water column as incident waves interact with it. The heaving induces movement in a turbine, which converts the motion to usable power.

**Figure 7.**Study locations (black dots with yellow outline) shown on a base map of gross wave power (Cornett, 2008).

**Figure 9.**Budal diagram showing Budal’s upper bound for different WEC sizes compared to the radiation power limit for the baseline scenario methods. Net power absorbable is outlined in a black star line. Each net power curve is labeled according to its corresponding WEC characteristic length (i.e., body diameter). The lowest curve is for the 1 m device, followed increasingly by the 2, 5, and 10 m device net power curves.

**Figure 10.**Budal diagram showing Budal’s upper bound for different WEC sizes compared to the radiation power limit and gross wave power for the expanded scenario methods. Net power is outlined in a black star line. Each net power curve is labeled according to its corresponding WEC characteristic length (i.e., body diameter). The lowest curve is for the 1 m device, followed increasingly by the 2, 5, and 10 m device net power curves.

**Figure 12.**Radiation power limit, Budal’s upper bound, gross power, and net power for 1 m WECs for a PM spectrum of 1 m significant wave height and 8 s peak period. Both the baseline and expanded case results are shown.

**Figure 13.**Radiation power limit, Budal’s upper bound, gross power, and net power for 10 m WECs for a PM spectrum of 1 m significant wave height and 8 s peak period. Both the baseline and expanded case results are shown.

**Figure 14.**Radiation power limit, Budal’s upper bound, gross power, and net power for 1 m WECs for a PM spectrum of 1 m significant wave height and 12 s peak period. Both the baseline and expanded case results are shown.

**Figure 15.**Radiation power limit, Budal’s upper bound, gross power, and net power for 10 m WECs for a PM spectrum of 1 m significant wave height and 12 s peak period. Both the baseline and expanded case results are shown.

**Figure 16.**MAEP for the 5 m WEC at each study site for the (

**a**) NPA assessment and (

**b**) the IEC assessment methods.

**Figure 17.**Monthly variation of (

**a**) mean net power via NPA and (

**b**) COV according to the baseline and expanded cases for the 5 m WEC from 2000 to 2010. Each differently colored line corresponds to one of the five ocean test sites.

**Figure 18.**Monthly variation of (

**a**) mean net power and (

**b**) COV for Miami from 2000 to 2010 for all WEC sizes. Each differently colored line corresponds to one of the four test WEC sizes, described by characteristic length (i.e., body diameter) in the legend.

**Figure 19.**Monthly variation of (

**a**) mean net power and (

**b**) COV for Los Angeles from 2000 to 2010 for all WEC sizes. Each differently colored line corresponds to one of the four test WEC sizes, described by characteristic length (i.e., body diameter) in the legend.

**Figure 20.**Monthly variation of (

**a**) mean net power and (

**b**) COV for WETS from 2000 to 2010 for all WEC sizes. Each differently colored line corresponds to one of the four test WEC sizes, described by characteristic length (i.e., body diameter) in the legend.

**Figure 21.**Example of instantaneous power for 1 m WEC at all sites in January 2000. Each differently colored line corresponds to one of the five ocean test sites.

**Figure 22.**Example of instantaneous power for 10 m WEC at all sites in January 2000. Each differently colored line corresponds to one of the five ocean test sites.

**Figure 23.**Example of instantaneous power at Cape Cod in January 2000. Each differently colored line corresponds to one of the four test WEC sizes, described by characteristic length (i.e., body diameter) in the legend.

**Figure 24.**Example of instantaneous power at WETS in January 2000. Each differently colored line corresponds to one of the four test WEC sizes, described by characteristic length (i.e., body diameter) in the legend.

Location | Lat, Lon (Degrees) | Depth (m) |
---|---|---|

PacWave, OR, USA | 44.557, −124.229 | 68 |

Los Angeles, CA, USA | 33.854, −118.633 | 350 |

WETS, Oahu, HI, USA | 21.466, −157.751 | 34 |

Cape Cod, MA, USA | 41.140, −70.690 | 38 |

Miami, FL, USA | 25.460, −80.030 | 318 |

Baseline Scenario | Expanded Scenario | |
---|---|---|

Filters | ${P}_{a}$$,{P}_{b}$ | ${P}_{a}$$,{P}_{b}$$,{P}_{gross}$ |

Maximum stroke | ${s}_{max}=\{\begin{array}{c}25\%ofDH0.25D\\ HH0.25D\end{array}$ | ${s}_{max}=\{\begin{array}{c}25\%ofDH0.25D\\ AH0.25D\end{array}$ |

**Table 3.**Mean and maximum values for significant wave height, energy period, and omnidirectional wave power at each study location from 2000 to 2010.

Location | $\mathbf{Max}{\mathit{H}}_{\mathit{m}0}$ | $\mathbf{Mean}{\mathit{H}}_{\mathit{m}0}$ | $\mathbf{Max}{\mathit{T}}_{\mathit{e}}$ | $\mathbf{Mean}{\mathit{T}}_{\mathit{e}}$ | $\mathbf{Max}\mathit{J}$ | $\mathbf{Mean}\mathit{J}$ |
---|---|---|---|---|---|---|

PacWave, OR, USA | 9.70 m | 2.30 m | 19.80 s | 9.70 s | 719 kW | 36.8 kW |

Los Angeles, CA, USA | 4.03 m | 1.07 m | 16.5 s | 9.38 s | 80.3 kW | 5.81 kW |

WETS, Oahu, HI, USA | 4.46 m | 1.66 m | 15.4 s | 7.59 s | 145 kW | 12.6 kW |

Cape Cod, MA, USA | 7.44 m | 0.857 m | 12.9 s | 5.49 s | 256 kW | 3.24 kW |

Miami, FL, USA | 7.33 m | 1.55 m | 16.6 s | 6.78 s | 344 kW | 12.4 kW |

Location | 1 m WEC | 2 m WEC | 5 m WEC | 10 m WEC |
---|---|---|---|---|

PacWave, OR, USA | 47.8 kW | 176 kW | 1.01 × 10^{3} kW | 3.52 × 10^{3} kW |

Los Angeles, CA, USA | 7.00 kW | 37.1 kW | 140 kW | 349 kW |

WETS, Oahu, HI, USA | 12.2 kW | 41.6 kW | 236 kW | 815 kW |

Cape Cod, MA, USA | 27.8 kW | 106 kW | 581 kW | 1.80 × 10^{3} kW |

Miami, FL, USA | 16.4 kW | 63.0 kW | 329 kW | 825 kW |

Location | 1 m WEC | 2 m WEC | 5 m WEC | 10 m WEC |
---|---|---|---|---|

PacWave, OR, USA | 100% | 100% | 100% | 100% |

Los Angeles, CA, USA | 83.00% | 75.00% | 58.70% | 47.10% |

WETS, Oahu, HI, USA | 81.00% | 68.00% | 49.10% | 41.10% |

Cape Cod, MA, USA | 82.70% | 72.30% | 56.10% | 48.30% |

Miami, FL, USA | 77.90% | 67.70% | 56.80% | 56.20% |

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**MDPI and ACS Style**

Dunkle, G.; Zou, S.; Robertson, B.
Wave Resource Assessments: Spatiotemporal Impacts of WEC Size and Wave Spectra on Power Conversion. *Energies* **2022**, *15*, 1109.
https://doi.org/10.3390/en15031109

**AMA Style**

Dunkle G, Zou S, Robertson B.
Wave Resource Assessments: Spatiotemporal Impacts of WEC Size and Wave Spectra on Power Conversion. *Energies*. 2022; 15(3):1109.
https://doi.org/10.3390/en15031109

**Chicago/Turabian Style**

Dunkle, Gabrielle, Shangyan Zou, and Bryson Robertson.
2022. "Wave Resource Assessments: Spatiotemporal Impacts of WEC Size and Wave Spectra on Power Conversion" *Energies* 15, no. 3: 1109.
https://doi.org/10.3390/en15031109