Proper wind turbine design relies on the ability to accurately predict ultimate and fatigue loads of turbines. The load analysis process requires precise knowledge of the expected wind-inflow conditions as well as turbine structural and aerodynamic properties. However, uncertainty in most parameters is inevitable. It is therefore important to understand the impact such uncertainties have on the resulting loads. The goal of this work is to assess which input parameters have the greatest influence on turbine power, fatigue loads, and ultimate loads during normal turbine operation. An elementary effects sensitivity analysis is performed to identify the most sensitive parameters. Separate case studies are performed on (1) wind-inflow conditions and (2) turbine structural and aerodynamic properties, both cases using the National Renewable Energy Laboratory 5 MW baseline wind turbine. The Veers model was used to generate synthetic International Electrotechnical Commission (IEC) Kaimal turbulence spectrum inflow. The focus is on individual parameter sensitivity, though interactions between parameters are considered.

The results of this work show that for wind-inflow conditions, turbulence in the primary wind direction and shear are the most sensitive parameters for turbine loads, which is expected. Secondary parameters of importance are identified as veer,

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Wind turbines are designed using the International Electrotechnical Commission (IEC) 61400-1 standard (IEC, 2005), which prescribes a set of simulations to ascertain the ultimate and fatigue loads that the turbine could encounter under a variety of environmental and operational conditions. The standard applies safety margins to account for the uncertainty in the process, which comes from the procedure used to calculate the loads (involving only a small fraction of the entire lifetime), but also from uncertainty in the properties of the system, variations in the conditions the turbine will encounter from the prescribed values, and modeling uncertainty. As manufacturers move to develop more advanced wind technology, optimize designs further, and reduce the cost of wind turbines, it is important to better understand how uncertainties impact modeling predictions and reduce the uncertainties where possible. Knowledge of where the uncertainties stem from can lead to a better understanding of the cost impacts and design needs of different sites and different turbines.

This paper provides a better understanding of the uncertainty in the ultimate and extreme structural loads and power in a wind turbine. This is done by parameterizing the uncertainty sources, prescribing a procedure to estimate the load sensitivity to each parameter, and identifying which parameters have the largest sensitivities for a conventional utility-scale wind turbine under normal operation. An elementary effects (EE) methodology was employed for estimating the sensitivity of the parameters. This approach was chosen because it provides a reasonable estimate of sensitivity, but with significantly fewer computational requirements compared to calculating the Sobol sensitivity, and does not require increasing the uncertainty in the result through the use of a reduced-order model. Some modifications were needed to the standard EE approach to properly compare loads across different wind speed bins.

This work is a first step in understanding potential design process modifications to move toward a more probabilistic approach or to inform site-suitability analyses. The results of this work can be used to (1) rank the sensitivities of different parameters, (2) help establish uncertainty bars around the predictions of engineering models during validation efforts, and (3) provide insight to probabilistic design methods and site-suitability analyses.

To identify the most influential sources of uncertainty in the calculation
of the structural loads for utility-scale wind turbines, a sensitivity
analysis methodology based on EE is employed. The focus is on the
sensitivity of the input parameters of wind turbine simulations (used to
calculate the loads), not on the modeling software itself, which creates
uncertainty based on whether the approach used accurately represents the
physics of the wind loading and structural response. The procedure followed
is summarized in the following subsections. The caveats of the sensitivity
analysis approach employed are given as follows:

Only the National Renewable Energy Laboratory (NREL) 5 MW reference turbine is used to assess sensitivity (the resulting identification of most sensitive parameters may depend on the turbine).

Only normal operation under turbulence is considered (gusts, start-ups, shutdowns, and parked or idling events are not considered).

Minimum and maximum values of the input parameter uncertainty ranges are examined in the analysis (no joint probability density function is considered).

With the exception of wind speed, each parameter is examined independently across the full range of variation and is not conditioned based on parameters other than wind speed.

The sensitivity of the turbine load response to each input parameter is assessed through the use of a simulation model. The NREL 5 MW reference turbine (Jonkman et al., 2009) was used in this study as a representative turbine. This is a three-bladed upwind horizontal-axis turbine with a variable-speed collective pitch controller; it has a hub height of 90 m and a rotor diameter of 126 m. Though not covered in this work, it would also be useful to examine how the sensitivity of the turbine loads to the parameters is affected by the size, type, and control of the considered wind turbine.

The sensitivity of loads to input parameter variation could be influenced by the wind speed and associated wind turbine controller response. Therefore,
the EE analysis was performed at three different wind speeds corresponding
to mean hub height wind speeds of 8, 12, and 18 m s

Overview of the parametric uncertainty in a wind turbine load analysis. Includes wind-inflow conditions (subset shown in blue), turbine aeroelastic properties (subset shown in black), and the associated load quantities of interest (QoIs) (subset shown in red).

OpenFAST (2017), a state-of-the-art engineering-level aeroservoelastic modeling approach, was used to simulate the NREL 5 MW wind turbine using the developed wind files, allowing for aeroelastic response and turbine operation analysis. A simulation time of 10 min was used after an initial 30 s transient period per turbulence seed. Drag on the tower was not considered because it is negligible for an operational turbine. AeroDyn, the aerodynamic module of OpenFAST, determines the impact of the turbine wake using induction factors that are computed using blade-element momentum theory with advanced corrections. Steady and unsteady aerodynamic responses were considered. Steady aerodynamic modeling uses static lift and drag curves in the momentum balance to calculate the local induction. Unsteady airfoil aerodynamic modeling accounts for dynamic stall, flow separation, and flow reattachment to calculate the local aerodynamic applied loads. ElastoDyn, a combined multibody and modal structural approach that includes geometric nonlinearities, was used to represent the flexibility of the blades, drivetrain, and tower as well as to compute structural loading, which was used to compute ultimate and fatigue loads. The baseline controller of the NREL 5 MW turbine was enabled using ServoDyn. OpenFAST results were used to assess the change in response of quantities of interest (QoIs) to changes in the physical input parameters.

Input parameters were identified that could significantly influence the loading of a utility-scale wind turbine. These parameters were organized into two main categories (or case studies): the ambient wind-inflow conditions that will generate the aerodynamic loading on the wind turbine and the aeroelastic properties of the structure that will determine how the wind turbine will react to that loading (see Fig. 1). Within these two categories, a vast number of uncertainty sources can be identified, and Abdallah (2015) provides an exhaustive list of the properties. For this study, the authors selected those parameters believed to have the largest effect for normal operation for a conventional utility-scale wind turbine, which are categorized into the labels shown in Fig. 1.

To understand the sensitivity of a given parameter, a range over which that parameter may vary needed to be defined. For the wind conditions, a literature search was done to identify the reported range for each of the parameters across different potential installation sites within the three wind speed bins. For the aeroelastic properties, the parameters are varied based on an assessed level of potential uncertainty associated with each parameter.

To capture the variability in turbine response that results from parameter variation, several QoIs were identified. These QoIs are summarized in Table 1 and include the blade, drivetrain, and tower loads; blade-tip displacement; and turbine power. Ultimate and fatigue loads were considered for all load QoIs, whereas only ultimate values were considered for blade-tip displacements. The ultimate loads were estimated using the average of the global absolute maximums across all turbulence seeds for a given set of parameter values. The fatigue loads were estimated using aggregate damage-equivalent loads (DEL) of the QoI response across all seeds for a given set of short-term parameter values. For the bending moments, the ultimate loads were calculated as the largest vector sum of the first two components listed, rather than considering each individually. The QoI sensitivity of each input parameter is examined using the procedure summarized in the next section.

Quantities of interest examined in the sensitivity analyses.

There are many different approaches to assess the sensitivity of QoIs for a given input parameter. The best choice depends on the number of considered input parameters, simulation computation time, and availability of parameter distributions. Sensitivity is commonly assessed through the Sobol sensitivity (Saltelli et al., 2008), which decomposes the variance of the response into fractions that can be attributed to different input parameters and parameter interactions. The drawback of this method is the large computational expense, which requires a Monte Carlo analysis to calculate the sensitivity. To decrease the computational expense, one approach is to use a metamodel, which is a lower-order surrogate model trained on a subset of simulations to capture the trends of the full-order more computationally expensive model. This approach has been used in the wind energy field (Nelson et al., 2003; Rinker, 2016; Sutherland, 2002; Ziegler and Muskulus, 2016) but was deemed unsuitable for this work given the wind turbine model complexity and associated QoIs. Specifically, it may be difficult for a metamodel to capture the system nonlinearities and interaction of the controller, especially ultimate loads at the tails of the load distribution, limiting metamodel accuracy. Another approach to reduce computational expense is to use a design of experiments approach to identify the fewest simulations needed to capture the variance in the parameters and associated interactions, e.g., Latin hypercube sampling (Matthaus et al., 2017; Saranyasoontorn and Manuel, 2006, 2008) and fractional factorial analysis (Downey, 2006). These methods were considered for this application but such approaches are still too computationally expensive given the large number of considered input parameters. Instead, a screening approach was determined to be the best approach. A screening method provides a sensitivity measure that is not a direct estimate of the variance, but rather supplies a ranking of those parameters with the most influence. One of the most commonly used screening approaches is EE analysis (Campolongo et al., 2007, 2011; Francos et al., 2003; Gan et al., 2014; Huang and Pierson, 2012; Jansen, 1999; Martin et al., 2016; Saint-Geours and Lilburne, 2010; Sohier et al., 2015). Once the EE analysis identifies the input parameters that are most influential to the QoIs, a more targeted analysis can be performed using one of the other sensitivity analyses discussed above.

EE at its core is a simple methodology for screening parameters. It is based on the one-at-a-time approach in which each input parameter of interest is varied individually while holding all other parameters fixed. A derivative is then calculated based on the level of change in the QoI to the change in the input parameter using first-order finite differencing. Approaches such as these are called local sensitivity approaches because they calculate the influence of a single parameter without considering interaction with other parameters. However, the EE method extends this process by examining the change in response for a given input parameter at different locations (points) in the input parameter hyperspace. In other words, only one parameter is varied at a time, but this variation is performed multiple times using different values for the other input parameters, as shown in Fig. 2. The derivatives calculated from the different points are considered to assess an overall level of sensitivity. Thus, the EE method considers the interactions between different parameters and is therefore considered a global sensitivity analysis method.

Radial EE approach representation for three input parameters. Blue circles indicate starting points in the parameter hyperspace. Red points indicate variation in one parameter at a time. Each variation is performed for 10 % of the range over which the parameter may vary, either in the positive or negative direction.

Each wind turbine QoI,

The basic approach for performing an EE analysis has been modified over the
years to ensure that the input hyperspace is being adequately sampled and to
eliminate issues that might confound the sensitivity assessment. In this
work, the following modifications to the standard approach were made:

A radial approach, where the EE values were calculated by varying each parameter one at a time from a starting point (see Fig. 2), was used rather than the traditional trajectories for varying all of the parameters, which has been shown to improve the efficiency of the method (Campolongo et al., 2011).

Sobol numbers were used to determine the initial points at which the derivatives will be calculated (blue circles in Fig. 2), which ensures a wide sampling of the input hyperspace (Campolongo et al., 2011; Robertson et al., 2018).

A set delta value equal to 10 % of the input parameter range (

A modified EE formula – different for ultimate and fatigue loads – was used to examine the sensitivity of the parameters across multiple wind speed bins. EE modifications are detailed in Sect. 3.3.1 and 3.3.2.

The most sensitive inputs were identified via thresholding of EE values rather than the classical method involving mean and standard deviation of EE values, as detailed in Sect. 3.4 and Appendix A.

This section provides the detailed formulas used to calculate the EE values for the ultimate and fatigue loads.

When considering the ultimate loads, only the single highest ultimate load
is of concern, regardless of the wind speed bin. Therefore, the standard EE
formula is modified so that the sensitivity of the parameters can be
examined consistently across different wind speed bins. This is accomplished
by keeping

To compute the fatigue loads, the same basic formulation is used as for the
ultimate loads but the DEL of the temporal response is considered in place
of the mean of the absolute maximums:

Wind-inflow condition parameters (18 total).

The EE value is a surrogate for a sensitivity level. Therefore, a higher EE
value for a given input parameter indicates more sensitivity. Here, the most
sensitive parameters are identified by defining a threshold over which an
individual EE value would be considered significant, indicating the
sensitivity of the associated parameter. This approach differs from the
classical method of determining parameter sensitivity, as discussed in
Appendix A. The threshold is set individually for each QoI. For the wind
parameter study, the threshold is defined as

Two separate case studies were performed to assess the sensitivity of input
parameters to the resulting ultimate and fatigue loads of the NREL 5 MW wind
turbine. The categories of input parameters analyzed were the wind-inflow
conditions and the aeroelastic turbine properties. In both of the case
studies, loads were analyzed for three wind speed bins, using mean wind
speed bins of 8, 12, and 18 m s

Many researchers have examined the influence of wind characteristics on turbine load response, considering differing wind parameters and turbulence models, and using different methods to assess their sensitivity. The most common parameter considered is the influence of turbulence intensity variability, which past work has shown to have significant variability and a large impact on the turbine response (Dimitrov et al., 2015; Downey, 2006; Eggers et al., 2003; Ernst and Seume, 2012; Holtslag et al., 2016; Kelly et al., 2014; Matthaus et al., 2017; Moriarty et al., 2002; Rinker, 2016; Saranyasoontorn and Manuel, 2008; Sathe et al., 2012; Sutherland, 2002; Wagner et al., 2010; Walter et al., 2009). The shear exponent, or wind profile, is the next most common parameter examined, concluded to have similar or slightly less importance to the turbulence intensity (Bulaevskaya et al., 2015; Dimitrov et al., 2015; Downey, 2006; Eggers et al., 2006; Ernst and Seume, 2012; Kelly et al., 2014; Matthaus et al., 2017; Sathe et al., 2012). Other parameters investigated include the turbulence length scale, standard deviation of different directional wind components, Richardson number, spatial coherence, component correlation, and veer. Mixed conclusions are drawn on the importance of these secondary parameters, which are influenced by the range of variability considered (based on the conditions examined), the turbine control system, and the turbine size and hub height under consideration. The effects of considering the secondary wind parameters are also mixed, sometimes increasing and sometimes decreasing the loads in the turbine; however, most agree that the use of site-specific measurements of the wind parameters will lead to a more accurate assessment of the turbine loads, resulting in designs that are either further optimized or lower risk.

The focus of this case study is to obtain a thorough assessment of which wind characteristics influence wind turbine structural loads when considering the variability of these parameters over a wide sampling of site conditions.

A total of 18 input parameters were chosen to represent the wind-inflow
conditions, considering the mean wind profile, velocity spectrum, spatial
coherence, and component correlation, as summarized in
Table 2. The parameters used were identified
considering a Veers model for describing and generating the wind
characteristics because it provides a quantitative description with a known
and limited set of inputs. Each of these parameters is described in the
following subsections. Note that the Veers model differs from the other
commonly used Mann turbulence model.

The Mann turbulence model (also considered in the IEC 61400-1 standard) is based on a three-dimensional tensor representation of the turbulence derived from rapid distortion of isotropic turbulence using a uniform mean velocity shear (Jonkman, 2009). The Mann model considers the three turbulence components as dependent, representing the correlation between the longitudinal and vertical components resulting from the Reynolds stresses. In the IEC 61400-1 standard, the two spectra (Mann and Kaimal) are equated, resulting in three parameters that may be set for the Mann model. However, there is uncertainty in whether the loads resulting from these two different turbulence spectra are truly consistent.

Regardless, the Veers model is used here because it is more tailorable than the Mann model, i.e., there are more input parameters that can be varied.A standard power-law shear model is used to describe the vertical wind speed
profile and a linear wind direction veer model is used. The sensitivity of
these characteristics are captured through variation in the exponent of the
shear,

The Veers model uses a Kaimal spectrum to represent the turbulence. The
Kaimal spectrum is defined as (IEC, 2005):

The point-to-point spatial coherence (Coh) quantifies the frequency-dependent cross-correlation of a single turbulence component at different transverse points in the wind inflow grid. The general coherence model used in TurbSim is defined as

The component-to-component correlation (PC) quantifies the cross-correlation
between directional turbulence components at a single point in space. For
example, PC

Included wind-inflow parameter ranges separated by wind speed bin.

Identification of significant parameters using ultimate

To assess the sensitivity of each of the parameters on the load response, a range over which the parameters could vary was defined. The variation level was assessed through a literature search seeking the range over which the parameters could realistically vary for different installation sites around the world (Berg et al., 2013; Bulaevskaya et al., 2015; Clifton, 2014; Dimitrov, 2018; Dimitrov et al., 2015; Eggers et al., 2003; Ernst et al., 2012; Holtslag et al., 2016; Jonkman, 2009; Kalverla et al., 2017; Kelley, 2011; Lindelöw-Marsden, 2009; Matthaus et al., 2017; Moriarty et al., 2002; Moroz, 2017; Nelson et al., 2003; Park et al., 2015; Rinker, 2016; Saint-Geours and Lilburne, 2010; Saranyasontoorn et al., 2004; Saranyasontoorn and Manuel, 2008; Sathe et al., 2012; Solari, 1987; Sutherland, 2002; Teunissen, 1970; Wagner et al., 2010; Walter et al., 2009; Wharton et al., 2015; Ziegler et al., 2016). When possible, parameter ranges were set based on wind speed bins. If no information on wind speed dependence was found, the same values were used in all bins. The ranges, summarized in Table 3, were taken from multiple sources (references cited below the values), based on measurements across a variety of different locations and conditions. For comparison, the nominal value prescribed by IEC for category B turbulence is specified in the “Nom.” row.

To simplify the screening of the most influential parameters, all parameters were considered independent of one another. This was done because of the difficulty of considering correlations between a large number of parameters. Such correlations should be studied in future work once parameter importance has been established. Because each parameter was considered independently, except for the conditioning on wind speed bin, some nonphysical parameter combinations may arise. This was considered acceptable for the screening process.

The EE value was calculated for each of the 18 input parameters (

The EE values across all input parameters, input hyperspace points, and wind
speed bins were examined for each of the QoIs for ultimate and fatigue
loads. To identify the most sensitive parameters, a tally was made of the
number of times an EE value exceeded the threshold for a given QoI. The
resulting tallies are shown in Fig. 3, with the
ultimate load tally on the left and the fatigue load tally on the right. As
expected, based on the parameters of importance in IEC design standards,
these plots show an overwhelming level of sensitivity of the

Stacked histogram of the ultimate load EE values for each of the QoIs across all wind speed bins, input parameters, and simulation points. Black line represents the defined threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

Primary input parameters contributing to ultimate load sensitivity of each QoI. Values indicate the number of times the variable contributes to the sensitivity count.

Histograms of the EE values for each of the QoIs are plotted in Figs. 4 and 5 for the ultimate and fatigue load metrics (associated exceedance probability plots are shown in Appendix B, Figs. B1 and B2). Each plot contains all calculated EE values for a given QoI colored by wind speed bin. The threshold used to identify significant EE values is shown in each plot as a solid black line. All points above the threshold line indicate a significant event and are included in the outlier tally for each QoI. Note that although electric power is shown, it is not used in the outlier tally because its variation is strictly limited by the turbine controller rather than other wind parameters. Highlighted in these figures is that most of the outliers come from the below-rated wind speed bin.

Stacked histogram of the fatigue load EE values for each of the QoIs across all wind speed bins, input parameters, and simulation points. Black line represents the defined threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

Primary input parameters contributing to fatigue load sensitivity of each QoI. Values indicate the number of times the variable contributes to the sensitivity count.

Exceedance probability plot of ultimate

To understand why the below-rated wind speed bin would be creating the most
outliers, a more thorough examination was made for one of the QoIs.
Exceedance probability plots of blade-root loads are shown in
Fig. 6. Here, all input parameters are plotted
independently of each other to compare the behavior between parameters. Each
line represents a different input parameter with each point representing a
different location in the hyperspace. These plots show how the shear and

Histogram plots of blade-root bending moment EE values are shown in
Figs. 7 and 8. In
each figure, wind speed bins are displayed in different plots and EE value
histograms showing the contribution from all input parameters are shown in
each histogram. Ultimate load EE values are shown in
Fig. 7 and fatigue load EE values are shown in
Fig. 8. Highlighted in these plots is the large
sensitivity of the shear parameter and, to a lesser extent,

Histograms of ultimate load EE values for the blade-root bending moment. Each graph in the left column shows one wind speed bin and includes all input parameters. Right column is a zoomed-in view of the left.

Histograms of fatigue load EE values for the blade-root bending out-of-plane bending moment. Each graph in the left column shows one wind speed bin and includes all input parameters. Right column is a zoomed-in view of the left.

To summarize which parameters are important for which QoIs, the number of
times each input parameter contributed to the significant event count for a
given QoI was tallied. The top most-sensitive parameters are shown in Tables 4 and 5 for ultimate and fatigue loads, respectively. Overall, 46 %
of the outliers for both ultimate and fatigue loads are due to

The second case study focuses on which aeroelastic turbine parameters have the greatest influence on turbine ultimate and fatigue loads during normal turbine operation. These parameters are categorized into four main property categories: support structure, blade structure, blade aerodynamics, and controller.

It is widely acknowledged that uncertainty in the aerodynamic parameters can affect the prediction of turbine performance and structural loading (Abdallah, 2015; Abdallah et al., 2015; Madsen et al., 2010; Simms et al., 2001). Abdallah et al. (2015) demonstrated the impact of uncertainty in steady airfoil data on prediction of extreme loads and assessed the correlation between various static coefficient polars. Despite significant work to measure these parameters, considerable uncertainty remains in their prediction. Static lift and drag measurements almost exclusively come from wind tunnel tests of airfoils, which lack three-dimensional and unsteady effects that are instead estimated through the application of semiempirical engineering models, e.g., rotational augmentation (stall delay) and stall hysteresis (Abdallah et al., 2015; Simms et al., 2001). In Damiani et al. (2016), unsteady aerodynamic parameters were tuned for several airfoil sections to match experimental lift and drag unsteady hysteresis loops, but the consequences of parameter variation were not considered. Blade chord and twist ranges were chosen using the work of Loeven and Bijl (2008), who identified changes in blade chord and twist based on uncertainty in aerodynamic loading, icing, or wear of the blades.

Beyond the blade aerodynamic properties, other turbine properties also contribute to the uncertainty of the load response characteristics. Abdallah et al. (2015) provides a comprehensive assessment of the sources of uncertainty affecting the prediction of loads in a wind turbine. Researchers have not focused on these other parameters as significantly as the aerodynamic ones, but they could make a significant contribution to the uncertainty. Witcher (2017) examined uncertainty in properties such as the tower and blade mass/stiffness properties within the context of defining a probabilistic approach to designing wind turbines by examining distributions of the load from propagated input parameter uncertainties versus resistance distributions. Prediction of the reliability of the wind turbine has been studied through examination of the damping in the structure by Koukoura (2014) and a better understanding of the uncertainty in the properties of the drivetrain by Holierhoek et al. (2010). Limited information is available on what the actual ranges of uncertainty are for these different characteristics. For most studies, expert opinion is used to set a realistic bound. A better assessment of these bounds will be needed in future work to understand the relative importance of the physical parameters and to provide a more precise assessment of the uncertainty bounds in the load response of wind turbines.

For the turbine aeroelastic properties, 39 input parameters (

Turbine aeroelastic parameters (39 total).

The level of variation was based on the perceived level of uncertainty in the parameter values. Some of these levels of uncertainty are proposed within the literature, but when no other information was available expert opinion was used. The source for the information is provided below the values in each table summarizing the parameter ranges. “Exp.” is used to identify where expert opinion was used. The uncertainty levels are largely percentage based, but in some instances an exact value was used. The following subsections define the ranges of the parameters introduced in Table 6. All parameters were considered independent of one another, as was done for the wind parameter sensitivity analysis.

For the support structure, nine parameters were varied and summarized in
Table 6. These parameters included mass and center of
mass (CM) of the tower and nacelle, tower and drivetrain stiffness factors,
tower and drivetrain damping ratio, and shaft angle. To manipulate the tower
structural response, the frequency of the corresponding tower mode shapes
was changed by

Parameter value ranges of turbine support structure parameters.

Parameter value ranges of turbine blade structure parameters.

For the blade structural properties, nine parameters were considered, including
blade flapwise and edgewise stiffness (including stiffness imbalance), mass
(including mass imbalance), CM, damping, and precone angle, as detailed in
Table 8. Through ElastoDyn, blade structural
dynamics are modeled using two flapwise mode shapes and one edgewise mode
shape per blade. To manipulate blade structural response, the frequency of
the first flapwise and edgewise mode shapes was changed by

The blade aerodynamic properties were represented using 18 parameters: 3 associated with the blade twist and chord distribution; 10 associated with the static aerodynamic component; and 5 associated with the unsteady aerodynamic properties. Blade twist and chord distributions were manipulated by specifying a change in the distributions along the blade. Three parameters were defined, associated with changing the chord at the blade tip and root and twist at the blade tip. For each of these parameters, the associated distribution along the blade was modified linearly such that there was zero change at the opposite end. The root twist was not changed because the blade-pitch angle uncertainties are considered in the controller parameter section.

For the steady aerodynamic component, the lift and drag versus
angle-of-attack (AoA) curves were modified to examine the sensitivity on
resulting loads throughout the wind turbine. The turbine operated in normal
operating conditions, and therefore only relevant regions of the curves were
modified. The curves modified by parameterization using an
approach based on one introduced by Abdallah et al. (2015). The approach
used here parameterized the

beginning of linear

trailing edge separation (TES) point – AoA location at which

maximum (max) point – AoA location at which

separation reattachment (SR) point – AoA location at which slope of

The selected points of interest are similar to those selected by Abdallah et al. (2015). A notable difference is the consideration
of

Perturbation of points of interest in representative

Parameter value ranges of turbine blade aerodynamic parameters.

AoA deltas are applied to the original AoA values via the following
equations.

The new AoA values are fit to the nearest existing AoA value on the curve. The AoA resolution is fine enough that all perturbations are captured, though not precisely. This approach may need to be adjusted if the perturbations were to decrease.

For all new AoA values, the change in

The total change in

For

The

Sample original and perturbed

Parameter value ranges of turbine controller parameters.

Percentage of contribution to total number of significant events for ultimate and fatigue loads.

Identification of significant parameters using

A similar process was followed by modifying the

Stacked EE-value histograms of ultimate loads across all wind speed bins, input parameters, and simulation points for all QoIs. The black line represents the threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

There are several unsteady airfoil aerodynamic parameters that can be
modified in OpenFAST. By expert opinion (Rick Damiani, personal communication, May 2018), several of these
parameters have been identified as having the largest potential variability
or impact on turbine response and are therefore included in this study.
Several of the parameters in the Beddoes–Leishman-type unsteady airfoil
aerodynamics model used here are derivable from the (perturbed) static lift
and drag polars, i.e., when the lift and drag polars are perturbed, the
associated Beddoes–Leishman unsteady airfoil aerodynamic parameters are
perturbed as well. Additionally, there are several other parameters
associated with unsteady aerodynamics that are included in OpenFAST. These
parameters are

These quantities were varied over the ranges detailed in Table 9 and are constant across the blade.

Zoomed-in stacked EE-value histograms of ultimate loads across all wind speed bins, input parameters, and simulation points for all QoIs. The black line represents the threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

Turbine yaw error was incorporated by directly changing the yaw angle of the turbine (see Table 10). For the collective blade pitch error, the twist distribution of each blade was identically shifted uniformly along the blade independent of the twist change in Table 9. For the imbalance pitch error, modified twist distributions were applied to two of the blades: one with a higher-than-nominal tip twist, one with a lower-than-nominal tip twist, and one unchanged.

The EE value calculation and analysis process are the same as was used for
the wind parameter analysis. Sixty wind file seeds (

Stacked EE-value histograms of fatigue loads across all wind speed bins, input parameters, and simulation points for all QoIs. The black line represents the threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

The EE values across all input parameters, input hyperspace points, and wind
speed bins were examined for all QoIs for the ultimate and fatigue loads. For
each QoI, the number of times an EE value exceeded the threshold for a given
QoI was tallied. The resulting tallies are shown in
Fig. 11, with the ultimate load tally on the top
and fatigue load tally on the bottom. Note that nearly twice as many
significant events were counted for fatigue loads; fewer significant events
were counted for ultimate loads because of the limited threshold exceedance
in the below-rated wind speeds. The percentage that each relevant input
parameter contributed to the total significant event count is summarized in
Table 11. Ultimate turbine loads are most sensitive
to yaw error (

Zoomed-in stacked EE-value histograms of fatigue loads across all wind speed bins, input parameters, and simulation points for all QoIs. The black line represents the threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

Histograms of the EE values for each of the QoIs are plotted in Figs. 12–15 for the ultimate and fatigue load metrics (associated exceedance probability plots are shown in Appendix B, Figs. B3 and B4). Here, EE values are colored by wind speed and the black vertical line represents the threshold for each QoI. The sharp separation of ultimate load EE values between wind speed bins is evident in Fig. 12. A zoomed-in view of the lower count values is shown in Fig. 13. The more evenly distributed nature of the fatigue load EE values is further highlighted in the histogram plots depicted in Fig. 14 and zoomed-in views in Fig. 15. Unlike ultimate load EE values, all wind speed bins contribute to the outlier count for each QoI. Histogram plots of blade-root ultimate and fatigue bending moment EE values are shown in Figs. 16 and 17, respectively. The sharp separation of ultimate load EE values between wind speed bins is again evident. Highlighted in the fatigue load plots is the more even distribution of threshold-exceeding EE values across wind speed bins.

The grouping of the results by wind speed bin creates an unequal distribution of outliers resulting from each turbine QoI. Most notably, blade-root pitching moment accounts for 18 % of the total ultimate load significant events, whereas rotor torque accounts for only 5 %. This suggests that it may be better to tailor the threshold for each QoI but this was deemed overly complicated for this first pass at assessing the sensitivity. Additionally, for a given QoI, it is typical for all ultimate load significant events to occur from either the near- or above-rated wind speeds. However, fatigue load EE values are more evenly distributed across wind speed bins, as shown in Fig. 14. The lower significant event counts for ultimate loads is a result of the segregated nature of the ultimate load EE values, as opposed to the more evenly distributed nature of the fatigue load EE values. In fact, unlike ultimate load EE values, a large percentage of significant events result from below-rated wind speed cases because of the higher probability of low-wind-speed conditions. However, the distribution of fatigue load outliers resulting from each turbine QoI is approximately the same as the distribution for ultimate load outliers, with 14.6 % of outliers resulting from the blade-root OoP bending moment and only 4.3 % resulting from the blade-root pitching moment. Note that the QoI (blade-root pitching moment) that contributed the most outliers for ultimate load outliers contributes the least for fatigue load outliers.

EE-value histograms of blade-root bending ultimate moment. Each graph shows one wind speed bin and includes all input parameters. Right column is a zoomed-in view of the left column.

EE-value histograms of blade-root OoP bending fatigue moment. Each graph shows one wind speed bin and includes all input parameters. Right column is a zoomed-in view of the left column.

Primary input parameters contributing to ultimate load sensitivity of each QoI. Values indicate how many times the variable contributes to the sensitivity count.

Primary input parameters contributing to fatigue load sensitivity of each QoI. Values indicate how many times the variable contributes to the sensitivity count.

EE-value exceedance probability plots for the blade-root bending
ultimate moment

The behavior of blade-root loads are examined in more detail by plotting
exceedance probability distinctly for each input parameter in
Fig. 18. Highlighted in these plots is the
contribution of the individual input parameters to the outlier counts. For
blade-root bending ultimate moment EE values, blade twist and

For each QoI, the number of times each input parameter contributed to the significant event count was tallied. The top parameters are shown in Tables 12 and 13 for ultimate and fatigue loads, respectively. Overall, 63 % of the top sensitive parameters for both ultimate and fatigue loads are due to aerodynamic perturbations or yaw error. Blade-root and main shaft moments are especially sensitive to perturbations of inputs. However, blade mass imbalance and blade mass account for 44 % of the most sensitive parameters associated with tower moment fatigue loads. Rotor torque ultimate and fatigue loads are most sensitive to perturbation of structural input parameters, especially those related to blade mass. For both ultimate and fatigue loads, electrical power is most sensitive to blade mass imbalance, blade mass factor, and yaw error. These results can be used in future sensitivity analysis work to focus on perturbation of specific input parameters based on desired turbine loads.

A screening analysis of the most sensitive turbulent wind and aeroelastic parameters to the resulting structural loads and power QoI was performed for the representative NREL 5 MW wind turbine under normal operating conditions. The purpose of the study was to assess the sensitivity of different turbulent wind and turbine parameters on the resulting loads of the wind turbine. The sensitivities of the different parameters were ranked. The study did not consider specific site conditions but rather focused on understanding the most sensitive parameters across the range of possible values for a variety of sites.

To limit the number of simulations required, a screening analysis using the EE method was used instead of a more computationally intensive sensitivity analysis. The EE method is an assessment of the local sensitivity of a parameter at a given location in space through variation of only that parameter, examined over multiple points throughout the parameter hyperspace, making it a global sensitivity analysis. This work modified the general EE formula to examine the sensitivity of parameters across multiple wind speed bins. A radial version of the method was employed, using Sobol numbers as starting points, and a set delta value of 10 % for the parameter variations. The most sensitive input parameters were identified using the EE value threshold.

Two independent case studies were performed. For the wind parameter case
study, it was found that the loads and power are highly sensitive to the
shear and turbulence levels in the

The aeroelastic parameter case study showed that the loads and power are highly sensitive to the yaw error and the lift distribution at the outboard section of the blade. To a lesser extent, turbine loads are sensitive to blade twist distribution, lift distribution at the inboard section of the blade, and blade mass imbalance. Additionally, ultimate load EE values are typically separated by wind speed bin, whereas fatigue load EE values are more evenly distributed across wind speed bins.

Through the implemented EE method, different combinations of input parameters have been used. When specific input parameters are shown to be sensitive to one or more turbine loads, it is possible that only certain combinations of the input parameters will result in this sensitivity. This leads to opportunities for future work to further investigate which parameter combinations lead to higher turbine sensitivity. In future work, this ranking of most sensitive parameters could be used to help establish uncertainty bars around predictions of engineering models during validation efforts and provide insight into probabilistic design methods and site-suitability analysis. Although the most sensitive ranking results may depend on the turbine size or configuration, the analysis process developed here could be applied universally to other turbines. This work could also be further expanded in future work to include load cases other than normal operation.

While this study sought to minimize computational expense, hundreds of thousands of simulations were run to perform the analysis. The models that the work is based on are publicly available through the National Wind Technology Computer-Aided Tools website (

To identify which parameters are the most sensitive, some researchers compare the average of the EE values for the different parameters across all input starting points. Additionally, some look at the standard deviation of the EE values for a given parameter across the different starting points. This helps to identify large sensitivity variation at different points, indicating strong interaction with the values of other parameters. As commonly found in EE-related literature, EE analysis typically identifies the most sensitive parameters using a plot to pictorially show the standard deviation versus mean values of the EE values. However, it is difficult to systematically identify the most sensitive parameters using this approach.

The mean of the absolute EE value for the ultimate loads for each QoI with
input parameter

This is shown in Figs. A1 and A2 for the blade-root bending ultimate
moment and the blade-root bending OoP fatigue moment metrics for both the
wind parameter and turbine parameter case studies, respectively. Shown in
Fig. A1 is the large sensitivity of shear in the
lowest wind speed bin and the large sensitivity of the

EE standard deviation versus EE mean for blade-root bending
moment ultimate load

EE standard deviation versus EE mean for blade-root bending
moment ultimate load

Exceedance probability plot of ultimate load EE values for each of the wind-inflow parameter QoIs across all wind speed bins, input parameters, and simulation points. Black line represents the defined threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

Exceedance probability plot of fatigue load EE values for each of the wind-inflow parameters across all wind speed bins, input parameters, and simulation points. Black line represents the defined threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

EE-value exceedance probability plots of ultimate loads for aeroelastic turbine parameters, across all wind speed bins, input parameters, and simulations points for all QoIs. The black line represents the defined threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

EE-value exceedance probability plots of fatigue loads of aeroelastic turbine parameters across all wind speed bins, input parameters, and simulations points for all QoIs. The black line represents the defined threshold by which outliers are counted for each QoI. Color indicates wind speed bin (blue is below-rated speed, red is near-rated speed, green is above-rated speed).

JJ provided the conceptualization and supervision for this project. ANR developed the EE methodology approach used within both parameter studies. KS led the investigation of the wind turbine property sensitivity study, and LS led the investigation of the wind characteristics study. ANR and KS prepared the article, with support from JJ and LS.

The authors declare that they have no conflict of interest.

The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government.

This work was authored by Alliance for Sustainable Energy, LLC, the manager and operator of the National Renewable Energy Laboratory for the U.S. Department of Energy (DOE) under contract no. DE-AC36-08GO28308.

This research has been supported by the U.S. Department of Energy, National Renewable Energy Laboratory (contract no. DE-AC36-08GO28308). Funding was provided by the Department of Energy Office of Energy Efficiency and Renewable Energy, Wind Energy Technologies Office.

This paper was edited by Michael Muskulus and reviewed by Imad Abdallah and two anonymous referees.