An innovative second-order design method for the structural optimization of the SpiderFLOAT offshore wind Platform☆
Graphical abstract
Introduction
Nearly 60% of the calculated U.S. offshore wind energy resource potential is over waters more than 60 m deep, where development of fixed-bottom offshore wind turbines is both technically and economically prohibitive (Musial et al., 2016a). Though this area is estimated to be able to provide the equivalent of the entire U.S. annual electricity consumption if tapped with power plants composed of floating offshore wind turbines (FOWTs) (Musial et al., 2016b), the high cost of state-of-the-art FOWTs poses a formidable barrier to its exploitation.
In response to this problem, the U.S. Department of Energy (DOE)'s Advanced Research Projects Agency-Energy (ARPA-E) kicked-off a new program: Aerodynamic Turbines Lighter and Afloat with Nautical Technologies and Integrated Servo-control (ATLANTIS). This program, among other goals, seeks to promote the design of radically new FOWTs by maximizing their rotor-area-to-total-weight ratio while either maintaining or ideally increasing turbine generation efficiency. This would yield levelized cost of energy (LCOE) values that make deep water sites economically viable to FOWT wind development. The program encourages the application of control co-design (CCD) methodologies to integrate feedback control and dynamic interaction principles as the primary drivers of the design.
The Floating Wind Technology Company together with the department of Electrical Engineering at Colorado School of Mines (CSM) and a multidisciplinary team comprised of the National Renewable Energy Laboratory (NREL), the University of Colorado at Boulder (CU), the University of Virgina (UVA), and the American Bureau of Shipping (ABS) are involved in a project named Ultra-flexible Smart Floating OffshoreWind Turbine (USFLOWT). USFLOWT is funded by ARPA-E's ATLANTIS program and has the goal of reducing FOWT's LCOE via the innovative platform SpiderFLOAT (SF) supporting a state-of-the-art, 10-MW class wind turbine.
The SF substructure (Fig. 1) was conceived to enable CCD optimization including smart control systems for mass minimization, system stability, and performance. The components of the substructure are fully modular and designed for ease of manufacturing (through a combination of local-content prefab and onsite manufacturing), transport, and installation. The low fixity level of the joints transfers minimum bending loads among the members, thus reducing demand on structural resistance, and allowing for tunable system hydrodynamic stiffness. Rather than responding to the waves as a rigid unit, SF's compliant members can have individual dynamics, thus can mitigate wave hydrodynamic forces and damp unwanted energy with only a reduced portion transferred to the rotor-nacelle-assembly and tower. Compared to currently deployed heavy and stiff floaters of oil and gas (O&G) derivation (e.g., Fig. 2), SF's innovative ultracompliant approach becomes evident. However, this ultra-flexible layout gives rise to complex dynamics and therefore requires a robust control system to maintain stability and performance.
SF makes use of reinforced concrete (RC) with an effective pre-stressing strategy realized via the very same stay-cables that guarantee the structural shape and functional integrity of the floater. RC structures can offer ample versatility in design and construction, can take advantage of local material and labor resources, are virtually maintenance free, feature cost-competitive material (concrete and steel) utilization, and have excellent fatigue and dynamic damping properties. The SF can largely be manufactured at port and with relatively small footprint. The legs are modular, with three or more segments, precast or slipformed at port. The leg segments can be stacked in a relatively small staging area, and picked up and moved to the assembly dock where they are bolted and grouted at their connections and installed onto the SF. The central stem is also fabricated out of RC, assembled in bolted/grouted segments, and benefits from the pre-compression realized by the same stay (post-tensioning) cables as well as additional internal tendons. This modular, industrialized construction method allows for simultaneous multi-component fabrication and parallel staging with minimum real-estate usage, therefore mitigating the drawbacks often attributed to concrete construction. The buoyancy cans are comprised of bundles of glass-fiber reinforced plastic (GFRP) pressure vessels tied together and linked to the ends of the legs during assembly. The cans can also be fabricated on-site via filament winding.
In this study, we developed an engineering model to determine the internal loads on the cables and legs that can then be used to size both components. Whereas this model can help size the SF central stem, the stem design will be the object of a future article. In our approach, the classical linear elastic beam theory was analytically extended to include second-order effects (e.g., P-δ moment amplification) that could lead to both an amplification of the bending stresses and to global instability. The theory was used to help close a system of equations for the static balance of the leg-cable subsystem that would otherwise be indeterminate.
The new theory was developed from first principles and implemented into a Python code, i.e., SpiderFLOAT Offshore Floater Tool for Sizing (SOFT4S), that can leverage OpenMDAO's optimization framework (Gray et al., 2019) and the aero-hydro-servo-elastic (AHSE) tools OrcaFLEX (Orcina Ltd., 2020) and OpenFAST (Jonkman, 2013). SOFT4S can in fact produce input files for these AHSE codes after determining the preliminary dimensions of the SF. In turn, AHSE simulations provide more accurate estimates of the external loads needed to run SOFT4S. As such, SOFT4S allows for quick turn-around analyses of the USFLOWT support structure and system dynamics within the CCD iterations. Numerically efficient tools, such as the one we propose, are, in fact, needed to guide the floater preliminary design through a multidisciplinary optimization infrastructure thereby rendering an effective balance between system mass (thus costs) and performance. Additionally, within OpenMDAO's framework, when coupled to a system and plant cost model (e.g., Dykes et al., 2011), SOFT4S allows for the full gamut of component investigations to arrive at LCOE-optimized wind turbine and/or power plant layout.
In stand-alone mode, SOFT4S aids the designer in the search for an optimal preliminary configuration (e.g., stem, leg, stay cable geometry) for given environmental loading conditions. The optimization criteria (e.g., minimum subcomponent mass or overall total structural mass) are customizable depending on the user's needs. SOFT4S also allows for parametric investigations and sensitivity analyses of both external factors and geometric variables that may drive the characteristics of the structure, thereby illustrating their impact on the mass, stiffness, strength, reliability, and expected costs.
SOFT4S can determine, among other design variables, the required leg length, its outer and inner diameters, its embedded reinforcement, and the number, size, and prestress values of the cables. A set of functions implement structural code checks per ACI (2014) to verify the leg cross-section under serviceability limit state (SLS) and ultimate limit state (ULS) and at various stations along the span. The design (fixed) parameters (inputs to the tool) include: lumped and distributed hydrodynamic loads, joint geometry, buoyancy and weight of the cans, and material characteristics. The hydrodynamic distributed loads are derived from AHSE simulations. Acceptable ranges for the design variables (e.g., maximum and minimum diameters, prestress levels, rebar and hoop reinforcement size and numbers) must also be provided as input parameters.
The model has undergone preliminary verification. A future version of the model will include a refined fatigue treatment and automatic selection of standard dimensions for the various subcomponents.
This document discusses the geometry of the SF in Section 2, with an overview of the nomenclature used throughout this study. The load determination problem and its indeterminate nature are presented in Section 3. Section 4 first presents the newly developed analytical beam theory and then a compatibility approach to make the force system of equations determinate. Section 5 discusses the necessary steps for SLS and ULS leg verification. In Section 6, SOFT4S is used to derive a preliminary design for legs and cables of the SF, and a cross-verification of the newly developed model is performed against a commercial finite-element method (FEM) package. A summary of SOFT4S's development and planned future research are provided in Section 7.
Section snippets
Geometry and coordinate systems
The geometry of the SF main components is shown in Fig. 3. Also shown are the symbols used in this study to denote the main design variables. Due to the 120 deg symmetry, for simplicity we will focus on of the SF and analyze one leg with its cable systems. Although the analytical development is carried out in the vertical plane for increased clarity, the lateral plane statics is analogous and the axis-symmetric nature of the leg allow for a combination of the loads in a new coordinate system.
The load determination problem
The SF in Fig. 3 can be reduced to an assembly of beams and tension-only members (the cables). In Fig. 5, we examine the forces acting on the hinge B.
Here we consider the action of the twin cables (, and , ) in the vertical plane . As a simplification in the treatment of this structure, an equivalent single cable with a doubled cross-sectional surface area replaces each cable pair; these equivalent cables are denoted by C1 and C2, for the lower and upper cable, respectively.
Elastic beam theory extension and solution of the indeterminate structure
A new theory is developed that is nonlinear in terms of final configuration geometry, but still linear in terms of material stress-strain relationship. In this Section, we highlight the main equations of this new analytical method, with the full mathematical development offered in Appendix D. In Sections 4.1 Derivation of the beam internal loads and transverse deflection, 4.2 Nonlinear constitutive equation and derivation of the beam axial deflection, 4.3 Summary of the extended elastic beam
Leg dimensioning
The design verification against SLS and ULS of one of SF's RC legs is performed following the steps highlighted in this Section. Here, we focus solely on the structural design aspects, and assume that the leg hydrodynamic requirements have already been addressed, whereby specifying, for example, minimum leg length, maximum leg mass and/or buoyancy. The latter demands would be verified by the external optimization loop of SOFT4S (called 'SOFT').
Generally speaking, the structural verification
Case study and model cross verification
In this section, we show the results of a preliminary design iteration for the SF leg and cable assembly based on expected overall footprint, mass, and required buoyancy to support a 10 MW turbine, and a generic 70Mpa-strength concrete. As the SF is covered by sensitive intellectual property (IP), we present normalized loads and geometry quantities from SOFT4S's results.
Two loading scenarios were considered: the first is representative of the load transfer at post-tensioning during the assembly
Conclusions and future work
The floating substructure and mooring components comprise about one third of the capital expenditure (CapEx) of a typical floating offshore wind power plant and are responsible for 20% of the LCOE (Stehly and Beiter, 2019). Reducing the cost of the floating platform can therefore greatly influence the final commercial viability of floating offshore wind. The SF was conceived to reduce these costs via a modularized slender structure, an efficient load path, an effective use of materials
CRediT authorship contribution statement
Rick Damiani: Conceptualization, Conceptualization of this study, Methodology, Software, Writing – original draft, Original draft preparation. Max Franchi: Conceptualization, Conceptualization of this study, Methodology.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to extend their appreciation to Dr. Kathryn Johnson, Colorado School of Mines, for supporting this study and reviewing this article. More thanks go the entire USFLOWT team (NREL, CU, UVA) for their continued development of the control system and overall offshore wind turbine performance.
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This study was conducted during the Ultra-flexible Smart Floating Offshore Wind Turbine (USFLOWT) research project funded by the Advanced Research Projects Agency-Energy (ARPA-E).