Calculations of annual energy production (AEP) from a wind power plant – whether based on preconstruction or operational data – are critical for wind plant financial transactions. The uncertainty in the AEP calculation is especially important in quantifying risk and is a key factor in determining financing terms. A popular industry practice is to assume that different uncertainty components within an AEP calculation are uncorrelated and can therefore be combined as the sum of their squares. We assess the practical validity of this assumption for operational-based uncertainty by performing operational AEP estimates for more than 470 wind plants in the United States, mostly in simple terrain. We apply a Monte Carlo approach to quantify uncertainty in five categories: revenue meter data, wind speed data, regression relationship between density-corrected wind speed (from reanalysis data) and measured wind power, length of long-term-correction data set, and future interannual variability. We identify correlations between categories by comparing the results across all 470 wind plants. We observe a positive correlation between interannual variability and the linearized long-term correction; a negative correlation between wind resource interannual variability and linear regression; and a positive correlation between reference wind speed uncertainty and linear regression. Then, we contrast total operational AEP uncertainty values calculated by omitting and considering correlations between the uncertainty components. We quantify that ignoring these correlations leads to an underestimation of total AEP uncertainty of, on average, 0.1 % and as large as 0.5 % for specific sites. Although these are not large increases, these would still impact wind plant financing rates; further, we expect these values to increase for wind plants in complex terrain. Based on these results, we conclude that correlations between the identified uncertainty components should be considered when computing the total AEP uncertainty.

This work was authored by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE) under contract no. DE-AC36-08GO28308. Funding provided by the US Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US 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 US Government purposes.

Calculations of wind plant annual energy production (AEP) – whether based on preconstruction data before a wind power plant is built or on operational data after a wind plant has started its operations – are vital for wind plant financial transactions. Preconstruction estimates of AEP are needed to secure and set the terms for new project financing, whereas operational estimates of long-term AEP are required for important wind plant transactions, such as refinancing, purchasing/selling, and mergers/acquisitions. The need for AEP analyses of wind plants is increasing because global wind capacity increased to 539 GW in 2017, representing 11 % and 91 % increases over 1- and 5-year periods, respectively; capacity is expected to increase by another 56 %, to 841 GW, by 2022

This rapid growth of the wind energy industry is putting an increased spotlight on the accuracy and consistency of AEP calculations. For preconstruction AEP estimates, there has been considerable movement toward standardization. The International Electrotechnical Commission (IEC) is currently developing a standard

Documentation and standards for preconstruction AEP methods are of limited use for operational-based AEP methods given the many differences between the two approaches. In general, operational AEP calculations are simpler than preconstruction estimates because actual measurements of wind plant power production at the revenue meter replace the complicated preconstruction estimate process (e.g., meteorological measurements, wind and wake-flow modeling, turbine performance, estimates of wind plant losses). However, the two methods do share several similarities, including regression relationships between on-site measurements and a long-term wind speed reference, the associated long-term (windiness) correction applied to the on-site measurements, estimates of future interannual variability (IAV), and estimates of uncertainty in the resulting AEP calculation. The shared components between operational AEP calculations and preconstruction estimates

Main sources of uncertainty in an AEP estimate.

The uncertainty values from each component listed in Table

To better understand how uncertainties are combined in long-term operational AEP calculations, we reached out to several wind energy consultants who regularly perform these analyses. These conversations revealed that uncertainties in a long-term operational AEP calculation are also assumed uncorrelated and combined using Eq. (

The purpose of this study is to examine the extent to which the assumption of uncorrelated uncertainties – and, therefore, the combination of those uncertainties through a sum of squares approach – is accurate and appropriate for operational AEP calculations. Specifically, this study aims to identify potential correlations between AEP uncertainty components using data for over 470 wind plants. While in the analysis we focus on operational AEP calculations, we expect that the results from this analysis – namely, the potential identification of correlated uncertainty components – can be equally relevant for informing and improving preconstruction AEP methods.

In Sect. 2, we first describe the data sources used in this analysis (wind plant operational data and reanalysis products), the Monte Carlo approach to quantify single uncertainty components in operational AEP, and the approaches used to combine these uncertainty components. Section 3 presents the main results of our analysis in terms of uncertainty contributions and correlations among the different components. We conclude and suggest future work in Sect. 4.

Operational wind plant energy production data for this analysis are obtained from the publicly available Energy Information Administration (EIA) 923 database

Long-term wind speed data (needed to perform the long-term or windiness correction in an AEP estimate) are used from three reanalysis products over the period of January 1997 through December 2017:

Please note that this product is provided in MERRA-2 directly and no further interpolation was performed.

. Data are provided at an hourly time resolution.The wind speed data are density corrected at their native time resolutions to correlate more strongly with wind plant power production (i.e., higher-density air in winter produces more power than lower-density air in summer, wind speed being the same):

Map of the 472 wind plants that were considered in this study.

To lessen the impact of limited and/or poor-quality data on the results of our analysis, we filter for wind plants with a moderate-to-strong correlation with all three reanalysis products (

The fundamental step in an AEP calculation involves a regression between density-corrected wind speed (here, from the reanalysis products) and energy production (here, from the EIA-923 database). To investigate whether a simple linear function can be assumed to express the relationship between density-corrected wind speed and wind plant energy production when considering monthly data, we show a scatterplot between MERRA-2 density-corrected monthly wind speed and monthly energy production across all 472 sites in Fig.

We find that the difference between the normalized MAE values from the considered functions is less than 0.7 %. Therefore, the uncertainty connected with the choice of using a linear regression in the operational AEP methodology at a monthly time resolution appears minimal. Moreover, through conversations with wind industry professionals, we found that a linear regression based on monthly data is the standard industry approach when performing bankable

Results are accepted by banks, investors, and so on for use in financing, buying/selling, and acquiring wind plants.

operational AEP analyses.Scatterplot between normalized MERRA-2 density-corrected monthly wind speed and monthly energy production across all 472 selected sites, as well as linear, quadratic, and cubic best-fit lines.

Given the lack of existing guidelines for a standard approach for

Wind speed data (measured or modeled) are density corrected at their native time resolution using Eq. (

Monthly revenue meter data, monthly average availability and curtailment losses, and monthly average wind speeds from a long-term wind resource product are calculated.

Monthly revenue meter data are normalized to 30 d months (e.g., for January, the revenue meter values are multiplied by

Monthly revenue meter data are corrected for monthly availability and curtailment (i.e., monthly gross energy data are calculated).

A linear regression between monthly gross energy production and concurrent density-corrected monthly average wind speeds is performed.

Long-term density-corrected monthly average wind speed is then calculated for each calendar month (i.e., average January wind speed, average February wind speed, and so forth) with a hindcast approach using 10–20 years of the available long-term reference monthly wind resource data (reanalysis products, long-term reference measurements, etc.).

Slope and intercept values from the regression relationship are then applied to the long-term density-corrected monthly average wind speed data using the long-term or so-called windiness correction. A long-term data set of monthly (January, February, etc.) estimated gross energy production is obtained.

The resulting long-term monthly gross energy estimates, which are based on 30 d months, are then denormalized to the actual number of days in each calendar month (e.g., for January, the obtained value is multiplied by

Long-term estimates of availability and curtailment losses are finally applied to the denormalized long-term monthly gross energy data, leading to a long-term calculation of operational AEP.

In the EIA-923 database, availability and curtailment data are not available. Therefore, in our analysis, we omit steps 4 and 9 of the list and only perform calculations on net energy data.

Long-term AEP estimation process using operational data under a Monte Carlo approach; sources of uncertainty and points of Monte Carlo sampling are denoted by probability distribution images. Note that IAV denotes interannual variability.

To quantify the impact of the single uncertainty components on the long-term operational AEP estimate obtained using the methodology described in the previous section, we implement a Monte Carlo approach. In general, a Monte Carlo method involves the randomized sampling of inputs to, or calculations within, a method which, when repeated many times, results in a distribution of possible outcomes from which uncertainty can be deduced. This is usually calculated as the standard deviation or the coefficient of variation (i.e., standard deviation normalized by mean) of the resulting distribution

Sampling set of regression lines corresponding to the slope and intercept values derived from their standard errors in the Monte Carlo approach for two stations in the EIA data set.

In our analysis, we separately consider five operational-based uncertainty components so that only the sampling of one parameter is performed in each Monte Carlo configuration. The following uncertainty components are included in our proposed Monte Carlo methodology for long-term operational AEP.

To calculate these uncertainty components at each wind plant, we run the Monte Carlo simulation under five different setups, each of them having only a single sampling performed (i.e., either revenue meter, reference wind speed data, IAV, linear regression, or windiness correction). For each component, we run the Monte Carlo simulation 10 000 times. We quantify the impact of each single uncertainty component on the long-term operational AEP in terms of the coefficient of variation of the distribution of operational AEP resulting from the Monte Carlo simulation run. Convergence of the AEP distribution within 0.5 % of the true mean after the 10 000 Monte Carlo runs was verified for all projects with 95 % confidence.

The code used to perform the AEP calculations is published and documented in NREL's (National Renewable Energy Laboratory) open-source operational assessment software, OpenOA

Once the contribution from each uncertainty component to the long-term operational AEP uncertainty has been quantified, the different components need to be combined to obtain the total AEP uncertainty. As stated in the Introduction, it is common practice for wind energy consultants to assume that all uncertainty components are uncorrelated and combine them using Eq. (

We contrast the total AEP uncertainty calculated assuming uncorrelated components with what we obtain by taking into account these correlations in the calculation. Following the guidance in

The comparison between

Operational-based AEP uncertainty distributions across projects for the different uncertainty components; mean values across projects are shown in the legend. Uncertainty values are quantified as the percent coefficient of variation of the long-term operational AEP distribution.

Distributions of each uncertainty component, expressed in terms of the percent coefficient of variation of the resulting AEP distributions, across all 472 wind plants are shown in Fig.

Correlation coefficient heat map between operational AEP uncertainty components, as calculated from each pair of AEP uncertainty components across the 472 wind plants considered in the analysis. Note that “Rev.” denotes “Revenue”.

To be able to assess the validity of the uncorrelated assumption when combining different uncertainty components, we assess potential correlations between uncertainty components by analyzing the Pearson's correlation coefficients,

To assess which of the obtained correlations have statistical significance, we calculate the

The wind resource IAV and the long-term windiness correction uncertainties are moderately correlated (

The linear regression and reference wind speed data uncertainties are weakly correlated (

The wind resource IAV and the linear regression uncertainties appear weakly negatively correlated (

The first correlation noted earlier (wind resource IAV and long-term windiness correction) is explained simply by the fact that both uncertainty components are driven by wind resource variability. At a site with large wind variability, IAV will be large by definition and so will the uncertainty introduced by different lengths of time series used for the long-term AEP calculation.

The correlation between linear regression and reference wind speed data uncertainties can be justified given the dependence of both these uncertainty components on the number of data points used in the regression between energy production data and concurrent wind speed data (Fig.

Dependence of linear regression uncertainty and reference wind speed data uncertainty on the number of data points in the period of record for the 472 projects considered in the analysis.

Both the slope and intercept errors (Eqs.

Long-term time series of normalized wind speed for EIA station ID 60502 from the three reanalysis products used in the study. The period of record (POR) for the wind plant is highlighted in light blue.

Ratio of wind speed to the long-term, 20-year average for periods of record of different lengths (all ending in December 2017) for EIA station ID 60502 using data from the three reanalysis products in the study.

The number of data points used for the regression also has an impact on the reference wind speed data uncertainty. In fact, a short period of record of a wind plant's operation can lead to different interpretations from the reference wind resource data sets used as to whether that short period of record was above, equal to, or below the long-term average resource. Over a longer period of record, these potential discrepancies between different wind resource data sets (in our case, reanalysis products) tend to average out, leading, therefore, to a reduced uncertainty. We illustrate this phenomenon by exploring the long-term trend of the reanalysis products for the wind plant with one of the highest reported reference wind speed data uncertainties (EIA ID 60502 reported a 3.7 % reference wind speed data uncertainty). Figure

Dependence of linear regression uncertainty and IAV uncertainty on the

Finally, the (weak) negative correlation between linear regression and wind resource IAV uncertainties is linked to the fact that they respond differently to the

Relationship between IAV uncertainty and the total sum of squares, SS

After having revealed the correlations existing between different AEP uncertainty components and having explained their sources, we can compare the total operational AEP uncertainty calculated when allowing for these correlations (Eq.

This difference can be explained by comparing the contributions

Financial operations related to wind plants require accurate calculations of the annual energy production (AEP) and its uncertainty prior to the construction of the plant and, often, in the context of its operational analysis. As wind energy penetration increases globally, the need for techniques to accurately assess AEP uncertainty is a priority for the wind energy industry. Typically, current industry practice assumes that uncertainty components in AEP estimates are uncorrelated. However, we have shown that this assumption is not valid for the five components that comprise an operational-based uncertainty. We used a Monte Carlo approach to assess AEP; this provides quantitative insights into aspects of the AEP calculation that drive its uncertainty. We have applied this approach using operational data from 472 wind plants, mostly in simple terrain, across the United States in the EIA-923 database in order to study potential correlations between uncertainty components. Three pairs of uncertainty components revealed a statistically significant correlation: wind resource interannual variability (IAV) and long-term windiness correction (positive correlation); wind resource IAV and linear regression (negative); and reference wind speed data and linear regression (positive). Wind resource IAV and long-term windiness correction uncertainties are correlated because they both depend on wind resource variability. Wind resource IAV uncertainty is correlated with linear regression uncertainty because they are both inversely proportional to the number of data points in the period of record. Finally, reference wind speed data uncertainty and linear regression uncertainty show a negative correlation because they respond oppositely to the

Our results show that ignoring these correlations between uncertainty components causes an underestimation of the total operational AEP uncertainty of, on average, about 0.1 % with peak differences of 0.5 % for specific sites. These differences, though not large, would still have a significant impact on increasing wind plant financing rates. Moreover, we expect differences would become even larger for sites characterized by a more complex wind flow. Therefore, our results suggest that correlations between uncertainty components should be taken into account when assessing the total operational AEP uncertainty.

Additional components of uncertainty in an operational AEP were not considered in our study because of limited reporting in the EIA-923 database. These components include reported availability, curtailment uncertainty, and various uncertainties introduced through analyst decision-making (e.g., filtering high-loss months from analysis and regression outlier detection). Future studies could include the impact of these additional sources of uncertainty on the operational AEP assessment. Moreover, our analysis excluded sites, mostly in complex terrain, with a weak correlation between reanalysis wind resource data and wind power production. Future work could explore the magnitude of operational AEP uncertainty and the correlation between its components for such complex flow regimes. Finally, this study focused on correlations between operational AEP uncertainty components. Future work could explore correlations between the numerous preconstruction AEP uncertainty components (e.g., wake loss, wind speed extrapolation, wind flow model).

EIA data used in this study are accessible from

NB and MO are equal contributors to this work. MO performed the AEP estimates on the wind plants considered in the study. NB and MO analyzed the processed data. NB wrote the paper with significant contributions from MO.

The authors declare that they have no conflicts of interest.

This 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.

This paper was edited by Carlo L. Bottasso and reviewed by Mark C. Kelly and Curran Crawford.