*2.1. Procedure*

The method proposed is based on four phases, as shown in Figure 1: geographic phase (inputs in the figure), energy phase (power matrix and sea state location in the figure), economic phase (LCOE calculation in the figure), and restrictions phase (restriction of bathymetry in figure).

**Figure 1.** Method adopted [source: own]. P: depth in meters; PWEC: wave energy converter (WEC) electric power generated; LCOE: levelized cost of energy.

#### *2.2. Geographic Phase*

The geographic phase is the first stage of this methodology. The parameters that have been used as input maps to generate output economic maps were calculated in this phase. The parameters were the significant wave height and the energy period of the waves, the bathymetry, the distance from farm to shore [51], farm to shipyard, and farm to port.

The wave parameters—significant wave height (Hs) and wave period (Tm)—were obtained from a previous hindcast study [49,50] using WW III (Wave Watch III) and SWAN (Simulating Waves Nearshore) in a coupled system. In terms of the size of the grid, it is important that a floating offshore wave energy farm can be located inside the cell. The distance between offshore WECs is 87.5 times the diameter (D) of the WEC and the distance between lines of WECs is 47.5 times the diameter (D) of the WEC, as Figure 2 shows. In the WECs considered, the main dimension is the diameter of the device.

**Figure 2.** Distance between wave energy converters (WECs) (87.5D) and distance between lines of WECs (47.5D). [Source: own].

The restriction assessment was done using the bathymetry from GEBCO (General Bathymetric Chart of the Oceans), which was also used in the SWAN simulations of the hindcast study mentioned above.

The grid maps of the bathymetry and the parameters Hs and Tm were interpolated so as to have the size recommended for the wave energy farm implementation. The interpolation was from a resolution of 0.05◦ × 0.1◦ in the case of Hs, Tm and bathymetry, and 0.5◦ × 0.5◦ in the case of wind to a resolution of 0.15◦ × 0.3◦. The function interp2 of MATLAB was applied to the data in a linear interpolation.

#### *2.3. Energy Phase*

In the energy phase, the energy produced by each WEC (*E*1WEC) is calculated by Equation (1).

$$E\_{\rm INEC} = NHAT \cdot P\_{\rm WEC} \cdot \eta\_{available} \cdot \eta\_{transmission losses} \tag{1}$$

This calculation depends on the number of hours per year (*NHAT*), the WEC electric power generated (*P*WEC), the availability (*ηavailability*) and the losses due to transmission (*ηtransmissionlosses*). The *P*WEC is calculated by Equation (2).

$$P\_{\rm WEC} = \frac{1}{100} \cdot \sum\_{i=1}^{n\_T} \sum\_{j=1}^{n\_H} p\_{ij} \cdot P\_{ij} \tag{2}$$

The power matrix of the WEC is associated with the sea state probability of occurrence in the study location. In this equation, the *nT* is the number of period and *nH* is the number of wave height in the table, the *pij* is the probability of occurrence of the sea state corresponding to the bin defined by the line *i* and the column *j* and *Pij* is the electric power corresponding to the same sea state or energy bin for the WEC considered [21]. Therefore, it is necessary to have the power matrix of the WEC, given by the supplier of the WEC considered, and the probability distribution matrix of the sea states for each point of the geography of the region of analysis. The devices studied here have their power matrices given in open literature.

#### *2.4. Economic Phase*

In the economic phase, two types of parameters were calculated to measure the economic viability of a wave energy farm deployment: the life-cycle cost of the wave energy farm and the economic parameters. For that, the values calculated in the geographic phase (the height of the waves, the period of the waves, the bathymetry, the distance from farm to shore, farm to shipyard, and farm to port) and energy phase (energy produced by the WEC) were used as inputs, which have different values for different points in the map (*k*).

The calculation of the life-cycle cost of the floating offshore wave energy farm (FOWEF) was based on the methodology developed in previous studies [22,23]. The methodology was based on the life-cycle process of floating offshore renewable energy devices, composed by six phases, attributing to each phase of the process the inherent costs, called the Life-cycle Cost System (LCS).

The phases along the life-cycle process and whose costs will be taken into account are [52]: the concept definition (*C*1), the design and development (*C*2), the manufacturing (*C*3), the installation (*C*4), the exploitation (*C*5), and the dismantling (*C*6). The Life-cycle cost system (LCS) of a floating offshore wave energy farm (FOWEF) was then calculated as Equation (3) shows:

$$L\mathbb{C}S\_{\text{FOWE}}(k) = \mathbb{C}1(k) + \mathbb{C}2 + \mathbb{C}\mathfrak{S}(k) + \mathbb{C}4(k) + \mathbb{C}\mathfrak{S}(k) + \mathbb{C}\mathfrak{G}(k). \tag{3}$$

Another measure of costs is the levelized cost of energy (LCOE), which takes into account the Life-cycle costs (LCSFOWEFt), the energy produced by the wave energy farm (*E*t) (without considering losses due to individual WEC efficiency or near field effects) in MWh/year and the capital cost of the project (*r*) [53,54]. The formula to calculate LCOE is Equation (4).

$$LCOE = \frac{\sum\_{t=0}^{N\_{\text{form}}} \frac{LCS\_{\text{COMHEP}}}{(1+r)^t}}{\sum\_{t=0}^{N\_{\text{form}}} \frac{E\_t}{(1+r)^t}} \tag{4}$$

Also important is the parameter NPV (net present value, Equation (5)), which consists of the net value of the cash flows of the floating offshore wave farm, considering its discount from the beginning of the investment [54,55].

$$NPV = -G\_0 + \sum\_{\mathbf{t}=1}^{n} \frac{CF\_{\mathbf{t}}}{\left(1+\mathbf{r}\right)^{\mathbf{t}}} \tag{5}$$

The NPV depends on the cash flow (*CF*<sup>t</sup> = *R*<sup>t</sup> − *E*t, where *E*<sup>t</sup> is the expenses on year and *R*<sup>t</sup> the revenues on year), the life-cycle years (t), the initial investment (*G*0), and the discount rate (r) [26].

When the NPV is equal to zero, the IRR (internal rate of return) is calculated from Equation (6) [25,27].

$$1 - G\_0 + \sum\_{t=1}^{n} \frac{CF\_t}{\left(1 + \text{IRR}\right)^t} = 0\tag{6}$$

The WACC (weighted average cost of capital) has been developed based on Equation (7).

$$\% \text{MACC} = \frac{MV\_{\text{c}} \cdot \text{R}\_{\text{c}} + MV\_{d} \cdot \text{R}\_{d} \cdot (1 - T)}{MV\_{\text{c}} + MV\_{d}} \tag{7}$$

It is dependent on the variables of total equity (*MVe*) and its costs (*Re*), total debt (*MVd*) and its costs (*Rd*), and the tax shield ((1 − *T*)).The floating offshore wave energy farm (FOWEF) studied is economically feasible if the NPV > 0, the IRR > WACC, and LCOE presents low values.

#### *2.5. Restrictions Phase*

Once all the economic maps have been calculated, it is important to restrict the area where the wave energy farm is to be installed. This is due to the fact that there could be a good region in economic terms (IRR, NPV, and LCOE), but with limitations of usage (seismic fault lines, environmental protected areas, offshore electric cable lines, navigation areas, etc.). In this paper, the bathymetry is the only restriction taken into account.

The bathymetry restriction will be from (*Dc* + 20), *Dc* being the maximum draft of all the floating offshore WECs considered, to 1000 m of depth, which is considered an adequate value to install this type of wave farm. The type of floating offshore wave platform also restricts the economic maps.

Finally, territorial waters (22.2 km) will also be shown in the maps because there is no law about the offshore space for offshore waves at the moment.

## *2.6. Case Study*

The case study is the offshore area of Portugal, as shown in Figure 3, characterized by deep waters, as shown in Figure 4, and good wave energy resources.

**Figure 3.** Portugal and Spain.

**Figure 4.** Bathymetry of Portugal, with P being the depth in meters [56].

It is important to know the life-cycle of the project, which is considered 20 years, and the size of the grid, which is considered 16 km × 33 km.

Several floating offshore wave energy platforms have been taken into consideration: Pelamis, AquaBuOY, and Wave Dragon, as shown in Figure 5. The characteristics of the wave farm will depend on the type of WEC considered, as Table 1 shows. The final configuration (number of WECs per line, number of lines, total number of WECs in the farm) was assembled considering the total power of the farm, which in all the cases is close to 110 MW.


**Table 1.** Characteristics of the wave energy farms depending on the WEC taken into consideration.

**Figure 5.** Types of WECs considered: Pelamis (**a**) [57], AquaBuOY (**b**) [58], and Wave Dragon (**c**) [23].

Due to the fact that Portugal does not have a specific electric tariff for wave energy, several tariffs were considered and are presented in Table 2.

**Table 2.** Electric tariffs considered for a floating offshore wave energy farm.


The restriction considered for bathymetry was 50 m, based on adding +20 m to the maximum draft of all the WECs considered, as shown in Figure 6.

The energy produced by a particular WEC is dependent on its power matrix, as shown in Tables 3–5, and on the number of occurrences of each sea state at the point considered, as shown in Table 6.

**Figure 6.** Bathymetry restriction. The white area represents the region selected considering the bathymetry restriction. The dashed line represents the territorial waters. [Source: own].




**Table 4.** Power matrix of the AquaBuOY [59]. *Hs*: wave height; *Tp*: wave peak period.

**Table 5.** Power matrix of the Wave Dragon [59]. *Hs*: wave height; *Tp*: wave peak period.


**Table 6.** Example of the number of occurrences for different sea states (in % from the total) for a point of Portugal. *Hs*: wave height; *Tp*: wave peak period.


The electric power generated by each WEC, considering the power matrix of each WEC and the number of occurrences for different sea states for each point of the geography, are presented in Figure 7.

**Figure 7.** Power of Pelamis (**a**), AquaBuOY (**b**), and Wave Dragon (**c**). [Source: own].

#### **3. Results**

The results obtained for each WEC in terms of LCOE, but without the bathymetry restriction, are displayed in Figure 8a–c. The Wave Dragon, as shown in Figure 8c, was the one that presents the best value for this parameter, with 316.90 €/MWh, followed by 735.94 €/MWh for the Pelamis, as shown in Figure 8a, and 2967.85 €/MWh for the AquaBuOY, as shown in Figure 8b.

**Figure 8.** Results for LCOE without bathymetry restrictions for Pelamis (**a**), AquaBuOY (**b**), and Wave Dragon (**c**) platform. [Source: own].

However, it is important to notice that the installation of the WEC depends on the bathymetry, so the previous maps shown in Figure 9 cannot be used in their totality for the choice of the best deployment place. In this context, a restriction for bathymetry has been considered, as shown in Figure 9a–c. However, in this study, this will not affect the results for the best LCOE.

**Figure 9.** Results for LCOE with bathymetry restrictions for Pelamis (**a**), AquaBuOY (**b**), and Wave Dragon (**c**). [Source: own].

Considering Scenario 1 for the electric tariff with 300 €/MWh, the implementation of a wave farm is not economically feasible whatever the WEC used. The values of IRR for all the WECs considered are lower than the WACC value, and the values of NPV are less than zero, the opposite of the feasibility conditions. For IRR, the values are around 4.74% for Wave Dragon, 11.94% for Pelamis, and −50.94% for the AquaBuOY. In terms of NPV, the Wave Dragon had −67.56 M€, the Pelamis −561.52 M€, and the AquaBuOY 2732.93 M€, as shown in Table 7.


**Table 7.** Results for the 300 €/MWh tariff. IRR: internal rate of return; NPV: net present value.

Scenario 2, which takes into account a 400 €/MWh electric tariff, has better results than the previous one. The WACC, which is dependent of the location (the total equity (*MVe*) and the total debt (*MVd*) depends of the life-cycle costs of each location), has values from 6% to 7%, which is lower than the IRR value of Wave Dragon, as shown in Figure 10c, with 9.35%. For Pelamis, as shown in Figure 10a, this parameter assumes the value of −5.67% and for AquaBuOY, as shown in Figure 10b, a value of −36.29%. For the NPV, the Wave Dragon, as shown in Figure 11c, has a value of 246.80 M€ (NPV > 0), the Pelamis, as shown in Figure 11a, a value of −429.67 M€, and AquaBuOY, as shown in Figure 11b, a value of 2637.39 M€. Looking at the results, the Wave Dragon is the WEC that encompasses all the requirements for a viable wave farm project.

**Figure 10.** Results for IRR considering a tariff of 400 €/MWh and the bathymetry restriction for Pelamis (**a**), AquaBuOY (**b**), and Wave Dragon (**c**). [Source: own].

**Figure 11.** Results for NPV considering a tariff of 400 €/MWh and the bathymetry restriction for Pelamis (**a**), AquaBuOY (**b**), and Wave Dragon (**c**). [Source: own].

The last scenario, Scenario 3, which takes into consideration a 600 €/MWh electric tariff, gives the best results of all the three scenarios. For IRR, the Wave Dragon, as shown in Figure 12c, presents the best value with 17.25%, followed by Pelamis, as shown in Figure 12a, with 2.49%, and AquaBuOY, as shown in Figure 12b, with −22.97%.

**Figure 12.** Results for IRR considering a tariff of 600 €/MWh and the bathymetry restriction for Pelamis (**a**), AquaBuOY (**b**), and Wave Dragon (**c**). [Source: own].

In terms of NPV, the best value for Scenario 3 is 881.24 M€ for the Wave Dragon, as shown in Figure 13c, followed by −168.38 M€ for the Pelamis, as shown in Figure 13a, and −244.73 M€ for the AquaBuOY, as shown in Figure 13b. Therefore, with this electric tariff, a wave farm project with Wave Dragon WECs would be economically feasible.

**Figure 13.** Results for NPV considering a tariff of 600 €/MWh and the bathymetry restriction for Pelamis (**a**), AquaBuOY (**b**), and Wave Dragon (**c**). [Source: own].

With respect to the best area for the wave farm installation, the area located close to Lisbon, in the center of Portugal, seems to be the better choice, as can be seen in all the economic maps with bathymetry restrictions. In the future, this would be a good location to install this type of offshore wave energy technology, when the reduction of costs, due to the commercial phase, guarantees the economic feasibility of the project.

#### **4. Conclusions**

The goal of this paper was to develop a method to calculate the economic feasibility of floating offshore wave energy farms. Therefore, their internal rate of return (IRR), net present value (NPV), and levelized cost of energy (LCOE) have been calculated. The method proposed has four phases: geographic phase, energy phase, economic phase, and bathymetry restriction phase. The aim of the geographic phase is to calculate the input values that will be used in the economic phase: the significant height of the waves, the period of the waves, the bathymetry, the distance from farm to shore, farm to shipyard, and farm to port. The second phase is the energy phase, which determines the energy produced by each WEC. This can be calculated by several methods, depending on the data available and the precision required. The next phase is the economic phase, where the economic parameters are calculated using the parameter results of the previous phases as inputs. Finally, there is the bathymetry restriction phase, where the restriction by bathymetry will be added to the economic maps, whose value will be different depending on the floating offshore WEC.

The case study was the Portuguese continental coast, which has a good wave energy resource. Different WECs were used for the evaluation: the Pelamis, AquaBuOY, and Wave Dragon, as well as different scenarios for electric tariffs.

The results of LCOE, IRR, and NPV indicate what the best WEC to use in a wave farm is and what the best location is to install it. The Wave Dragon has the best LCOE, with 316.90 €/MWh, followed by Pelamis, with 735.94 €/MWh, and AquaBuOY, with 2967.85 €/MWh. This is due to the fact that Wave Dragon generates more energy for the location selected, as its power matrix shows. This is a result of being a larger device and benefiting from the effect of the scale of the energy produced, which then makes it cheaper. According to the IRR and the NPV results, only Scenario 2 (400 €/MWh) and 3 (600 €/MWh) for the electric tariff are economically feasible when using a Wave Dragon platform.

The layout considered is similar for all the WECs, considering that each device is separated from the other, taking into account the main dimensions of the platform. In the future, it can be improved considering the different energy production systems that each WEC has.

This study presents a novelty compared to other studies because it takes into account the economic aspects of wave energy, not only their technical aspects. It is very important to know the areas where the farms can be installed in economic terms, and whose use can help to analyze maritime planning of the countries in the future.

Portugal has good wave energy potential. In the future, areas close to Lisbon would be good locations to install this type of offshore technology, when the reduction of costs, due to the commercial phase, guarantees the economic feasibility of the project.

**Author Contributions:** All authors have been involved in either calculations or writing, as follows: Introduction, L.C.-S., D.S. and C.G.S.; Methodology, L.C.-S.; Case study, L.C.-S., D.S., A.R.B., N.S. and C.G.S.; Results, L.C.-S.; Discussion, L.C.-S., D.S., A.R.B., N.S. and C.G.S.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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