NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency

and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

A Monte Carlo-Based Approach to Assessing Annual Energy Production and Uncertainty

Anna Craig, Mike Optis, M. Jason Fields, Patrick Moriarty

National Renewable Energy Laboratory (NREL)

Motivation and Approach

The information contained in this poster is subject to a government license.

American Wind Energy Association Wind Resource and Project Energy Assessment Conference 

Austin, Texas

September 11‒12, 2018

NREL/PO-5000-72233

This work was authored by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. 

Funding provided by the U.S. Department of Energy, within the Atmosphere to Electrons research program. The views expressed in the article do 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.

Conclusions

The industry standard approach to assessing annual energy production (AEP) uncertainty can be 

limited because of the assumption of uncorrelated uncertainty categories and subjectivity in 

calculations. A Monte Carlo approach to uncertainty quantification can largely overcome these 

limitations and provide a more robust assessment of energy uncertainty. 

Here, we demonstrate the Monte Carlo approach in the context of AEP estimation using 

operational data. Monthly net energy production for all reporting wind power plants in the United 

States was taken from the Energy Information Administration (EIA) 923 database. Atmospheric 

data from three reanalysis products were also considered. After filtering for wind plants that had 

at least 8 months of data and moderate-to-strong correlation with all three reanalysis products 

(R2 > 0.6), we assessed 472 wind power plants total.

Uncertainty Correlations Uncertainty Contributions

Mike Optis, Senior Scientist, National Renewable Energy Laboratory (NREL)

Uncertainty Category Incorporation under Monte Carlo

Revenue meter accuracy Sample revenue meter data based on 0.5% uncertainty

Wind measurement accuracy Consider multiple reanalysis products:

• Modern-Era Retrospective analysis for Research and Applications 

v2 (MERRA-2)

• European Reanalysis Interim (ERA-interim)

• National Centers for Environmental Prediction v2 (NCEP2) 

Wind interannual variability (IAV) Sample calendar monthly wind speeds based on corresponding 

monthly uncertainties

Regression model Sample slope and intercept values from their standard errors and 

covariance

Windiness adjustment Sample the number of years to use in the windiness correction 

(between 10 and 20)

Figure 2 outlines the process of estimating AEP using operational data under a 

Monte Carlo approach. Table 1 shows a summary of the uncertainty categories 

considered and how they are incorporated in a Monte Carlo analysis. 

Figure 2. AEP estimation process using operational data under a Monte Carlo approach; source of 

uncertainty and points of Monte Carlo sampling are denoted by probability distribution images

Table 1. Uncertainty Categories Considered and Their Incorporation under a Monte Carlo Approach

• Wind IAV and windiness correction uncertainties are moderately correlated

• Regression and wind measurement uncertainties are weakly correlated

• Wind IAV and regression uncertainties appear weakly negatively correlated.

Regression Uncertainty

• Wind resource IAV dominates the uncertainty

• Regression uncertainty is significant

• Wind resource product can be influential

• Windiness adjustment uncertainty is relatively small.

Figure 1. Correlation coefficient heat map between uncertainty categories. 

Note: “Rev.” denotes “Revenue”

Figure 3. Uncertainty distributions across projects for the different 

uncertainty categories; mean values across projects are shown in the legend

Figure 4. Dependence of regression uncertainty on both the strength of correlation between 

energy and wind speed and the number of data points

A Monte Carlo approach to assessing AEP not only directly accounts for correlations between uncertainty categories, but also provides quantitative insight into aspects of the 

AEP process that drive uncertainty (e.g., regression relationship and number of years in windiness correction). Furthermore, the added computational expense of running 

Monte Carlo relative to the industry standard AEP method is easily managed by a typical computer.

Several additional categories of uncertainty in an operational AEP were not considered because of limited reporting in the EIA-923 database. These categories include 

reported availability and curtailment uncertainty and various uncertainties introduced through analyst decision-making (e.g., filtering high loss months from analysis and 

regression outlier detection). Uncertainty in analyst decision-making in operational energy assessments is an active research area at NREL (e.g., Craig et al. [2018]1). This 

aspect of uncertainty has, to our knowledge, not previously been explored in the industry.

1 Craig, A., M. Optis, M. J. Fields, P. Moriarty. Uncertainty Quantification in the Analyses of Operational Wind Power Plant Performance J. Phys.: Conf. Ser. 1037 (2018) 052021

• Standard error of slope and intercept inversely proportional to 

number of data points (i.e., more data gives lower uncertainty)

• Uncertainty inversely proportional to regression strength

• Explained variance of regression uncertainty improves to 0.85 when 

considering both regression strength and number of data points. 

Standard error of regression 

(i.e., residual)

Standard error of slope

Standard error of intercept eebb = eeyyeeaa

xxii

2

nn

eeaa = eeyy

∑ xxii − ̅xx 2

eeyy = ∑ yyii − �yyii 2

nn − 2