WO2017131953A1 - Design optimization for a wind turbine tower - Google Patents

Abstract

The structure of a wind turbine tower is optimized (22) based on cost. Following rules, the optimization (22) is constrained (22A) based on physical effect of the design. An initial design of the structure is updated (22C) in the optimization (22) and each update is checked (22A, 26A) for constraint violation and cost. The constraint violation and cost evaluation is determined from three-dimensional modeling (26C) of the structure.

Description

DESIGN OPTIMIZATION FOR A WIND TURBINE TOWER

RELATED APPLICATIONS

[0001] The present patent document claims the benefit of the filing date under 35 U.S.C. §119(e) of Provisional U.S. Patent Application Serial No. 62/286,722, filed January 25, 2016, which is hereby incorporated by reference.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] The U.S. Government has a paid-up license in this invention and the right in limited circumstances to require the patent owner to license others on reasonable terms as provided by the terms of grant no. CFDA# 81.087; Projection # 401 -20-12B awarded by DOE.

BACKGROUND

[0003] The present embodiments relate to wind turbine tower design.

Major costs involved during the lifecycle of a wind turbine structure include material costs, manufacturing costs, fabrication costs, transportation costs, installation costs, operation and management (O&M) costs, and decommissioning costs. The aggregation of these or other costs divided by the total kilowatts of energy produced during the lifetime of a tower is the levelized cost of energy (LCOE). This LCOE cost is directly dependent on the selected design for the wind tower structure. A wind tower structure may have an optimal design, which meets all the desired physical properties, but may not be cost effective. Alternatively, a wind tower may have an LCOE that is comparatively cheaper than other designs but might not have the structural characteristics suitable for long operation timeframes. For tall towers (e.g., over 80 or over 100 meters), the stringent requirements of physical attributes as well as lifecycle costs become very important. Any compromise of physical attributes may be risky, whereas ignoring lifecycle costs may lead to financially unviable solutions.

[0004] Research has been conducted to optimize the design of various pole and tower structures for wind turbines. These research efforts have provided valuable insights into the optimal design of wind turbine structures as well as into the effectiveness of various optimization strategies. Generally, a certain criterion is selected for design optimization. Examples of some commonly used criteria are - minimization of the tower's mass, maximization of the tower's stiffness, maximization of the tower's stiffness to mass ratio, minimization of vibrations, and maximization of separation between the structure's natural frequency and the turbine's exciting or operation frequency. Functional approximations for structural properties may be used with LCOE to objectively optimize the design, but the functional approximations may result in sub-par optimization.

SUMMARY

[0005] By way of introduction, the preferred embodiments described below include methods, computer readable media, and systems for design optimization for a wind turbine tower. The structure of the wind turbine tower is optimized based on cost. The optimization is constrained based on physical effect of the design. An initial design of the structure is updated in the optimization and each update is checked for constraint violation and cost. The constraint violation and cost evaluation is determined from three- dimensional modeling of the structure.

[0006] In a first aspect, a method is provided for design optimization for a wind turbine tower. A three-dimensional model of the wind turbine tower is generated based on values of parameters of structure of the wind turbine tower. A response of the wind turbine tower is simulated based on the three- dimensional model and a tower load. The response is a deflection and a resonant frequency of the wind turbine tower. The values for the parameters are optimized as a function of the deflection, the frequency, and a levelized cost of energy of the structure of the wind turbine tower. The optimized values for the parameters are transmitted as a design for the wind turbine tower.

[0007] In a second aspect, a non-transitory computer readable storage medium has stored therein data representing instructions executable by a programmed processor for design optimization for a wind turbine tower. The storage medium includes instructions for initializing a design and wind load for the wind turbine tower, analyzing effect of the wind load on the design with a three-dimensional representation of the design, updating the design with an optimization objective function based on the effect and a lifecycle cost of the design, repeating the analyzing with the updated design, repeating the updating with the effect from the repeating of the analyzing, and determining the updated design with a minimum of the lifecycle cost and the effect within a constraint.

[0008] In a third aspect, a system is provided for design optimization for a wind turbine tower. A memory is configured to store initial dimensions of the wind turbine tower and a load on the wind turbine tower. A processor is configured to: generate multiple variations of the initial dimensions of the wind turbine as part of an optimization, the optimization using a cost as the objective function and using deflections and frequencies from three- dimensional modeling of the variations as constraints, identify at least one of the variations based on minimization of the cost, and store the identified at least one of the variations in the memory as a cost minimized version of the wind turbine tower satisfying the constraints.

[0009] The present invention is defined by the following claims, and nothing in this section should be taken as a limitation on those claims.

Further aspects and advantages of the invention are discussed below in conjunction with the preferred embodiments and may be later claimed independently or in combination.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The components and the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like reference numerals designate corresponding parts throughout the different views.

[0011] Figure 1 is a flow chart diagram of one embodiment of a method for design optimization for a wind turbine tower;

[0012] Figure 2 is a flow chart diagram of another embodiment of a method for design optimization for a wind turbine tower;

[0013] Figure 3 is a flow chart diagram of yet another embodiment of a method for design optimization for a wind turbine tower; [0014] Figures 4A-C are example parameterizations of a wind turbine tower for three-dimensional modeling;

[0015] Figures 5A and 5B show tower and column diameter for initial and optimized tower designs;

[0016] Figure 6 is a block diagram of one embodiment of a system for design optimization for a wind turbine tower; and

[0017] Figure 7 represents one embodiment of modules of rules for design optimization for a wind turbine tower.

DETAILED DESCRIPTION OF THE DRAWINGS AND PRESENTLY PREFERRED EMBODIMENTS

[0018] A design optimization framework examines design variations. The optimization uses the LCOE of the tower as the objective function and tower tip deflection and natural frequency as constraints of the model. Instead of using approximation equations, a CAD model of the tower is used and actual structural simulations are run for calculating deflection and natural frequency. Rules for this new combination of acts in wind turbine tower optimization provide for feasible structure relative to minimized cost.

[0019] In one embodiment, the framework is applied for a tall tower, such as a tower over 80 or 100 meters. The tower cost may be reduced by refining the design parameters, while at the same time considering the design influence on the tower's structural characteristics, transportation, and/or construction limitations. The modular nature of the tower allows the design space to be easily parameterized to support exploration of design variations. The goal of the optimization is to explore variations of the tower design to minimize the tower cost while ensuring structurally suitable designs that are feasible to construct.

[0020] A fully automated optimization workflow may be implemented. The initial tower design and tower loads are input, and optimization using an automated tower structural simulator coupled with an optimization module is performed. In one approach, the optimization is performed by utilizing DAKOTA (an open source optimization toolkit designed and developed by Sandia National Labs) in conjunction with Siemens NX Open (a collection of application programming interfaces (APIs) that allows users to create custom applications for Siemens project lifecycle management (PLM's) NX software through an open architecture). The genetic algorithm toolbox in DAKOTA is used to perform a population-based search of the best design candidate. An NX Open executable is developed to perform automatic finite element analysis (FEA) using Siemens NX CAE and Nastran. Other optimization and physics modeling may be used.

[0021] This simulation and optimization based approach is not wind tower specific, but may be used in diverse design optimization problems where a certain objective such as minimization of cost needs to be achieved under certain structural requirements. The tool is generic enough to handle single or multi-objective problems, linear problems, nonlinear problems, and non- analytical functions through a standalone simulation interface. In cost calculations, distributions or certain ranges for cost parameters may also be specified for applying stochastic optimization or robust optimization techniques.

[0022] Figure 1 shows a method for design optimization for a wind turbine tower. Optimization in combination with three-dimensional simulation determines a design for a wind turbine tower. The objective of the

optimization is to minimize the total tower cost.

[0023] Figures 2 and 3 show two example implementations of the method. Generally, Figure 2 uses Dakota for optimization and NX Open for simulation, with constrain checks, cost calculation, and design aggregation being performed in or as needed relative to the optimization and three-dimensional simulation. Generally, Figure 3 is directed optimization of one parameter (e.g., base radius) by three-dimensional simulation of the tower with calculation of cost occurring only for valid designs. Other parameters are determined form the optimized primary parameter.

[0024] The methods are implemented by a computer or workstation, such as an engineering workstation. For example, the processor, memory, and display of Figure 6 are used. As another example, the modules of Figure 7 are implemented by a processor, server, or computer. The computer uses rules to optimize. [0025] The methods are implemented in the orders shown or different orders. For example, Figures 1 and 2 show input of the initial design to the optimization of act 22, but the initial design may be input to the three- dimensional simulation of act 26. As another example, the constraint check on the tower response (e.g., frequency and/or deflection) is performed in the simulation (see Figure 3), in the optimization (see Figure 2), or separately from the simulation and optimization.

[0026] Additional, different, or fewer acts may be performed. For example, act 26A is combined with act 22A. As another example, both acts 22A and 26A are implemented as part of the objective function optimization in act 22C. In yet another example, acts 20 and 21 are combined, such as where the executable is the input without conversion from a design of act 20.

[0027] Some (e.g., all but act 20) or all the acts are performed

automatically by the model system. The user causes the input of an initial design (e.g., engineer created design) and tower load due to wind. The user may activate the process. Once activated, the method is performed without any user input, such as without user input of creating or modification to the three-dimensional model for simulation. Alternatively, the user assists in a semi-automated process, such as the user indicating update values to be used, cost information, and/or constraints. Other user input may be provided, such as for changing modeling parameter values, correcting output, and/or to confirm accuracy.

[0028] In act 20, initial design and wind load for the wind turbine tower are input. The input is from a user interface, such as a keyboard, and/or a memory (e.g., file transfer).

[0029] The design for optimization is initialized. This initial design has any parameterization. For example, only one or fewer than all parameters are input (see Figure 3 where the input is base diameter). The other parameters are determined by logic. As another example, all the parameters for the design are input. Example design parameters include: 1 ) height of sections, 2) tower diameter at sections, 3) column diameters at sections, 4) panel thicknesses, 5) number of post-tensioning strands, and 6) panel and column material. In one embodiment, the optimization includes a subset of the design parameters (e.g., tower diameters at each section, column diameters at each section, and the number of post-tensioning strands) as design variables that have the most impact on tower cost and design.

[0030] The wind load or load on the tower is computed based on computational aerodynamics simulations using wind profiles from weather data. Alternatively, the wind load is input by the user, such as based on tests conducted at an installation location, or looked up.

[0031] In the method of Figure 2, the optimization receives two files as input in act 20. The files include (i) the dimension file of the initial design, in the form of panel thickness, and tower and column diameters at each horizontal plane (at section height) of the tower; and (ii) load input file, which includes the magnitudes of forces and moments at different locations of the tower. The dimension file may be a CAD representation of the tower or may be the values for the parameters in the initial design.

[0032] In act 21 , an executable file including the input information is generated by the computer. The executable file may be used to automatically generate a design in act 24A.

[0033] Figures 4A-C show example parameterization of the wind turbine tower. Figure 4A shows an example of a tower cross section with a number of columns and corresponding panels between columns, and a diameter of that section. Figure 4B shows a three-dimensional representation of the section of Figure 4A, including panel thickness and section height. Ruled surfaces are created as panels by joining lines from two adjacent cross- sections. Figure 4C shows a CAD model of the tower generated from the values of the parameters. The CAD model is generated in act 26 from parameter values provided in act 20 or as updated in act 22.

[0034] In one embodiment, the parameters are for a tall tower. Typical wind turbine towers are 80 meters in height. By designing tall towers (e.g., greater than 100 meters), more wind energy may be harvested. For example, the initial design input in act 20 is for a hub height of 140m (459ft) to support a 2.3 MW turbine or for a hub height 140m (459ft) to support a 3.2 M W turbine. In each case, the optimization objective is to explore more cost-effective design solutions while satisfying certain tower design constraints. In consideration of the smoothness of the tower geometry, the number of tower diameter design variables at different sections is restricted to two in one embodiment. Tower diameters at other sections are linearly interpolated with a constant relationship for tapering of the tower. Other approaches for inputting and/or parameterizing the initial tower design may be used, such as providing separate diameters for the sections between the tip and base.

[0035] In act 24, the initial tower design and wind load are passed to the three-dimensional simulation of act 26. The tower design is passed as input in act 20. Alternatively, the executable file of act 21 is processed, providing an instantiation or initial extraction of the values of the parameters for the tower in act 24A. Where the input values are for a sub-set of parameters, the design point of act 24A provides values for other parameters, such as based on look-up, assignment of default values, and/or calculation from the input values. The repetition of the optimization of act 22 is used to generate multiple tower design variations in act 24. Alternatively, multiple tower design variations are created in the initial and/or each performance of act 24 to more rapidly provide many variations for analysis.

[0036] In act 24B, the computer creates a dimension input file. The dimension input file provides dimensions for various components or structural parts of the tower. In one embodiment, the values from the design of act 24A are formatted for three-dimensional simulation. In other embodiments, the dimensions are for aspects of the tower based on the values of the

parameters but not represented directly by the values of the parameters. A dimension input file is created for each of the variations.

[0037] In act 26A, the dimensions are checked against constraints. Prior to generating a three-dimensional model, the values of the parameters and/or dimensions derived from the values are verified to be acceptable. The design or structure represented by the dimensions is subjected to geometric constraints. Any constraints may be used, such as constraints on geometric design (e.g., size of parts matches), transportation (e.g., limit on size and/or weight), and/or construction constraints (e.g., size, weight, and/or type of material). Based on the input dimensions, the simulation (e.g., NX Open executable) evaluates whether the design violates the geometric and/or other constraints. Any number of constraints may be used.

[0038] When one or more constraints are violated (e.g., diameter too large for transport or construction at a given location), the tower cost, three- dimensional representation, and/or three-dimensional analysis are not performed to minimize computation. Instead, the process returns to act 22C for optimization, randomization, and/or other alteration of one or more values of the parameters to create a different design. Figure 2 shows skipping acts 26B-D and 22A-B. Figure 3 shows skipping act 26B, but not acts 26C and D.

[0039] When the dimensions satisfy the constraints, then the current design of the structure may be manufactured, transported, and/or constructed. The method proceeds to three-dimensional simulation of act 26. In Figure 2, the method proceeds to cost calculation in act 26B prior to the three- dimensional simulation acts 26C and D. In Figure 3, the method proceeds to cost calculation in act 26B and then optimization in acts 22D and C as the simulation is a precursor to the constraint check in act 26A.

[0040] In act 26, the computer analyzes an effect or effects of the wind load on the design. The analysis uses a three-dimensional representation of the design. A physics model calculates the response of the designed structure to the load using the three-dimensional representation. The analysis is repeated for each updated design provided by the optimization in act 22. The repetitive interaction between optimization of the values of the

parameters and the effect of the load on the structures defined by the values optimizes the design of the wind turbine tower.

[0041] In act 26B, the cost of the tower of the current design is calculated. The cost includes costs for any one or more of material costs, manufacturing costs, fabrication costs, transportation costs, installation costs, operation and management (O&M) costs, and de-commissioning costs. The costs are based on estimates from experts and/or empirical data. The costs are stored as a table relating various dimensions or combinations of dimensions to cost. Alternatively, the costs are modeled, such as with a function, and calculated from the model given the dimensions. [0042] The cost may include energy return. For example, LCOE is calculated. The energy estimated to be provided based on the expected wind load and the life expectancy is used with the costs of the tower. Cost of other structure, such as the blades and turbine, may be included. In other embodiments, the lifecycle cost (cost over life) with or without energy consideration is used.

[0043] In one embodiment, the total cost of the tower is computed using standard cost estimating procedure accounting for both material and assembly costs of the tower, as represented by:

^Total ⁼ C Material ^Assembly (Ό

The unit prices of the costs in this formula are listed in Table 1 . Assembly cost is assumed to be linearly deductible from initial design if weight is reduced by 350kips. Other cost formulas based on functions (e.g. , $/m) or look-up may be used. Additional cost terms may be used.

Table 1 . Total cost breakdown

[0045] In act 26C, the computer generates a three-dimensional model of the wind turbine tower based on the values of parameters of structure of the wind turbine tower. The dimensions input to the three-dimensional simulation are used to generate a three-dimensional representation of the current design of the tower. For the initial design, the three-dimensional representation is of the design input by the user in act 20. For subsequent designs updated by optimization, the three-dimensional representation is of the updated design.

[0046] The three-dimensional representation is generated as a computer assisted design (CAD) model. Objects, interconnections, and/or materials are represented as pieced together to form the tower. In an embodiment, the three-dimensional representation is a finite element model, such as a mesh of interconnected nodes. Other meshes, such as a collection of triangular patches, may be used. The values of the parameters as represented by the dimensions are used to generate the mesh. Assemblies of standard parts fit to the dimensions may be used.

[0047] In one embodiment, an executable program (e.g., the NX Open executable) automatically creates the computer-aided design (CAD) model. The CAD software encodes the design parameters to create the CAD model, such as represented in Figure 4C. Given the cross-section dimensions at a height along the tower, a cross-section (i.e., sketch) (see Figure 4A) is created in NX. On each cross-section, the necessary components (e.g.

panels) are drawn based on the given dimensions. CAD model geometric constraints (e.g. location of the center of the tower) are set on each cross- section. Then, ruled surfaces are created to connect the sketch components between two horizontal planes. The geometric parameters (e.g. the height of the sketch plane and/or tower diameter) are encoded as expressions in software.

[0048] The NX Open executable generates the initial CAD model from scratch if the model has not been created previously. Alternatively, the executable updates the expressions of an existing CAD model as the new design. The generation of the three-dimensional model is repeated for each design output by the optimization.

[0049] In one embodiment, the finite element model of the tower has two parts, columns and panels. The columns have hexagonal cross-sections, and the panels have rectangular cross-sections. To speed up the analysis, the CAD model uses beams (1 D element) and shells (2D element) to perform FEA simulation, instead of three-dimensional solid elements. The 1 D and 2D elements connected together provide a three-dimensional representation of the tower. By reducing the number of degrees of freedom (DOF), this simplification significantly accelerates the meshing and solving processes without loss of accuracy.

[0050] Each section may be the same or different height as other sections. Section size may be any value, such as 1000 mm. Larger sizes may minimize the computation time. [0051] In act 26D, the computer simulates a response or responses of the wind turbine tower. The response is a deflection and/or a resonant frequency of the wind turbine tower. The deflection is an amount of movement in response to the load at any location, such as at a top or location of greatest movement. Other deflections may be used, such as an amount of bend or curvature. The resonant frequency is a frequency at which the tower with or without the generator and blades resonates. Multiple modes or resonances at different frequencies or ranges of frequencies may be used. Other responses may be used, such as shear, expansion, or twist.

[0052] In the embodiment of Figure 2, the NX Open simulator calculates the tower deflection and frequency for each tower design. The deflection and frequency are transferred back or used for optimization. The goal of performing the simulation is to obtain the frequency and the deflection of a tower design under the wind load conditions. NX Nastran "SOL 101 Linear Statics" solver or other simulator calculates the deflection. NX Nastran "SOL 103 Real Eigenvalues" solver or other simulator evaluates the frequency of the tower.

[0053] For simulation, a physics model uses the three-dimensional model (e.g., finite element model) and a tower load. The three-dimensional model and boundary conditions account for the size, shape, and/or material of the structure of the design. A finite element analysis is a physics model that calculates response of the three-dimensional model subjected to the tower load. The finite element analysis is applied to the finite element model. For example, computer-aided engineering (CAE) analysis uses finite element analysis based on the specific tower design.

[0054] In one embodiment, in a statics analysis, wind loads are applied at specific locations on the columns according to the conditions provided in the wind load input file. To ensure that a node is present at the locations specified in the load input file, mesh points are first created on the CAD model. These mesh points serve as mesh seeds when generating 1 D mesh of beam elements and mapped 2D mesh of shell elements. Other static analysis may be used. [0055] The locations of the load application for the statics and modal analyses may be at mesh nodes and/or other locations. All the mesh nodes or subsets may be used.

[0056] In modal analysis, the inertia of the nacelle and rotor is included by adding a 0D concentrated mass at the location of rotor neutral axis. A 1 D linking element is used to fix the element to the top plane of tower. The post- tensioning force compresses the concrete columns and the tower sections are connected. To include the connectivity between sections in the finite element model, the nodes of the panels between adjacent sections are merged so that the entire tower is joined as a single unit.

[0057] Any boundary conditions may be used, such as to define the nacelle and rotor as discussed above or to fix the base to the earth or support. For example, displacement boundary conditions are applied in the finite element analysis to constrain the tower base. The horizontal plane of the tower base (Z=0) is fixed in all directions and the rest of the tower sections are left unconstrained. These boundary conditions are applied to both statics analysis and modal analysis. As another example in the statics analysis, the wind loads include bending moment and shearing force. Bending moment is distributed to the nodes of the six columns at the corresponding heights defined in the wind load input file. Linear distribution of normal stresses on the horizontal plane is assumed to calculate the forces that generate the moment, but non-linear distribution may be used. These force values are applied to each column. In the modal analysis, gravity is applied as pre-stress in the longitudinal direction. Post-tensioning force may be included or may be neglected because post-tensioning force has little effects on the frequency.

[0058] To automate the CAD creation of act 26C and the finite element simulation of act 26D, an executable may be created. For example, an NX Open executable is created. The executable uses the tower dimensions and wind loads as input. The geometric dimensions and wind loads are used to determine the deflection and frequency. For example, a design for a 140- meter tower has a deflection in a given direction or maximum deflection of 564.31 mm and a first bending mode frequency of 0.318 Hz. [0059] The generation and simulation of act 26 (e.g., acts 26C and D) are repeated in conjunction with the optimization. As the optimization determines updated values for the design of the structure, new dimensions result. These new dimensions are used to generate the three-dimensional representation and simulate the response due to wind load or another load on the tower.

[0060] In act 22A, the computer checks one or more constraints on the deflection, the resonant frequency, and/or other response prior to optimizing. The deflection and/or frequency are constrained. The deflection is prevented from being larger than a threshold. The resonant frequency of the tower is prevented from being within a range of operating frequencies of the turbine. The optimization is subjected to structural characteristic constraints on deflection, stress, moment, and/or frequency. Other constraints may be used.

[0061] The verification is a pre-condition to optimization or incorporated as part of the optimization. In Figure 1 , constraints are not checked or the checks are incorporated into the simulation of act 26 or the optimization of act 22. In Figure 2, the constraints of the simulated response are checked in act 22A and the constraints on the structure (geometric constraints) are checked in act 26A. In Figure 3, one check is provided for either or both of acts 22A and 26A.

[0062] In Figure 2, when the constraints are not violated for a given design, the design is stored as a feasible design in act 22B. The process then continues with the update of act 22C. When the constraints are violated for a given design, the process then continues with the update of act 22C. In Figure 3, the design (e.g., radius as the primary parameter) is discarded in act 22E for violation of the constraints. The constraints being satisfied or not is passed as information for the optimization. The optimization may use feasibility of the design to guide selection or creation of another design (i.e., updating of values of one or more parameters).

[0063] In act 22C, the computer updates the design with an optimization objective function. The optimization uses the cost for the design to determine updated values. The amount of change and/or what values to change may be based on statistical information from previous iterations. Both the effect (i.e., response) and a lifecycle cost of the design are used to optimize. Alternatively or additionally, the feasibility and cost are used. The objective function of the optimization includes these variables for solving for new values of the parameters.

[0064] In one embodiment, the values for the parameters are optimized using the deflection, frequency and LCOE or other cost for the structure of the wind turbine tower. Each design has a corresponding deflection, frequency and cost. A collection of designs and corresponding costs and responses are used to optimize. Alternatively, the current design's costs and responses are used without others.

[0065] This updating with the effects output by repetition of the analyzing of act 26 of the immediately previous design is repeated. For example, the optimization generates random designs from an input design. This

randomization creates the updated values. The updating may be guided by feasibility and cost. The analyzing of act 26 and the updating in optimization of act 22 are iteratively repeated to create and test different designs of the wind turbine tower, optimizing the design. After confirming whether any geometric, deflection and frequency constraints are being violated, the optimization is performed.

[0066] The optimization provides updated values for the parameters.

Different parameters may be updated by different amounts. For each parameter, whether to hold constant or the amount of change is provided by the optimization. The values for all, just some, or only one of the parameters may be altered. The updating results in a new design for the tower, which results in a subsequent generation of a corresponding three-dimensional model and simulation. The optimizing is performed again using the frequency, the deflection, and the cost (e.g., LCOE) for the updated values. A collection of feasible tower designs results, each with a measure of desire or benefit based on the cost function. The design or designs with the best or better measures of the objective function are output as the optimized designs. The optimization updates as a prediction of values that may return better designs as measured by the cost function. The optimization module explores the optimal design parameters for the tower, such as values for diameters, column diameters, and the number of post-tension strands connecting the tower sections.

[0067] Any optimization may be used. In one embodiment, the general tower design optimization is stated as:

minimize: f(x)

T

x— [ -L · · · D_it · ·· cf/, n_s]

subject to: c^x < Def_max (2)

Freq₁≤ c₂(x)≤ Freq₂

c₃(x) = 0

X_j^ ^ X %u

In this formulation, f(x) is the objective function, x is a vector of real-valued design variables (i.e. , parameters) describing the geometry of the tower,

[D_j ··· D is a vector of tower diameters from base to top, [d_j ··· d_j] represents the column diameters at each tower horizontal cross section, n_s is an even integer number of post-tension strands in each column, the vectors x_L and χ_υ are the lower and upper bounds on the design variables, respectively, constraint function c_x examines if the maximum deflection of the tower is below requirement Def_max (maximum deflection limit), the frequency constraint c₂ has both lower and upper bounds Freq_x and Freq₂, respectively, and the equality constraint c₃ contains geometry requirements. Other optimizations may be used, such as including different parameters and/or not including constraints.

[0068] The optimization is a function of the cost, such as the LCOE. The cost is a function of the design, such as different values of the parameters resulting in different cost of the tower. The optimization creates various designs to find one that is feasible and has a lowest cost. The cost (e.g. , lifecycle cost) is minimized, so the objective function f is defined in terms of the cost. In Figure 3, if the constraints are satisfied, the tower cost is calculated to be used in the optimization of act 22C. In Figure 2, if the constraints are satisfied, the previously calculated cost of act 26B is used in the updating of act 22C. The objective of the optimization is to minimize the total cost function, f, while satisfying any constraint functions. [0069] The nonlinear constraint functions c_x and c₂ are evaluated from the simulation, q is the deflection of the tower, and c₂ is the frequency of the tower. The bounds of and c₂ are set based on expert opinion, default, or empirical information. The geometric constraint function c₃ covers any design rules regarding the tower design. These design rules are summarized in Table 2. M_wind is the wind-load induced bending moment in g_x, the section moment. The moment capacity of each section, , is to exceed the wind-load moment as the first check.

Table 2 Geometry Constraints Summary

The non-negative c₃ constraint function includes these geometry constraints and gives an overall metric reflecting the geometric feasibility of the tower design, such as represented by:

c₃(*) = p(∑Li(max[0, -^(x)])²)^{0 5} (3)

A penalty term p with a value of 10⁴ or other value is added to capture the small geometry constraint violations. Geometry feasibility is strictly

maintained if c₃ is zero, otherwise one or several geometric constraint functions listed in Table 2 are violated, resulting in an infeasible design. Other combinations of the different geometric constraints may be used.

[0070] Any type of optimization may be used, such as gradient descent or simulated annealing. In one embodiment, the objective function (e.g. , cost minimization) is solved by genetic optimization. The values are updated or adjusted in act 22C using genetic optimization. For example, a single objective genetic algorithm (SOGA) is adopted as the global optimizer. SOGA is one of the evolutionary algorithms inspired by natural evolution.

Evolutionary algorithms are distinguished using natural selection and a population of candidate designs to evolve to an optimal design solution.

[0071] The genetic algorithm (GA) is a gradient-free optimizer. Gradient information is not required in the search process. In this simulation-driven optimization process, there may be a practical difficulty in computing accurate gradient information from simulations. In addition, this design optimization problem involves discrete design variables, for which it is challenging to obtain the gradients. The GA allows the designer to explore a design space without any gradient computation.

[0072] GA is a population-based optimizer. While traditional optimizers iterate with a single design point, the genetic algorithm examines a population of candidate design points simultaneously. This strategy makes the genetic algorithm more powerful in searching for the optimal design point. A population-based optimization is also intuitive for parallel implementation and thus, significant speed up may be obtained by utilizing parallel computing resources, such as provided by a graphics processing unit or multi-core processor. A population-based optimizer has more advantages in searching for multiple optimal design points. When multiple design solutions are equally important for decision makers to make trade-off analysis between multiple objectives, a GA is more suitable for multi-objective optimization. In this sense, adopting the genetic algorithm provides a good foundation for future multi-objective optimization studies on tower trade-off design analysis.

[0073] Pseudo code for SOGA is outlined below:

Algorithm 1 : Pseudo code for singe objective genetic algorithm.

Begin

Initialize a population of candidate designs

Evaluate each candidate design

While Termination criteria is not met do

Generate new individual designs by Crossover and Mutation

Evaluate new individuals Select best individuals to form new population end While

Output the best individual in current population

End

The optimization may be initiated with a random population of designs. Then, the algorithm starts the iterative process that evaluates and updates the current population to create a new population of individual designs. In GA, the iteration counter is represented with generation number. The creation of new individual designs relies on three main GA operators: crossover, mutation, and selection. When the stopping criteria of SOGA are met, the best design in the current population is considered as the optimal design point.

[0074] In the implementation of the proposed tower design optimization problem, several computing management strategies may be utilized to improve the efficiency of the optimization. The computational cost of the proposed optimization is directly associated with the number of simulations. Therefore, avoiding invoking the simulation procedure when the candidate design is infeasible may reduce computation. Before each candidate design is being evaluated in the simulation, the geometric constraint c₃ is evaluated first to pre-screen this candidate solution (see act 26A of Figure 2). If the equality constraint c₃ is not satisfied, the constraint function c and c₂ will be assigned with constant values p₁ and ₂, rather than evaluating via simulations.

(4)

where constant values p₁ and p₂ are specified with infeasible values outside the bounds of deflection and frequency of the tower. This prevents many infeasible designs from being evaluated in time-consuming simulations, thus helping to improve the efficiency of SOGA implementation.

[0075] To achieve the maximum efficiency of SOGA implementation, the computational process is parallelized for individual evaluations. Parallel computing implementation of genetic algorithm is the most direct way to make the proposed real-world engineering design optimization computationally tractable. For example, an 8-core or 8-processor parallelization is implemented. This parallelization strategy may be easily extended when higher performance computational resources are available.

[0076] The optimization parameters used by SOGA to solve the optimization problem in one example are listed in Table 3.

Table 3 SOGA Parameters

Other values may be used. As the proposed design optimization problem involves discrete design variables, the SOGA implementation is specified as binary encoded. The crossover is performed at 4 crossover points in the binary gene of two candidate design individuals while mutation is introduced with random variation on a random design variable using uniformly distributed value. The selection criterion for offspring reproduction favors feasible designs. This makes sure that SOGA always prefer a more feasible design over less feasible designs. Other optimization parameters specifications may be used.

[0077] For a given current input design, the optimization is completed after enough generations have been evaluated. Each randomly generated design is passed for simulation as the updated design. The optimization determines the best design from the candidates randomly derived from the current design. This best design provides the determined design for output.

Alternatively, the best design is output as the updated values of the parameters for passing to the simulation. The best design is then used to simulate in act 26 for a repeat of the optimization. This iterative process continues until a stop criterion is reached.

[0078] In act 22D, the computer determines the updated design with a minimum of the lifecycle cost and the effect within one or more constraints. The optimization and simulation of acts 22 and 26 are repeated until it is determined in act 22D that optimization is complete. Any criteria may be used to determine if the objective is optimized, such as a number of iterations. In one embodiment, the objective measure of recent iterations remains unchanged or changes little over a given number of iterations, indicating completion.

[0079] In alternative embodiments, act 22 is performed once based on one input design and simulation results for that design. Act 26 is performed for the one input design and to verify compliance of the response to load for the selected best structure of the tower from the optimization. The optimization generates various random designs, only one of which is simulated for response after completion of the optimization.

[0080] In an example design optimization, a tall tower of 140 meters is designed. The general design optimization problem is specified as:

minimize: f(x)

x— [D₁, D₂, d₁ - - - d₁₅, n_s]^T

subject to: c^x) < 700mm

0.268Hz < c₂(x)≤ 0.360Hz

c₃ (x) = 0

Xj_^ ^ ^ %u

There are 15 column diameter design variables, along with tower diameters and strand number for this design problem. The design domain for these variables is shown in Table 4.

Table 4 Design variables used for optimization

Deflection at the top of the tower is constrained to be less than 700 mm.

Tower and nacelle combined frequency range is restricted within an interval of [0.268 Hz, 0.360 Hz]. [0081] The optimization problem is solved in the optimization scheme discussed above using SOGA. The optimal design found by the SOGA optimizer is presented in Table 5, comparing to the initial or user created and input design.

Table 5 HT2 initial design vs. optimal design

Descriptor Initial design Optimal

design

D₁ 25.00 26.66

D₂ 11.50 1 1 .90 d₁ 3.33 3.45 d₂ 3.33 3.29 d₃ 3.31 3.28 d₄ 3.29 3.19 d₅ 3.27 3.16 d₆ 3.25 3.10 d₇ 3.23 3.10 d₈ 3.20 3.07 d₉ 3.18 3.03 d₁₀ 3.16 3.02 da 3.14 3.02 d₁₂ 3.12 3.01 d₁₃ 3.1 1 3.01 d₁₄ 3.09 3.01 d₁₅ 3.09 3.00 n_s 76 64

Weight 3493 kips 3387 kips

Deflection 643.2 mm 636.9 mm

Frequency 0.266 Hz 0.268 Hz

Total Cost 1.908 1.883 million

million

The difference between the optimal design and the initial design parameters is also plotted in Figures 5A and 5B. The optimal column diameters are much lower compared to the initial design. The number of post-tensioning strands within each concrete column is also reduced from 76 to 64.

[0082] In the exploration of the best solution through SOGA optimization, the finite element analysis evaluation ensures the engineering performance of the optimal design. The presented simulation-driven optimization effectively reduces the material needed for the tower while satisfying the geometric and performance requirements of the tower. To evaluate the cost performance of the optimized design with respect to the net energy production value, the LCOE ($/MWh) may be calculated following the standard NREL formula based on installed cost and operating cost:

LCOE =

net

ICC Installed Capital Cost ($/kW) Tower cost included

FCR Fixed Charge Rate (%) 9.5%

AOE Annual Operating Expenses ($/kW/yr) 35

AEPnet Net Annual Energy Production HT2=6235; HT3a=7697

(MWh/MW/yr)

The LCOE of the initial design is 46.93 while the LCOE of the optimal design is 46.76. The optimal design shows a reduction of total cost from the initial design. Optimization reduces the LCOE. Considering this optimization focuses on the installation cost of the tower, a refined cost objective function involving other costs and/or life-cycle cost may potentially achieve larger LCOE reductions through optimization. Where many towers are to be constructed and given the cost in 100s of thousands or millions of dollars for each tower, this reduction is significant.

[0083] In act 22F, the optimized design is output. The computer transmits the optimized values for the parameters as the design for the wind turbine tower. The transmission is over a bus, network, or wireless. The

transmission is to a memory for storage, to a display for viewing by a user, or over a network for serving the results.

[0084] The design with the lowest cost that also satisfies the constraints is output. For example, once the values satisfying the optimization stop criteria (e.g. , the maximum evaluation or best LCOE is determined to have been reached of act 22F) are determined, the design with the best LCOE is output. Additional designs may be output, such as providing a given number of designs with the lowest costs or all the feasible designs in cost ranking. The output is of the values of the parameters. The CAD model, simulation video, dimensions, or other derived information may be output for the design or designs. Comparative information may be output, such as contrasting cost and/or values between the optimized design and the initial or input design.

[0085] In one embodiment, an integrated tool automatically generates tower CAD models, performs finite element analysis simulation, calculates tower cost, evaluates constraints, and performs optimization of the tower cost. Tower diameters, column diameters and the number of post-tensioning strands are included as design variables, but other parameters may be included. Tower geometric constraints, tower frequency, and tower deflection constraints are evaluated, but other constraints may be used. Parallel computing increases the speed of the optimization.

[0086] Any cost reduction through design optimization may be provided, such as 1.31 % or 5.96% for two example towers. The tower diameters as optimized do not deviate much from the initial designs. For both, column diameters are significantly reduced after the optimization. The lower bound of the tower frequency is the active governing constraint in the optimization of these example towers, while tower deflection had a lesser impact on the optimization.

[0087] The optimization framework improves the initial designs without violating the geometric and structural constraints. Since the optimization is automated and parallelized, the optimization took less than one day to complete on a desk-top computer with an 8-core processor. Setting up the initial tower design, determining the appropriate wind load conditions, and providing LCOE model may take more time than the optimization process. More detailed and realistic cost models may be introduced in the objective function when such data is available. In addition, the genetic algorithm is complex and time consuming. When the number of design variables is large, high performance computing may be utilized to increase the speed of the optimization.

[0088] Figure 6 shows a system for design optimization for a wind turbine tower. The system is a workstation, computer, or server for optimizing a design of a wind turbine tower. The system includes a processor 12, a memory 14, and a display 16. Additional, different, or fewer components may be used. For example, a user input device is provided for receiving user selection of values of parameters, wind load, and/or other inputs. As another example, a network interface is provided for receiving the initial design (e.g., values of parameters), wind load, and/or other inputs. [0089] The computing components, devices, or machines of the system, such as the processor 12, are configured by hardware, software, and/or design to perform calculations or other acts implementing rules for

optimization. The computing components operate independently or in conjunction with each other to perform any given act, such as the acts of Figures 1 , 2 or 3. The acts are performed by one of the computer

components, another of the computing components, or a combination of the computing components. Other components may be used or controlled by the computing components to scan or perform other functions.

[0090] The memory 14 is a buffer, cache, RAM, removable media, hard drive, magnetic, optical, database, or other now known or later developed memory. The memory 14 is a single device or group of two or more devices. The memory 14 is part of a computer with the processor 12 (e.g., cache, RAM, or hard drive) or is outside or remote from other components. The memory 14 is configured by formatting by the processor 12 or another processor. The storage of data in the memory 14 configures the memory 14 for that storage.

[0091] The memory 14 stores initial dimensions of the wind turbine tower and a load on the wind turbine tower. The initial design parameters or file is received by the system and stored in the memory 14. Other input information may also be stored in the memory 14. Design, dimensions, constraints, cost information, calculated costs, three-dimensional models, analysis data, calculated responses, candidate designs, feasibility, optimization calculations, stop criteria, or other information may be stored in the memory 14. The memory 14 stores data resulting from or used in the processes described herein, such as storing the constants, initial values, intermediate values, computed metrics, or other properties. The storage may be short term, such as associated with a buffer, or may be for long term, such as associated with an output of an optimized design.

[0092] The memory 14 is additionally or alternatively a non-transitory computer readable storage medium with processing instructions. The memory 14 stores data representing instructions executable by the

programmed processor 12 for design optimization for a wind turbine tower. The instructions for implementing the processes, methods and/or techniques discussed herein are provided on computer-readable storage media or memories, such as a cache, buffer, RAM, removable media, hard drive or other computer readable storage media. Computer readable storage media include various types of volatile and nonvolatile storage media. The functions, acts or tasks illustrated in the figures or described herein are executed in response to one or more sets of instructions stored in or on computer readable storage media. The functions, acts or tasks are independent of the particular type of instructions set, storage media, processor or processing strategy and may be performed by software, hardware, integrated circuits, firmware, micro code and the like, operating alone or in combination.

Likewise, processing strategies may include multiprocessing, multitasking, parallel processing and the like. In one embodiment, the instructions are stored on a removable media device for reading by local or remote systems. In other embodiments, the instructions are stored in a remote location for transfer through a computer network or over telephone lines. In yet other embodiments, the instructions are stored within a given computer, CPU, GPU, or system.

[0093] The processor 12 is a general processor, application specific integrated circuit, field programmable gate array, graphics processing unit, digital signal processor, graphics card, or combinations thereof. In one embodiment, the processor 12 is a multi-core processor (e.g., 8 or 16 cores) or a graphics processing unit capable of parallel operations for simulation and/or optimization. The processor 12 is a single device, a plurality of devices, or a network. For more than one device, parallel or sequential division of processing may be used. Different devices making up the processor 12 may perform different functions, such as simulating by one device and optimization by another device. The processor 12 operates pursuant to stored instructions to perform various acts described herein.

[0094] The processor 12 is configured to generate multiple variations of initial dimensions of the wind turbine as part of an optimization. The optimization uses a cost as the objective function and uses deflections and frequencies from three-dimensional modeling of the variations as constraints. The variation that satisfies the deflection, frequency, other response, and/or other constraints with a lower or lowest cost relative to other feasible variations is found. At least one of the variations is identified based on minimization of the cost. This identified variation or variations are stored in the memory 14 as a cost minimized version of the wind turbine tower satisfying the constraints.

[0095] To identify the variation of the design, the processor 12 implements a model system as the analysis model 13 and an optimization model 15. These two modules interact where the analysis module 13 provides three- dimensional modeling and analysis to determine response and/or cost used in the optimization module 15 to identify the feasible variation with reduced or lowest cost.

[0096] Additional, different, or fewer models may be included, such as also including constraint check, format conversion (e.g. , input data to an executable), and/or modules for any of the acts of Figures 1 -3. The different modules communicate, such as the optimization module 15 providing updated values of parameters or dimensions for simulation and the analysis module 13 providing response of the design to load for optimization. The communication may be through shared access to a memory location or buffer. Alternatively, the communication is by transmission over a bus or network. Other communication may be used.

[0097] The models are rules configured by software, hardware, and/or firmware. The model system is implemented on one or more processors (e.g. , processor 12) or other computing components. The model system is code structures, algorithms, programs, or representations of the wind turbine tower.

[0098] Figure 7 shows another embodiment of the module system. The model system includes an optimization module 70, implemented using DAKOTA; a cost calculator module 72 implemented in C++; an analysis module 74 implemented in C++; a secondary tower parameter module 76 implemented in MATLAB, a three-dimensional representation module 78 implemented with CAD, and a simulation module 80 called by the analysis module 74. The standard DAKOTA installation includes a set of optimization solvers. The optimization capabilities may be extended by compiling available open source code with various third party solvers. The analysis and cost objective calculator modules 72, 74 are coupled with DAKOTA via a black-box interface so that DAKOTA and analysis/cost code remain independent, with data being transferred to and from DAKOTA via text files. The cost calculator module 72 encodes the tower costs as a function of the tower design and evaluates the tower costs by querying the parametric models in NX for volume and/or other information. The cost calculator module 72 computes the LCOE. The analysis module 74 interfaces with NX to update the parametric models, perform finite element analysis using NX, query the results from NX

(frequency and deflection), and use NX in the optimization framework for structural constraints.

[0099] One embodiment of this modular approach is represented in Figure 3. LCOE is minimized by varying the base radius. At each step of the optimization, the optimization module 70 updates the base diameter according to the optimization algorithm. This value is sent to the analysis and cost calculator modules 72 and 74. The analysis module 74 invokes the secondary parameter optimization module 76. In the completed framework, column diameters and panel thicknesses are considered secondary tower parameters that are dependent on the tower base diameter. The parameter optimization module 76 determines the optimal parameters for the tower such as column diameters and panel thicknesses for a given tower base diameter so that a design is structurally suitable. In the embodiment for Figure 2, the secondary parameters are treated as primary parameters with the base diameter, so the optimization solves for values without further calculation as secondary by the parameter module 76.

[00100] New design parameters are sent to the parametric models in the CAD module 78 where the geometry is updated. The analysis module 74 also triggers an update of the finite element models and simulation models, accordingly. The analysis module 74 then initiates finite element analysis by the simulation module 80 to perform frequency and deflection analysis on the updated model. The resulting natural frequency and deflection values are sent back to analysis module 74 for structural compliance check. If the natural frequency of the updated model falls inside a user-specified interval and if the deflection is less than the value defined by standards, the tower cost is calculated using the cost calculator module 72. Otherwise, the base radius value is rejected. The process repeats with a new base radius value until a maximum number of iterations is reached or the optimal cost value is attained.

[00101] Referring again to Figure 6, the display 16 is a CRT, LCD, plasma, projector, printer, or other output device for showing an image or report. The display 16 displays the optimized design, values of parameters for the optimized design, or other information (e.g., one or more images from a rendering of the CAD model for the optimized design). More than one design may be displayed for comparison, such as providing a table of different values of the parameters for the different designs. The cost or cost difference may be displayed. A comparison of the initial or input design and the optimized design may be displayed.

[00102] While the invention has been described above by reference to various embodiments, it should be understood that many changes and modifications can be made without departing from the scope of the invention. It is therefore intended that the foregoing detailed description be regarded as illustrative rather than limiting, and that it be understood that it is the following claims, including all equivalents, that are intended to define the spirit and scope of this invention.

Claims

I (WE) CLAIM:

1 . A method for design optimization for a wind turbine tower, the method comprising:

generating (26C) a three-dimensional model of the wind turbine tower based on values of parameters of structure of the wind turbine tower;

simulating (26D) a response of the wind turbine tower based on the three-dimensional model and a tower load, the response being a deflection and a resonant frequency of the wind turbine tower;

optimizing (22C) the values for the parameters as a function of the deflection, the frequency, and a levelized cost of energy of the structure of the wind turbine tower; and

transmitting (22F) the optimized values for the parameters as a design for the wind turbine tower.

2. The method of claim 1 wherein generating (26C) comprises generating (26C) the three-dimensional model as a computer assisted design model.

3. The method of claim 1 wherein generating (26C) comprises initially generating (26C) the three-dimensional model from a user input, and wherein optimizing (22C) comprises updating (22C) the values for a subsequent generating (26C) of the three-dimensional model.

4. The method of claim 1 wherein generating (26C) comprises generating (26C) the three-dimensional model as a mesh using the values of the parameters, the parameters comprising at least two of a height of sections, a diameter of one of the sections, a column diameter, a panel thickness, a number of post-tensioning strands, and material.

5. The method of claim 1 wherein simulating (26D) comprises applying a physics model of the three-dimensional model subjected to the tower load.

6. The method of claim 1 wherein generating (26C) comprises generating (26C) a finite element model and wherein simulating (26D) comprises applying a finite element analysis to the finite element model.

7. The method of claim 1 wherein optimizing (22C) comprises adjusting at least one of the values with a genetic optimization.

8. The method of claim 1 wherein optimizing (22C) comprises optimizing (22C) as a function of the levelized cost of energy, the levelized cost of energy being a material cost and assembly cost, the material cost and assembly cost being a function of the values of the parameters.

9. The method of claim 1 wherein optimizing (22C) updates the values of the parameters, wherein generating (26C) and simulating (26D) are repeated with the updated values, and where optimizing (22C) is performed again using the frequency, the deflection, and the levelized cost of energy for the updated values.

10. The method of claim 1 further comprising:

checking (26A) constraints on the values prior to the generating (26C) of the three-dimensional model.

1 1 . The method of claim 1 further comprising:

Checking (22A) constraints on the deflection and the resonant frequency prior to optimizing (22C).

12. The method of claim 1 wherein transmitting (22F) comprises transmitting (22F) the optimized values satisfying a stop criteria of the optimizing (22C).

13. The method of claim 1 wherein transmitting (22F) comprises transmitting (22F) the optimized values for a lowest of the levelized cost of energy.

14. The method of claim 1 wherein generating (26C) comprises generating (26C) for the wind turbine tower being over 100 meters.

15. A non-transitory computer readable storage medium having stored therein data representing instructions executable by a programmed processor (12) for design optimization for a wind turbine tower, the storage medium comprising instructions for:

initializing (20) a design and wind load for the wind turbine tower;

analyzing (26D) effect of the wind load on the design with a three- dimensional representation of the design;

updating (22C) the design with an optimization objective function based on the effect and a lifecycle cost of the design;

repeating the analyzing (26D) with the updated design;

repeating the updating (22C) with the effect from the repeating of the analyzing (26D); and

determining (22D) the updated design with a minimum of the lifecycle cost and the effect within a constraint.

16. The non-transitory computer readable storage medium of claim 15 wherein analyzing (26D) comprises performing a finite element analysis.

17. The non-transitory computer readable storage medium of claim 15 wherein updating (22C) comprises minimizing the lifecycle cost of the design constrained by the effect.

18. The non-transitory computer readable storage medium of claim 15 wherein repeating the analyzing (26D) and the updating (22C) comprises optimizing (22C) the design.

19. A system for design optimization for a wind turbine tower, the system comprising:

a memory (14) configured to store initial dimensions of the wind turbine tower and a load on the wind turbine tower; and

a processor (12) configured to:

generate multiple variations of the initial dimensions of the wind turbine as part of an optimization, the optimization using a cost as the objective function and using deflections and frequencies from three-dimensional modeling of the variations as constraints,

identify at least one of the variations based on minimization of the cost, and

store the identified at least one of the variations in the memory (14) as a cost minimized version of the wind turbine tower satisfying the constraints.

20. The system of claim 19 wherein the frequencies are resonant frequencies constrained to be different than operating frequencies of a turbine.