The floating wind turbine assumed for the reference array designs is the IEA Wind 15 MW reference turbine . It is a widely used reference wind turbine design, developed through a collaborative effort as part of the IEA Wind Task 37 on Wind Energy Systems Engineering. The platform is the University of Maine VolturnUS-S reference semisubmersible , which was specifically designed for the IEA Wind 15 MW turbine. The VolturnUS-S is a generic steel semisubmersible with three radial columns and a central column that holds the tower. The platform and wind turbine are shown in Fig. , and their properties are summarized in Table . The VolturnUS-S platform with the IEA Wind 15 MW turbine provides a well-established floating wind turbine system for the reference array designs.

The VolturnUS-S was originally designed with a chain catenary mooring system for a 200 m depth. We replaced the mooring system with designs from to suit the water depths of the reference array designs. Section discusses the mooring designs in more detail. We also added dynamic power cables (Sect. ), which were not included with the original VolturnUS-S design.

The floating offshore substation design used in these arrays is a rectangular semisubmersible high-voltage alternating current (HVAC) substation developed by . This design has a capacity of 1.2 GW. The platform comprises four square columns connected in a square with four pontoons. The dimensions and mass properties of the floating substation platform are shown in Table . The geometry of the floating substation platform is visualized in Fig. .

As with the floating wind turbine, we applied the mooring line and dynamic cable designs developed in to the floating substation; however the substations feature a larger number of mooring lines to ensure redundancy of the design. A substation failure would have a more significant impact on farm revenue than a single turbine failure, so a redundant mooring system is of greater importance. We verified the performance of each mooring system and substation under a 500-year return period of extreme wind, wave, and current loading in the open-source frequency domain modeling tool RAFT to ensure acceptable platform offsets for the dynamic cable designs. The dynamic performance of the substation platform, which was designed and evaluated in , is not a focus of the present work. All substations feature intra-array cable connections on a maximum of three of the four sides; one side is free of cables to allow maintenance vessel access.

The mooring systems in the reference array designs were previously developed in for the same sets of site conditions. These designs each have a different configuration (catenary, semitaut, and taut in order of increasing depth). They were optimized for the extreme and fatigue site conditions in a multifidelity modeling process consisting of (1) the optimization of line dimensions to minimize costs subject to initial constraints checked in the quasi-static mooring model MoorPy , (2) extreme and fatigue load analyses using the dynamic floating wind turbine modeling tool OpenFAST , and (3) adjusting tuning factors in the quasi-static optimization and iterating until all constraints were satisfied. The design constraints included maximum tensions, fatigue life of chain sections, avoiding polyester rope contact with the seabed, yaw stability, avoiding vertical loading on drag-embedment anchors, and platform offset. The extreme load analysis applied aligned wind and wave directions to obtain peak loading on the mooring system, while the fatigue load cases considered site-specific wind–wave misalignment. The fatigue and extreme load cases are provided in , and the methodology used to develop these datasets is described in . This design process and the resulting designs are detailed further in .

We used these mooring system designs directly for the floating wind turbines in the reference array designs, relying on the extreme and fatigue load analyses and constraint checks that were performed in ; however, for the floating substations, we used the same mooring line designs but increased the number of mooring lines to six or eight to provide increased restoring stiffness and redundancy. We verified that the substation mooring systems keep the platform offsets within acceptable limits under extreme current loading.

Detailed anchor design was not a focus of this work, but anchor costs significantly contribute to the overall array cost; therefore, approximate anchor masses were directly pulled from , which sized anchors based on maximum anchor loads from extreme load cases performed in OpenFAST and general soil types. We input these approximate anchor masses into our anchor cost modeling assumptions described in Sect. to estimate the anchor material costs.

The reference array designs include intra-array cables between the turbines and from the turbines to the substation. Each intra-array cable connecting two floating wind turbines or a floating wind turbine and a substation consists of a dynamic cable on either end to connect to the platform and a static cable routed along the seabed between the dynamic cables.

The dynamic cable designs were developed in following a similar design process to the moorings. That work initially optimized the cable dimensions and checked constraints in MoorPy, and then it checked the dynamic cables in OpenFAST against constraints for extreme tensions and allowable curvature in extreme load cases, iterating until all constraints were met. More details on the design process of the dynamic cables can be found in .

For the gigawatt-scale reference floating wind farms, additional dynamic cable designs were needed for larger conductor sizes. These larger conductor sizes are necessary to meet the power transmission needs when many turbines are connected in series within the wind farm. We adapted the dimensions of the initial designs from , which use a cable with a 300 mm² conductor cross-sectional area, for larger conductor sizes (630 and 1000 mm²) by increasing the number of buoyancy modules to compensate for the increased cable weight. This approach maintains approximately the same cable profile shapes and ranges of motion. We then simulated these additional cable designs in conjunction with the floating wind turbine and mooring system for extreme load cases in OpenFAST to ensure compliance with the allowable cable tensions and curvatures. The extreme load cases featured aligned wind and waves to obtain peak loading.

The properties for each dynamic cable are shown in Table . For all dynamic cable designs, we assumed a buoyancy module with a volume of 0.57 m³, consistent with the original reference designs. The buoyancy module properties are shown in Table .

The static cables are represented by their routing along the seabed and their cross-sectional properties. Cable burial and environmental loadings are beyond the reference design scope. The properties for each static cable are shown in Table .

Each reference array layout follows a uniform-grid approach with seven key design variables that control the grid geometry. We chose a uniform grid to maintain navigability within the array, following the United States Coast Guard recommendations . The design variables we used for these uniform-grid layout optimizations are as follows:

Dx′, Dy′: grid x, y spacing (m)

The grid variables are shown in Fig. . The platform rotation variable, γ, is defined as 0° when one platform leg (or mooring line) is due north. Platform rotation definitions are independent of the grid rotation angle α. All angles are measured clockwise positive.

The substation rotation is defined at 0° when one pontoon faces each cardinal direction. We set the substation heading after the optimization process based on the spatial requirements of the array and the direction of the incoming dynamic cable strings.

We altered the uniform-grid layout optimization methodology in to improve the computational efficiency and give more consistent results. The previous method tested each potential platform location against spatial constraints before adding that grid location to the layout, and it stopped adding points when the required number of platforms was met. In the current method, we develop a grid of all possible platform location points inside the lease area without determining if the constraints are met. In cases where more grid points than the required number of platforms fit inside the boundary, points closest to the boundary are removed until the required number of platforms remain. This ensures that the array layout is approximately centered within the lease area.

Platforms closest to the boundary are generally most at risk of violating spatial constraints, such as mooring system components crossing the boundary; therefore, when generating the layouts, we keep the platform locations with the best chance of passing spatial constraint checks without checking the constraints of every possible grid point. Layout constraints are checked all together at a later step for the grid platforms to improve efficiency. When less than the required number of platforms fit in the boundary, the layout is excluded from consideration.

Cable routing within the array is dependent on the location of the substation(s), and the intra-array cables are an important contributor to cost; therefore, it is important to accurately represent the substation placement during the layout optimization.

To maintain navigability of the array, we assume that substations must be positioned on the same uniform grid as the turbines. The approach in kept the substation location constant during the optimization process, which does not allow the substation location to be part of the grid. Our current approach places substations in the uniform grid at the grid points closest to the user-inputted substation positions. This allows the user to choose the general substation locations while ensuring that the substations fit within the layout's uniform grid. The total number of grid points maintained when developing the platform locations, as described in Sect. , includes the total number of turbines plus the number of substations to accommodate substations in the grid.

Once the substation positions are defined, an approximate cable routing is automatically performed within the optimization loop. This cable routing allows for an approximation of the cable costs during the optimization. We then refine the cable routing after the optimization is finished, as discussed in Sect. .

When there are multiple substations in the array, we first assign each turbine to a substation before determining the cable routing. This differs from , which only supported one substation. To support multiple substations, we use an assignment algorithm that allocates turbines to their closest substation to reduce cable costs. If the number of turbines connected to a substation exceeds the substation's capacity, turbines that have the smallest difference in distance to an alternate substation from the overwhelmed substation are re-allocated to the alternate substation until each is at or below capacity.

After each turbine is assigned to a substation, we apply the cable routing approach described in for the pool of turbines assigned to each substation. First, the clusters of turbines to be connected in series are determined using spectral clustering around the substation. Then, the routing within the clusters is determined using Prim's algorithm , a minimum spanning tree method. describe this intra-array cable routing algorithm in detail. The conductor size for each cable is determined based on the power requirements from the number of upstream turbines, which affects the cost, as described in Sect. .

The objective of the layout optimizations is to minimize the LCOE. To improve computational efficiency, the optimization framework only calculates the LCOE for layouts that meet all constraints described in Sect. . The LCOE can be described as 1LCOE=FCR×CapEx+OpExAEP, where FCR is the fixed charge rate, defined as the fraction of capital expenditure (CapEx) that will be paid each year; CapEx is the total capital expenditure for the array, including the installation and component costs; OpEx is the annual operational expenditure; and AEP is the annual energy production.

The array AEP is calculated using the Gaussian curl hybrid wake model within the steady-state wake modeling tool FLORIS (v4.2) . The wind roses we used in the AEP calculations cover each direction at intervals of 5° for every wind speed at intervals of 1 m s⁻¹.

For the layout optimization, all CapEx costs except for those of the intra-array cables are assumed constant throughout the optimization. The intra-array cable material costs are updated for each feasible layout considered in the optimization based on the output cable routing. During the optimization, these cable costs are approximated by the two-dimensional distance between turbines multiplied by the dynamic cable cost per meter. This simplification is used to improve computational efficiency. It results in shorter cable lengths than a three-dimensional representation; however, the cost reduction is partially offset by the higher dynamic cable cost in comparison with static cables. The cable cost per unit length for a 66 kV dynamic cable is modeled as 2Costiac=(0.7845USDmm-2m-1)A+257.3USDm-1, where Cost_iac is the dynamic intra-array cable cost per unit length, and A is the cable conductor area. The dynamic cable cost values are based on a linear regression of the costs provided in .

The mooring material cost is calculated as follows: 3Costchain=(2.585USDkg-1m-1)m,4Costpoly=(23USDMN-1m-1)MBL, where Cost_chain is the mooring chain cost per unit length, m is the linear mass density of the chain, Cost_poly is the mooring polyester cost per unit length, and MBL is the minimum breaking load of the polyester. The chain cost coefficient is based on the value provided in , and the polyester cost coefficient is based on industry-provided estimates.

The anchor material costs are determined based on the material cost per kilogram as follows: 5CostDEA=(5.705USDkg-1)m,6CostSPA=(4.435USDkg-1)m, where CostDEA is the material cost of the drag-embedment anchors, CostSPA is the material cost of the suction pile anchors, and m is the anchor mass. These material cost coefficients are based on the average cost per mass value provided in . Because of the constant bathymetry in the arrays, one mooring and anchor design is used for all platforms in a given array, so the mooring and anchor cost remains constant for each array optimization.

The remaining CapEx costs and the OpEx costs are based on the data and assumptions provided in . The CapEx costs excluding mooring, cable, and anchor materials are calculated at a rate of 3749 USD kW⁻¹ of capacity. Annual OpEx costs are calculated at a rate of 62.5 USD kW⁻¹ of capacity. The FCR is set at 5.82 %.

After the optimization, we implement realistic three-dimensional cable designs with lazy-wave cable configurations at each platform connected to static cable sections along the seabed, as described in Sect. . Additionally, we refine the cable routing around the substation and to avoid moorings and anchors, which is described in Sect. . The additional component cost calculations used in the three-dimensional representation of the cables are described in the following.

Buoyancy module costs are calculated as 7Costbuoy=(8590USDm-3)V+USD3080, where Costbuoy is the buoyancy module cost, and V is the buoyancy module volume. These values were determined from industry estimates.

Static cable costs are calculated as 8Coststatic=(0.719USDmm-2m-1)A+239.57USDm-1, where Coststatic is the cost per unit length, and A is the cable conductor area.

The estimated costs of the cable connectors, which include bend stiffeners, are as follows for each cable: 9Costconnectors=(212.22USDmm-2)A+USD139831, where Costconnectors is the cable connector cost per cable.

Cable joints, found at the transition between the dynamic and static cable sections, are modeled as a constant cost of 237×103 per turbine. The static cable, cable connectors, and cable joint costs are based on the data provided in . The static cable and cable connector costs are a linear regression of the data provided in .

We have collected cost data from various sources to compare the assumed component costs with values from a limited literature search. The limited number of publicly available cost estimates for different components is a challenge when comparing cost estimates, as is the wide range of costs reported for certain component types. Table summarizes costs gathered from the literature compared to the cost values used in this work. Where possible, we have attempted to use data sources that allow for fair comparisons between components, and converted costs to 2024 US dollars (USD). In the process of developing these cost comparisons, we have included some assumptions to allow for consistent cost comparisons when the only component costs available were reported using different units of measure than those used in the present work. The discussion following the table provides more details on these assumptions.

Dynamic cable cost data are particularly challenging to find, especially cost data that vary with conductor size. A 2007 study , which gathered cable costs from two companies, reported intra-array cable cost ranges for a variety of conductor sizes. The cost values reported in Table from have been adjusted for inflation from 2007 USD to 2024 USD. Note that this literature source does not differentiate between static and dynamic cable costs, so the same values are applied to the static and dynamic cables for the purposes of comparison. The cost values from are higher than the utilized cost in general. Significant supply chain development and innovation in the offshore intra-array cable industry since 2007 may have led to reduced costs.

Buoyancy modules are another component with limited cost data available. provide buoyancy module costs per cable for an array of conductor sizes. To compare costs with those used in this work, we assumed the cable (which has two dynamic cable sections, one to connect to each platform) has the same volume of buoyancy modules as the dynamic cable designs used in this work. We estimated the cost per volume of buoyancy module from the cable buoyancy module cost divided by the total buoyancy module volume for each dynamic cable size. The range of buoyancy module costs is based on the minimum and maximum values from the three cable sizes used in this work. The buoyancy module costs estimated from are somewhat higher than the values used in this work, but it is difficult to directly compare them due to the required assumptions.

Relevant cost data for cable connectors and joints, especially for conductor sizes similar to those used in this work, were not found in the limited literature review. provided costs for static and dynamic bend stiffeners, which convert to approximately USD 120 000 in 2024 USD for all required bend stiffeners in one cable. However, this cost is not comparable to the value used in this work because it is for a different cable conductor size and does not include costs of other cable connection parts. It is therefore not included in Table .

provided a cost estimate of suction pile anchors, which was obtained from an industry estimate. We converted the value to USD using 2021 exchange rates and adjusted for inflation from 2021 to 2024 USD. Van Koten's reported cost coefficient is similar to the value used in this work.

Two cost sources were found for drag-embedment anchors in addition to the source used in this work. provided a range of drag-embedment anchor cost coefficients, and the average value was used in this work. reported a lower cost coefficient, while a report from Wind Energy Scotland provided an approximate cost coefficient closer to the utilized value after converting to 2016 USD and adjusting for inflation to 2024 USD.

Three chain cost per mass coefficients are reported in Table  in addition to the value used in this work. reported a cost range of 2.54–6.34 USD kg⁻¹, and reported a cost coefficient near the center of this range. provided a lower estimate at 1.68. The value used in this work, 2.585, is within the range of other reported values.

The polyester cost coefficient used in this work is in between the cost coefficient values provided in and .

Spatial constraints are checked during the array layout optimization to ensure realistic and feasible designs. The spatial constraints apply buffer zones around the mooring lines, anchors, and platforms to ensure that these components do not cross each other and stay within the boundaries of the lease. Figure shows the buffer zones that are applied around a single floating wind turbine.

We use the same approach to buffer zones as laid out in . Anchor buffer zones have a 100 m diameter centered around the anchor, which ensures that no two anchors are less than 100 m apart, per . The mooring buffer zones have a 40 m diameter centered along the axis of the mooring line. Mooring buffer zones may not cross anchor buffer zones or other mooring buffer zones, and anchor buffer zones may not cross other anchor buffer zones. Platforms also have a buffer zone with a 400 m diameter. The spacing between turbines is set to a lower limit of 0.6 nautical miles or 1111 m, but the platform buffer zone ensures a minimum distance from the lease boundary edge. Mooring line and anchor buffer zones may cross the platform buffer zone. To keep the design within the lease area boundaries, no buffer areas are permitted to cross a boundary.

We do not check if cables cross mooring lines or other components in the optimization process because the cable routing developed in the optimization is designed to estimate cable costs by simply determining the shortest distance between connected platforms rather than determining the exact route of a cable between two platforms; therefore, cables do not have buffer zones within the optimization. This simplification is used to improve the computational efficiency of the optimization. After the optimization is completed, a full three-dimensional representation of the cables is implemented. The dynamic cable headings and the static cable routing points are then adjusted to avoid mooring and anchor clashing, as described in Sect. . As discussed in Sect. , the cost difference is limited and does not greatly affect the total.

The layout optimization, where the grid parameters are adjusted to minimize the LCOE while meeting spatial constraints, can be done with many types of optimizers. We chose a particle swarm optimizer for its ability to find the global minimum even when there are discontinuities and many local minima. A particle swarm optimizer is a gradient-free optimization method developed by , based on the natural phenomenon of animals' collective behavior in a swarm, such as schooling fish. An initial randomized group (swarm) of particles, each representing a potential solution in the design space, is evaluated, and each particle moves within the design space at each iteration. Each particle considers its best known solution and the swarm's best known solution at the end of each iteration when new particle positions are generated. If a particle's position fails any constraints, the particle's best position will not be updated, and the particle is not considered when updating the overall swarm's best position at the end of the iteration. Therefore, the optimizer does not allow the solutions of non-feasible positions to influence the future velocity of the particle or swarm. This method requires many function evaluations per iteration, but it allows the optimizer to move past local minima.

For this work, we used a swarm size of 200 evaluated for a minimum of 100 iterations. The Gulf of Maine and Gulf of America optimizations were run for 100 iterations, while the Humboldt Bay optimization was run for 364 iterations due to the increased complexity of the layout, which increased the required number of iterations to achieve a general convergence.

The evolution of the particle positions and best solution were monitored throughout the optimizations. In the case of the Gulf of Maine and Gulf of America optimizations, the optimization was consistently unable to find better solutions well before 100 iterations, and the swarm's particle positions were concentrated around the swarm’s best known solution, so only 100 iterations were used for those designs. In the case of the Humboldt Bay optimization, new best solutions were frequently being discovered by the optimization at around the 100 iteration mark, so the optimization run time and number of iterations were increased until new iterations were consistently unable to determine a better solution.

Note that the goal of this work is to develop and present detailed, open-source array layout designs that approximately minimize the LCOE while meeting the constraints and design requirements of each region; therefore, a detailed study of the optimization algorithms, settings, and convergence criteria that lead to the global minimum LCOE is out of scope.

After the layout optimization is completed, we refine the preliminary intra-array cable routing with an algorithmic approach that identifies and adjusts cables that are at risk of clashing with mooring lines. We apply an angular buffer on all mooring lines along the mooring line heading, and we examine if a dynamic cable heading lies within the angular buffer zones of the platform it is attached to. A 30° angle is used by default, but we adjust this value to fit the unique spatial requirements of each array. The angular buffer begins at the center of the platform and extends for 500 m past the cable attachment point on the platform. Cables that cross the buffer are adjusted to follow the outside of the angular buffer for 500 m from the cable attachment point or for the horizontal span of the dynamic cable, whichever is longer.

After this distance, cables begin routing toward the next turbine, even if the mooring radius is larger than 500 m, because the angular buffer increases the distance from the mooring with length. Continuing the angular buffer for the entirety of the mooring line length could cause the cable to interfere with the moorings of other turbines for locations with large mooring footprints, such as Humboldt Bay. Figure shows this process.

If a static cable overlaps with an anchor buffer zone, we reroute the cable around the anchor with an additional routing point placed 100 m from the anchor point in a direction perpendicular to the initial cable heading, as shown in Fig. .

We also apply some manual routing adjustments to cables at the substation. Cables attaching to a substation are rerouted to ensure that one side of the substation is clear of cables and to avoid acute angles when possible for the static cable routing. The headings of the dynamic cables entering the substation are spaced at 5° intervals to prevent clashing between dynamic cables.

Humboldt Bay is located off the coast of California. The water depths in the Humboldt Bay lease areas range from 550 to 1100 m , with a uniform 800 m reference depth assumed for the array design. We selected a square lease area of 256 km² based on the size of the Humboldt Bay northeast lease area.

The Humboldt Bay area has large extreme current speeds, ranging from 0.92 to 1.44 m s⁻¹. The wind rose is mostly unidirectional, with the wind coming predominantly from the north. The wind, wave, and current roses for the Humboldt Bay reference site conditions are shown in Fig. . The extreme load case conditions, including the design load cases (DLCs) 1.6 and 6.1 and a survival load case (SLC), are shown in Table .

The Humboldt Bay mooring design, developed in , is taut with suction pile anchors. In this work, we assume lazy-wave cables throughout the array. Figure shows the Humboldt Bay mooring and dynamic cable configuration.

The Humboldt Bay mooring design is taut, consisting mostly of polyester rope with chain sections at the anchor and fairlead connections. The anchoring radius of the mooring system is 1400 m, which is significantly larger than the Gulf of Maine and Gulf of America designs. The mooring design is summarized in Table . Further details on the Humboldt mooring design performance can be found in .

The Humboldt Bay dynamic cable configuration is a lazy wave. The initial dynamic cable design for a 300 mm² cable was optimized by with a cable span of 800 m (the horizontal distance between the platform connection and the joint or transition point to the static cable) and a buoyancy section length of 400 m. When evaluating the cable routing within the full array, we found that the large cable span made it difficult to fit mooring lines and cables without crossing. To address this, we decreased the cable span from 800 to 500 m while keeping the other cable dimensions the same. This effectively reduced the length of the dynamic cable that is always lying on the seabed. The dynamic cable designs for the 630 and 1000 mm² conductor areas have the same span, total cable length, buoyancy section length, and buoyancy section midpoint location; however, we optimized the number of buoyancy modules, and consequently the buoyancy module spacing, for each design. The 300, 630, and 1000 mm² designs require 34, 50, and 74 buoyancy modules, respectively. The buoyancy module spacing ranges from 12.1 to 5.5 m. The three dynamic cable designs are summarized in Table .

We optimized the Humboldt Bay array layout to maximize the LCOE. The parameters of the optimized array design are listed in Table . The x and y spacings are 1847.2 and 1431.3 m, respectively, and there is a small amount of skew. The grid is rotated 36.7°, maximizing spacing in the predominant wind direction of due north. The substation is located in the center of the array.

The Humboldt Bay mooring system has a large anchoring radius of 1400 m, which required careful positioning of the mooring systems to fit 67 turbines within the area. As a result, the turbine rows alternate between two opposite mooring orientations to fit the turbines more closely together. To avoid interference with mooring lines that run along the columns, we used an angular buffer of 30° to reroute the lazy-wave cables away from the mooring line heading, as described in Sect. . In some locations, the static cable is routed beneath the mooring lines. This maintains acceptable clearances because the taut mooring system is mostly suspended. The array layout and cable routing are shown in Fig. . The static cables were automatically rerouted to avoid intersecting with anchors, as shown in Fig. . The rerouting follows the logic outlined in Fig. .

The Humboldt Bay substation design features six mooring lines, with two corners supported by two mooring lines and the opposite corners supported by one mooring line each. Though it would be preferable to have two mooring lines on each corner for improved symmetry, we implemented a six-line design for Humboldt Bay due to spatial constraints. This mooring design adheres to the maximum allowable offsets dictated by the dynamic cable designs when modeled under extreme current loading. To provide sufficient clearances around this mooring system, we rerouted the dynamic cables to two sides of the substation with headings 5° apart, as shown in Fig. .

We designed the Humboldt Bay array layout to avoid the predominant wind direction of north–south, as shown by the wake plot in Fig. a. Figure b shows the wake losses for the array with a 12 m s⁻¹ wind speed for every wind heading at 1° intervals. The wake losses are at a maximum of approximately 30 % when the wind is oriented along the columns (i.e., northwest to southeast). The wake losses are slightly less along the rows because the spacing is larger. The wind rose shows that the wind is predominantly coming from the north to northwest directions, which have minimal wake losses. This shows that the Humboldt Bay array layout was well designed to minimize wake effects.

To understand how different wind rose discretizations affect the AEP calculations, we investigated the sensitivity of the number of wind directions to the output AEP for the Humboldt Bay array. Figure  shows the AEP for 12, 18, 36, 72, 180, and 360 wind directions, which corresponds to intervals of 30, 20, 10, 5, 3, 2, and 1°. The highest granularity, 360 directions, produced a 0.007 TWh (0.13 %) decrease in AEP compared to the chosen granularity (72 directions, starred in Fig. ). Lower numbers of wind directions produced more varying results, with 12 directions producing a largely underestimated AEP compared to the smallest discretization. While a wind rose discretization with 360 wind directions may produce a slightly more accurate AEP than the chosen discretization of 72 wind directions, the chosen granularity produces a reasonably close result for significantly less computational expense.

The final values affecting the LCOE calculations in the optimization process are described in Table . These cost values are based on the cost curves in Sect. and reflect the final design, which includes the refined cable routing. The cable material costs are significantly higher than the mooring and anchor material costs. Although there are more mooring lines than cables, the cost per length of cable is approximately 2–4.5 times that of polyester (which composes the majority of each mooring line) depending on the conductor size.

The Gulf of Maine wind energy call area features water depths of approximately 100–300 m . We chose a constant water depth of 200 m for this reference array. The wind, wave, and current roses for the Gulf of Maine reference site conditions are shown in Fig. . The extreme load case conditions are described in Table .

Figure shows the mooring and dynamic cable configuration for the Gulf of Maine.

The Gulf of Maine array design uses a three-line semitaut mooring system consisting of chain and polyester with drag-embedment anchors from . The chain section is approximately 500 m long, and the polyester section is 200 m long, with an anchoring radius of 700 m. Table details the mooring configuration.

The dynamic cable is a lazy-wave configuration, also adopted from . We directly implemented the 300 mm² cable conductor size from , and then we adapted the number of buoyancy modules for the larger conductors sizes. The 300 mm² cable includes 6 buoyancy modules over the buoyancy section, while the 630 mm² cable includes 10, and the 1000 mm² cable includes 14. All cables have a constant buoyancy section length of 60 m, meaning the buoyancy module spacing decreases as the conductor size increases. The design parameters for the three different cable conductor sizes are shown in Table .

We optimized the Gulf of Maine reference array to minimize the LCOE for 132 turbines within a 504.5 km² area. Table shows the grid transformation design variables for the Gulf of Maine optimized reference array layout. The spacing in the x direction is 1442 m, and the spacing in the y direction is 2564 m. The grid has a 180° rotation with a skew of -18°, and all turbines are rotated to 60°.

The optimized reference array layout is shown in Fig. .

There are two substations in this array to accommodate the larger number of turbines. The substations are located at a slight offset from the center of the farm, with one closer to the northwest corner and one closer to the southeast corner. We chose these locations prior to the optimization to reduce the lengths of cables connected in series. The optimizer then placed the substations at the grid points closest to the user-defined locations.

Each substation mooring system features eight lines, with two on each corner spaced 20° apart. One side of each substation is free of cables to allow space for a maintenance vessel to approach. The intra-array cables enter at headings spaced 5° apart for each side. The substations are rotated 25°, which is 35° less than the turbine platforms. We chose this heading after the optimization process to prevent sharp angles when rerouting the cables entering the substation. Figure shows a close-up view of this rerouting on the northwest substation.

The algorithm described in Sect. rerouted the dynamic cables to be at least 25° offset from the mooring line headings of their associated platforms to avoid clashing, and then it rerouted the static cables to follow the dynamic cable heading for an additional 300 m before routing toward the next platform to ensure that the mooring lines and cables would not cross.

Figure a visualizes the FLORIS wake model with winds at 12 m s⁻¹ from the predominant wind direction, 205° clockwise from due north. Figure b shows a polar plot of the wake losses for a wind speed of 12 m s⁻¹ at each angle with a 1° interval. Though some directions produce significant wake losses, the wake losses dramatically decrease with even slight changes in the wind direction. When comparing the major wake loss directions in subplot (b) to the uniform-grid layout in subplot (a), the largest wake losses are along the east–west directions at up to 35 % loss due to the small grid spacing in this direction. Figure a shows that the wind resource is limited in this direction, so there is limited impact on the AEP.

There are also notable wake losses in the northwest–southeast and northeast–southwest directions, which can be attributed to the cross-wise grid direction; however, these wake losses are less than 10 %. Near the predominant wind direction, there is a wake loss of less than 1 %. The layout largely avoids wake losses in directions with significant wind resource. The wind rose of the Gulf of Maine is more spread than that of Humboldt Bay, making it difficult to completely avoid wake losses in all relevant wind directions. Notably, the wind rose data used to calculate AEP used 5° direction intervals to balance computational efficiency with AEP accuracy. When those same 5° intervals are used to calculate wake loss percentages, no wake losses appear in the interval covering the predominant wind direction due to the drastic decay in the wake losses around a specific angle. This suggests that a more granular wind rose discretization might be needed to better capture the wake losses in the AEP calculations within layout optimizations.

We repeated the AEP sensitivity analysis for the Gulf of Maine design, applying the same wind direction discretizations as in Sect. . The highest granularity, 360 directions, produced a 0.01 TWh (0.1 %) decrease in AEP compared to the chosen granularity (72 directions, starred in Fig. ). Lower numbers of wind directions produced more varying results, while the chosen granularity produces an adequate result for significantly less computational expense.

The final values affecting the LCOE calculations in the optimization process are described in Table . These cost values reflect the final design, which includes the refined cable routing. The Gulf of Maine total anchor material costs are an order of magnitude less than the total cable material costs. The cable material costs are similar to the mooring system material costs, unlike the Humboldt Bay design. These costs are based on the cost curves in Sect. . The AEP, at nearly 10 TWh, is significantly larger than that of the Humboldt Bay design due to the increased number of turbines.

The Gulf of America has a wide range of water depths within the federal exclusive economic zone. The wind energy call area developed for the Gulf of America is mostly shallow water suitable for fixed-bottom wind turbines, but some portions are deep enough (greater than 60 m) to require floating wind . We chose a water depth of 80 m for the Gulf of America reference array. The wind, wave, and current roses are shown in Fig. . The extreme load cases used to evaluate the mooring and cable designs are described in Table . The extreme load case parameters in this reference site dataset use the same approach as the other sites in . This approach, which involves fitting probability distributions to the maxima or peaks in time series data, is a simplification that is not well suited for the extreme tropical cyclone conditions that can occur in this region. Designing specifically for tropical cyclone conditions was left for future work because the intent of the reference array designs is to suit the already-defined reference site conditions.

We adopted the three-line catenary chain mooring system with drag-embedment anchors and lazy-wave dynamic cables developed in for use in the Gulf of America reference array. The anchoring radius is 400 m with a total line length of 364.5 m. Figure shows the mooring and dynamic cable configurations used in the Gulf of America reference array.

The dynamic cables used in the Gulf of America reference array are 80 m depth lazy-wave cable designs adopted from . From the original optimized design for the 300 mm² cable conductor size, we adapted the number of buoyancy modules for the larger sizes. The 300 mm² cable includes 5 buoyancy modules over the buoyancy section, while the 630 mm² cable includes 8, and the 1000 mm² cable includes 12. All cables have a constant buoyancy section length of 50 m, meaning the buoyancy module spacing decreases as the conductor size increases. The cable design parameters are shown in Table .

We optimized the Gulf of America reference array layout to minimize the LCOE for 67 turbines in a 280.7 km² square lease area. The layout is a uniform grid with 1189 m spacing in the x direction and 3991 m spacing in the y direction. There is no grid rotation, but there is a 6° skew. Each turbine platform has a heading of 60.3°. Table shows the grid transformation variables for the Gulf of America reference array layout. The predominant southeast wind direction led to a significantly larger spacing in the y direction than in the x direction.

The optimized layout for the Gulf of America reference array is shown in Fig. .

It is notable that there are extra grid locations without turbines. The location of the unused grid points is based on the optimization process's method of filling in the grid, which removes turbines closest to the lease area boundary until the correct number of turbines are remaining. It is possible that the placement of these unused grid points and the substation in another part of the grid could improve the AEP; however, these considerations are an additional variable that is out of the scope of this optimization. We placed the substation in the center of the array to reduce the cable lengths and sizes.

The substation mooring system features eight mooring lines, with two on each corner of the substation spaced 20° apart. Figure provides a close-up view of the rerouting around the substation. Cables are routed to three sides, with three cables on each. In each side, cable headings entering the substation are spaced 5° apart to prevent clashing between cables. The substation is rotated 35.3°, 25° less than the turbine platforms. We chose this heading after the optimization process to prevent sharp angles when rerouting the cables entering the substation.

Figure a visualizes the Gulf of America FLORIS wake model with winds at 12 m s⁻¹ from the predominant southeast wind direction. Figure b shows a polar plot of the wake losses, where the array wake losses were calculated for every angle at an interval of 1° when the wind speed is 12 m s⁻¹. When comparing the major wake loss directions in subplot (b) to the uniform-grid layout in subplot (a), it is clear that the main wake loss directions are east–west along the x direction of the grid, as this direction affords the least distance between turbines. Comparing subplot (b) with the wind rose in Fig. a, the predominant southeast wind direction does not align with the major wake loss directions. Though there is significant wind coming from the south, which aligns with the y direction of the grid, there is no significant wake loss due to the large north–south spacing in the grid.

We replicated the AEP sensitivity analysis for the Gulf of America array design, with results shown in Fig. . The highest granularity, 360 directions, produced a 0.002 TWh (0.05 %) decrease in AEP compared to the chosen granularity (72 directions, starred in Fig. ). Therefore, the chosen granularity produces a reasonably close AEP estimate for significantly less computational expense.

The final values affecting the LCOE calculations in the optimization process are described in Table . The cable material costs are similar to the total mooring material costs. These costs reflect the material cost of the final design, including the refined cable routing. The AEP is less than that of Humboldt Bay, which has the same total capacity, consistent with the reduced wind resource in the Gulf of America.