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The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations (e.g., for design-standards-based loads analysis). Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system properties and exploit well-established methods and tools for analyzing linear systems. This paper presents the development of the new linearization functionality of the open-source engineering tool OpenFAST for floating offshore wind turbines, as well as the concepts and mathematical background needed to understand and apply it. INTRODUCTION To support design and analysis—so that wind turbines are innovative, optimized, reliable, and cost-effective—the wind industry and research communities rely on engineering software (i.e., design tools) capable of predicting the coupled dynamic loads and responses of the wind system. OpenFAST (formerly known as FAST), developed by the National Renewable Energy Laboratory (NREL) via support from the U.S. Department of Energy, is an open-source multiphysics tool that enables the design of wind turbines [1]. OpenFAST models the important physical phenomena and system couplings, including the environmental excitation (wind, waves, and current) and full-system dynamic response (rotor, drivetrain, nacelle, support structure, and controller) under both normal (for fatigue) and extreme (for ultimate) loading conditions. The OpenFAST model enables the analysis of a range of wind turbine configurations, including twoor three-bladed horizontal-axis rotors, pitch or stall regulation, rigid or teetering hub, upwind or downwind rotor, and lattice or tubular towers. The wind turbine can be modeled on land or offshore on bottom-fixed or floating substructures. The primary use of OpenFAST is to run nonlinear timedomain simulations (e.g., for design-standards-based loads analysis). Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system response and exploit well-established methods and tools for analyzing linear systems. For example, linear state-space models can be transformed to transfer functions, impulseresponse functions, or frequency-response functions. The ability to generate linearized models is important for eigenanalysis (to derive structural natural frequencies, damping ratios, and mode shapes), controls design (based on linear statespace models), stability analysis, gradients for optimization problems, and support for the development of reduced-order models. Previous FAST linearization work focused on 1) structuring the FAST v8 source code to enable linearization (FAST v8 is the predecessor of OpenFAST); 2) developing the general approach to linearizing the mesh mapping within the module-to-module, input-output coupling relationships, including rotations; 3) linearizing core (but not all) features of the land-based modules of FAST (InflowWind, AeroDyn, ServoDyn, and ElastoDyn) and their coupling; and 4) verifying this implementation by applying the tool to sample cases [2]. More recently, the ability to linearize OpenFAST models with advanced structural dynamics for aeroelastically tailored blades using the BeamDyn module was introduced and verified [3]. This work extends these efforts to linearizing core (but not all) features of the floating offshore wind turbine (FOWT) modules in OpenFAST and their coupling, including the hydrodynamics in HydroDyn and moorings in MAP++, and verifying the updated implementation. The HydroDyn hydrodynamics module of OpenFAST [1] allows for multiple approaches for calculating the hydrodynamic loads on floating platforms, including a potential-flow theory solution, a strip-theory solution, or a hybrid combination of the two. Waves may be regular (periodic) or irregular (stochastic), and long crested (unidirectional) or short crested (with wave energy spread across a range of directions). Second-order terms in the wave kinematics and/or potential-flow solution are available options. The MAP++ module of OpenFAST [1] models mooring systems quasi-statically, considering geometric nonlinearities of catenary or taut lines, elastic stretching, line weight, and buoyancy as well as clump weights and buoyancy tanks, lineto-line interconnections, and seabed friction. 1The offshore linearization functionality of older versions of FAST (v6 through v7) was limited to structural linearization only, requiring disabling or assuming a quasi-static treatment of other physics, and linearization of waveexcitation and wave-radiation loads was not possible.

Full-System Linearization for Floating Offshore Wind Turbines in OpenFAST: Preprint