We examine the effect of rotor design choices on the power capture and structural loading of each major wind turbine component. A harmonic model for structural loading is derived from simulations using the National Renewable Energy Laboratory (NREL) aeroelastic code FAST to reduce computational expense while evaluating design trade-offs for rotors with radii greater than 100 m. Design studies are performed, which focus on blade aerodynamic and structural parameters as well as different hub configurations and nacelle placements atop the tower. The effects of tower design and closed-loop control are also analyzed. Design loads are calculated according to the IEC design standards and used to create a mapping from the harmonic model of the loads and quantify the uncertainty of the transformation.

Our design studies highlight both industry trends and innovative designs: we progress from a conventional, upwind, three-bladed rotor to a rotor with longer, more slender blades that is downwind and two-bladed. For a 13 MW design, we show that increasing the blade length by 25 m, while decreasing the induction factor of the rotor, increases annual energy capture by 11 % while constraining peak blade loads. A downwind, two-bladed rotor design is analyzed, with a focus on its ability to reduce peak blade loads by 10 % per 5

Christopher J. Bay's copyright for this publication is transferred to Alliance for Sustainable Energy, LLC.

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)

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

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

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

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)

A couple of 20 MW rotor designs have been proposed in the literature.

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

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

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.

It is useful to start from established designs when doing comparative analysis. In Sect.

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

Turbine models and environmental parameters used throughout this article.

Illustrations of the turbines in this study, along with the National Renewable Energy Laboratory (NREL) 5 MW reference turbine

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

increasing the energy capture and

reducing the wind turbine component loads.

Aerodynamic design was performed using two inverse design tools: PROPID and PROFOIL. PROPID

Aeroelastic simulations were performed using the latest version of FAST

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

To simulate turbine design loads and power capture, a closed-loop control scheme is necessary. In below-rated conditions, the generator torque

Baseline control block diagram, where

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

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.

Baseline control illustration of a problematic gust for the SUMR-13A baseline rotor in extreme turbulence (DLC 1.3) with a mean wind speed of 14 ms

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.

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

The harmonic loads are derived from FAST simulations with a sheared wind inflow such that the wind speed

Load harmonic magnitude

From the components in Eqs. (

The forces and moments on a component drive its design: larger loads require greater reinforcement, leading to greater component mass and cost. We analyze component loads in terms of the maximum (or peak) load:

Structural loads evaluated in this article. Each component has loads in multiple directions and experiences the peak load and greatest contribution to fatigue loads at different wind speeds.

N/A indicates “not applicable”.

Fatigue loads are computed in terms of the damage equivalent load (DEL): the constant amplitude of a sinusoidal load signal that results in the same total accumulated damage from a more complex load signal. The accumulated damage in simulations with different wind speeds is extrapolated over the turbine lifetime using the wind speed probability distribution

Illustration of the load axes used in this article. The non-rotating load axes – tower, main bearing, and yaw bearing – are all parallel and are denoted by subscripts “t”, “s”, and “y”, respectively. Note: the blade, hub, and main-bearing axis origins are collocated; the blade and hub load axes rotate with azimuth angle, as shown in Fig.

The structural loads on a wind turbine originate from constant and periodic effects, modeled by the harmonic load, as well as from dynamics due to turbulence, which are not necessarily correlated with the azimuthal position of the rotor and are not modeled in this transformation. In some cases, the effect of turbulence greatly outweighs the constant and periodic effects, but in all cases, the harmonic loads can be mapped to the design loads determined by the DLCs. We quantify this relationship in Sect.

To balance the computational efficiency of the harmonic load estimation in Sect.

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

DLC 1.3: extreme turbulence, for peak loads, using the same number of turbulent wind seeds and wind speeds.

DLC 1.4: extreme coherent gust with direction change, for peak loads near rated, above-, and below-rated wind conditions. Different rotor azimuthal initial conditions are simulated to account for the rotor being in different positions when the gust occurs.

DLC 1.5: extreme wind shear, for peak loads near rated and at cut-out wind speeds. The same azimuthal initial conditions as in DLC 1.4 are used.

First, we compare the harmonic loads, calculated using the methods in Sect.

Peak main-bearing loads computed using DLC simulations versus the harmonic load

In Fig.

For example, all peak main-bearing loads found using DLC simulations are shown in Fig.

We also see a difference in how turbulence affects two- versus three-bladed rotors, illustrated by the different lines of fit in Fig.

We transform from the harmonic loads to the design loads by fitting a linear model,

We analyze the uncertainty of the transformation by computing the residuals between the estimated loads, which are fit using the linear relation (Eq.

In general, the standard deviation of the residual is less than 12 % of the mean value, which indicates decent agreement between the transformed load estimates and the DLC-computed design loads. The cases with lowest uncertainty tend to have lower turbulence factors, like the blade edgewise (blade X) DEL and the hub

The most erroneous load component is the peak yaw-bearing load about the

In the remainder of this article, we use these mapped load estimates to analyze the structural loading and power capture of the various rotor configurations in Table

Set of turbines designed and analyzed in this article.

Overview of the design studies performed in this paper. The loads on each component (blue) transfer from the blades to the tower base as shown. Design studies (yellow) that affect each component are performed in Sects.

In this section, we outline the design and simulation results of the 42 turbines shown in Table

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.

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 (

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.

We evaluate rotors with longer blade lengths, lower axial induction factors, and large, downwind cone angles, using the SUMR-13A design described in Sect.

Summary of aerodynamic design studies: the blade length, axial induction (in combination with blade length, chord, and twist), and cone angle are varied, while the AEP and peak blade load are calculated and compared to the base case (SUMR-13A, black dot in all). The standard deviations of the residuals for AEP and peak flapwise load are normalized to the SUMR-13A values and apply across all design studies. All rotors here are two-bladed, and positive cone angles correspond to downwind rotors. Unless otherwise specified, the available rotor power is 13.9 MW, the axial induction is 0.333, and the cone angle is 5

Blade length is changed indirectly in PROPID by increasing the available rotor power at 11.3 ms

The available rotor power of 13.9 MW at 11.3 ms

The rotors used to evaluate axial induction (red, center column in Fig.

The cone angle design study is performed using the same baseline SUMR-13A blades for each rotor but with different cone angles, including upwind (negative) and downwind (positive) cone angles. With a fixed blade length, downwind, highly coned rotors decrease the rotor-swept area, resulting in both reduced power capture and blade loads. The load decrease is significant: 25 % compared with a 7 % decrease in power capture. In comparison with the blade length design study, it is clear why highly coned rotors are attractive for large rotor designs: an increased cone angle will decrease operational loads faster than an increase in blade length will increase them.

For all the aerodynamic design studies, there is a trade-off between power capture and blade loading. Each design study is plotted together in Fig.

The trade-off between power capture and blade loads. The AEP is plotted on the

The SUMR-13A blade design was found to be driven by extreme loading along a combined flapwise and edgewise direction, where DLC 1.4 (extreme coherent gust with direction change) caused the greatest blade load. Since edgewise loads are largely deterministic, varying with a near-constant amplitude with respect to the rotor azimuth, the design goal of the next rotor iteration, the SUMR-13B, was to constrain peak flapwise loads and increase power capture using the aerodynamic design changes previously described. The SUMR-13B is not necessarily cost optimal. Using larger blades with both greater power capture and structural loading could potentially result in a net cost benefit compared to the SUMR-13B. However, in the absence of a detailed cost model, these design choices are difficult to make and depend on a wide array of factors. Larger rotors with both increased loading and power capture will be investigated in future design iterations.

The SUMR-13B does, however, provide a demonstration for using the harmonic loads and results in Fig.

A set of three-bladed rotors (shown with dotted lines in Fig.

Despite the larger blade loads on two-bladed rotors compared to three-bladed rotors with the same power capture, we will be analyzing the two-bladed SUMR-13B for the remainder of this article. When comparing similarly powered rotors, e.g., the CONR-13 and the SUMR-13A, two-bladed rotors reduce the total blade mass by as much as 25 %, which reduces the capital expenditures associated with blade material costs

As a wind turbine blade increases in length, its mass and stiffness increase to account for the additional structural loading. The structural properties of a blade are described by its distributed parameters along the blade span, which include mass, stiffness, and inertia per unit length. In the previous section, these distributed structural parameters were constant for different blade lengths. In this section, we will change the distributed mass and stiffness values through various scaling rules to observe the effect each parameter has on the blade loads. However, changes to the mass and stiffness are not necessarily independent of each other. We will analyze the dependency between blade mass, stiffness, and load using the results of the initial parameter study to determine an initial guess for the distributed parameters of the SUMR-13B blade. The initial guess can then be used for the load simulations that are used to do a more detailed structural lay-up design and determine the final distributed structural parameters for the blade.

To model blades with different lengths, we start with classical similarity scaling rules

mass per unit length, which scales with

stiffness per unit length in the flapwise, edgewise, and torsional directions, which scales with

stiffness per unit length in the spanwise direction, which scales with

inertia per unit length in the flapwise and edgewise directions, which scales with

These parameters can be more flexibly scaled to account for innovations or changes to the structural design. For instance, we scale the mass per unit length distribution by

With

Ultimately, the final structural parameters will be determined by the structural lay-up, but this model could be used to more quickly analyze trade-offs between blade mass, stiffness, loads, and power. In general, mass scaling has the greatest impact on loads. Since this article only considers operational load cases, the effect is most apparent when analyzing fatigue loading. Loads during shutdown events and fault cases are also expected to increase with blade mass. Increased flapwise stiffness contributes to a small increase in energy capture (about 1 %; not shown) due to decreased blade deflection. We also observe that the change in load due to each individual scaling parameter (

The most significant impact of positive structural scaling is the increase in edgewise DELs due to the increased blade mass. Theoretically, the additional mass increase of the larger blade would provide additional reinforcement against these loads, through trailing edge reinforcement or increased root diameter. We see that changes to the blade mass result in a change in edgewise load

The linear system determined by Eqs. (

Blade structural coefficients for the SUMR-13B blade determined using the relationships described in Fig.

The relationship between blade mass, edgewise loads, and edgewise stiffness, as well how each value was derived.

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,

The hub axis (

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:

To compare with the two-bladed SUMR-13B, a three-bladed SUMR-13B was designed using the same blade parameters described in Table

Comparison of the 8.5 ms

Loads on other turbine parts are, however, affected by the change in the number of blades. Hub loads on the two-bladed SUMR-13B are mostly about the

Three-bladed rotors are advantageous due to these balanced hub loads, which effectively nullify the 2P load components and only contain a small 3P load on the non-rotating turbine components. The difference in magnitude of the 1P hub load harmonics is responsible for the greater loading on the non-rotating components of two-bladed rotors. Figure

Change in peak main-bearing loads

Historically, some two-bladed turbines have used a mechanical teeter hinge, which allows for rotation about an axis perpendicular to the main shaft at the shaft tip. Recently, with the advent of pitch regulated turbines, individual pitch controllers have been designed in order to mimic this action by changing the aerodynamic loads on the blades as they rotate. Both solutions reduce loading on the hub, which translates into reduced loading on the main bearing and other non-rotating components.

We have modeled a free-teetering hinge in FAST by enabling the teeter degree-of-freedom and setting a zero damping coefficient to the teeter motion. This free-teetering setup would provide the best configuration for reducing blade loads. A more realistic teeter hinge must account for friction, damping, and end stops (see, e.g.,

The free-teetering hinge configuration completely eliminates the coupling between blade and hub loads, resulting in zero hub loads about the

A more ideal teeter design could be achieved by selecting an appropriate teeter damping coefficient

Alternatively, IPC can be used to mimic the rotor balancing of a teeter hinge by adding a time-varying pitch angle offset to each blade. An IPC algorithm was initially designed to focus on blade loads, which we call blade IPC in Table

Using the relationship in Eq. (

If used in below-rated conditions, these load mitigation techniques reduce power capture, as shown in Fig.

The main bearing must support the weight of the rotor and thrust imbalance on the rotor due to shear, i.e.,

The harmonic loads in Table

The tower clearance

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

Large mean loads on the yaw bearing (

To compare peak yaw-bearing loads across rotors, we adjust the nacelle center of mass so that mean yaw-bearing loads (

Component masses for placing the nacelle center of mass atop the tower.

Peak tower loads in the fore–aft (F-A) direction (

Rotors with large downwind cone angles must have nacelle center of masses further upwind (negative values in Fig.

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

Peak fore–aft tower loading is similar to the peak blade loads described in Sect.

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

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.

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.

When analyzing the design studies of Sects.

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

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.

As rotor size increases, due to increasing blade mass, edgewise blade loading becomes a critical design-driving load and may ultimately constrain the size of wind turbine rotors.

Downwind, coned rotors can significantly reduce peak operational blade loads but capture less energy than rotors with lower cone angles.

Downwind, coned rotors will experience slightly larger (about 15 %–25 %) peak main-bearing loads than upwind turbines, but the effect is amplified with increasing blade length, mass, and cone angle.

Peak yaw-bearing and tower loads are not problematic for downwind rotors as long as the nacelle is properly balanced on the tower.

Two-bladed rotors experience significantly greater loading on the non-rotating parts compared to three-bladed rotors, unless a teeter hinge or individual pitch control is utilized. In these cases, the loading is comparable but with a loss in power.

Two-bladed rotors will require either speed avoidance control or a different tower design to avoid resonance with the 2P frequency of the rotor.

The code and/or data from this study can be made available upon request.

All authors contributed to the baseline models and design direction of the SUMR rotors. DSZ developed the harmonic model, transformation, and closed-loop controllers, carried out simulations, and prepared the visualizations and manuscript. GKA designed the aerodynamic properties of the various rotors, MC investigated the structural properties, DPM investigated the teeter configurations, and CJB visualized the design studies. KEJ provided a thorough review of initial and the final drafts. EL developed the original rotor concept and outlined system-level goals. DTG provided experience on edgewise loading for large rotors, guided the structural design process, and reviewed the article. MSS reviewed the article. LYP had a supervising function and guided the study, helped formulate the article concept, and reviewed multiple drafts of the article.

The authors declare that they have no conflict of interest.

The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency – Energy (ARPA-E), US Department of Energy, under award no. DE-AR0000667. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Support from the Hanse-Wissenschaftskolleg Institute for Advanced Study (Delmenhorst, Germany) and a Palmer Endowed Chair Professorship are also gratefully acknowledged. The authors would also like to acknowledge Paul Veers for his helpful review of this article on behalf of the National Renewable Energy Laboratory and the entire SUMR team for the discussions that ultimately motivated these design studies, as well as their work on the many design aspects of the baseline rotor models.

This research has been supported by the Advanced Research Projects Agency – Energy (grant no. DE-AR0000667).

This paper was edited by Raúl Bayoán Cal and reviewed by Christopher Kelley and one anonymous referee.