# Techno-Economic Related Metrics for a Wave Energy Converters Feasibility Assessment

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Device Specifications

#### 2.2. Techno-Economic Model

#### 2.3. Assumptions

- Power matrices are scaled with the Froude scale (further explained below).
- For all ratings, the device is in survival mode in sea states where H
_{s}> 10 m. - No interaction effects are considered among devices (q factor = 1).
- CAPEX is scaled based on the following equation:$${\text{CAPEX}}_{2}={\text{CAPEX}}_{1}\times {\text{Scale}}^{\text{Scaleparameter}},$$
_{1}corresponds to the CAPEX of the 25 kW device, Scale corresponds to the scale of the device calculated through the rated power conversion, and Scale parameter corresponds to the CAPEX Scale parameter that is further explained below. - 1st OPEX calculation approach:For the sake of simplicity, and due to the absence of adequate O&M data for wave energy converters, OPEX is calculated as a percentage of the CAPEX. O’Connor et al. [6] showed different figures of OPEX calculated as a percentage of CAPEX. In this case, following Guanche et al. [7], it was assumed that the initial OPEX was 8% of CAPEX.
- 2nd OPEX calculation approach:As a second approach, OPEX is calculated based on the real cost of the repair actions through the life-cycle of the device. The assumption of one major repair being performed every two years is used. Costs are based on consultations with a vessel company in Orkney. It is assumed that the same type of vessel is used for the repair action, independently of the rating of the device.
- For both OPEX approaches it is assumed that OPEX is the same for all locations.
- The same level of availability is assumed for all locations, and is taken to be 95% based on Guanche et al. [17].
- It is assumed that the wave energy farm is designed for a 20-year life-cycle.
- A discount rate of 8% has been chosen following Guanche et al. [7].
- A feed in tariff of 375 Eur/MWh has been selected, as this is the current feed in tariff in the United Kingdom for wave and tidal projects.
- It is assumed that this will be the first 20 MW farm developed and so the selection of interest rate, availability, and OPEX has been made with this in mind.
- A learning rate is applied to CAPEX due to bulk production. In this case, as the first units produced, a factor of 0.82 is selected as suggested as an optimistic scenario in Guanche et al. [7]. For OPEX, a learning rate of 0.92 is applied (normally OPEX shows slower learning than CAPEX).

#### 2.4. Power Matrix Scaling Methodology

_{1}= Fr

_{2}as represented in Equation (4):

_{1}/l

_{2}based on Froude similitude. Force is defined in Equation (5) and velocity is defined in Equation (6). This results in the power being expressed in terms of λ in Equation (7). The wave heights scale linearly with the scale ratio (Equation (8)) and the wave period scales as a square root to the scale ratio (Equation (9)).

#### 2.5. CAPEX Scaling

## 3. Sites

## 4. Results

#### 4.1. The 20 MW Farm Analysis

_{s}–low T

_{e}area. It is noticeable how, in Wavehub, the smaller rating versions perform much better than the high ratings. In contrast, for instance in Yeu, the medium rating version performs as well as the small rating version

_{e}between 5.5 and 6.5 s make up nearly 50% of the annual occurrences, while they only represent 16% of the annual available energy. Most of the energy comes from high-energy, low-probability sea states that are not captured by the CorPower Ocean device. It should be noted that the specific device model being studied had been equipped with a PTO optimized for the lower end of the wave period range. A PTO optimized for longer waves would likely perform better at EMEC. It should be emphasized that the reference power matrix is optimized for Yeu and this penalizes the other locations. For future studies the power matrices will be calculated numerically and will be optimized for each location.

_{s}, high T

_{e}area.

#### 4.2. Sensitivity Analysis: CAPEX and OPEX

#### 4.3. Metrics Comparison among Devices

^{2}that represents the absorbed energy per surface unit, and the ACE that is a proxy for LCOE.

^{2}).

## 5. Relation of LCOE to Other Indicators

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Wave climate scatter plots for the five selected sites (number of occurrences per year). EMEC (

**top left**), WaveHub (

**top right**), Bimep (

**mid left**), Yeu (

**mid right**), and DK North Sea Point 2 (bottom) [12].

Module & Parts | Scale Parameter |
---|---|

M1_Pretension | 3 |

M2_Wave_Spring | 3 |

M3_Gearbox | 3 |

M4_Flywheel | 3 |

M5_Generators | 3.5 |

M7_6 Control & Power_Electronics | 3.5 |

M8_Software & Communications | 1 |

M9_PTO frame, boxes and routing | 2 |

M10_Buoy | 2 |

M11_FAT_Rigs | 1 |

M12_Cooling_System | 1 |

M13_Lubrication_System | 1 |

M14_Humidity_System | 1 |

M15_Gas_Refill_System | 1 |

M16_PTO_Frame | 2 |

M17_Hydraulic_Power_Pack | 1 |

M21_Tethers | 3 |

M22_Anchors | 3 |

M23_Tidal_Module | 0.5 |

M24_Umbilical & connectors | 1 |

Weighted Scale Coefficient | 2.39 |

Location | Mean Power | Waver Depth Range | Distance to Shore |
---|---|---|---|

EMEC (United Kingdom) | 28.5 kW/m | 12–50 m | 1–2 km |

Wavehub (United Kingdom) | 16 kW/m | 50–60 m | 16 km |

Bimep (Spain) | 21 kW/m | 50–90 m | 1.7 km |

Yeu Island (France) | 26 kW/m | --------- | ---------- |

DK, North Sea point 2 (Denmark) | 12 kW/m | 31 m | 100 km |

**Table 3.**Rating option (kW) associated with minimum LCOE with OPEX calculated with the first approach.

Scale Parameter | EMEC | Wavehub | Bimep | Yeu | DKNorth Sea Point 2 |
---|---|---|---|---|---|

0.5 | 2000 | 250 | 250 | 500 | 250 |

1 | 100 | 100 | 250 | 250 | 100 |

1.5 | 100 | 25 | 100 | 100 | 100 |

2 | 25 | 25 | 25 | 25 | 100 |

2.5 | 25 | 25 | 25 | 25 | 25 |

3 | 25 | 25 | 25 | 25 | 25 |

3.5 | 25 | 25 | 25 | 25 | 25 |

4 | 25 | 25 | 25 | 25 | 25 |

**Table 4.**Rating option (kW) associated with minimum LC with OPEX calculated with the second approach.

Scale Parameter | EMEC | Wavehub | Bimep | Yeu | DKNorth Sea Point 2 |
---|---|---|---|---|---|

0.5 | 2000 | 2000 | 2000 | 2000 | 1500 |

1 | 2000 | 1500 | 2000 | 2000 | 1500 |

1.5 | 2000 | 1500 | 1000 | 1000 | 1500 |

2 | 2000 | 500 | 1000 | 100 | 1500 |

2.5 | 2000 | 500 | 750 | 750 | 1000 |

3 | 1000 | 500 | 750 | 750 | 750 |

3.5 | 1000 | 500 | 750 | 500 | 500 |

4 | 500 | 500 | 500 | 500 | 250 |

RST (m) | Width (m) | Surface Area (m^{2}) | Capture Width Ratio (%) | kWh/kg | MWh/m^{2} | ACE (m/M€) | |
---|---|---|---|---|---|---|---|

Small bottom-ref heaving buoy | 0.094 | 3 | 42 | 4.1 | 0.92 | 0.68 | 6.44 |

Bottom-ref. submerged heave-buoy | 0.115 | 7 | 220 | 13 | 0.97 | 0.88 | 7.38 |

Floating two-body heaving converter | 0.342 | 20 | 2120 | 36 | 0.3 | 0.79 | 2.04 |

Bottom-fixed heave-buoy array | 0.0468 | 17 | 4350 | 17 | 1.5 | 0.56 | 2.93 |

Floating heave-buoy array | 0.140 | 18 | 4750 | 11 | 0.67 | 0.79 | 0.61 |

Bottom-fixed oscillating flap | 0.239 | 26 | 2020 | 72 | 1 | 1.9 | 7.99 |

Floating three-body oscillating flap | 0.095 | 25 | 2160 | 20 | 0.69 | 0.46 | 5.00 |

Floating OWC | 0.035 | 24 | 6500 | 52 | 1.6 | 1.8 | 11.26 |

CorPower 250 kW | 0.029 | 8.54 | 328.03 | 37 | 9.05 | 2.21 | 25.92 |

© 2016 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/).

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**MDPI and ACS Style**

De Andres, A.; Maillet, J.; Hals Todalshaug, J.; Möller, P.; Bould, D.; Jeffrey, H.
Techno-Economic Related Metrics for a Wave Energy Converters Feasibility Assessment. *Sustainability* **2016**, *8*, 1109.
https://doi.org/10.3390/su8111109

**AMA Style**

De Andres A, Maillet J, Hals Todalshaug J, Möller P, Bould D, Jeffrey H.
Techno-Economic Related Metrics for a Wave Energy Converters Feasibility Assessment. *Sustainability*. 2016; 8(11):1109.
https://doi.org/10.3390/su8111109

**Chicago/Turabian Style**

De Andres, Adrian, Jéromine Maillet, Jørgen Hals Todalshaug, Patrik Möller, David Bould, and Henry Jeffrey.
2016. "Techno-Economic Related Metrics for a Wave Energy Converters Feasibility Assessment" *Sustainability* 8, no. 11: 1109.
https://doi.org/10.3390/su8111109