Explaining the decline of US wind output power density

US wind power generation has grown significantly over the last decades, in line with the number and average size of operating turbines. However, wind power density has declined, both measured in terms of wind power output per rotor swept area as well as per spacing area. To study this effect, we present a decomposition of US wind power generation data for the period 2001–2021 and examine how changes in input power density and system efficiency affected output power density. Here, input power density refers to the amount of wind available to turbines, system efficiency refers to the share of power in the wind flowing through rotor swept areas which is converted to electricity and output power density refers to the amount of wind power generated per rotor swept area. We show that, while power input available to turbines has increased in the period 2001–2021, system efficiency has decreased. In total, this has caused a decline in output power density in the last 10 years, explaining higher land-use requirements. The decrease in system efficiency is linked to the decrease in specific power, i.e. the ratio between the nameplate capacity of a turbine and its rotor swept area. Furthermore, we show that the wind available to turbines has increased substantially due to increases in the average hub height of turbines since 2001. However, site quality has slightly decreased in this period.

ρ air density, constant value of 1.225 kg m −1 is used R loss factor to account for wake effects, downtime and other losses P in power input of all turbines (at hub height) P in,refh,avg wind power at a reference height assuming long-term average wind conditions P in,avg wind power at hub heights assuming long-term average wind conditions

Introduction
Wind power generation has been expanding rapidly in the US in the past two decades. Between 2001 and 2021, the number of operating turbines increased fivefold (see section 3). At the same time, new wind turbine models with larger hub height, rotor swept area and capacity were deployed (see figures 1(a)-(c)), which also contributed to more wind power being generated. However, while total output increased, output power density declined. Output power density can be measured in terms of power output per rotor-swept area or per spacing area. Miller and Keith [1,2] have shown a decline in power output per spacing area, implying higher land requirements for wind power, while we show here that power output per rotor swept area also declined.
We explore the factors which contributed to the decline in output power density. In particular, we assess how input power density, i.e. the wind available to turbines, changed-due to new location choices, but also due to the increase in average hub heights. Furthermore, we assess the contribution of system efficiency to the decrease in output power density. System efficiency measures how much of the wind available to turbines is converted to electricity. One main factor determining system efficiency is the specific power of turbines, i.e. the ratio of nameplate capacity to rotor swept area: a decrease in the average specific power of turbines will decrease, everything else equal, system efficiency. The relation between specific power and system efficiency is illustrated in figure 2. Wind power generation of a single turbine at a certain point in time is capped by its rated capacity. Therefore, turbines with lower specific power inevitably use less of the available wind resources compared to turbines with higher specific power when high wind speeds occur. When comparing turbines with equal rotor Figure 1. Evolution of turbine characteristics: average hub height, capacity and rotor swept area of operating wind turbine models increases over time, but not at the same pace. Specific power, the ratio between capacity and rotor swept area, shows a declining trend. (Data source: USWTDB, see section 6.5. 2) diameter but different capacity, the one with higher capacity and therefore higher specific power has higher power output at high wind speeds.
Specific power has decreased strongly in the US in the recent 20 years (see figure 1(d)), because turbines with lower specific power are economically more profitable for operators [6] and easier to integrate into the system [7]. This development can explain potential decreases in system efficiency.
Here, we therefore assess historic trends in output power density, i.e. how much electric power can be generated per rotor swept area, considering the whole US fleet, to deepen our understanding of declining landuse efficiency of wind turbines. Furthermore, we show how the change in output power density is related to: (a) the change in the wind available to the fleet, measured by power in the wind per rotor swept area (i.e. input power density) and (b) how efficiently the fleet converts the power in the wind to electric power (system efficiency). Furthermore, we decompose the change in input power density into change due to new locations, due to increasing average turbine heights and due to annual variations in wind conditions. To derive those indicators, we introduce a novel decomposition approach, which we apply to the complete US fleet in the period 2001-2021. This allows us to answer (a) if more wind is available to wind turbines compared to previous periods, (b) why wind availability changed, and (c) how the efficiency of converting wind to electric power has evolved over time. It also explains why spacing area requirements of wind turbines have increased recently, as rotor swept area and spacing area requirements are intrinsically related.

Definition of wind power metrics
Here, we first introduce several metrics to conceptualize our understanding of trends in US wind power generation. The yield of wind power generation, i.e. the total generated electric power averaged over a certain period of time for all operating wind turbines in the US, will be denoted as power output or with the symbol P out . Power output is the part of available wind resources which is converted to electricity. Power input P in is the primary energy in wind which is harnessed. It is the total kinetic power of moving air flowing through the rotor swept areas of all operating wind turbines in the US, neglecting disturbances introduced by turbines themselves, e.g. wake effects. For a single wind turbine, power input is proportional to the rotor swept area of the turbine (see appendix A.6.3). Therefore, at fixed turbine heights, turbine locations can be compared by the power input relative to the given area. Total rotor swept area of operating turbines is denoted by A and input power density P A in is the power input normalized by the total rotor swept area. Furthermore, we define output power density as the . At wind speeds above about 8 m s −1 , the Gamesa model has a higher power output. Despite economic advantages of turbine models with lower specific power, higher specific power turbines generate more power per rotor swept area if generated energy can be stored or transmitted. Wind speeds above 8 m s −1 are less likely than lower wind speeds (third panel of the figure), but higher wind speeds play a larger role because wind power depends on the cube of the wind speed. In total, output power density decreases due to the decline of specific power as will be shown in the following. (Data sources: power curve model [3], ERA5 [4] bias-corrected with GWA2 [5], see also section 6.5). amount of generated electric power per unit of rotor swept area P A out . Note that A can be interpreted as the total size of the wind power fleet which is linked to land use requirements and impacts, because both length of turbine blades of turbines and number of operating turbines contribute to it.
With system efficiency we denote the share of power input converted to electricity, i.e. the ratio of power output and power input P P out in . System efficiency is bound by the Betz' limit and results from different influencing factors, such as mechanical and technical efficiency, but also system effects such as input power density, wakes, curtailing and downtime due to maintenance, as discussed in more detail in section 3.2.
Output power density can be viewed as a combination of input power density and system efficiency: The introduced terminology allows for a multiplicative decomposition of wind power output into the total number of operating turbines, average rotor swept area per turbine, input power density, and system efficiency. Denoting the total number of operating turbines with N, the decomposition can be formally described by In appendix A.1, we show how our decomposition is motivated by the physics behind wind to power conversion for deriving wind power generation from wind speeds. For each of the introduced variables, a time series will be calculated for the period 2001-2021. P in is computed by estimating the kinetic power in wind at all known US wind turbine locations from reanalysis wind speed data which is bias corrected with the global wind atlas. P out uses the wind speed data in combination with a generic power curve model, based on specific power, to derive wind turbine power output for all known turbines in the US (see section 6.2).
However, there are no precise turbine commissioning dates available, but only the year of installation for each turbine, which is why we cannot calculate time series for A and N with a resolution higher than yearly. Additionally wind speeds are subject to large seasonal variations. We therefore define the variables P in , P out , N, and A as yearly aggregated time series for all wind turbines in the US and use them for all further computations. That means the time series P in , P out , N, and A are functions of the year Y.
For Y being the set of all hours in a year and L being the set of all turbine locations, the aggregated time series P in is given by is the kinetic power in wind flowing through the rotor swept area at location l during hour t (see appendix A.1) and b Y,l indicates whether turbine l was already built and operating in year Y (see section 6.1). Due to the coarse resolution of the wind speed data, we assume that wind speed reductions and wake effects caused by the turbines are not reflected in the wind speed data and therefore also not part of P in . Hence, system efficiency relates generated electric power to the theoretically available wind resources, which can be captured by the turbine.
Similarly, ( ) P Y out is the average generated electric power in time period Y of all wind turbines. A power curve model is used to estimate ( ) p v t l out , l and a constant loss correction factor is applied to account for downtime, wakes and other losses not reflected in the power curve or climate data, see section 6.2. Furthermore, in appendix A.2.1 we show all metrics derived when using observed time series for power output instead of simulated generation.
Note that the factors in equation (2), are ratios of averages and not averages of ratios. A ratio of averages can be interpreted as weighted averages (see appendix A.6.1). Output power density and input power density are average power output and input power, weighted by rotor swept area. System efficiency is weighted by power input of each turbine. This means that turbines with larger rotor swept area have a larger influence on the resulting time series, which is not the case for other measures of efficiency, such as the average coefficient of power (see appendix A.6.3).

Results
The growth of wind power generation during the last decades was mostly driven by an increasing number and size of turbines. If only the number of operating turbines had changed, all other factors in equation (2)  Besides number and size of turbines, wind power output is affected by input power density and the system efficiency (see equation (2)). Output power density is the combination of input power density and system efficiency as shown in equation (1). These three characteristics will be analyzed in the following subsections.
Note that a validation of simulated power output with observed data suggests a greater confidence of results in the period after 2009, see section 4 and appendix A.2.1.

Output power density
As expected, generated electric power per rotor swept area, i.e. the output power density, is subject to strong annual variations. In years with high average wind speeds, wind power output is higher than in years with lower average wind speeds. Using long-term average wind power to calculate output power density allows identifying the underlying trends without variations caused by annual changes in wind conditions (see section 6.2). In this scenario, output power density increased from 85.9 W m −2 to 94.9 W m −2 in the period between 2001 and 2009. Since 2009 output power density then dropped to 90.9 W m −2 in 2021 ( figure 4). This implies that in 2021, around 4.2% less power output was generated per unit of rotor swept area than in 2009. Annual variations in output power density due to changes in average wind speeds range from −6.4 W m −2 to 5.6 W m −2 when compared with the scenario using long-term average wind power. Output power density is a combination of two opposing trends (see equation (1)). As shown in the next sections, system efficiency declines, but input power density shows an increase since 2001 and stabilizes after 2009. In combination, additional input power density was able to offset the decrease of system efficiency until 2009, but between 2009 and 2021 the decline of system efficiency prevails.

System efficiency
System efficiency, i.e. the share of power output compared to power input, has declined over the past two decades from 32.3% in 2001 to 28.4% in 2021, with substantial variability between years (figure 5), caused by annually changing wind conditions. Annual variations are eliminated when system efficiency is calculated from power input and power output using long-term average power in the wind. In this scenario, system efficiency decreases 0.14 percentage points per year on average.  System efficiency, as defined here, is subject to various characteristics of wind power generation. Firstly, system efficiency is negatively correlated to input power density. In times of low wind speeds, system efficiency tends to increase, while it tends to decrease in years with high wind speeds. The reason is that the system efficiency of converting power in the wind into electricity is not uniform over the whole range of wind speeds for wind turbines. For low wind speeds, this conversion efficiency is low, it increases with higher wind speeds and decreases again for very high wind speeds. For the US, we find that relatively low wind speeds move the fleet of wind turbines into a more optimal range of the conversion efficiency, while higher wind speeds tend to move the fleet out of that range. This effect is partly explained by temporal and spatial aggregation, as high power input or power output values have a larger impact on the average as defined here (see appendix A.6.1). In conclusion, we find that the system efficiency is lower in wind resource-rich years. The correlation coefficient between yearly aggregated time series of system efficiency and input power density of all turbines is ρ = − 0.935 (see also figure A.9 in the appendix).
Besides input power density, system efficiency is largely affected by specific power. Lower specific power 2 can reduce system efficiency, as it increases the share of the input wind power, which is not converted to electricity by wind turbines compared to a turbine with higher specific power. At the same rotor size, a turbine with a smaller rated capacity but similar slope in its power curve will reach the upper limit of the turbine capacity more often than one with a higher rated capacity-this implies that implicitly, input wind power is curtailed by turbines with a lower specific power. We find that the specific power decreased from 426 W m −2 to 301 W m −2 during 2001-2021 (see figure 1(d)), which is in accordance with other results [6]. Hence, we conclude that the decline of specific power is one of the reasons for lower system efficiency.
Other factors can affect system efficiency too. However, lack of detailed data, and the high correlation between factors prevent us from drawing conclusions on their individual contribution to the change in overall system efficiency. A change in efficiency can be caused by aging effects of turbines, which are not included in our main model. However, we tested if the identified trends in our results changed when adding a aging loss correction factor (see appendix A.4), and our analysis is robust to these changes. Wake effects, curtailment of wind energy, downtime due to maintenance, and downtime due to extreme weather conditions other than wind speeds such as icing or snow also reduce system efficiency. In our computation these effects are assumed to be constant over time and are controlled for by adding a constant loss factor. This assumption is discussed in detail in section 4, section 6.2 and appendix A.2.1.
All other losses can be summarized as technical efficiency, i.e. losses in the electrical generator and transmission or mechanical losses. These losses can be expected to decrease due to technical progress and therefore may partially offset the decline of system efficiency caused by specific power. The extent to which technological progress is correctly identified by our power curve model, is uncertain 3 . Nevertheless, a comparison with reported wind power output confirms our results (see appendix A.2.1). We conclude, that technological progress is either not significant for the declining trend of system efficiency or that it is properly reflected in the used power curve model. This trend is the result of a combination of opposing effects: the effect of higher wind speeds due to larger turbine towers and the effect of new locations with lower wind speeds. In addition, input power density is affected by annual variations of wind speeds at the turbines locations. An additive decomposition was used to quantify these effects (see section 6.4 for further details). Figure 6(b) shows the decomposition.

Input power density
As expected, the growth of average hub heights has a positive effect on input power density. Since 2001 an increase of 98.2 W m −2 can be attributed to higher wind turbines, i.e. input power density would have increased by that amount if only hub heights changed. At the same time the deployment of turbines at locations with less wind resources, compared at the same reference height, had a negative effect on input power density. Between 2001 and 2021, input power density would have decreased by 52.4 W m −2 if only changes due to new locations were considered. This result is, however, sensitive to the data set used for wind speed bias correction: the trend is clear when using 50 m and 100 m wind speeds from the global wind atlas, but vanishes once the 200 m version is 2 Specific power is the ratio between the nameplate capacity, i.e. the size of the generator, and the rotor swept area of a wind turbine. 3 Specific power is a parameter in the power curve model we use and due to the strong correlation between time and specific power, in average modern turbine models have a lower specific power. As the power curve model is estimated from existing power curves using a regression model, a lower specific power may implicitly imply a higher technical efficiency as mainly newer turbines will be used in the estimation. As this is implicit, we cannot understand to which extent technological progress is included in our computation of system efficiency.

Discussion
The rotor swept area indicates the spacing area necessary in-between turbines, and thus the size of land necessary for deploying a wind park. If the distance between turbines required to reduce wake effects to an acceptable level is proportional to the rotor diameters, the total rotor swept area is also proportional to the spacing area if effects at the borders of wind parks are neglected. A simplified rule of thumb based on rotor sizes is often used to estimate spacing area requirements: it is assumed that a spacing of 7-12 times the rotor diameter in prevailing wind direction and 2-5 times the rotor diameter in the perpendicular direction between wind turbines has to be guaranteed [3,8,9], pp. 76, 77, [10], p. 423. Lower distances will increase losses due to wake effects too much. Hence, output power density can be used as proxy for land use requirements for wind power generation.
Miller and Keith showed that power output per land area decreased from 0.93 W m −2 in 2010 to 0.90 W m −2 in 2016 [1,2]. The decline in output power density identified by us is in accordance with their results. In figure  A.2, we show a direct comparison of Miller and Keith to our results by assuming a fixed ratio between rotor diameter to the spacing between turbines in prevailing wind direction and perpendicular to it. In addition to confirming the results by Miller and Keith and extending their analysis for a longer time period, we furthermore deepen our understanding of the reasons for increasing land-use requirements: falling system efficiency, which outperforms increases in input power density in the last ten years, is identified as the main reason. The falling specific power of US wind turbines is one of the drivers of falling system efficiency.
Our approach of simulating wind power generation allows to simulate theoretical scenarios, such as wind power production using long-term average wind conditions, which enables us to remove noise due to annual variations in wind speeds. Nevertheless, this method does not allow to derive conclusions about losses due to curtailing, downtime, wake effects and aging of turbines. We therefore introduced a constant loss factor to account for these effects which are not reflected otherwise in the estimation of power output via a power curve model (see section 6.2), while we show that the effects of aging do not have a strong effect on the trends observed in our results (appendix A.4).
We furthermore validated the simulated time series for power output against measured power output time series provided by the EIA [11] and created a separate model to estimate output power density and system efficiency using the EIA data for power output, instead of our power curve simulations (see appendix A.2.1). Both approaches confirm a decrease in system efficiency and a stabilization or slight decrease in output power density in the period 2008-2019. However, the models deviate in the years before 2008 and after 2019. EIA data reflect earlier mentioned losses and technological progress, but the approach of simulating power output using power curves allows for more internal consistency, as errors in the US Wind turbine database are canceled 4 . In contrast, the observation approach captures all relevant effects, but missing turbines or missing or flawed metadata in the US Wind Turbine Database and errors in the observational wind power generation data may contribute to noisy results (see appendix A.3).
We consider other limitations of minor importance, but list them here anyway. Turbine characteristics are missing for some turbines in the USWTDB. Data imputation techniques were applied to estimate missing values. Some turbines had to be removed completely during the data cleaning process, because the year of commissioning is missing or the turbine's specific power is not in a plausible value range. Furthermore, to estimate input power, a constant value for air density has been used. It has been shown that variations in air density over space and time can lead to errors, when an average air density is used for simulating wind power output [12]. However, a validation of simulated power output using constant air density against observation data showed a good fit of simulation to observation, indicating that errors from the assumption of constant air density are low [13].

Conclusions
Concluding, we have shown that wind power was not able to increase its power output harmonized by rotor swept area-this is in stark contrast to solar PV, where power generation per panel area doubled in the past decade [14]. This implies higher specific land-use requirements and higher externalities linked to wind turbine rotors. We identify that higher land-use requirements are driven by declining system efficiency, which itself is partly a result of a fall in specific power. Increasing availability of input wind power was not sufficient to offset this decrease in system efficiency. At the moment, the market clearly favors wind turbines which are less efficient in using the wind available to them-but also are less costly in terms of levelized costs of electricity (LCOE) and provide more benefits to the power system. If specific power decreases further, windy locations become less available, and further increases in hub-heights are limited, input power density for new projects will stabilize or even decrease, and output power density will therefore also decrease further. This implies that the area swept by rotors required to produce one unit of electricity will increase, as will land-use requirements of onshore wind power-we therefore identify an inherent trade-off between minimizing cost and minimizing land-use of wind turbines.

Methods and Data
In the following sections, details about the computation of the presented results and used data sets are described. Our code is published under the MIT license on Github 5 and can be used to reproduce the results.

Computation of power input
In a first step, wind velocities at 10 m and 100 m at the precise turbine location were estimated from raw ERA5 data (see section 6.5.1) using bilinear interpolation in the directions of longitude and latitude. Directionless wind speeds were then computed from u and v components for each turbine location l and hour t.
Subsequently, the wind power law In the following we will use v t,l to denote the wind speed at time stamp t and turbine location l. The height h is omitted here in the notation for simplicity. The calculation of power input is done at a constant reference height and at hub heights of the installed turbines (see section 6.4).
To increase spatial resolution, a bias correction was applied to the wind speeds using average wind speed data provided by the Global Wind Atlas 2 (GWA2). Bias correction factors are given by 4 The simulated model uses the USWTDB to compute A, P out and P in . On the other hand, the USWTDB is not used for P out EIA . If turbines are completely missing in the USWTDB, if decommissioned turbines are not correctly removed or if metadata is wrong, the error is smaller in P out /P in and P out /A than in P P out EIA in and P A out EIA . 5 Peter Regner, Katharina Gruber, Sebastian Wehrle, Johannes Schmidt 2023 Code and Data repository Explaining the decline of US wind output power https://github.com/inwe-boku/windpower-decomposition-usa 6.4. Decomposition of input power density Input power density P A in is subject to large climatic variations. An additive decomposition is used to observe underlying trends unrelated to the climate. In the following, we describe the decomposition in more detail.
Note that input power density P A in is proportional to the weighted average of v t l , 3 with weights A l (see section 6.1, note that a constant value is used for the air density ρ). Therefore, input power density changes precisely if wind speeds v t,l at locations with operating turbines change. Hence, changes in input power density are thoroughly explained, if changes can be attributed to different reasons for changing wind speeds at turbine locations. The average wind speed at the hub height at turbine locations changes because of turbines being added at new locations, a change of the average hub height, or a change of climate conditions (either annual or multiannual variability or trends due to, e.g. climate change). In order to analyze these different components, power input is computed under different hypothetical conditions. P in,refh,avg is the power input at turbine locations at a reference height of 80 m using average power input over the entire period. P in,avg is the total power input at all turbine locations at the hub height of installed turbines when also assuming average climate conditions. P in is the actual power input captured by all installed wind turbines (see section 6.1). These definitions can be used for the following decomposition: The baseline is an arbitrary value. It is chosen as the average of P in,refh,avg over the complete time span. Similarly, the reference height of 80 m is the median of all turbine hub heights. Both values, baseline and reference height, do not change the trends of the time series, but only add an offset. To get an additive decomposition of the input power density P A in , we divide the equation on both sides by A. This allows quantifying the effect of changes in wind speeds due to new locations, the effect of change in hub heights and the effect of annual variations in available wind resources.
Note that the annual variations of climate conditions is not independent of the effect of hub height change. Average wind speeds at hub height are increasing over time, since average hub heights of new turbines are increasing over time and average wind speeds are higher at larger heights. Therefore also the difference P in − P in,avg exhibits larger variations over time, when compared with variations of input wind power at the same heights. However, due to the increasing number of operating turbines, annual variations at hub height can be expected to decrease over time. These two opposing trends can cancel each other out to some extent.
A graphical explanation of the additive decomposition of input power density is given in the appendix in figure A.8.

Data
We aimed at mainly using publicly available data sets to compute the presented results. However, the turbine data set was extended by non-public data as explained in section 6.5.2 in more detail. External input data were validated using additional data sets as described in appendix A.2.

Wind speed data
To estimate the power input at turbine locations, wind speeds from the ERA5 data set [4] were used. ERA5 is an openly available global reanalysis data set. Wind velocities are provided at 10 m and 100 m height with hourly temporal resolution and 0.25°spatial resolution-in the US this results in tiles with a size of approximately 25 km × 25 km.
To increase spatial resolution, the Global Wind Atlas Version 2 (GWA2) was used [5]. It provides average wind speeds at a resolution of 0.0025°, so each ERA5 tile is covered by 10 000 GWA2 tiles.

Wind turbine data
The United States Wind Turbine Database [16] is a collection of 81,075 wind turbines located in the USA. Every turbine is annotated with a precise location, i.e. longitude and latitude, and several other meta parameters such as hub height, rotor diameter, capacity, model name and commissioning year.
However, many of the meta parameters are missing. For 14.9% of the turbines in the data set, there is no hub height or no rotor diameter available. Simply discarding turbines with missing data would lead to a significant underestimation of aggregated values such as the total rotor swept area of operating turbines, which is essential in most parts of the computation. Instead, we used mean data imputation for each year to estimate values for the missing meta parameters for hub height, rotor diameter and capacity. The parameters are missing not at random (MNAR), as there are more missing parameters for older turbines (see appendix A.3). The distribution of missing parameters for turbines built in the same year is unknown, which is why there is no way to find an optimal way of estimating missing values. However, computation of minimum and maximum introduced error -similar to a sensitivity analysis-shows that the introduced error can be neglected.
The public USWTDB data set contains currently operating wind turbines only. This study aims to analyze the historical development of turbines, which naturally requires also knowledge about decommissioned turbines. Via personal communication, we received an extension to the USWTDB data set [17], which consists of turbines that have been removed from the USWTDB by now due to their decommissioning. These turbines have been merged with the publicly available data set. However, there are turbines appearing in older versions of the USWTDB which are neither part of the latest version nor of the extension data set, which contains decommissioned turbines. We therefore merged the USWTDB versions 3.01, 4.1, 5.0 and 5.1 and then removed duplicates by using the longitude and latitude of the turbines.
For some of the turbines in the data set, the commissioning year is missing. These turbines cannot be used in the calculation of the time series and are therefore removed in a preprocessing step. This affects 1.6% of all turbines or 8.7% of turbines operating in 2001. We assume that these are mostly older and therefore smaller turbines, since the share of turbines other meta parameters missing is higher for the ones with commissioning year before 2008 (see appendix A.3). Therefore, the discarded total capacity can be assumed to be below 1.6% of the total capacity or below 8.7% relative to capacity installed in 2001.
Decommissioning dates are missing for most turbines. For only 1,716 turbines a decommissioning year is available, but 7,928 turbines are marked as decommissioned and further 4,223 turbines were older than 25 years in 2021. However, since this affects mostly smaller turbines, the effect on the total installed capacity is quite small (see appendix A.2 and figure A.4). Therefore, all turbines were used without taking decommissioning into account.
One turbine with a capacity of 275 kW located on the Mariana Islands has been removed from the data set because it significantly reduces the size of the bounding box of turbine locations and, therefore, also the size of required wind speed data.

Power curve model
A power curve maps wind speeds to the expected power output of a wind turbine. Here we used the power curve model introduced by Ryberg et al [3]. They used power curves provided by turbine manufacturers to fit a model with specific power as parameter. A lower specific power shifts the peak in system efficiency to lower wind speeds, i.e. a turbine with a low specific power can generate more electric power per unit of power input for lower wind speeds and a turbine with higher specific power can generate more electric power per unit of power input for higher wind speeds. The power curve model is provided via a table of two parameters [3], table A.6. Discrete steps and linear interpolation were used for specific power and wind speed to calculate the power output for a certain turbine and wind speed.