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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Linearized modeling and optimization of shared mooring systems

Shared mooring systems, where adjacent platforms are tethered directly to each other, can reduce anchor quantities and mooring line lengths in a floating array but also introduce new modeling and design challenges. This paper presents and demonstrates a first-order approach to modeling and designing shared mooring systems that simplifies these challenges. We formulate a general, linearized model for the force-displacement response of shared mooring systems, including inter-platform couplings. Using this linearization, we realize significant simplifications to the shared mooring system design problem and propose a corresponding design optimization approach. Finally, we demonstrate the complete approach on a variety of shared-mooring floating wind farm layouts with generic design assumptions and constraints. Some fundamental observations about shared mooring systems can be made from the results. Polygonal array layouts with perpendicular anchor positions appear to maximize shared mooring system efficiency. Also, arrays with greater levels of sharing tend to exhibit larger deviations in offsets between platforms. Overall, the results show how the linearized approach can be applied to efficiently evaluate and systematically optimize preliminary shared mooring system designs.

17 WIND ENERGY↗
DOE OSTI2022

Coupled loads analysis of a novel shared-mooring floating wind farm

Shared mooring lines are a method to reduce the stationkeeping cost of floating offshore wind farms; however, their impacts on floating array dynamics are not yet well understood. Here this article presents advancements to floating wind farm simulation capabilities that allow the dynamic modeling of shared-mooring floating wind arrays - specifically, platform coupling through shared lines and proper phasing of wave loads across the array. These capabilities are demonstrated on a 10-turbine shared-mooring array featuring two staggered rows of wind turbines. A baseline array design with individually moored turbines is used as a basis for comparison. Coupled analysis using FAST.Farm shows that the shared-mooring design has smaller fluctuations in surge when compared to the baseline design. The mean and maximum platform offsets are highest in normal operating conditions, but the maximum mooring line tensions are highest in 50-year storm conditions. Power spectral density analysis of platform surge and sway motions shows that the shared mooring configuration does not introduce any significant inter-platform resonances. The tower-base bending moment statistics and the line tension damage equivalent loads indicate no consequential differences in turbine loading or mooring fatigue life. Anchor load analysis shows that the total required anchor capacity for the shared-mooring array is decreased by approximately 25% when shared anchors are used. Dynamic simulations of the shared mooring system under line failures show that remaining line tensions stay within bounds and that offsets are significantly smaller when compared to the baseline design. Overall, the results show that shared moorings do not introduce any dynamic response concerns in this floating wind array design.

17 WIND ENERGY↗
DOE OSTI2022

Design and analysis of a ten-turbine floating wind farm with shared mooring lines

This paper discusses the development and analysis of a novel design for a 10-turbine floating wind farm with shared mooring lines. Shared mooring lines tether adjacent floating platforms together, reducing the number of anchors required but increasing system complexity. We present a systematic, multistage design process for shared mooring systems, involving linearized analysis of array layout options, quasi-static mooring line optimization, and design refinement based on coupled dynamic loads analysis. The design developed from this process is thought to represent one of the most advantageous shared-mooring configurations for this scale of floating wind array. It features perpendicular anchor line pairs and allows shared, multiline anchors, making it an example of a shared-mooring-and-anchor array. Comparing the performance and cost characteristics of the shared-mooring design with more conventional three-line individual mooring systems shows equivalent dynamic response characteristics and stationkeeping system cost savings of 25% when using shared mooring lines and shared anchors. The design is also advantageous in the case of a mooring line failure, with offsets and redundancy characteristics similar to four-line individual mooring systems.

17 WIND ENERGY↗
DOE OSTI2024

Shared mooring system designs and cost estimates for wave energy arrays

For floating renewable energy devices to become more cost-efficient and commercially scalable, their mooring system designs must be low-cost and suited for large-scale installations. Large arrays of floating devices, such as wave energy converters (WECs), will likely be designed with an individual mooring system for each device in the array. However, new mooring technology advancements provide options to use shared mooring lines to connect adjacent devices to one another, reducing the total number of anchors in the array, thereby reducing material use and cost. Here, this paper explores the design, modeling, and cost analysis of shared mooring systems for various sizes of arrays consisting of heaving oscillating water column (OWC) WECs. Shared mooring systems for WEC arrays sized in 2 x N and N x N grid layouts are designed to meet the relevant design standards, checking their performance with a nonlinear time-domain dynamic simulation, and the costs of each are calculated and compared. Several assumptions are taken in the design process to produce efficient results, providing a preliminary optimization for guidance on design decisions rather than a full, detailed design analysis. Mooring system costs per WEC were found to decrease as the number of WECs in the array increase, up to certain array sizes. The 2 x 3 array had the lowest mooring system cost per WEC out of all arrays considered, with a 60% cost reduction relative to using individual mooring systems. The 3 x 3 and 4 x 4 arrays achieved a 50% cost per WEC reduction. In addition to these significant cost reductions, the shared mooring system designs can provide advantages through smaller mooring system footprints, lower installation times, and less seabed disturbance.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Frequency-domain modeling of floating wind arrays with shared mooring lines

A frequency-domain model for floating wind turbine dynamics has been extended to model floating wind farms with couplings from shared mooring systems. The model, called RAFT, could previously calculate the mean offsets and wave-induced response spectra for single floating wind turbines. Now, the model supports multiple floating wind turbines, each with their own properties and responses, along with mooring lines that run directly between floating wind turbines in the array, meaning that shared mooring lines or fully suspended dynamic power cables can be included. This capability is achieved by setting up an array-level solution of the system mean offsets and assembling the full system matrices for solving the dynamic response. The quasi-static mooring model MoorPy is used to linearize the mooring system properties. To compute the floating wind turbine relative motions, phase offsets are applied to each turbine's response as a function of wave frequency based on the wavelength and relative positions in the array. These differential motions are then applied to mooring system tension Jacobians to compute the tension loads in the shared mooring lines. Overall, the capability provides a frequency-domain analog to the modeling capabilities of the floating support structure in FAST.Farm. Mean offsets and power spectral density plots of responses are compared between RAFT and FAST.Farm to verify the implementation. The results indicate good agreement within the expectations of a frequency-domain modeling approach and suggest correct implementation of the shared mooring aspects. Additionally, a unique comb-like frequency response in the shared mooring line tensions has been observed. This phenomenon has a clear physical basis and may be an important design consideration for future shared mooring systems.

17 WIND ENERGY↗
DOE OSTI2022

Mooring System Cost Estimates for Wave Energy Farms in Shared Mooring Arrays

As wave energy converters (WECs) become more advanced and cost-efficient, so too must their mooring systems. A key question in the development plans for WECs is the cost of the mooring system, particularly for large wave farms. WEC devices deployed in a WEC farm array, where each device can be connected by shared mooring lines in various array layouts, have potential to reduce mooring system costs significantly. This paper presents the modeling and designing of mooring systems for large WEC arrays and the calculation of the cost of each mooring system to determine the change in cost as the number of WECs in a farm increases. A baseline mooring system for a single floating oscillating water column (OWC) WEC was developed for this analysis. The mooring system utilizes four anchored mooring lines connected to a square assembly of wire rope mooring lines, supported by four floating buoys, and attached to the floating WEC by four polyester rope mooring lines. This assembly, referred to as a floating cell, can be tiled to form various rectangular WEC arrays. The objective of this analysis is to determine how the mooring system cost changes as more WECs are added to an array layout, each with their own interconnected floating cell. To do this, complete mooring systems need to be designed for each WEC array layout. To narrow down the design space of a WEC array mooring system, a couple assumptions were made. It was assumed that the floating cell parameters of the baseline design were to stay constant across all floating cells in the WEC array. It was also assumed that the anchored mooring lines would be of the baseline configuration, a predominantly chain mooring line with a short section of polyester rope near the fairlead, and a drag-embedment anchor. These anchored lines were assumed to extend from the outer edges of the WEC array, inline with the headings of the wire rope mooring lines of the floating cells, or diagonal if extending from a corner of the WEC array. Full mooring systems were designed for 2xN and NxN WEC array layouts and efficiently simulated in the mooring dynamics simulation tool, MoorDyn, to ensure all dynamic constraints were met. The system costs were calculated and then refined by shortening unnecessary chain line lengths and reducing the chain diameters of the downstream anchored mooring lines. It was found that, in general, mooring system costs per WEC decrease when WECs are installed in an array. Compared to the baseline mooring system for a single WEC, the 2x3 mooring system array had the lowest mooring system cost per WEC, reducing the cost per WEC by 59%. The 3x3 and 4x4 array mooring systems also saw significant reductions in cost per WEC but had negligible cost savings between the two designs, primarily because the larger 4x4 mooring system requires larger chain diameters, which increases cost. These results provide an interesting glimpse into modeling, designing, and calculating the cost of mooring systems for large WEC arrays.

cost↗
DOE OSTI2026

FAD-Toolset (Floating Array Design Toolset) [SWR-26-056]

The Floating Array Design (FAD) Toolset is a collection of tools for modeling and designing arrays of floating offshore structures. It was originally designed for floating wind systems but has applicability for many offshore applications. A core part of the FAD Toolset is the floating array model, which serves as a high-level library for efficiently modeling a floating array, such as a floating wind array. It combines site condition information and a description of the floating array design, and contains functions for evaluating the array's behavior considering the site conditions. For example, it combines information about site soil conditions, mooring line loads, and an array's anchor characteristics to estimate the holding capacity of each anchor. The library works in conjunction with the tools RAFT, MoorPy, and FLORIS to model floating platforms, wind turbines, mooring systems, power cables, and array wakes respectively. Layered on top of the floating array model is a set of design tools that can be used for algorithmically adjusting or optimizing parts of the a floating array. Specific tools existing for mooring lines, shared mooring systems, dynamic power cables, static power cable routing, and overall array layout. These capabilities work with the design representation and evaluation functions in the floating array model, and they can be applied by users in various combinations to suit different purposes. In addition to standalone uses of the FAD Toolset, a coupling has been made with Ard, (https://github.com/NLRWindSystems/Ard) a sophisticated and flexible wind farm optimization tool. This coupling allows Ard to use certain mooring system capabilities from FAD to perform layout optimization of floating wind farms with Ard's more advanced layout optimization capabilities. The FAD Toolset works with the IEA Wind Task 49 Ontology (https://github.com/IEAWindTask49/Ontology), which provides a standardized format for describing floating wind farm sites and designs. See example use cases in our examples folder (https://github.com/NLRWindSystems/FAD-Toolset/blob/main/examples/README.md) For working with the library, it is important to understand the floating array model structure, which is described more here: https://github.com/NLRWindSystems/FAD-Toolset/blob/main/fad/README.md.

Sirkis, Leah [National Laboratory of the Rockies (↗
DOE OSTI2024

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices. While quasi-static mooring models are well established, most published formulations are focused on specific applications, and no publicly available implementations provide efficient handling of large mooring system networks. The present formulation addresses these gaps by: (1) formulating solutions for edge cases not typically supported by quasi-static models; (2) creating a fully generalized model structure such that any combination of mooring lines, point masses, and floating bodies can be assembled; and (3) deriving analytic expressions for the system Jacobians (stiffness matrices) so that systems with many degrees of freedom can be solved efficiently. These techniques form the theory basis of MoorPy, an open-source mooring analysis library. The model is demonstrated on nine scenarios of increasing complexity with features of interest for offshore renewable energy applications. When compared with steady-state results from a lumped-mass dynamic model, the results show that the quasi-static formulation accurately calculates profiles and tensions and that its analytic approach provides more efficient and reliable computation of system stiffness matrices than finite-differencing methods. These results verify the accuracy of the MoorPy model.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

2025 Continuing Incubator Final Report: Active Hybrid Mooring

This project advanced the development of an active hybrid mooring system integrating experimental testing with numerical simulation to capture complex mooring dynamics not feasible in existing wave basins, including deep-water and shared mooring interactions. Verification testing of the complete hybrid system yielded good agreement in mooring tension and platform translation responses, though discrepancies in platform pitch response indicate that further refinement may be needed in future work.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

2024 Incubator Final Report: Active Hybrid Mooring

This Incubator project has defined and developed a representation of an active hybrid mooring (AHM) system in Simulink to assess whether the speed and accuracy of AHM is sufficient to warrant further investigation in a larger project. We first built a representative mooring system for the VolturnUS-S 15MW floating offshore wind turbine (FOWT) in 1,000-meter water depth to provide baseline loads and displacements needed in the AHM system, with the results showing off-the-shelf actuators would be practical. We then defined model configurations for the numerical and physical substructures, using standalone MoorDyn v2 with a novel input strategy and chained hydraulic actuators represented in Simulink Simscape, respectively. The remainder of the project has focused on verifying the existing models for speed and accuracy against OpenFAST simulations, increasing their complexity to enable six degree of freedom (6DOF) operation, and connecting the numerical and physical substructures into a single holistic model. The verification phase of the project has shown promising results, though further refinement is needed to resolve accuracy discrepancies and for robust performance across a wider range of metocean conditions. The numerical model we developed is computationally stable and operates faster than real time using a time step of 0.01 seconds or shorter, indicating the model is likely fast enough for our AHM design to operate successfully. Additionally, the Simscape model of a hydraulic actuator operates with less than 0.3% relative error when actuating mooring loads from an OpenFAST simulation of the VolturnUS-S 1,000-meter mooring system. The aforementined refinements will be performed in the next year as a Continuing Incubator, with key remaining tasks include programming the predictor-corrector loop to minimize movement error, testing against more complex nonlinear wave cases, and expanding to enable loads from connected shared mooring lines.

17 WIND ENERGY↗
DOE OSTI2024

Assessing the impacts of wakes on floating wind farms with shared anchors

This paper examines wake effects for floating wind farms with shared anchors. Three 20-turbine farms are examined: a grid-formation baseline with no shared anchors, a farm based on 3-line anchors, and a farm based on 6-line anchors, governed by a wind turbine spacing of 8 rotor diameters. The IEA 15 MW reference turbine on the UMaine semisubmersible platform was used with a taut mooring system in deep- water depths representative of U.S. west coast lease areas. A steady-state wake model showed that, when evaluating a sweep of wind headings, the baseline design had the lowest wake losses, with a value of 11.7 %, followed by the 6-line at 12.9% and the 3-line at 13.8%. Dynamic simulations were run in FAST.Farm to analyse the effects of wakes on mean anchor loads for wind headings that showed significant wake losses. The baseline farm showed the largest anchor load reductions due to wake effects (up to 16%), followed by the 3-line farm (up to 8%), and the 6-line farm, which showed relatively consistent load magnitudes on the 6-line anchors across all headings.

17 WIND ENERGY↗
DOE OSTI2025

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

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.

17 WIND ENERGY↗
DOE OSTI2024

Levelized Cost of Energy Comparison of Floating Wind Farms With and Without Shared Anchors

As part of the Innovative Deep-Water Mooring Systems for Floating Wind Farms (DeepFarm) R&D project, led by Principle Power Inc., the National Renewable Energy Laboratory (NREL) performed an LCOE analysis to compare the changes in LCOE between floating wind farms with individual anchors versus shared anchors. This report presents a comparative analysis of the LCOE of two different wind farms with different mooring systems: one with taut mooring lines each connected to individual suction pile anchors, and one with taut mooring lines connected to shared anchors. A brief description of the methodology employed to conduct the LCOE comparison is given, including the underlying assumptions. Then, results are presented with a compilation of key findings.

16 TIDAL AND WAVE POWER↗
NASA NTRS2012

Global Energetics of Large Solar Eruptive Events

We have evaluated the energetics of the larger solar eruptive events recorded with a variety of spacecraft instruments between February 2002 and December 2006. All of the energetically important components of the flares and of the accompanying coronal mass ejections and solar energetic particles have been evaluated as accurately as the observations allow. These components include the following : (1) the total energy in the high temperature plasma determined from the RHESSI thermal X-ray observations; (2) the total energies in accelerated electrons above 20 keV and ions above 1 MeV from RHESSI hard X-ray and gamma-ray observations, respectively; (3) the potential and kinetic energies of the CME from SOHO/LASCO observations; (4) the solar energetic particle (SEP) energy estimates from in situ measurements on ACE, GOES, and SOHO; (5) the total radiated energy from the SORCEITSI measurements where available, and otherwise from the Flare Irradiance Spectral Model (FISM). The results are assimilated and discussed relative to the probable amount of non potential magnetic energy estimated to be available in the flaring active regions from MDI line-of-sight magnetograms.

Dennis, Brian R.↗
DOE OSTI2023

Mooring latch for marine structures

A mooring latch includes a passive foundation portion and a latching portion. The latching portion includes a mechanism, a conical surface shaped to mate with a conical surface of the passive portion, a connector for connection to a mooring structure and permitting rotation about a horizontal axis. The mechanism has a latched configuration that mates the conical surfaces and permits rotations about a shared vertical axis of the conical surfaces. A mooring line threaded through the passive and latching portions and equipped with one or more stops may be used to guide the latching portion to or from the passive portion and to actuate latching or unlatching or the mooring latch.

Siegel, Stefan G.↗
NASA NTRS1989

A logical model of cooperating rule-based systems

A model is developed to assist in the planning, specification, development, and verification of space information systems involving distributed rule-based systems. The model is based on an analysis of possible uses of rule-based systems in control centers. This analysis is summarized as a data-flow model for a hypothetical intelligent control center. From this data-flow model, the logical model of cooperating rule-based systems is extracted. This model consists of four layers of increasing capability: (1) communicating agents, (2) belief-sharing knowledge sources, (3) goal-sharing interest areas, and (4) task-sharing job roles.

Bailin, Sidney C.↗