Addendum: Observation-based solar and wind power capacity factors and power densities (2018 Environ. Res. Lett. 13 104008)

‘Observation-based solar and wind power capacity factors and power densities’ (Miller and Keith 2018 Environ. Res. Lett. 13 104008) contained a methodological error in how we estimated wind plant area, leading to an underestimate of wind power densities. The method and revised results were published as a Corrigendum (Miller and Keith 2019 Environ. Res. Lett. 14 079501). Given the importance of these estimates to energy policy, here in this Addendum, we expand on these corrected results, while also describing the public release of data to allow verification by third-parties. Specifically, here we: (1) illustrate our method by showing in greater detail how it works for the 2 wind power plants from figure 1 of the original study, (2) identify potential selection biases in the sampling of wind power plants used in our study, (3) provide a comparative overview of the various prior published estimates in graphical form, and, (4) conclude with a description of the data we are releasing publicly.

shows the Bull Creek and Fenton wind power plants. Bull Creek (Plant_Code=56956) is comprised of 180 Mitsubishi MWT62/1.0 turbines, with a per-turbine rated capacity of 1.0 MW i and 69 m hubheight. Based on our Methods (main text and supplemental information of Miller andKeith 2018a, 2019), we calculated a Voronoi polygon around each wind turbine location. Each Voronoi polyon delineates the area closer to an individual turbine than to any other wind turbine in the entire USGS data set (Hoen et al 2018). As shown in figure 1(C), some Voronoi polyons are unrealistically large if considered as estimates of their wind turbine footprint. Indeed, a wind plant consisting of a single isolated turbine would have a huge Voronoi polyon area. This is the reason our method uses the area of the median Voronoi polygon as the basis for estimating the area of the wind plant which is computed by multiplying the median area (in this case 0.22 km 2 ) by the number of turbines (180) to yield an estimate for the total area (39.2 km 2 ).
Our method provides an estimate of the wind plant area, but it does not provide a unique outline of that area.
As an aid to visualizing and understanding our results, we can compute an outline that contains the same total area as our estimate while having a constant minimum offset between each turbine and the perimeter. This is computed by constructing disks of equal radii around each turbine, dissolving their overlapping area to prevent double counting, and adjusting the radii until the total area inside one or more disks is equal to the area we computed. The resulting perimeter for Bull Creek is shown in figure 1(A). This is a useful illustration of a wind-plant perimeter, particularly as compared to methods that use a fixed radius from each turbine.
The same approach was used for Fenton (Plant_Code=56617). Fenton is comprised of 137 GE1.5-77 turbines, with a per-turbine rated capacity of 1.5 MWi and an 80 m hub-height. Just like the method for Bull Creek, Fenton's median Voronoi polygon area of 0.53 km 2 was multiplied by the turbine count, yielding a total area of 73.2 km 2 ( figure 1(D)). This equivalent area is shown around the Fenton wind turbines in figure 1(B).
We investigated the impact of selection bias in our sample of wind plants. In the 2016 data, for example, Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
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total capacity of wind plants that passed our qualityassurance filters was only 51% of the total capacity reported by EIA at the end of 2016. How representative is our sub-sample of the full data set? We first examine spatial sampling. Figure 2 shows the map of the all wind power plants from the EIA Power Plants (US Energy Information Administration EIA 2018a) and our subset (see public data release below:  MillerKeith2018Data1.csv). Some locations, like Massachusetts appear to be missed. Upon further analysis, many of these 'plants' are actually 1 or 2 wind turbines, which because of their rated capacity >1 MW are included in the Power Plants dataset, but were excluded from our analysis because the Voronoi polygons containing these wind power plants were large, so the filter for capacity densities 0.1 MW i km −2 excluded these wind plants. Figure 3 compares the capacity cumulative distribution of wind plant size in the full data and our subset. Our sample is biased towards larger wind power plants. This highlights the fact that our method is not applicable to very small wind plants.
Assuming, as seems likely, that continued expansion of wind power will be associated with larger wind plants, then our under-sampling of small wind plants does not impact the applicability of our estimates. Moreover, the uncertainty or arbitrariness of the median-Voronoi method decrease with increasing scale. For a single turbine, we know of no unambiguous way to define the area over which it is extracting power. Calculating power density for small wind plants is inherently arbitrary, as the benefits of being isolated on a ridgeline or in a coastal region are clear, but the ability to later deploy additional wind turbines downwind is often limited. But the methodological errors in estimating the power density of medium sized wind power plants (30-200 km 2 ) using the median-Voronoi method are small as these plants typically contain 10-100 s of wind turbines all co-located into one region, often in rows (e.g. figure 1).
Large wind power plants (>300 km 2 ) should also be easily defined in the future, but as today's wind plants are just now growing to these dimensions via adjacent deployment in windy locations, we suspect that our results for these large wind power plants are also not perfect. In our analysis, the power densities associated with these large wind power plants are quite low (figure 7(B) of Corrigendum), leading us to believe that these are regions with very low capacity densities rather than low power densities resulting from wind plants operating upwind. As these regions are builtout with turbines, we would expect the area estimate for large wind plants to improve as well.
Finally, figure 4 compares results from this study with earlier estimates of wind's power density. The power densities from this study are consistent with physically-based models, and inconsistent with wind resource estimates that ignore interactions between wind turbines and the atmosphere.
To facilitate independent validation of these results, we have placed 2 datasets on OpenEI, a public  USWTDB_ID-unique ID (text name) which also appears in MillerKeith2018_Data1.csv for matched wind power plants