Wind turbines are large, dynamic structures that experience significant structural loading on their component parts. Design choices impact the loading on each of these parts. We present a model for the rapid computation of wind turbine design loads, which we use to quantify the effect of design trade-offs associated with different rotor concepts. The economics of wind energy have enabled larger wind turbine sizes, generator ratings, and blade lengths. Longer blades are economical simply because they capture more power more often. A wind turbine's annual energy production (AEP) is the total amount of energy captured by a wind turbine during one year. Increasing the power capture is the primary driver of reducing the cost of wind energy (COE) 1COE=CapEx+OpExAEP, where capital expenditures (CapEx) and operational expenditures (OpEx) make up the cost of building and running a wind turbine. Our goal is to minimize the cost of wind energy, enabling the sale of more wind turbines in an effort to make low-cost energy more available.

Operational expenditures are non-negligible but make up roughly 15 % of the total cost, according to a study of the average 2015 offshore wind turbine . Capital expenditures include the wind turbine parts and balance-of-station costs. Balance-of-station costs account for about 55 % of the total cost and include electrical infrastructure, assembly, and substructure costs. Wind turbine parts (tower, nacelle, blades, etc.) comprise about 30 % of the overall cost of an offshore, fixed-bottom wind plant . The small cost contribution of the wind turbine blades, which is only a fraction of the cost of the wind turbine parts, and the significant effect of wind turbine blades on AEP contribute to the economics that enable larger and larger blades.

However, longer blades require additional structural reinforcement, which increases the blade weight, resulting in larger loads experienced by other wind turbine components like the hub, main bearing, yaw bearing, and tower. Various innovations have enabled lower weight blades; these innovations are then used to subsequently design larger blades that capture more power. Still, the wind turbine components must survive extreme structural loading and last 20–30 years. Wind turbine components are often designed by various engineering teams based on loads from aeroelastic simulations, making wind turbine design a large, distributed design task.

The aerodynamic and structural aspects of wind turbines must be designed and controlled so that the structural loading for a design is feasible. There is a large interdependence between these design aspects (aerodynamic, structural, and controls) and on the various wind turbine components, which has led to numerous design optimization studies. These studies focus primarily on blade aerodynamic and structural design, e.g., in and . Some incorporate dynamic control effects, like and . System engineering tools, like HAWTOpt2 , WISDEM , and Cp-Max , have been developed to handle the large number of design variables but often compute structural loads using simplified scaling rules, conservative static calculations, or many nonlinear aeroelastic simulations. A full set of design load cases (DLCs), specified by the (IEC) in design standards, and simplified for research purposes in , can include up to 2000 simulations, which can be costly in terms of computational effort, resulting in long design cycle times. Often the results of these simulations do not fully elucidate the root cause of problematic load cases on the affected turbine component. An attempt to distill the DLCs into a reduced basis for design loads in an optimization framework was presented in .

We describe an alternative load estimation procedure, based on a set of simulations with a constant, sheared wind inflow that reflects the main drivers of wind turbine loads and the effects of design changes on global wind turbine loads. Since both turbulent and constant wind effects contribute to structural loading and the effect of turbulence has been well studied recently, e.g., in and , we will focus our effort on how turbine model changes impact the harmonic loads caused by wind shear and turbine self-weight. We do this by decomposing the turbine loads from constant, sheared wind inputs into their harmonic components, i.e., the load amplitude of the ith per revolution (iP) load signal. These signals have been used for control , stability analysis , and wind field estimation . Here, we use the same signals to develop a mapping, or transformation, from the harmonic loads to the DLC-simulated design loads to understand the effect that changing the underlying turbine model has on structural loading.

The power and load estimation procedure developed in this study is used to analyze concepts for enabling rotor radii greater than 100 m. Recently, large rotor concepts have been studied in the European projects UpWind and INNWIND. The Danish Technical University (DTU) 10 MW reference wind turbine (RWT) was provided as a design basis for large rotors to test design methods and tools. The DTU 10 MW RWT has motivated studies that focus on optimization methods and active and passive load control methods, but the resulting designs from these studies do not deviate far from the base rotor model. A two-bladed, downwind, teetering hub configuration of the DTU 10 MW RWT was developed, which shows that a teetering hub can greatly reduce the unbalanced loading on the main shaft and blade root . suggest that the tower stiffness distribution needs to be redesigned in order to avoid a resonance at the twice-per-revolution (2P) rotor harmonic and that two-bladed rotors (without teeter) increase loading on the main shaft significantly.

A couple of 20 MW rotor designs have been proposed in the literature. and use classical similarity scaling rules to upscale conventional turbines. Both conclude that loads due to self-weight will increase significantly with blade length and drive component design as turbines grow larger. Specifically, edgewise blade loads and the effect of wind shear are magnified for larger rotor sizes.

A series of design studies at Sandia National Laboratories (SNL) detailed the structural design of a 100 m blade with the goal of reducing the blade mass. First, a classically upscaled blade was given a detailed composite lay-up and tested against DLCs . Next, a series of design innovations reduced the blade mass from 76 metric tons to 49 metric tons, utilizing carbon-fiber reinforcement , advanced core materials , and flatback airfoils .

Another concept to reduce mass-scaling issues is a highly coned, downwind rotor, which has shown that blade loads can be reduced by converting large cantilever loads at the blade root into tensile loads along the span of the blade . We will analyze this concept and its effect on the structural loading of the other wind turbine components besides the blades.

There are few openly published documents that quantify the effects of significant design changes and detailed rotor upscaling on the various wind turbine components. We will quantify the effect of aerodynamic changes, including the blade length, axial induction, cone angle, and number of blades, as applied to both upwind and downwind rotors. A simplified structural model will demonstrate the effect of structural reinforcement on blade mass and loads. The upscaled structural model must provide enough stiffness to compensate for the increasing edgewise blade loads of large rotors. We quantify the effect of changes to the hub by looking at three-bladed and two-bladed rotor configurations, and consider the relative benefits of a teeter hinge or individual pitch control for the latter. Finally, we show how the nacelle placement atop the tower and control schemes can impact the loads on the tower and yaw bearing.

We believe this study will contribute an early stage design model for evaluating design concepts with less computational effort by eliminating hundreds of DLC simulations. The simplified load model provides a qualitative understanding of the relationship between wind turbine structural loads as they progress from the blades to the substructure, highlighting the wind speeds where peak and fatigue loads are most problematic. A designer could use the simplified model to explore the design space and develop an initial wind turbine model for use in a more detailed load analysis. We map the harmonic loads to a set of loads found using operational design load case simulations and quantify the uncertainty. Quantitative design studies evaluate the effect of increased blade size and power capture on global wind turbine loads, as well as the design trade-offs associated with two-bladed wind turbines, teeter hinges, and individual pitch control.

We will present the baseline models used for comparison and our general design direction in Sect. . Section  will outline the tools used for design and simulation and will also provide environmental site specifics. A description of the control scheme used throughout the article is presented in Sect. . The harmonic model is described in Sect. , and in Sect.  the transformation from harmonic loads to DLC-simulated design loads is described. The set of design studies is described in Sect. , leading to studies of blade loads and power capture (Sect. ), hub and main-bearing loads (Sect. ), yaw-bearing loads (Sect. ), and tower loads (Sect. ). A discussion of the model's limitations and potential use is provided in Sect. , followed by conclusions in Sect. .

It is useful to start from established designs when doing comparative analysis. In Sect. , in lieu of a full structural lay-up design, we will use these baseline models for scaling the distributed structural properties of rotor blades. For three-bladed rotors, we will use a conventional rotor design (CONR-13) as a starting point. The CONR-13 is the culmination of a series of design studies aimed at designing a lightweight 100 m blade; it utilizes flatback airfoils, carbon-fiber reinforcement, and advanced core materials to reduce the blade mass below state-of-the-art scaling trends. The full design is described in . The distributed blade structural properties of the CONR-13 will be used for all three-bladed rotors in this study.

A downwind, two-bladed rotor was developed with similar structural advances but with the goal of reducing the total blade mass by at least 25 % compared to the CONR-13 . The blade was designed to enable segmentation, ultralight design, and a morphing rotor; we refer to this design as the SUMR-13A. The initial aerodynamic design is presented in . We have slightly modified the initial design to have a downwind cone angle of 5∘ for the purposes of the design studies presented later. The distributed structural parameters of the SUMR-13A blade were used as a basis for scaling all two-bladed rotors in this study. A summary of both baseline models is shown in Table  and are drawn to scale in Fig. . Both rotors were structurally validated to check strain limits, panel buckling, flutter, and fatigue.

In the remainder of this paper, we will evaluate designs aimed at

increasing the energy capture and

Aerodynamic design was performed using two inverse design tools: PROPID and PROFOIL. PROPID is an inverse rotor design tool that enables a rotor geometry to be designed based on desired performance specifications like available power, tip speed ratio, wind speed distribution, axial induction, airfoils used, and desired lift distribution along the blade. PROFOIL is an inverse airfoil design tool. It allows for the design of airfoil geometries based on prescribed velocity distributions and desired geometric (thickness and camber) and aerodynamic properties. Airfoil geometries output using PROFOIL are analyzed using XFOIL and iterated on using PROFOIL until a final converged design is obtained.

Aeroelastic simulations were performed using the latest version of FAST . Different FAST modules couple the wind inflow with aerodynamic and elastic solvers that compute the structural loading on the wind turbine. Turbulent wind inputs are generated using TurbSim . A recent FAST-based, wind-tunnel-validated approach has shown that, compared with turbulence, tower shadow effects are relatively small . Thus, for simplicity, we have omitted the tower shadow model from our analysis in order to focus on the influence of the more important harmonic and turbulent loads. Control inputs are provided to FAST through a Matlab/Simulink interface that processes FAST outputs and performs closed-loop control. Fatigue results are computed using MLife , which uses a rain-flow-counting algorithm to determine load cycles and extrapolates them over the lifetime of the wind turbine.

To properly compute lifetime fatigue and annual energy production, the wind turbine environment must be provided. The rotors in this study are all designed to be placed off the coast of Virginia, USA. The site corresponds to a Class IIB turbine rating , with mean and turbulent wind speed characteristics shown in Table .

To simulate turbine design loads and power capture, a closed-loop control scheme is necessary. In below-rated conditions, the generator torque τg is controlled so that the rotor speed ω is optimal for power capture, following the typical τg=kω2 law for most of the below-rated operating region, before transitioning to above-rated conditions . For simplicity, this is implemented as a look-up table, though more sophisticated methods exist. The look-up table is altered to avoid a critical rotor speed for two-bladed rotors only (see Fig. b; Sect.  provides more details). The generator rated power of 13.2 MW and rated speed of 1173.7 rpm are assumed to be constant for all the turbines in this study. The gearbox ratio of each turbine is changed to enable operation at the aerodynamically optimal rated rotor speed.

In above-rated wind speeds, the pitch angle is controlled to regulate the rotor speed to its rated value using a gain-scheduled proportional-integral (PI) controller. The gains of the PI controller are set so blade fatigue is minimized, subject to a constraint on the maximum generator speed . We have chosen this control architecture, which is the same for all rotors, so that it can be easily tuned for many rotors in the same way. The optimal generator torque control gain k is computed using rotor parameters, and the PI pitch control gains are tuned using a subset of the DLC 1.2 turbulent simulations. The control architecture (as shown in Fig. a) is adapted from the National Renewable Energy Laboratory (NREL) 5 MW baseline controller , which is commonly used as a reference to compare new controller designs. While this baseline control may not necessarily be the best possible controller, it allows us to focus on the power and load sensitivity to model changes.

Using closed-loop control for load simulations is important because peak loads often occur near the transition between below- and above-rated operation. With a constant generator rating (13.2 MW), different rotors transition from below- to above-rated conditions at different wind speeds. Additional control signals, like individual pitch control (IPC) signals, are added to the baseline control signals in Fig. a.

A controller is also necessary for computing design loads in turbulent DLC simulations, where wind speed changes, or gusts, must be adequately controlled. Often, peak loads are caused by a negative gust, or lull, which we show in Fig. . During a decrease in wind speed, the rotor slows and the pitch decreases to its optimal power position. When the decrease in wind speed is followed by a positive gust, the pitch control must react quickly to regulate rotor speed. We model the actuator of each rotor in this study as a second-order Butterworth filter with a cut-off frequency of 0.25 Hz. The pitch actuator has a maximum pitch rate limit of 4∘ s-1; maximum pitch rates between 1 and 3∘ s-1 were recorded in the turbulent simulations that were run. This decrease and then increase in wind speed creates a condition where there is an above-rated wind speed but a below-rated pitch angle setting, resulting in a large thrust force on the rotor and high loads. To capture the effect that closed-loop control has on design loads as rotor changes are made, we use the same control architecture for computing loads using the harmonic model (Sect. ) and for turbulent DLC simulations (Sect. ), updating the controller parameters based on the rotor parameters.

Load simulations according to the DLCs can be time consuming, so we have developed a simplified model to estimate the loads on wind turbine components more quickly for evaluating design trade-offs across a wide range of parameters. In this section, we describe harmonic loads mH, which are derived from constant and periodic loads that arise due to steady wind loading, wind shear, and turbine self-weight. These harmonic loads can be mapped, or transformed, into estimates mEst of design loads mDLC that are computed using operational DLC simulations in Sect. . The key simplification of the harmonic load model compared to design loads computed using DLC simulations is the omission of load variations that occur at frequencies that do not correspond to the rotor speed. These non-harmonic load variations arise because of wind speed and direction changes, as well as the component's natural frequencies. All frequency components of a load are required to determine the design load for a final, detailed design, but for exploring potentially large numbers of design trade-offs, simplified harmonic loads provide enough information about the various turbine loads.

The harmonic loads are derived from FAST simulations with a sheared wind inflow such that the wind speed u at height z is 2u(z)=uhzzhα, where zh is the hub height, uh is the wind speed at hub height, and α=0.14, which is representative of an offshore wind field . Because of the wind shear, the turbine's structural load signals contain harmonic components that depend on the rotor azimuth ψ; i.e., a load signal m(ψ) can be expressed as 3m(ψ)=m0+mc1Pcos⁡(ψ)+ms1Psin⁡(ψ)+…+mciPcos⁡(iψ)+msiPsin⁡(iψ)+… The components are computed by 4m0=12πNR∫ψ-2πNRψm(ψ)dψ,5mciP=1πNR∫ψ-2πNRψm(ψ)cos⁡(iψ)dψ, and 6msiP=1πNR∫ψ-2πNRψm(ψ)sin⁡(iψ)dψ, where NR is the number of rotations used in the calculation . We have found that load signals can be reconstructed closely using the first four harmonics; the most energy is usually in either the first, second, or third harmonic depending on the component (see Table ) and number of blades.

From the components in Eqs. () and (), the magnitude and phase of each harmonic can be computed: 7miP=mciP2+msiP2, and 8ϕiP=tan⁡-1msiPmciP. An example for the blade flapwise load is shown in Fig. ; most of the load magnitude is in the constant m0 and once-per-revolution m1P load component (101–102 MNm), with some in the 2P load component due to shaft tilt and gravity (∼100 MNm), and very little in the higher harmonics (<10-1 MNm). We will use these harmonic coefficients, calculated via Eqs. ()–(), to estimate fatigue and extreme loads for the various wind turbine components.

To balance the computational efficiency of the harmonic load estimation in Sect.  with the more expensive and realistic design loads computed using DLC simulations, we present the following transformation procedure. In this article, we focus on the moments on the turbine components during power-producing design load cases and simulate the following DLCs specified by the IEC standard :

DLC 1.2: normal turbulence, for fatigue loads, using six random seeds at mean wind speeds from cut-in to cut-out, spaced 2 ms-1 apart.

In this section, we outline the design and simulation results of the 42 turbines shown in Table . The design loads for each rotor are estimated using harmonic loads from Sect.  and the transformation method in Sect. . Additionally, gross AEP is calculated using the generator power P(u) at mean wind speed u by 15AEP=8760∑u∈Up(u)P(u), where p(u) is the Weibull distribution in Table  and 8760 is the number of hours in a year.

We first examine changes to the blade loads and power capture of the SUMR-13A due to variations in the aerodynamics, including the blade length, axial induction, and cone angles. Both upwind (negative) and downwind (positive) cone angles are evaluated. The aerodynamic changes lead to a larger, heavier but more powerful SUMR-13B rotor, which we use to study the effect of mass and stiffness scaling on blade loads. Next, non-rotating component loads will be compared for different hub configurations, considering the number of blades, a teetering hinge, individual pitch control, and rotor placement (upwind versus downwind). Finally, the effect of a downwind rotor on yaw-bearing design loads will be presented and the effect of a two-bladed rotor on tower design will be investigated. A summary of the design parameters considered in this article and the process for incorporating their interconnections is shown in Fig. ; details are given in Sects. –.

We begin by analyzing the effect of changing rotor aerodynamics on blade loads and energy capture. Blade loads are computed at the blade root in both the flapwise (mby) and edgewise (mbx) directions. Blade flapwise loads are primarily aerodynamic in nature and depend on the thrust force exerted on the blades from the wind inflow. Peak blade flapwise loads occur near rated wind speed, which represents the worst combination of wind speed and orthogonal blade surface area but before the blade begins pitching to regulate power in the above-rated operation. Blade pitch has a significant influence on the mean blade flapwise load and control actions can often cause peak loads, e.g., when the pitch angle decreases towards its fine pitch angle to maximize power and then a wind speed gust occurs. The dependence of this load on the control system highlights the necessity of including control design at an early stage.

Flapwise fatigue loads are driven by blade thrust, wind shear, and, to a small degree, blade weight and cone angle. Edgewise fatigue loads, on the other hand, have a nearly constant load cycle amplitude, unless the rotor torque is rapidly changing. The load cycle amplitude of edgewise blade loads depends on the blade weight, creating a large positive and then negative load when the blade is in each horizontal position during a rotor revolution. Edgewise fatigue loads increase with blade length and mass and influence the design of the baseline blade structures used in this study (CONR-13, SUMR-13A). Additional stiffness must compensate for increased edgewise loads but at the cost of increased blade mass, leading to even greater loads. We will explore this relationship in Sect. .

Blade loads are transferred through the blade root to the hub at the pitch actuator. In this section, we analyze the load cycle amplitudes of the hub loads and how they transfer to the non-rotating turbine components. The hub load axes, yh and zh, rotate with the hub (Fig. ). About the yh axis, hub loads are directly related to the blade loads for both two- and three-bladed configurations; they peak when the rotor is near ψ=0∘ due to vertical wind shear, resulting in a large cosine–cyclic component of the hub load about the yh axis (mhy,c1P). A teeter hinge reduces the coupling between blade and hub loads, except in cases of very large rotor deflections, where “hard” end stops increase the coupling and result in large peak loads. About the zh axis, the source of loading depends on whether the rotor has two or three blades (see Fig. ). For three-bladed rotors, the hub load about the zh axis is driven by the blade aerodynamic loading due to wind shear and has a similar magnitude to the load about the yh axis (Fig. , top right). This symmetry is not inherent in a two-bladed configuration; the mhz load is primarily determined by the weight of the blades unless there is a horizontal wind shear. The mismatch between the load cycle amplitudes of mhy and mhz results in larger non-rotating loads, e.g., msy, for two-bladed rotors (Fig. , bottom right). The hub load about the zh axis, for both hub configurations, peaks when the rotor is at ψ=90∘, resulting in a large mhz,s1P component. The magnitude of these loads in relation to each other is important for determining their impact on the non-rotating load components.

The rotating hub is connected to the main shaft, which is supported by a main bearing close to the hub and also may consist of additional bearings between the hub and gearbox. A rotation matrix models the transfer of loads from the rotating to non-rotating frame: 23msymsz=cos⁡ψ-sin⁡ψsin⁡ψcos⁡ψmhymhz, which results in the 1P hub loads mapping to large 0P and 2P load components. The large 2P loads result in large fatigue DELs on the non-rotating parts of two-bladed turbines. The hub configuration, including the number of blades, whether a teeter hinge is used, and IPC all have an impact on the fatigue loading of the main bearing.

The main bearing is mounted to the bedplate of the nacelle, which attaches to the yaw bearing, responsible for rotating the entire nacelle and rotor to align with the wind direction. The yaw bearing experiences similar loads to the main bearing; they peak near rated and at cut-out due to thrust effects and wind shear, respectively. A potential issue with downwind turbines is a large, mean yy-axis moment leading to large peak yaw-bearing loads, similar to the peak main-bearing load. However, peak loads on the yaw bearing can be counteracted by properly balancing the nacelle center of mass atop the tower. We will study the different cone angle designs from Sect.  for two- and three-bladed rotors, as well as our SUMR-13B final design to investigate the effect of rotor cone angle and increased mass on nacelle design and yaw-bearing loads.

Large mean loads on the yaw bearing (myy0P) cause large peak loads that can be overcome by properly choosing the hub-to-tower overhang xOH and the nacelle center of mass xcm (as shown in Fig. ). We use a simple method for determining the nacelle overhang: for upwind turbines, the nacelle overhang was set to that of the CONR-13 (-8.61 m), and for downwind turbines, we used the minimum possible overhang (3.15 m, equal to the radius of the tower at the nacelle). These hub-to-tower overhang values result in adequate tower clearance (the minimum perpendicular distance between the blade tip and the yaw axis yz) when the cone angle is at least 5∘ away from the tower (Fig. a). However, such an important design parameter would certainly be subject to verification using a detailed tower design and the full set of DLCs before deeming the tower safe from blade strike. Rotors with larger cone angles have large tower clearances, which is part of the motivation for their design.

To compare peak yaw-bearing loads across rotors, we adjust the nacelle center of mass so that mean yaw-bearing loads (myy0P) are minimized in still air. The mean yaw-bearing load is linearly dependent on the component masses and center of masses: 30myy0P=gmnacxcm+mrotxcm,rot, where g is the acceleration due to gravity, mnac is the nacelle mass, mrot is the total rotor mass, and xcm,rot is the rotor center of mass. The nacelle center of mass xcm that sets the mean overturning yaw-bearing load to zero is 31xcm=-mrotxcm,rotmnac. The hub and nacelle masses are approximated using a length-to-mass scaling factor of 100633 from the NREL 5 MW reference turbine and shown in Table . The hub and nacelle masses are constant for all rotors throughout this study, but the rotor mass and center of mass vary.

Rotors with large downwind cone angles must have nacelle center of masses further upwind (negative values in Fig. , center). Given the nacelle mass in Table , moving the nacelle center of mass 1 m upwind reduces the mean (and peak) yaw moment by about 10 MNm. Due to the extra overhang necessary for upwind turbines, the center of mass location for the downwind turbines is closer to the tower than for the upwind turbines. By designing the proper hub-to-tower overhang and nacelle placement, the peak yaw loads are no more problematic for downwind rotors than upwind rotors. Once properly balanced, the peak yaw loads are primarily driven by the thrust imbalance due to wind shear, which decreases with increased cone angle (Fig. c). However, changing the nacelle center of mass is a non-trivial task that involves a detailed drivetrain and nacelle design. Fatigue loads (not shown) on the yaw bearing also depend on rotor thrust and decrease with increasing cone angles. The methods presented in Sect.  also reduce yaw-bearing loads.

The yaw bearing is attached to the top of the tower, which must support the rotor–nacelle assembly and withstand large moments. We focus on the effect of rotor axial induction, cone angle, and the number of blades on peak loads in the fore–aft direction mtyPeak and fatigue loading in the side-to-side direction mtxDEL.

Peak fore–aft tower loading is similar to the peak blade loads described in Sect. ; with a maximum near rated wind speeds, they are largely driven by rotor thrust, which is most sensitive to changes in axial induction and cone angle. Lower axial induction rotors and downwind rotors can both reduce the peak tower load by as much as 20 % (Fig. , left). Tower loads are not as sensitive to blade length. Longer blades increase the rotor thrust in below-rated wind speeds, but with a constant generator power, the pitch controller activates at lower wind speeds, constraining the peak tower load near rated. For rotors that capture the same amount of power, two-bladed rotors experience about a 30 % increase in peak tower fore–aft load when compared to three-bladed rotors because of a large difference in the turbulent sampling of the wind due to the increased chord lengths, an effect that is also present when looking at the tower DELs.

Besides having larger chord lengths that sample more turbulence than three-bladed rotors, two-bladed rotors also experience a resonance due to the tower design. Modern wind turbine towers are usually designed to be “soft–stiff”, with a natural frequency between the 1P and 3P harmonics of the rotor . When the 2P rotor speed interacts with the natural frequency of the tower, there are high fore–aft and side-to-side loads. Side-to-side tower DELs increase the most, since there is less aerodynamic damping from the rotor in this direction . One idea is to use a high-compliance tower structure or a floating substructure with a natural frequency below the 1P harmonic. However, a very low tower natural frequency causes tower motion to be perceived as a wind speed disturbance, resulting in speed regulation issues. Several studies have considered this, given the emergence of floating wind turbines , but to simplify our analysis, we have kept the same tower for all turbines: a scaled version of the NREL 5 MW three-bladed reference model .

Our solution is to implement a speed avoidance controller that reduces the rotor speed as it approaches the critical rotor speed from below and increases it after, avoiding the critical speed as much as possible (Fig. b). Similar approaches have been used in two-bladed rotor field testing . While this controller does reduce side-to-side fatigue loading, two-bladed rotors still experience 3 to 4 times the DELs that similar three-bladed rotors experience (Fig. ). Longer, heavier blades with lower axial induction factors amplify this effect. Changing hub architectures also impacts the tower fatigue loads. Both teeter and IPC decrease the fore–aft loading while increasing the side-to-side loading.

The harmonic load simulations predict the same peak tower loads for both two- and three-bladed rotors, but turbulent simulations show a clear difference in the design load, as indicated in Fig. . Compared with other turbine parts, the transformed estimates of the tower loads have a large amount of uncertainty (Fig. ). This uncertainty can be attributed to the source of these tower loads, which are highly dependent on turbulent gusts.

When analyzing the design studies of Sects. –, we have come across a few sources of uncertainty in the estimates of the transformed loads. When mapping the harmonic loads to the loads calculated using DLCs (Sect. ), we see that a large component of the design load is due to turbulence, which primarily depends on the number of blades on the rotor, leading to different transformation coefficients for two- and three-bladed rotors in Eq. (). However, the turbulent component is also correlated with other model parameters, most notably rotor thrust. Highly coned downwind rotors reduce the rotor thrust and have a lower turbulent component than upwind rotors. Different levels of turbulence, besides Class IIB that was analyzed in this study, would result in different turbulent components and residuals of the transformation from harmonic to design load. Additionally, dynamic effects, like the problematic gust in Fig. , are not explicitly modeled in the harmonic model of Sect. . Thus, dynamic control solutions that appear promising in constant wind inputs should be ultimately verified in turbulent simulations.

Several improvements to the harmonic model could be made. For instance, the problematic gust events follow a similar profile in many instances; this could be an additional simulation added to the model's set of simulations. While outside the scope of this study, parked, fault, and shutdown cases can result in the largest design loads in practice, e.g., in ; they could be added with little computational expense. The transformation procedure could be streamlined by perhaps doing a single, exemplary turbulent simulation for each case to determine the turbulent component of each load.

The harmonic loads and their mapping to design load estimates used to evaluate design trade-offs provide a potential middle ground for wind turbine system engineering tools. The method is more realistic than simple scaling rules and static estimates but requires less computational effort than full sets of DLC simulations and therefore allows for an initial optimization over a wider range of configurations.

In this article, we presented a method for estimating wind turbine power capture and structural loads, which uses the harmonic components of signals from aeroelastic simulations in FAST with a constant, sheared inflow. The power and load estimates are mapped to design loads from power-producing design load cases and could be used for initial wind turbine system design or sensitivity analyses to model changes. We designed 42 different rotors with the goal of reducing the cost of wind energy through increased power capture and reduced capital expenditures. Power capture and structural loads are analyzed for blades longer than 100 m in both upwind and downwind configurations, with two- and three-bladed rotors, leading to an updated design, the SUMR-13B, with longer, more slender blades that align with industry trends. A series of detailed design studies was performed, with the following conclusions:

Low axial induction rotors using longer blades with smaller chord lengths can capture more energy while constraining peak operational blade loads.