The case study considers a scenario of marine current turbine implantation in the Iroise Sea located in the north-west of France, where areas with high marine current velocity have been identified. Two areas are particularly well-known: the “Raz de Sein area” near Sein Island and the Fromveur pass area near Ouessant Island.

Figure 6 shows the locations where several current velocity surveys were performed and the velocity is higher than 1 ms

^{−1} at least during 30% of the time for a year. Our study is focused on “Raz de Sein”, which is also a high-density human activity area and particularly for fishery. In order to find the place generating the fewest conflicts between sea users, the first step consists of classifying the study area in different zones according to the social acceptance criteria.

#### 4.1. Social Acceptance Evaluation Using Electre III

Let us apply the strategy described by Step 1 of the methodology in order to evaluate the social acceptance criteria. The Electre III outranking MCA method has been applied. In this example, the demonstration is restricted to professional fishery activities, which are the principal human activity nearby the Sein area. Different kinds of fishery practices are identified in the study area. The knowledge of the location of the fishery activities comes from the regulation and seabed properties [

20]. These locations are approximated, as they do not take into account the time/seasonal dimension for the fishery activities, but nevertheless, they give some useful information on the practice geographical breakdown. The fishery activities in the study area are grouped into four categories, which constitute four constraints. The first constraint groups floating longlines and floating lines (

Figure 7). The derived map shows potential overlapping areas. This means that, if two activities overlap in a given location, conflicts may arise. The three other constraints are derived under the same principles. They group net, trawling and dredge and ground line areas, which are respectively shown by

Figure 8,

Figure 9 and

Figure 10 (on top of the map of currents exhibited in

Figure 6).

**Figure 7.**
Floating line fishing areas.

**Figure 7.**
Floating line fishing areas.

**Figure 8.**
Net fishing areas.

**Figure 8.**
Net fishing areas.

Electre III also incorporates the fuzzy dimension of a decision-based process. The outranking relation,

S, is derived for each pair of alternatives (

a,

b) of a set of solutions,

A. The assertion,

a outranks

b,

aSb, is based on two indexes. The concordance index evaluates if a majority of criteria is in favor of

aSb, and the discordance index evaluates if in the minority of criteria; none of them is strongly opposed to

aSb. The fuzzy value is introduced using different thresholds (indifference,

q, preference,

p and veto,

v) in the outranking relation [

5]. The outranking is then defined as follows:

where

g(

x) is the performance of the alternative,

x, regarding a given constraint.

**Figure 9.**
Dredge and trawling areas.

**Figure 9.**
Dredge and trawling areas.

**Figure 10.**
Ground line fishing areas.

**Figure 10.**
Ground line fishing areas.

The veto threshold,

v, is used in the discordance index calculation and defines the case where the performance of

b regarding a given criteria is so high that it constitutes a veto for the assertion

aSb. The threshold values and constraint weight used for the four constraints related to fishing activities are shown in

Table 1. The weight of the floating line has been defined as the lowest, as we assume that this activity has a lesser impact on the potential location of a marine current turbine. Conversely, we assume that trawling and dredge activities are the most-conflicting activities, so those are valued with the highest weights. Indeed, and as part of a real marine spatial planning process, these values should be confirmed by experts and stakeholders. As previously introduced in Step 1 (

Figure 3), before running the MCA, a multi-criteria map is derived. Accordingly, the four constraint maps are overlapped in order to create a new subdivision of the study area made by the intersection of the maps related to the different fishing activities. Electre III allows one to classify all subareas into six categories: the first one denotes the least-impacting areas, while the sixth one denotes the most important conflicting areas (

Figure 11). Therefore, the whole region considered is classified according to the social acceptance criteria. The next step of the methodology develops the cost evaluation.

**Table 1.**
Threshold values and weights.

**Table 1.**
Threshold values and weights.
Constraints | Weight (k) | Indifference Threshold (q) | Preference Threshold (p) | Veto Threshold (v) |
---|

Trawling/dredge | 3 | 0 | 1 | 3 |

Nets | 2 | 0 | 1 | 3 |

Floating lines | 1 | 0 | 1 | 3 |

Ground lines | 2 | 0 | 1 | 3 |

**Figure 11.**
Classification of the study area according to fishery activities.

**Figure 11.**
Classification of the study area according to fishery activities.

#### 4.2. Cost and Energy: Evaluation Using a Genetic Algorithm

As for the previous steps and before applying the optimization algorithm, a multi-criteria map has to be built by taking into account the geographical constraints involved in the estimation of the cost and energy. These constraints modify the suitability resources map. The new map is generated by an overlay of bathymetry, current resource and social acceptance.

Figure 12 shows the current map overlapped by these constraints and where 180 spatial units are obtained. Firstly, locations where the depth is too low have been removed (

i.e., under 15 m). Secondly, spatial units with small areas (

i.e., less than 2600 m

^{2}) are spatially aggregated when they have similar current characteristics. Each spatial unit is, at this step, a homogenous part of the study area according to the social acceptance criteria and the two parameters involved in the estimation of the cost and energy produced. In order to estimate these two parameters, other attributes are added to each of these spatial units: their area, distance to the harbor and distance to the electric grid. The area allows one to define the maximum number of turbines,

NT_{max}, which can be installed in the spatial unit (

NT_{max} is at least equal to one, as the installation of a single turbine does not need a large area). This number depends on a minimum distance between two devices, which also depends on the turbine radius,

R. The turbines are supposed to be placed as a patchwork with a device spacing approximated to seven times its diameter,

D.

NT_{max} is defined as follows:

where

A_{su} is the area of the spatial unit.

The maximum radius allowed for a specific spatial unit is denoted as

R_{max} and is evaluated as a function of the water depth in the area and surface and bottom margins:

Next, the installation and maintenance costs depend on the harbor distance. For the considered case study, this harbor is that of Brest, which is planned to house a complete set of specific marine energy maintenance and installation devices.

**Figure 12.**
(**a**) Multi-criteria map social acceptance ranking visualization. (**b**) Multi-criteria map current resource visualization.

**Figure 12.**
(**a**) Multi-criteria map social acceptance ranking visualization. (**b**) Multi-criteria map current resource visualization.

In fact, the design of a marine current turbine cannot be treated by a classic and deterministic optimization method. Due to the non-linearity of the variables considered and the high number of possible combinations, stochastic methods, such as inductive learning, neural networks and genetic algorithms, should be preferred [

21]. In particular, genetic algorithms perform very well at optimizing a search process with a relatively high number of variables and combinations, and those have been already used for the design of wind turbines [

22]. We retain the solution of a genetic algorithm to best adapt a marine current turbine farm to a specific site according to the technical feasibility and economic viability. The parameters retained for the optimization process are presented hereafter with their corresponding variation domain and variation step (note that the approach is flexible enough to be extended towards some additional parameters):

- -
the turbine type (TT): VA or HA without yaw or HA + yaw

- -
the rotor radius (R): 2.5 m to R_{max} with a step of 0.5 m

- -
the drive train configuration (DT): Direct-drive PMSG or DFIG + gearbox

- -
the rating power (P_{n}) of DT: 0.1 to 3MW with a step of 0.1 MW

- -
the number of turbines (NT) one to NT_{max}

In the case of a VA turbine, the rotor radius corresponds to half the turbine’s height. The width of the VA turbine is calculated in such a way that its area is the same as that of an HA turbine with an equivalent radius.

In order to illustrate the solution exhibited by the application of the optimization algorithm, let us consider a spatial unit (green contour in

Figure 12). This spatial unit is characterized by an area of 310,000 m

^{2} and a mean depth of 24 m. The distance of this unit from Brest harbor and from the fictive grid connection point are, respectively, 48 km and 10 km. The marine current distribution is described by

Figure 13. A surface of (

7D)

^{2} is reserved for one turbine. A top margin of 5 m is suggested to allow small boat navigation and to minimize turbulence and swell effects. Moreover, a five-meter bottom clearance is recommended as a minimum distance to avoid damage by materials moving at the seabed and to minimize the hydrodynamic effects related to the boundary layer [

23]; as the minimum radius considered is 2.5 m and 10 m are allocated for bottom and top clearance (this explains why depths under 15 m have been previously removed).

**Figure 13.**
Distribution of current.

**Figure 13.**
Distribution of current.

For the spatial unit considered, the current is characterized by a dissymmetric distribution.

Figure 13 shows the ideal orientation and the cone of extraction in the case where an HA turbine (without yaw) is taken. In this particular case, various current orientations are hence not harnessed efficiently. The optimization applied to that spatial unit characteristics and algorithm parameters presented previously gives the results shown in

Table 2. As expected, solutions that allow one to harness the current in all directions are selected by the optimization algorithm. No solution with a VA turbine is found; however, a VA solution with the same design of the lowest cost solution (Alternative 1) should be considered by the Pareto optimum, but with a lower value of the produced energy (due to a lower power coefficient). Another observation is that the rotor radius tends to take the entire place that is allocated to it (24 m depth with 10 m of top/bottom clearance that leads to a 7-m turbine radius). In this case, the maximal number of turbines is

NT_{max} = 32. It can also be noticed that the cost of the energy decreases when the number of turbines increases, due to equipment sharing effects.

#### 4.3. Final Ranking

The genetic algorithm, applied with the same parameters, is performed for all spatial units (

Figure 12). This process generates a set of turbine solutions for each spatial unit (as in

Table 2). This results in 2265 possible solutions overall (alternatives) for 180 spatial units. Each of these alternatives is characterized by the energy produced, its cost and the social acceptance of the area to which it belongs (determined by Step 1). Electre III is applied to these alternatives. The weight and threshold values used in the MCA are shown in

Table 3. In this example, a preference for low-cost alternatives grading the highest weight is chosen. The energy indifference threshold is set to 10 MWh; this roughly corresponds to the annual energy needed by a 70-m

^{2} house. That means that if, for two alternatives, the difference of the energy is less than 10 MWh, these two alternatives are considered as equivalent under this criterion. When the difference lies between the indifference and preference thresholds, a linear interpolation is performed. This allows one to derive a fuzzy outranking relation that permits one to state how an action weakly outranks another one. The cost preference threshold is set to 100 k€ (this being the lowest value that can be attributed, due to the cost approximation). The 2265 possible solutions are sorted into 1376 ranks for each spatial unit. The best alternative for a given spatial unit is having the lowest rank among the alternatives belonging to that unit.

Figure 14 gives the classification of the study area, according to the best alternative of the spatial unit, based on the three criteria considered.

In

Figure 14, the four most suitable spatial units are qualified from

A to

D (

A being the best one). The characteristics of the best alternatives and their ranks are given in

Table 4.

A has its alternative ranked as one, but the second spatial unit,

B, has its alternative ranked as three. This means that the alternative, which belongs to

A, has a better ranking than the alternative related to

B. A similar observation can be seen for

C. A gap of three ranks exists between

B and

C. There are two alternatives of

A or

B that can be taken into consideration before considering the spatial unit,

C.

The results show that a majority of the most suitable spatial units have currents, whose velocities are superior to 1 ms^{−1} during at least 50% or 60% of the time, except for C, for instance. The two first spatial units considered (A and B) are located in the lowest fishery area and correspond to a low cost.

**Table 2.**
Results of the genetic algorithm optimization. PMSG, permanent magnet synchronous generator; TT, turbine type; NT, number of turbines; DT, direct-drive turbine.

**Table 2.**
Results of the genetic algorithm optimization. PMSG, permanent magnet synchronous generator; TT, turbine type; NT, number of turbines; DT, direct-drive turbine.
Alternatives | Energy (MWh/year) | Cost (M€) | P_{n} (MW) | R (m) | TT | NT | DT | €/MWh (20 years) |
---|

1 | 1068 | 5.7 | 0.3 | 7 | HA + yaw | 1 | PMSG | 267 |

2 | 1210 | 5.8 | 0.4 | 7 | HA + yaw | 1 | PMSG | 240 |

3 | 1469 | 6.2 | 1 | 7 | HA + yaw | 1 | PMSG | 211 |

4 | 1478 | 6.3 | 1.1 | 7 | HA + yaw | 1 | PMSG | 213 |

5 | 1493 | 6.4 | 1.4 | 7 | HA + yaw | 1 | PMSG | 214 |

6 | 1496 | 6.9 | 2.1 | 7 | HA + yaw | 1 | PMSG | 231 |

7 | 2137 | 8.3 | 0.3 | 7 | HA + yaw | 2 | PMSG | 194 |

8 | 2420 | 8.4 | 0.4 | 7 | HA + yaw | 2 | PMSG | 174 |

9 | 2956 | 9.3 | 1.1 | 7 | HA + yaw | 2 | PMSG | 157 |

10 | 2985 | 9.7 | 1.4 | 7 | HA + yaw | 2 | PMSG | 162 |

11 | 2993 | 10.2 | 1.8 | 7 | HA + yaw | 2 | PMSG | 170 |

12 | 3205 | 10.8 | 0.3 | 7 | HA + yaw | 3 | PMSG | 168 |

13 | 3630 | 11 | 0.4 | 7 | HA + yaw | 3 | PMSG | 152 |

14 | 4407 | 12.2 | 1 | 7 | HA + yaw | 3 | PMSG | 138 |

15 | 4433 | 12.4 | 1.1 | 7 | HA + yaw | 3 | PMSG | 140 |

16 | 4478 | 13 | 1.4 | 7 | HA + yaw | 3 | PMSG | 145 |

17 | 4489 | 13.8 | 1.8 | 7 | HA + yaw | 3 | PMSG | 154 |

18 | 8867 | 21.6 | 1.1 | 7 | HA + yaw | 6 | PMSG | 122 |

**Table 3.**
Threshold values and weights.

**Table 3.**
Threshold values and weights.
Constraints | Weight (k) | Indifference Threshold (q) | Preference Threshold (p) | Veto Threshold (v) |
---|

Energy | 1 | 10 (MWh) | 300 (MWh) | 3000 (MWh) |

Cost | 3 | 0 | 0.1 (M€) | 1 (M€) |

Social acceptance | 1 | 0 | 1 | 3 |

**Figure 14.**
Areas ranked considering energy, cost and acceptance.

**Figure 14.**
Areas ranked considering energy, cost and acceptance.

In the case study, no information about the budget allocated for the marine current turbine has been considered so far. As the cost is a minimized criterion with the highest weight, the alternatives generated as best solutions tend to be low-cost projects (i.e., including a single turbine). When and if a budget is allocated, one might search in the project ranking for which one has the best corresponding cost. This actually shows the role of the decision aid component of our approach: the final ranking provides an ordered classification of possible solutions, the final decision being in the hands of the decision-maker. Another method to consider if the budget is given as a straight constraint is to apply the value, project cost-budget, as a minimized criterion.

**Table 4.**
Spatial unit ranking and turbine characteristics.

**Table 4.**
Spatial unit ranking and turbine characteristics.
Spatial Unit | Rank | Energy (MWh/year) | Cost (M€) | P_{n} (MW) | R (m) | TT | NT | NT_{max} | DT | €/MWh (20 years) |
---|

A | 1 | 2710 | 6.3 | 0.5 | 11 | HA | 1 | 5 | PMSG | 116.2 |

B | 3 | 2860 | 6.5 | 1.1 | 11 | HA + yaw | 1 | 4 | PMSG | 113. 6 |

C | 6 | 7426 | 11.9 | 0.6 | 12 | HA | 3 | 10 | PMSG | 80.1 |

D | 7 | 3221 | 7.3 | 2.1 | 11 | HA + yaw | 1 | 7 | PMSG | 113.3 |