Sensitivity Analysis of Turbine Fatigue and Ultimate Loads to Wind and Wake Characteristics in a Small Wind Farm

. Wind turbines are designed using a set of simulations to determine the fatigue and ultimate loads, typically focused solely on unwaked wind turbine operation. These structural loads can be signiﬁcantly inﬂuenced by the wind inﬂow conditions. When placed in the wake of upstream turbines, turbines experience altered inﬂow conditions, which can additionally inﬂuence the fatigue and ultimate loads. It is important to understand the impact of uncertainty on the resulting loads of both non-waked and waked turbines. The goal of this work is to assess which wind-inﬂow-and wake-related parameters have the 5 greatest inﬂuence on fatigue and ultimate loads during normal operation for turbines in a three-turbine wind farm. Twenty-eight wind inﬂow and wake parameters were screened using an elementary effects sensitivity analysis approach to identify the parameters that lead to the largest variation in the fatigue and ultimate loads of each turbine. This study was performed using the National Renewable Energy Laboratory (NREL) 5 -MW baseline wind turbine, simulated with OpenFAST and synthetically generated inﬂow based on the International Electrotechnical Commission (IEC) Kaimal turbulence spectrum with IEC 10 exponential coherence model using the NREL tool TurbSim. The focus was on sensitivity to individual parameters, though interactions between parameters were considered, and how sensitivity differs between waked and non-waked turbines. The results of this work show that for both waked and non-waked turbines, ambient turbulence in the primary wind direction and shear were the most sensitive parameters for turbine fatigue and ultimate loads. Secondary parameters of importance for all turbines were identiﬁed as yaw misalignment, u-direction integral length, and the exponent and u components of the IEC co-15 herence model. The tertiary parameters of importance differ between waked and non-waked turbines. Tertiary effects account for up to 9 . 0% of the signiﬁcant events for waked turbine ultimate loads and include veer; non-streamwise components of the IEC coherence model; Reynolds stresses; wind direction; air density; and several wake calibration parameters. For fatigue loads, tertiary effects account for up to 5 . 4% of the signiﬁcant events and include vertical turbulence standard deviation; lateral and vertical wind integral lengths; non-streamwise components of the IEC coherence model; Reynolds stresses; wind direction; 20 and all wake calibration parameters. This information shows the increased importance of non-streamwise wind components and wake parameters in fatigue and ultimate load sensitivity of downstream turbines.


Introduction
When examining the feasibility of a wind farm design for a desired location, simulation models are run to assess the loading that the turbines will encounter given the conditions of that site. These simulation models include a large number of parameters 25 to try to represent the complex conditions the turbine will encounter, and many times much of this wind characterization is not available. It is therefore useful to identify those parameters that have the most significant influence on the load response, to prioritize measurement campaigns and analysis studies. The focus of this paper is to identify those parameters that have the most influence on the load responses of wind turbines when situated in a farm environment. This paper builds off our previous work and case studies related to the sensitivity of loads on a single wind turbine in 30 isolation. Our first study focused on assessing the sensitivity of wind inflow parameters on a single turbine (Robertson et al. (2019)). To perform this work, a sensitivity analysis methodology was developed, which employs elementary effects (EE) to provide a sensitivity estimate, requiring significantly fewer simulations than a full sensitivity analysis. For more information on why this method was chosen, including a review of other methods and the benefits and drawbacks of the EE method, see Robertson et al. (2019). This EE-based sensitivity approach has been employed in all subsequent studies, including the 35 one considered in this paper. The single turbine inflow study found that the primary parameters of importance to the fatigue and ultimate loading of the NREL 5-MW baseline wind turbine under normal operation were turbulence in the primary wind direction and shear, followed by veer, u-direction integral length, and exponent and u components of the IEC coherence model.
The second case study focused on assessing the sensitivity of the aerodynamic parameters of the wind turbine blades, such as lift and drag coefficients as well as unsteady aerodynamic parameters ). This study found the primary 40 parameters of importance to be blade twist and lift coefficient distributions (both outboard and inboard), followed by the maximum lift coefficient location, blade chord length, and drag coefficient distributions. The most recent study built upon the blade aerodynamics study to include additional turbine properties such as blade-mass and pitch imbalance, blade and tower center-of-masses, and stiffness and damping uncertainty, on the wind turbine loads (Robertson et al. (2019)). This study found the primary parameters of importance to be yaw misalignment and outboard lift coefficient distribution, followed by inboard 45 lift distribution, blade-twist distribution, and blade mass imbalance.
To perform these case studies, an extensive literature review was conducted to identify the appropriate parameters to study and bounds over which to vary them. Refer to Robertson et al. (2019) to learn about previous efforts in the sensitivity of loads in wind turbines based on wind and aeroelastic parameters. Building off the methods and findings from these previous studies, the work in this paper assesses how waked turbine fatigue and ultimate load sensitivity differs from that of unwaked 50 turbines for varying wind inflow and wake conditions. Many other studies that have been conducted to understand loads on downstream turbines, with researchers in wide agreement that those in the wake of upstream turbines will have higher loads than the upstream ones. Additionally, wind farm sensitivity analysis studies have been conducted for cost modeling and optimization purposes (Rezaei et al. (2020); Diaz et al. (2020); Martin et al. (2016); Dykes et al. (2014)) and well as wind farm power (?Tautz-Weinert et al. (2019)). These papers tend to focus on the wind farm as a whole and do not distinguish between 55 waked versus non-waked turbine impact. However, the authors were unable to find research regarding the sensitivity of how downstream turbine loads differ based on the wind and aerodynamic parameters.
In this work, the inflow study that was previously conducted for a single turbine is expanded to include several turbines in a small wind farm. Additionally, parameters that effect the wind turbine wake evolution, such as yaw misalignment and model parameters that change wake evolution, were included. An additional wind inflow parameter, air density, was also added. This work aims to highlight the relative importance of inflow and wake parameters for fatigue and ultimate load sensitivity. This is accomplished by developing metrics to assess the sensitivity of several turbine load measurements, and assessing how this sensitivity changes with varying inflow and wake conditions. The sensitivity is assessed using the EE method developed in the first case study, considering a wide range of possible wind inflow and wake conditions. From these sensitivity values, a threshold is used to determine when a sensitivity value is classified as a "significant event". From this, the number of "significant events" triggered by varying each parameter are analyzed, along with which aeroelastic quantities of interest (QoI) are most effected. The results from this work can be used to better inform not only the turbine design process and site-suitability analyses, but also help identify important measurement quantities when designing wind farm experiments.

Approach and Methods
To identify the inflow wind and wake parameters that structural loads of waked and unwaked utility-scale wind turbines are 70 most sensitive to, a sensitivity analysis based on an EE methodology is used. The procedure is summarized in the following section. However, there are several caveats to this work that must be noted. First, only the NREL 5-MW reference turbine was considered. Thus, this study does not examine the dependency of the sensitivity findings on the size and design of the turbine. Secondly, only normal turbine operation was considered; gusts, start-ups, shutdown, and parked or idling events were not included, which can often lead to the high loading experienced by a turbine. Thirdly, input parameter variation was done 75 independently, with no joint-probability functions or conditioning based on any parameter other than wind speed. Developing joint-probability distributions across the large number of parameters considered was not feasible. And finally, only three laterally aligned turbines are considered, as opposed to a more extensive wind farm, so some wind farm effects such as deep array effects are not present. Despite these caveats, this work still provides insight into the sensitivity of fatigue and ultimate loads based on the variation of a wide range of wind inflow and wake conditions.

Wind Turbine Model and Tools
The sensitivity study was performed considering a small wind farm with three laterally aligned NREL 5-MW reference wind turbines (Jonkman et al. (2009)) separated by 7 rotor diameters in the zero-degree wind direction, as shown in Figure 1.
Parameter sensitivity was assessed using simulations from FAST.Farm, a multi-physics engineering tool that accounts for wake interaction effects on turbine performance and structural loading in wind farm applications based on advancements to the 85 Dynamic Wake Meandering (DWM) model. FAST.Farm is an extension of the NREL software OpenFAST, which solves the aero-hydro-servo-elasto dynamics of individual turbines (OpenFAST; Jonkman and Shaler (2020)).
Each wind turbine was modeled in OpenFAST, using the NREL 5-MW reference turbine as a representative turbine. This is an upwind three-bladed horizontal-axis turbine with a 90 m hub height, and 126 m rotor diameter. AeroDyn, the aerodynamic module of OpenFAST, was applied to calculate the aerodynamic loads on the rotor using blade-element momentum (BEM) 90 theory with advanced corrections, including unsteady aerodynamics. ElastoDyn, a combined multi-body and modal structural approach that includes geometric nonlinearities, was used to represent the flexibility of the blades, drivetrain, and tower. (Elas- Past work has shown that the sensitivity of loads to input parameter variation is influenced by the wind speed and associated wind turbine controller response (Robertson et al. (2019)). Therefore, this study considered three different wind speeds at mean hub height wind speeds of 8, 12, and 18 m/s, representing below-, near-, and above-rated wind speeds, respectively. Wind inflow was synthetically generated using TurbSim (Jonkman (2014)), which creates time-varying two-dimensional turbulent 100 flow fields that are convected through the domain using Taylor's frozen turbulence hypothesis. Turbulence was simulated using the Kaimal turbulence spectrum with an exponential coherence model. TurbSim generation involves two stages of simulations, one each for the low-resolution and high-resolution domains of FAST.Farm and using the suggested FAST.Farm discretization recommendation (Jonkman and Shaler (2020)). The low-resolution TurbSim domain throughout the wind farm had a spatial resolution of 10, 20, and 25 m for the below-, near-, and above-rated wind speeds, respectively, and a temporal resolution of 105 0.1 seconds to match the suggested high-resolution FAST.Farm discretization. A high-resolution TurbSim domain around each wind turbine was then generated for each turbine, derived from the hub height time series extracted from the low-resolution TurbSim domain with a spatial resolution of 5 m and temporal resolution of 0.1 seconds. Many turbulence seeds were used for each input parameter variation to ensure any variation in results was independent of the selected turbulent seed. The number of seeds was determined via a seed convergence study that considered each QoI. The generated inflows were used as input to 110 FAST.Farm using a simulation time of 600 seconds after an initial 600 seconds transient period was removed.

Case Study Description
In previous case studies (Robertson et al. (2019)), ambient wind-inflow parameters were identified that significantly influence the loading of a single wind turbine. This study extends that work to identify the inflow and wake parameters most influencing downstream wind turbines in a small wind farm. The ambient wind inflow input parameters were selected to be the same 115 ones used in our previous work (Robertson et al. (2019)). Additional wake parameters were added that relate to turbine wake  Many QoIs were identified, as detailed in Table 1, including the blade, tower, and drivetrain moments; blade-tip displacement; rotor power; and inflow turbulence intensity (TI) of each turbine. Inflow TI, which is often related to fatigue loads, was 120 computed using Equation 1 (where t is the turbine number) and treated in the sensitivity assessment as if it were a fatigue load.
The total wind farm electrical power, which is important of cost of wind energy, was treated in the sensitivity assessment as if it were an ultimate load.
The fatigue loads were calculated using aggregate damage-equivalent loads (DEL) of the QoI response across all turbulence 125 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 listed components. The ultimate loads were calculated using the average of the global absolute maximums across all turbulence seeds for a given set of parameter values. See Robertson et al. (2019) for more details on the fatigue and ultimate loads calculations. All quantities associated with electrical power and inflow TI were excluded from the significant event count, but were examined for other purposes. The QoI sensitivity of each input parameter was examined using 130 the procedure summarized in Section 3.

Elementary Effects Procedure
An EE method (Gan et al. (2014); Martin et al. (2016); Saranyasoontorn and Manuel (2006)) was used to assess which parameters have the largest influence on turbine loads. This is a simple methodology for screening parameters, based on a one-at-a-time approach where each parameter is varied independently while all other parameters remain fixed. In this way, the EE method 135 is a local sensitivity approach because the influence of a single parameter is calculated without considering interaction with other parameters. The change in response QoIs based on the change in the input parameter was used to compute a derivative, which together with the possible range of the input parameter variation was used to assess the sensitivity of the parameter. This variation and derivative computation was performed several times for each parameter at different points in the hyperspace of all input parameters, as shown in Figure 3. In this way, the EE approach used in this work is considered a global sensitivity When considering the EE method, each wind turbine QoI, Y , was represented as a function of different characteristics of the inflow and wake input parameters, U, as follows: where I is the total number of input parameters. For a given sampling of U, the EE value of the ith input parameter was found by varying only that parameter by a normalized amount, ∆: Because of the normalization of U, clarified below, the EE value (EE i ) can be thought of as the local partial derivative of the output (Y ) with respect to an input (u i ), scaled by the range of that input. Thus, the EE value has the same unit as the output QoI.

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In a radial sensitivity approach, the EE value is calculated for all input parameters at a given point, R, in the parameter hyperspace by varying each parameter individually from that point. A representative schematic of this approach is depicted in Figure 3. Each variation is performed for ±10% of the range over which the parameter may vary (∆ = ±0.1). This ±10% range (∆ = ±0.1 normalized or ∆ ib = ±0.1u ib,range dimensional) is used to ensure the finite difference calculation occurs over an appropriate range to meet the linearity assumption required by this method. Note that this is different than the original 160 EE methodology, which creates a trajectory by varying each new parameter from the ∆ point of the previous parameter. This process is repeated for R starting points in the input parameter hyperspace (blue points in Figure 3), creating a set of R different calculations of EE value for each parameter. The R starting points are determined using Sobol numbers (blue circles in Figure 3), which ensures a wide sampling of the input hyperspace.
Because EE value is analogous to a sensitivity level, a higher value for a given input parameter indicates more sensitivity.

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Here, the most sensitive parameters were identified by defining a threshold value, above which an individual EE value would be considered significant. The threshold was set individually for each QoI and turbine and defined as EE r + 2σ. Here, EE r was the mean of all EE values across all starting points R, inputs I, and wind speed bins B for each QoI and σ was the standard deviation of these EE values.

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A total of 28 input parameters represented the wind-inflow and wake conditions, considering the mean wind profile, velocity spectrum, spatial coherence, component correlation, and wake parameters, as summarized in Table 2. The wind inflow parameters were detailed in previous work (Robertson et al. (2019)). Wind direction was used to essentially introduce lateral offset distances for downstream turbines, with zero degrees direction indicating flow directly down the row of turbines. Wind direction was simulated by changing the locations of the wind turbines in the FAST.Farm simulations. This way, the same inflow 175 turbulence files could be used for various wind direction values. Changing the wind direction does not result in a mean yaw misalignment of the wind turbines; the yaw misalignment is considered in independent parameter. Air density was specified in AeroDyn and represents the change due to temperature or humidity variations. Yaw misalignment was specified by rotating the nacelle-yaw angle of each wind turbine individually in ElastoDyn. Wake calibration parameters are FAST.Farm user-specified parameters that modify wake dynamics evolution and meandering. C N earW ake adjusts the wake deficit and expansion correc-180 tion for the otherwise neglected pressure gradient zone directly behind the rotor in the near wake. C M eander influences the spatial averaging used to calculate how the wake meanders and specifically defines the cut-off wave number for the spatial filter.
k vAmb and k vShr modulate the relative contribution of the ambient turbulence and wake shear layer to the eddy viscosity. f c defines the cutoff frequency for the low-pass time filter used in the wake evolution model to ensure high-frequency fluctuations do not pass into the quasi-steady wake-deficit increment model.

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To understand the sensitivity of a given parameter, a range over which that parameter may vary must be defined, as summarized in Tables 3 and 4. A literature search was done to identify the range for each of the parameters across varying onshore installation sites, with additional details provided in Robertson et al. (2019). 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 for all bins. Many of these ranges were chosen based on our previous study (Robertson et al. (2019)). Air density ranges were based on the work 190 of (Ulazia et al. (2019)) and represents the changes due to temperature or humidity variations. The wind direction was chosen based on the work of Gaumond et al. (2014), which looked at wind direction uncertainty in experimental measurements. Yaw misalignment ranges were based on the work of Quick et al. (2017). For the wake parameters, ranges were chosen based on a calibration study used to determine the default FAST.Farm parameters (Doubrawa et al. (2018)).

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The EE value was calculated for each of the 28 input parameters ( line were included in the significant events tally, discussed next. From these plots, it was seen that the shear exponent heavily dominates the results, especially for the below-rated wind conditions. This was seen in previous work (Robertson et al. (2019)) Table 3.
Wind inflow parameter ranges separated by wind speed bin. The nominal value prescribed by IEC for category B turbulence is specified in the "IEC" row.
Below-Rated Wind Speeds   Unique symbols are used for parameters that primarily contributed to the significant events count. The vertical lines on each plot correspond to the threshold value used to identify significant events. and was largely due to the sizeable range considered for this value. These plots also demonstrate the differences in EE values across wind turbines. For instance, the maximum EE value for ultimate loads at below-rated was due to the shear parameter for all turbines. However, this EE value was 32% higher for WT3 compared to the value for WT1, thus demonstrating the potential 215 differences in parameter importance for waked conditions.
To identify the most sensitive parameters, a tally was made of the number of times an EE value exceeded the threshold for each QoI. The resulting tallies are shown in Figure 5, with the ultimate load tally on the left (a, c) and the fatigue load tally on the right (b, d). The top figures (a, b) show the cumulative values for each turbine. These results indicate substantial sensitivity to the u-direction turbulence standard deviation (σ u ) and vertical wind shear (α) for all wind turbines. These results were 220 expected based on our past studies (Robertson et al. (2019)) and the parameters of importance in the IEC design standards.
Considering the lower tally values in this plot highlights the secondary level of importance of yaw misalignment (Θ T 1,T 2,T 3 ), streamwise u-direction integral length (L u ), u-direction components of the IEC coherence model (a u and b u ), and the IEC coherence model exponent (γ). As expected, wake calibration parameters have no effect on the unwaked turbine, but do appear with significant events for the waked turbines. Additional insights shown here that were not seen in the previous study was the 225 changing effect of yaw misalignment for downstream turbines. Results for each turbine show high sensitivity to that turbine's yaw misalignment. However, there was little to no dependence on the yaw misalignment of other turbines. It was expected that the yaw misalignment of a downstream turbine would not effect an upstream turbine result, but less expected that the reverse was not also true; i.e., that the yaw misalignment of an upstream turbine has little to no effect on the sensitivity of the turbine directly downstream of it considering recent work on wake steering in the wind energy community. There was a 230 slight effect of Θ T 2 on WT3, but this effect was minimal, especially relative to the effect of Θ T 3 on WT3. The primary and secondary importance parameters were the same for fatigue and ultimate loads, as well as for each turbine, with WT1 results being consistent with the results in Robertson et al. (2019). The distinction between "primary", "secondary", and "tertiary" parameters of importance were mostly made by visually inspecting the significant count results.
However, the relative importance of these parameters between fatigue and ultimate loads and between wind turbine does 235 change, as shown in Figures 5(c) and 5(d). Here, the differences between the waked and non-waked turbine response were explored by showing the difference in the percentage a certain parameter makes up of the total number of significant event counts for that turbine, relative to WT1. These values were computed using Equation 5, where t = 2 or 3, and i was the input parameter being varied.
The percent difference results show when input parameters lead to a higher or lower percentage of significant events counts in waked turbines, relative to the non-waked turbine. For ultimate loads, WT2 and WT3 show reduced sensitivity for many of the input parameters, but also increased sensitivity for parameters that show little to no significance for the non-waked turbine, such as lateral wind components and wake parameters. Similar results were seen for fatigue results. From here, tertiary effects can be identified for waked turbines. Tertiary effects for ultimate loads show the importance of veer (β), non-streamwise components 245 of the IEC coherence model (a w and b v ), Reynolds stresses (P C uv ,P C uw , and P C vw ), wind direction (WD), air density (ρ), and several wake calibration parameters (C M eander , k ν,Amb , k ν,Shr , and f c ). For WT1 and WT2, these tertiary parameters accounted for 3.2% and 3.6% of the total significant events count, respectively, and nearly triple that for WT3, with 9.0% of the significant events resulting from tertiary parameters. This suggests that the importance of these other parameters would likely grow if additional wind turbines where added to the wind farm. Tertiary effects for fatigue loads show the importance 250 of vertical turbulence standard deviation σ w , lateral and vertical wind integral lengths (L v and L w ), lateral and vertical wind components of the IEC coherence model (a w , b v , and b w ), Reynolds stresses (P C uw and P C vw ), wind direction (WD), and all wake calibration parameters (C N earW ake , C M eander , k ν,Amb , k ν,Shr , and f c ). For WT1, these tertiary parameters accounted for 4.1% of the total significant events count. For WT2 and WT3, this percentage increases to 5.4% and 5.3% of the significant events, respectively. These results indicate the increased influence of non-streamwise inflow components, including wake 255 meandering, in fatigue and ultimate loads sensitivity of waked turbines. Table 5. Percentage of contribution to total number of significant events for fatigue and ultimate loads. Cells are colored by the percentage value, with darker blue representing a higher percentage. This point was further made by comparing the percentage of contribution to the total number of significant event for fatigue and ultimate loads for each turbine, shown in Table 5. These results show that most of the tertiary parameters contribute at least twice as much to the significant events count for waked turbines, compared to unwaked turbines. This indicates that, though still tertiary parameters, fatigue and ultimate loads of waked turbines were generally twice as sensitive to non-streamwise 260 inflow components.
Histogram plots of blade-root pitching moment EE values are shown in Figures 6 and 7 for ultimate and fatigue loads, respectively. These figures show EE value histograms showing the contribution from all input parameters, with wind speed bins and turbines shown in separate subplots. Here, tertiary parameters are highlighted in bright colors to better recognize when they contribute to the significant event count. For ultimate loads, the distribution of outliers were consistent across the 265 turbines, with most outliers occurring at below-rated wind speeds. Tertiary effects do, however, occur the most for WT3, in particular at above-rated wind speeds. Similar results were seen for the fatigue load results in Figure 7, with overall distributions remaining consistent across the turbines, but tertiary effects occurring the most for WT3 and near-rated wind speeds.  To further investigate which QoI were influenced by the input parameters,  Table 7 for fatigue loads. For all turbines, the top three QoIs that contribute to load sensitivity were tower-top bending, tower-top yaw moment, and low-speed shaft bending, though the exact ranking was different for all turbines. For each turbine, 14-18% of the significant events resulting from these load channels. The frequency with which QoIs triggered significant events 275 differs, as summarized in Figure 8, which shows the percent difference in significant event counts for WT2 and WT3 relative to WT1 as calculated by Equation 5, but based on QoI instead of input parameter. For WT2, the most differences occur for blade-root pitching moment, reduced by 1.5% and tower-top yaw moment, increased by 1.8%. For WT3, the most differences occur for tower-base bending moment, reduced by 3.3%, and shaft bending moment, increased by 2.6%. Similar results were seen for fatigue results, though to a lesser extent.

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When looking only at the contribution of tertiary parameters in Tables 6(b) and 6(c), blade-root pitching moment stands out the most for all turbines, though nearly twice as much for WT3 compared to WT1. Overall, WT3 loads were up to 8× more sensitive to tertiary parameter variation as compared to WT1, with this highest increase occurring for low-speed shaft bending ultimate loads. Tower-top bending, tower-top yaw moment, and low-speed shaft bending contributed the most to load sensitivity for all turbines. Though the top QoIs were the same, the exact ranking and amount of events differed. 285 Table 7 shows tabulated results for the number of fatigue load significant events for each input parameter, separated by QoI. For all turbines, the top three QoIs that contribute to load sensitivity were blade-root in-plane bending, low-speed shaft 0 • bending, and low-speed shaft 90 • bending. For each turbine, 26-28% of the significant events resulting from these load channels. The QoI that were most sensitive for WT1 were in-plane blade-root moment and low-speed shaft bending. For

Tower-Top Yaw
Tower-Base Bend.

Generator Power
waked turbines, the most sensitive QoIs were in-plane blade-root bending moment, inflow TI, and 0 • low-speed shaft bending.

Tower-Top Yaw
Tower-Base FA Bend.
Tower-Base SS Bend.

Generator Power
This work aimed to highlight the relative importance of inflow and wake parameters for fatigue and ultimate load sensitivity.
This was accomplished by developing metrics to assess the sensitivity of several turbine load measurements, and assessing 295 how this sensitivity changes with varying inflow and wake conditions. The sensitivity was assessed using an EE method, considering a wide range of possible wind inflow and wake conditions. From these sensitivity values, a thresholding method was used to determine when a sensitivity value was classified as a "significant event". From this, the number of "significant events" triggered by varying each parameter was analyzed, along with which aeroelastic QoI were most effected. The results from this work can be used to better inform not only the turbine design process and site-suitability analyses, but also help 300 identify important measurement quantities when designing wind farm experiments.
The results of this work show that for both waked and non-waked turbines, ambient turbulence in the primary wind direction and shear were the most sensitive parameters for turbine fatigue and ultimate loads. Secondary parameters of importance for all turbines were identified as yaw misalignment, u-direction integral length, and u components of the IEC coherence model, as well as the exponent. The tertiary parameters of performance differ between waked and non-waked turbines. Tertiary effects 305 for ultimate loads of waked turbines were veer; non-streamwise components of the IEC coherence model; Reynolds stresses; wind direction; air density; and several wake calibration parameters, with these tertiary effects accounting for up to 9.0% of the significant events for waked turbines. For fatigue loads, the tertiary effects of waked turbines were the vertical turbulence standard deviation; lateral and vertical wind integral lengths; lateral and vertical wind components of the IEC coherence model; Reynolds stresses; wind direction; and all wake calibration parameters, with these tertiary effects accounting for up to 5.4% of 310 the significant events of waked turbines. This information shows the increased importance of non-streamwise wind components and wake parameters in fatigue and ultimate load sensitivity of downstream turbines. Additionally, the most effected QoIs differed between waked and unwaked turbines.
Author contributions. KS led the investigation. ANR developed the EE methodology approach used in the parameter study. JJ provided the conceptualization and supervision for this project. KS prepared the article, with support from ANR and JJ.
not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.
The research was performed using computational resources sponsored by the Department of Energy's Office of Energy Efficiency and Renewable Energy and located at the National Renewable Energy Laboratory.