Comparison of Coupled and Uncoupled Modeling of Floating Wind Farms with Shared Anchors

Abstract

As design options for floating wind farms continue to be explored, shared (or multiline) anchors that secure mooring lines from multiple turbines remain a promising technology that can potentially reduce the number of anchors and overall mooring costs. This study evaluates two methods for analyzing the loads on shared anchors: one in which floating offshore wind turbines are simulated individually (using the software OpenFAST), and one in which an entire floating wind farm is simulated collectively (using the software FAST.Farm). A three-line shared anchor is evaluated for multiple loading scenarios in deep water, using the International Energy Agency 15 MW turbine on the VolturnUS-S semisubmersible platform. While the two methods produce broadly comparable results, the coupled wave loading on platforms within the farm results in wave force cancellations and amplifications that decrease multiline force directional ranges and increase multiline force extreme values (up to 7%) and standard deviations (up to 11%) for wave-driven load cases. The inclusion of wakes in FAST.Farm also reduces the net load on the shared anchor due to the velocity deficit, leading to larger differences between OpenFAST and FAST.Farm (up to 3% difference in mean loads) for load cases with operational turbines.

1. Introduction

Shared anchors for floating wind farms are increasingly being considered as a method to reduce mooring costs and optimize layouts. Their viability has been proven as an operating floating offshore wind farm, Hywind Tampen, already uses them. In a traditional floating wind farm, each mooring line has its own anchor. For a shared anchor, mooring lines from different floating offshore wind turbines are connected to the same anchor. Shared anchor layouts depend on the number and configuration of mooring lines used for each platform. A commonly evaluated layout is a three-line nonredundant mooring system arranged so that three-line shared anchors connect adjacent turbines [1,2,3], as pictured in Figure 1.

Sharing anchors reduces the total number of anchors needed for a farm [5]. For example, for a 100-turbine farm with three-line shared anchors, the total number of required anchors would be reduced by 60% [1]. Shared anchors even have the potential to reduce anchor loads compared to their single-line counterparts [1,2]. For an array with shared mooring lines in addition to shared anchors, Lozon and Hall [6] found that, while shared anchors resulted in larger anchor loads than single-line anchors, it reduced the overall farm anchor capacity by 25%. Shared anchors can also reduce seabed footprints [7]. Chen and Yang [8] found that shared anchors can reduce the required seabed surface area by 24% compared to a single-line anchor design. Shared anchors must be able to withstand omnidirectional loads, thus anchors with a vertical axis of symmetry are adaptable [5,6,7,8,9,10]. Suitable anchors have been discussed in many studies and include suction piles [3,11,12,13], ring anchors [14], and gravity anchors [15].

The reduction in the total number of anchors needed for a farm has the potential to reduce costs [5]. Shimada et al. [12] found that, in a water depth of 120 m with catenary mooring systems, shared suction pile anchors reduced installation costs compared to single-line drag embedment anchors. The primary cost driver was the reduction in chartering work vessels due to the decreased number of anchors required. Shared anchors also offer cost savings by reducing the number of geotechnical site investigations needed [9]. A report by the Carbon Trust [16] found that, for challenging environments (deep and shallow water depths), shared anchors are the most significant way to reduce costs. Potential downsides of shared anchors include a decrease in system reliability and the potential for cascading failures [16], but increasing anchor capacities by an additional factor of safety of as little as 1.1 can mitigate these risks [3,11,17].

Previous studies have used a number of different tools and evaluation methods to analyze shared anchors. OpenFAST [18] is an open-source wind turbine simulation tool developed by the National Renewable Energy Laboratory, while FAST.Farm [19] couples OpenFAST instances to model multiple turbines simultaneously, allowing for the inclusion of wake effects and spatial coherence of wind and wave fields. MoorDyn [20], the lumped-mass mooring dynamics module of OpenFAST, is used to model the mooring systems. When using OpenFAST, mooring line time series are taken from independent simulations of each turbine in the array and summed together during postprocessing to represent multiline loads on a shared anchor. With this method, there is no spatial coherence between wind and wave time series on adjacent wind turbines, and wake effects are not captured. Unlike OpenFAST, FAST.Farm allows for the modeling of multiple turbines and, therefore, platforms in a single simulation; wind and wave time series between platforms are coupled based on their locations in the array. In terms of modeling setup, OpenFAST offers a simpler approach, as only one platform is modeled. FAST.Farm coupled with TurbSim, the National Renewable Energy Laboratory’s wind simulation tool, requires a more complex inflow wind setup, requiring a low-resolution grid that spans the entire farm and a high-resolution grid for each turbine. OpenFAST is also typically less computationally expensive than FAST.Farm and has quicker runtimes. OpenFAST has been widely used for shared anchor studies, such as in [1,21,22]. As FAST.Farm is a newer software, it has fewer published studies on shared anchors: Lozon and Hall [6] used FAST.Farm to evaluate a 10-turbine shared mooring array with multiline anchors, and Coughlan et al. [7] used it to analyze wake effects for floating wind farm layouts with shared anchors.

OrcaFlex [23], developed by Orcina, allows for the modeling of offshore marine systems and is being increasingly used for offshore wind analysis. Pillai et al. [2] used OrcaFlex, coupled with TurbSim for wind loads, to evaluate three-line shared anchors for the 15 MW VolturnUS semisubmersible in shallow waters with catenary systems. OrcaFlex was also used by Chen and Yang [8] and in a COREWIND report [24] to analyze shared anchor loads for two sites. Chemineau et al. [25] used OrcaFlex coupled with OpenFAST for wind loads to evaluate three shared anchor and mooring configurations at moderate and deep water sites.

The Horizontal Axis Wind turbine simulation Code 2nd generation (HAWC2) [26] is an aeroelastic code in the time domain developed by the Technical University of Denmark. HAWC2Farm, like FAST.Farm, allows for the modeling of multiple turbines in a single simulation. Gozcu et al. [27] used HAWC2Farm to model two floating offshore wind turbines with a shared anchor and shared mooring line in deep waters.

The Sesam module Sima [28], developed by Det Norske Veritas, is a software that allows for modeling and simulations for marine operations and mooring systems, which has been extended to include offshore wind turbines. Chow [29] used Sima to investigate shared anchor configurations with catenary systems in deep water.

Additionally, Connolly and Hall [30] used quasi-static modeling methods to compare different shared mooring configurations. Van Koten [13] scaled loads from the National Renewable Energy Laboratory 5 MW turbine for the International Energy Agency 15 MW turbine, both on semisubmersible platforms. Lastly, shared anchors have been evaluated in wave basin experiments [8].

The majority of previous OpenFAST studies have been decoupled, and there have been limited farm-level simulations of shared anchor loading. Previous studies of shared anchors have been inconsistent in their wake modeling and quantification. Some studies had large enough turbine spacings to deem wake effects negligible [1], while others noted that wakes were captured but did not provide further details [2,8]. Lozon and Hall [6] noted that wakes reduced power output and resulted in greater fatigue loads, but this study focused more on shared mooring lines than shared anchors. One published work on the effect of wakes on shared anchors [22] was performed in OpenFAST using the Jensen model, while another was performed in FAST.Farm [7]. Spatial coherence was evaluated by Fontana et al. [21] in terms of downstream turbines in the farm but was found to be negligible due to the large turbine spacings; turbines at the same x-locations received the same wave trains (the environmental loading came from the positive x-direction).

This study aims to compare decoupled (OpenFAST) and coupled (FAST.Farm) simulation methods for modeling shared anchor loading in floating wind farms, evaluating differences and assessing the suitability of both approaches for shared anchor analyses. The modeling methodologies are applied to a three-turbine wind farm with a three-line shared anchor. Shared anchor loads are simulated in U.S. West Coast site conditions and compared between the different modeling methodologies. The comparison will determine if wind coherence, wave coherence, and wakes have any significant effects on the shared anchor forces.

2. Case Study Description

This section describes the turbine and platform selected for this study, site details and environmental conditions, mooring system design, and metrics used to compare simulation results for shared anchors.

2.1. Platform, Site Selection, and Load Cases

The turbine and floating platform used for this study are the International Energy Agency 15 MW reference turbine [31] and the UMaine VolturnUS-S semisubmersible platform [32]. The turbine features a 150 m hub height and a 240 m rotor diameter, with a rated wind speed of 10.6 m/s. It is installed on a steel semi-submersible platform, with the turbine positioned on a central column and three radial columns spaced 120° apart. The platform is designed with a draft depth of 20 m. Humboldt Bay, a U.S. offshore lease area off the coast of California with water depths ranging from 550 m to 1100 m [33], was selected as the site for this study. At these water depths, the mooring geometry and turbine spacings are more likely to create arrays that are more natural fits for shared anchors. A representative water depth of 850 m was selected.

Marine structure design standards require consideration of ultimate, accidental, and fatigue limit states [34]. However, evaluating every design load case is impractical for a study of this scope. To strike a balance between comprehensiveness and feasibility, we selected three critical ultimate limit state (ULS) load cases: DLC 1.6, DLC 6.1, and SLC (DLC I.1). These load cases were chosen because they represent a range of operational and extreme conditions likely to govern mooring system performance, providing a meaningful overview of system behavior. This focused approach is consistent with prior studies on mooring system design [1,2,17]. DLC 1.6 captures extreme operational conditions, with the turbine operating at its rated wind speed of 10.6 m/s under 1-year storm conditions. DLC 6.1 accounts for a 50-year storm scenario, while SLC represents the most extreme case, a 500-year storm. For both DLC 6.1 and SLC, the turbine is feathered and parked or idling.

The metocean conditions for these three IEC DLCs, summarized in

Table 1. Humboldt Bay environmental conditions for three IEC DLCs [35].

Load Case	Wind Speed (m/s)	Significant Wave Height (m)	Spectral Peak Wave Period (s)	Surface Current (m/s)
DLC 1.6	10.6	6.6	14.3	0.92
DLC 6.1	34.5	9.3	14.9	1.28
SLC	36.5	10.8	15.1	1.49

, were sourced from a proprietary environmental report provided by Principle Power. To ensure a conservative analysis, wind, waves, and currents were assumed to be fully aligned.

2.2. Mooring System and Farm Design

The mooring system was designed in a previous study [36]. Mooring system dimensions were governed by the water depth of 850 m and an assumed turbine spacing of 2000 m (approximately 8 rotor diameters), as pictured in Figure 2 and Figure 3. In that study, a studless chain-polyester-chain taut mooring system with a length ratio of 1:8:1 was designed as per industry recommendation; chain lengths were included at the anchor and fairlead to prevent rope abrasion from contact with the seafloor and platform. Polyester was selected as it has been used extensively in the offshore oil and gas industry for deep water installations and its properties are better understood than other rope types [37]. In its equilibrium position, the angle between the seafloor and each mooring line (taut angle) is 36°. Pretensions were kept between 10 and 20% of the minimum breaking load as per [37]. Simulations were run for the DLCs in Table 1 to ensure that the maximum offset did not exceed 5% of the water depth and that the maximum tension did not exceed 50% of the minimum breaking load for unidirectional turbulent wind, irregular waves, and current loading with a 0° heading. Selected mooring line properties are provided in

Table 2. Mooring line properties [36].

Line Type	Length Per Segment (m)	Diameter (mm)	Dry Mass Density (kg/m)	EA (MN)	Min. Breaking Load (kN)
Chain	138	110	242	1071	13,629
Polyester	1097	193	23.6	276	12,184

.

2.3. Shared Anchor Terminology

Fontana et al. [1] and Balakrishnan et al. [38] defined terms for describing shared anchors, as presented in

Table 3. Multiline anchor terminology defined.

Variable	Units	Definition
T1	kN	Mooring Line 1 tension, from Turbine 1
T2	kN	Mooring Line 2 tension (primary loaded line for 0° WWC), from Turbine 3
T3	kN	Mooring Line 3 tension, from Turbine 2
θ	°	Taut angle, the angle from the seafloor that the line is at in the undisplaced equilibrium position
Fx	kN	Summation of forces on anchor in x-direction
Fy	kN	Summation of forces on anchor in y-direction
Fz	kN	Summation of forces on anchor in z-direction
Fm	kN	Multiline anchor net force, sum of all forces on shared anchor
Fh	kN	Horizontal component of the multiline force
Fv, Fz	kN	Vertical component of the multiline force
Φd	°	Direction of the multiline force in the x-y plane, can range from 0° to 360°
Φi	°	Inclination (from seafloor) of the multiline force, can range from 0° to 90°

. The mooring lines connected to the shared anchor (T1, T2, and T3) are visually represented in Figure 2. As this study focuses on shared anchors, mooring line tension values presented here (mainly T2) were calculated at the anchor, not the fairlead. The multiline-specific metrics are visually represented in Figure 4. The x-, y-, and z-force components from each connected mooring line are first summed to calculate the overall F_x, F_y, and F_z acting on the shared anchor. These directional force components are then vector-summed to calculate the multiline force magnitude (F_m). Similarly, F_x and F_y are vector-summed to obtain the horizontal component of the multiline force (F_h). The multiline force direction (Φ_d) is the direction of the multiline force vector projected onto the x-y plane. The multiline inclination angle (Φ_i) describes the ratio between the horizontal (F_h) and vertical (F_v) components of the multiline force vector.

3. Simulation Setup

OpenFAST v3.3.0 [39] was used as the foundational software. Core modules utilized were AeroDyn for aerodynamic effects, ServoDyn for control and electrical elements, ElastoDyn for blade and tower flexibility, HydroDyn for platform hydrodynamics, and MoorDyn v2 for mooring line dynamics. Turbulent wind inputs were created with TurbSim [40] in AeroDyn, applying the Kaimal spectrum and IEC coherence model, with each simulation using a unique random wind seed. The turbulence intensity was set to 10, and a power law exponent of 0.11 was used.

For controls, the NREL Reference OpenSource Controller [41] was used, with nacelle yaw aligned to match the direction of the wind, waves, and current (WWC). ElastoDyn was used to model the flexibility of both the tower and the blades. In HydroDyn, irregular waves followed the JONSWAP spectrum with a peak shape factor of 2, and each realization had unique random wave seeds. Second-order wave forces were applied to the platform using the full quadratic transfer function (QTF) matrix. Current was applied as a preload to the platform in HydroDyn, and to the mooring lines through MoorDyn, following the profiles provided in [35]. The current loading was constant and did not vary with time.

The anchor loads were calculated from the mooring line tensions at the seabed, neglecting any portion of the mooring line that would be embedded under the mudline (for anchors with padeyes below the mudline). This approximation is based on the capabilities of the models and still allows a clear comparison of how the two modeling options compared in this paper affect the anchor loads. Inclusion of the chain– or anchor–soil interaction would have similar effects on both options compared in this paper, and is a step better left to more detailed mooring and anchor design work. An additional 10 min of simulation time was included at the beginning of all simulations and excluded from the analysis to eliminate non-physical startup transient phenomena.

3.1. Uncoupled Modeling with OpenFAST

To model multiline anchor forces in OpenFAST, we ran three uncoupled simulations to simulate each turbine individually. Per load case, eighteen 1 h realizations were run to form six sets of data. Each realization had unique turbulent wind time series and unique, irregular wave trains. For each mooring line attached to the shared anchor, a unique mooring line tension time series was taken from a realization (T1, T2, and T3). This approach allowed for a comparison of independent, non-correlated wind and wave seeds against the correlated wind and wave fields provided by FAST.Farm. While using correlated wind and wave fields for each individual simulation may have offered a more physically consistent input, the goal of the analysis was to assess how the choice of wind-wave correlation influences the modeling results.

3.2. Coupled Modeling with FAST.Farm

The FAST.Farm model consists of three platforms with 2000 m spacing between the turbines, as shown in Figure 2. Each turbine had its own high-resolution turbulent wind input grid around the rotor area, with 16 m spacing in all directions and 33, 32, and 25 grid points in the x-, y-, and z-directions, respectively. The low-resolution grid that encapsulated the farm had 30.4 m spacing in the x-direction and 32 m spacing in the y- and z-directions, with 133, 96, and 25 grid points in the x-, y-, and z-directions, respectively.

In FAST.Farm, the three wind turbines were modeled in the same simulation, meaning that only six 1 h simulations had to be run per load case. The low-resolution grid coupled the high-resolution grids for each turbine to each other so that the turbulence and wakes propagate through the array; wake-added turbulence is not included in this version of FAST.Farm. The waves experienced by each platform also have consistent propagation through the array, where the wave spectrum and direction are constant, and the phases are adjusted based on the turbine positions and the wavelengths (see Lozon and Hall [6] for the model formulation). The use of second-order wave loads makes the inclusion of directional spreading computationally impractical, so wave spreading is not included. Overall, FAST.Farm is more spatially coherent than OpenFAST, but FAST.Farm is more than three times more computationally expensive than OpenFAST and takes longer to set up properly due to the added grid complexities.

3.3. Impact of Current and Wave Loading on Mooring Line Dynamics

MoorDyn supports the modeling of current and wave forces specifically on the mooring lines [42], complementing the current loading and wave kinematics already modeled on the platform through HydroDyn. We evaluated how these additional modeling capabilities affected the multiline anchor metrics by analyzing results from a 1 h FAST.Farm SLC simulation. The SLC case was selected as it represents the most extreme wave and current loading conditions.

Current profiles were provided in a proprietary site environmental report [35]. We compared the results for a 1 h simulation in FAST.Farm with and without current loading on the mooring lines to understand the general effect on the multiline force metrics, as displayed in

Table 4. Multiline statistics with and without current loading on the mooring lines, SLC in FAST.Farm.

	With Current			Without Current			Percentage Difference
Metric	Max.	Mean	St. D.	Max.	Mean	St. D.	Max.	Mean	St. D.
T2 (kN)	4962	3969	327	4919	3907	327	0.9%	1.6%	0.0%
Fm (kN)	4876	3778	329	4809	3715	329	1.4%	1.7%	0.1%
Fh (kN)	3488	2566	300	3421	2486	302	1.9%	3.1%	−0.6%
Fv (kN)	3924	2761	291	3925	2749	292	0.0%	0.4%	−0.7%
Φd (°)	11	0	3.4	12	0	3.5	−4.7%	−3.0%	−5.2%
Φi (°)	60	47	3.9	62	48	4.1	−2.9%	−1.7%	−3.6%

. Percentage differences up to 3.1% were observed for the tension metrics; F_h showed the largest changes due to the current addition. Regarding single-line tensions, current loading increased tensions on the primary loaded line, while tensions on the non-primary loaded lines decreased. Due to the magnitude of the differences observed, we decided to include current loading on the mooring lines in the simulations.

Additionally, we ran 1 h SLC simulations to compare multiline metrics with and without wave loading on the mooring lines. These simulations also included current loading on the mooring lines because the remainder of the simulations in this study included current loading. Results are displayed in

Table 5. Multiline statistics with and without wave loading on the mooring lines, SLC in FAST.Farm.

	With Wave Loading			Without Wave Loading			Percentage Difference
Metric	Max.	Mean	St. D.	Max.	Mean	St. D.	Max.	Mean	St. D.
T2 (kN)	4960	3972	327	4962	3969	327	0.0%	0.1%	0.2%
Fm (kN)	4866	3781	329	4876	3778	329	−0.2%	0.1%	−0.1%
Fh (kN)	3499	2571	304	3488	2566	300	0.3%	0.2%	1.2%
Fv (kN)	3904	2760	287	3924	2761	291	−0.5%	0.0%	−1.4%
Φd (°)	11	0	3.3	11	0	3.4	−0.6%	−0.5%	−1.3%
Φi (°)	60	47	3.9	60	47	3.9	−0.1%	−0.1%	0.0%

. For single-line tensions and multiline metrics, all maximum and mean percentage differences were less than 0.7%. Standard deviations showed the largest differences, with a 1.4% difference for F_v; F_v and Φ_d also had similar percentage differences. Due to the relatively small impact of wave kinematics on the statistics evaluated here and the extra computational time that it would take to generate the wave elevation time series, we decided not to include wave loads on the mooring lines in the simulations.

4. Results

We ran simulations for WWCs of 0° to evaluate wave coherence and 30° to evaluate wakes (Figure 2). For each WWC and load case, we ran the equivalent of six 1 h simulations in OpenFAST and FAST.Farm to match the recommendations in IEC standards [34]. The results are presented for all 6 h of simulation time, and extreme values were calculated by averaging the maximum and minimum values from each hour. This section presents results for both the 0° and 30° WWC simulations, analyzing the differences between OpenFAST and FAST.Farm in anchor force metrics and force directionality for the three load cases.

Loads for DLC 1.6 are wind-driven, as this is the only load case with an operating turbine; this results in DLC 1.6 typically showing the largest mean values. DLC 6.1 (50-year storm) and SLC (500-year storm) are more wave-driven, which typically results in larger standard deviations and extreme values, with SLC showing the largest maximums. These patterns are reflected in the results.

4.1. Wave Field Impacts

The analysis for 0° WWC investigates the impacts of the wave field on the system. In this FAST.Farm setup, the two upwind turbines (WT 1 and WT 2) experience the same wave-elevation time series, enabling an evaluation of how the wave field affects their response. The upwind mooring lines (T2) receive the largest loads and thus have the highest tensions.

4.1.1. Anchor Forces for 0° WWC

We analyzed four force metrics (T2, F_m, F_h, and F_v), and their means, maximums, and standard deviations in each time series are presented in

Table 6. Force statistics for 0° WWC.

		OpenFAST			FAST.Farm			Percentage Difference (OpenFAST–FAST.Farm)/OpenFAST
Metric	Load Case	Max.	Mean	St. D.	Max.	Mean	St. D.	Max.	Mean	St. D.
T2 (kN)	DLC 1.6	4923	4183	227	4892	4240	195	0.6%	−1.4%	13.9%
	DLC 6.1	4507	3363	290	4444	3350	275	1.4%	0.4%	5.2%
	SLC	5182	3982	337	5380	3974	344	−3.8%	0.2%	−2.2%
Fm (kN)	DLC 1.6	4688	3951	226	4668	4003	196	0.4%	−1.3%	13.4%
	DLC 6.1	4381	3236	289	4272	3223	277	2.5%	0.4%	3.9%
	SLC	5021	3793	337	5173	3785	345	−3.0%	0.2%	−2.2%
Fh (kN)	DLC 1.6	3392	2771	187	3379	2823	167	0.4%	−1.9%	10.7%
	DLC 6.1	2987	1983	262	2975	1964	264	0.4%	1.0%	−1.0%
	SLC	3566	2585	290	3800	2571	322	−6.6%	0.5%	−11.1%
Fv (kN)	DLC 1.6	3339	2815	158	3378	2836	151	−1.2%	−0.8%	4.6%
	DLC 6.1	3496	2548	250	3553	2543	267	−1.6%	0.2%	−6.7%
	SLC	3801	2768	274	4003	2764	302	−5.3%	0.1%	−10.0%

and Figure 5. In Figure 5, the central black lines represent the mean values, the color blocks represent the standard deviations, and the bounding black lines represent the averaged maximum and minimum values.

For each load case, several statistical patterns were observed across all force metrics. The largest differences between means were observed for DLC 1.6 when the turbine is operating; FAST.Farm had higher means, with percentage differences ranging from 0.8% to 1.9%. For DLC 6.1 and SLC, OpenFAST had slightly larger mean values, but the percentage differences were all less than 1%. SLC showed the largest differences in maximum values and FAST.Farm had larger maximum values for all metrics, with percentage differences ranging from 3.0% to 6.6%. Differences in standard deviations were largest for DLC 1.6, ranging between 4.6% and 13.9%; OpenFAST had larger standard deviations than FAST.Farm for all metrics in DLC 1.6. Standard deviations were largest for SLC, as standard deviations are wave-driven, and SLC had the largest waves. FAST.Farm had larger standard deviations than OpenFAST in SLC.

Comparing single-line (T2) and multiline (F_m) forces, the multiline forces had a small mean load reduction for all load cases and for both OpenFAST and FAST.Farm, with percentage differences ranging from 4 to 6%. This matches previous studies that found that multiline anchors can offer a load reduction over their single-line counterparts [1,43].

The vertical force (F_v) stayed relatively consistent across all load cases. However, the horizontal force (F_h) showed more variation, with the largest means in DLC 1.6 and a significant drop in DLC 6.1. The horizontal force is more sensitive to changes in the mean turbine loading; the drop between DLC 1.6 and DLC 6.1 signifies a change in the operating condition of the turbine (operating to parked). The increase in horizontal force from DLC 6.1 to SLC is caused by the increase in current loading. This change in horizontal loading drives the differences in the multiline force between load cases, which is a product of its vertical and horizontal components.

One noticeable time series difference was observed in F_y; the F_y component in FAST.Farm exhibited a reduction in frequency content compared to OpenFAST, as depicted in Figure 6. The power spectral densities of F_y for OpenFAST and FAST.Farm, shown in Figure 7, reveal a noticeable drop in frequency content around the peak wave period (T_p) in the FAST.Farm results. To investigate this phenomenon further, we plotted the individual F_y time series for each mooring line (Figure 8). The results suggest that the cross-wave force components (y-forces) from the two upwind turbines, which are subject to identical wave trains, cancel each other out, thereby reducing wave-frequency contributions in the multiline anchor system.

To validate this observed cross-wave cancellation, we conducted a 1 h DLC 1.6 simulation in FAST.Farm with regular waves and steady wind. The mooring line tension time series are shown in Figure 9a, and their corresponding y-force components are presented in Figure 9b. The tension time series for T1 and T3 are identical, while their y-force components are equal in magnitude and opposite in direction, confirming the cancellation effect. Additionally, the simulation revealed amplification effects in the in-wave force components (x-forces). The x-force components from T1 and T3 are identical and in phase, which increases amplitudes in the multiline F_x. This amplification is evident in Figure 9c, where the multiline F_x has a larger amplitude than the individual x-force components of the mooring lines; F_x for T1 and T3 have amplitudes of 80 kN, F_x for T2 has an amplitude of 360 kN, and the multiline F_x reaches an amplitude of 390 kN. These findings align with those of Fontana et al. [15], who observed maximum multiline force amplitudes due to in-phase waves acting on turbines in a three-line multiline anchor configuration. The amplified x-force components likely explain why FAST.Farm produced larger standard deviations and maximum values than OpenFAST for wave-dominated load cases.

4.1.2. Multiline Force Directionality for 0° WWC

FAST.Farm had smaller multiline force directional ranges than OpenFAST, as displayed in Figure 10 and

Table 7. Directionality statistics for 0° WWC.

		OpenFAST			FAST.Farm			Percent Difference (OpenFAST–FAST.Farm)/OpenFAST
Metric	Load Case	Max.	Mean	St. D.	Max.	Mean	St. D.	Max.	Mean	St. D.
Φd (°)	DLC 1.6	7.6	0.1	2.0	1.5	0.1	0.4	80.4%	−12.0%	80.9%
	DLC 6.1	24.9	−0.1	6.8	17.9	−0.2	4.7	28.2%	−76.2%	30.5%
	SLC	21.4	−0.2	5.6	15.3	−0.2	3.6	28.8%	−43.9%	35.0%
Φi (°)	DLC 1.6	51.4	45.5	1.4	52.1	45.1	1.6	−1.3%	0.7%	−16.3%
	DLC 6.1	67.4	52.1	3.9	68.5	52.3	4.5	−1.5%	−0.3%	−16.3%
	SLC	59.2	47.0	3.2	64.8	47.1	4.2	−9.5%	−0.3%	−29.2%

. This difference is also linked to the effect of the wave trains on the y-component of the multiline force, as the multiline force direction is a function of the y-component of the multiline force (Figure 4). Directional time series for FAST.Farm and OpenFAST are displayed in Figure 11, and the reduction in wave frequencies observed in Φ_d is shown in Figure 12. The multiline force direction is aligned with the WWC direction, as directional means varied by less than 1° about 0°. Directional percentage differences between OpenFAST and FAST.Farm are large, but this is because the values themselves are quite small in magnitude.

FAST.Farm had larger inclination angle ranges than OpenFAST, as displayed in Figure 13 and Table 7. This could also be linked to wave coupling in FAST.Farm, as the inclination angle is a function of the horizontal component of the multiline force (Figure 4), which is influenced by x-amplifying effects. However, mean values varied by less than 1° between OpenFAST and FAST.Farm load cases.

4.2. Wake Impacts

To capture wake effects and out-of-phase wave loading, we ran simulations for a WWC of 30° (clockwise, as shown in Figure 2). We conducted the same simulations and analyses as those performed for 0° WWC. Wake effects were only captured for DLC 1.6, as that is the only load case with an operating turbine. In this loading scenario, T2 receives the largest load and thus has the highest tensions.

4.2.1. Evaluation of Wake Effects

One significant advantage of FAST.Farm over OpenFAST for wind farm modeling is its ability to capture wake effects. This study used the polar wake model in FAST.Farm [13]. For 0° WWC, no turbines are directly downwind of each other, which meant that no wake effects were captured. As FAST.Farm does not currently support nonzero wind headings, the array was rotated 30° counterclockwise to model a 30° clockwise WWC where WT 3 is directly downwind of WT 2. Wake visualizations for 0° and 30° WWCs are mapped in Figure 14, based on a DLC 1.6 simulation.

To analyze the quantitative effects of wakes on the turbines, the generator power and mean wind velocity of the three turbines were checked for the six 1 h DLC 1.6 simulations. Values for the two upwind turbines were practically identical, while the downwind turbine showed reductions in power and wind velocity, as seen in

Table 8. Energy and mean wind velocities for DLC 1.6 in 30° WWC.

	Energy Output over 6 h (kWh)	Mean Wind Velocity x (m/s)
WT 1	13,773	10.6
WT 2	13,774	10.6
WT 3	9562	8.8

. The downwind turbine experienced a reduction in mean wind velocity of approximately 1.8 m/s, which led to a reduction of approximately 4000 kWh over the 6 h time period.

4.2.2. Anchor Forces for 30° WWC

The 30° WWC force results are presented in Figure 15 and

Table 9. Force statistics for 30° WWC.

		OpenFAST			FAST.Farm			Percentage Difference (OpenFAST–FAST.Farm)/OpenFAST
Metric	Load Case	Max.	Mean	St. D.	Max.	Mean	St. D.	Max.	Mean	St. D.
T2 (kN)	DLC 1.6	4815	4245	192	4664	4087	177	3.1%	3.7%	7.7%
	DLC 6.1	3975	3267	217	3973	3256	211	0.1%	0.3%	2.6%
	SLC	4801	3952	251	4752	3943	244	1.0%	0.2%	2.7%
Fm (kN)	DLC 1.6	5062	4477	193	4949	4346	171	2.2%	2.9%	11.2%
	DLC 6.1	4206	3428	226	4137	3417	217	1.7%	0.3%	4.0%
	SLC	5066	4167	266	4991	4159	250	1.5%	0.2%	5.9%
Fh (kN)	DLC 1.6	3174	2768	135	3100	2663	124	2.3%	3.8%	8.4%
	DLC 6.1	2558	1961	176	2571	1952	174	−0.5%	0.4%	1.2%
	SLC	3221	2557	191	3200	2549	187	0.7%	0.3%	2.3%
Fv (kN)	DLC 1.6	4012	3519	157	3879	3434	132	3.3%	2.4%	15.6%
	DLC 6.1	3522	2808	204	3474	2801	192	1.4%	0.2%	5.9%
	SLC	4062	3288	229	4011	3283	214	1.3%	0.2%	6.6%

. In DLC 1.6, the downstream turbine (WT 3) experiences a decrease in wind speed, which decreases the thrust force and, therefore, the magnitude of T2, which is connected to WT 3 and the shared anchor. As T2 is the mooring line with the largest load connected to the shared anchor, it has the largest impact on multiline statistics. This decrease in loading on T2, due to the presence of wake effects in FAST.Farm, results in OpenFAST having larger values for all force metrics and statistics, which is contrary to what was observed for the 0° WWC results. Maximum percentage differences ranged from 2 to 3%, mean percentage differences ranged from 2 to 4%, and standard deviation percentage differences ranged from 7 to 16% across all force metrics in DLC 1.6. These trends match the results observed by Balakrishnan et al. [22] and Coughlan et al. [7]. Differences between OpenFAST and FAST.Farm were less pronounced for the extreme nonoperating load cases, and the two software showed better alignment than for 0° WWC. This is because the turbines are all receiving phase-shifted wave trains in FAST.Farm, which reduces the y-force cancellation and x-force amplification seen in 0° WWC. Unlike 0° WWC, OpenFAST had larger maximums, means, and standard deviations for almost all force metrics.

4.2.3. Multiline Force Directionality for 30° WWC

Multiline force direction and inclination results for 30° WWC are displayed in Figure 16 and Figure 17 and in

Table 10. Directionality statistics for 30° WWC.

		OpenFAST			FAST.Farm			Percentage Difference (OpenFAST–FAST.Farm)/OpenFAST
Metric	Load Case	Max.	Mean	St. D.	Max.	Mean	St. D.	Max.	Mean	St. D.
Φd (°)	DLC 1.6	39.7	29.9	33.1	36.7	28.1	32.8	7.6%	5.9%	1.0%
	DLC 6.1	49.9	29.8	36.5	49.6	29.8	36.4	0.7%	0.1%	0.3%
	SLC	46.0	29.8	35.5	46.2	29.8	35.5	−0.4%	0.3%	−0.1%
Φi (°)	DLC 1.6	55.3	51.8	1.0	55.0	52.2	0.8	0.4%	−0.8%	18.4%
	DLC 6.1	65.4	55.1	2.5	65.4	55.1	2.4	0.1%	−0.1%	3.2%
	SLC	60.1	52.1	1.9	60.0	52.2	1.8	0.3%	−0.1%	0.8%

. The FAST.Farm multiline force direction in DLC 1.6 experiences a negative shift, with the mean decreasing 2° compared to OpenFAST due to wake effects. However, the directional ranges for both extreme nonoperating load cases show little variation between OpenFAST and FAST.Farm.

The FAST.Farm inclination angles showed a slight positive shift in DLC 1.6, as wake effects change the ratio between horizontal and vertical loading on the anchor by decreasing the horizontal loading. Like direction, inclination ranges varied little between OpenFAST and FAST.Farm for both extreme nonoperating load cases.

5. Discussion

Overall, the differences in multiline metrics between the two methods were relatively small in magnitude. The results of this study show that, for WWC headings with in-phase waves hitting multiple turbines, the differences between OpenFAST and FAST.Farm will be more pronounced. Cancellation of wave-frequency oscillations in the anchor tension component perpendicular to the wave propagation direction can reduce cyclic loading calculations on the shared anchor, potentially underpredicting cyclic anchor loads relative to more realistic seas that include wave spreading. WWC headings that result in turbines being directly downstream of each other will also show larger differences between coupled and uncoupled modeling methods due to the impacts of wakes on multiline anchor loading. Wakes reduce mean loads on downwind turbines, reducing loading on the downwind mooring line(s) attached to the anchor and thus reducing the forcing that the multiline anchor experiences. While wind coherence was not evaluated in isolation, the minor differences in results between OpenFAST and FAST.Farm for both loading directions and across all load cases implies that wind coherence does not drive differences in shared anchor loading.

Each method has advantages and disadvantages for farm modeling. In a coupled array-level model like FAST.Farm, modeling long-crested waves can result in an idealized and unrealistic phase-matching of wave loads on adjacent turbines that are aligned in the cross-wave direction. For this study, a coherent wave field was modeled in FAST.Farm, but it is also possible to specify different sea states and realizations for each turbine. The issue of wave coherence in floating wind farms with shared anchors should be researched further to understand whether it is realistic to model adjacent turbines with identical wave trains; while some wave fields have strong directionality and coherence, certain locations have a high prevalence of multimodal sea states, and only a minor shift in wave spreading or direction would reduce this effect. Thus, because FAST.Farm has the ability to model both coherent and non-coherent waves as well as various wake models with ease [43], it may prove the superior software for shared anchor analyses. However, if modeling an array in which turbines are spaced far enough apart to neglect wake effects, a coupled array-level simulation with wakes may not offer any advantages over simulating individual turbines, meaning a simpler model like OpenFAST can be used without issue.

There are also methods for including wake effects in individual turbine simulations. For example, wakes can be modeled manually in OpenFAST, as Balakrishnan et al. [22] demonstrated by using the Jensen wake model to calculate the decrease in wind velocity and increase in turbulence intensity, then input those into OpenFAST simulations. FAST.Farm can also be coupled with MannBox [44], a wind simulation software developed for HAWC2, which does not require low-res and high-res grids, potentially simplifying the FAST.Farm setup process.

6. Conclusions

This study compared two shared anchor modeling methodologies using OpenFAST (uncoupled) and FAST.Farm (coupled). Overall, the methods produced similar results, with a few notable differences. The key findings were as follows:

• Including current loading on the mooring lines increased tension metrics on primary-loaded lines by up to 3.1%, while wave loading on the mooring lines had a minimal impact (less than 0.7%). However, it is worth noting that the influence of current and wave loading on mooring tensions could vary with mooring system types and environmental conditions, with systems exposed to higher currents or stronger waves potentially experiencing greater effects;
• For environmental load headings in which multiple platforms receive the same wave train, cross-wave force components from the mooring lines connected to the shared anchor cancel each other out, while in-wave force components compound, resulting in decreased multiline directional ranges and increased extreme multiline force values;
• For environmental load headings with downstream turbines, wake effects will decrease the loading on downwind turbines, leading to reductions in the multiline force magnitude (a 3% difference in the mean load for this study) and directional ranges (such as an 8% difference in maximum multiline force direction) that will not be captured if simulating turbines individually.

Note that these results are for a specific platform, water depth, and turbine spacing; changing any of these parameters may reveal different patterns. Semisubmersibles are more sensitive to wave loading than spars [45], so wave cancellation effects may not be as prominent if using a spar platform. If using a taut mooring system, changing the water depth may lead to a change in the ratio of horizontal to vertical loads on the multiline anchor. Decreasing turbine spacings would increase wake effects. Future work comparing the two methods could investigate accidental limit states, which may prove critical to shared anchor designs [13,17]. Future work could also investigate a wider range of sea states with prevalent wakes and consider shallow water sites where snap loading may be a challenge.