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.

10th International Workshop on 

Large-Scale Integration of Wind 

Power into Power Systems

October 25, 2011

Bri-Mathias Hodge

Erik Ela

Michael Milligan

Transmission and Grid Integration 

Group

National Renewable Energy Laboratory

Golden, Colorado USA

NREL/PR-5500-53410

The Distribution of Wind Power 

Forecasting Errors from 

Operational Systems

Photo by Warren Gretz, NREL/PIX 10926

Photo from Tom Hall, NREL/PIX 06588
Topics

• Introduction

• Statistical Background

• Datasets

• Normal Distribution 

Comparison

• Persistence Model 

Comparison

• Distribution Modeling

• Conclusions

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Photo from Native 

Energy, Inc., 

NREL/PIX 17593
Renewable Energy Portfolio Standards

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Renewable Generation Integration Background

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Statistical Background

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4

4 ( )

σ

ε

κ

E

=















 



 



 − =

3

σ

μ γ

X E

• Skewness – 3rd

Statistical 

Moment

• Kurtosis – 4th

Statistical 

Moment
Datasets

• ERCOT data

• Day-ahead forecasts

• Hourly power output

• 13 months of data

• Forecasts made at 16:00 the day prior 

• ~ 9,000 MW wind capacity

• Xcel Energy data

• Forecasts produced every 15 minutes for the next 

72 hours

• Hourly power output

• 3 months of data

• Single wind plant ~ 300 MW capacity

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ERCOT Day-Ahead Histogram

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γ = -0.62; κ = 1.03
ERCOT Day-Ahead Normal Q-Q Plot

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Xcel Plant 1-Hour Normal Q-Q Plot

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Xcel Hour-Ahead Persistence Comparison

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γ = -0.51; κ = 5.97 γ = -0.01; κ = 17.62

Persistence Model Operational Model
Xcel 24-Hour-Ahead Persistence Comparison 

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γ = -0.03; κ = 0.15 γ = -0.65; κ = 1.05

Persistence Model Operational Model
Persistence Comparison – Multiple Timescales

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Persistence Operational

Timescale Skewness Kurtosis Skewness Kurtosis

15 Minutes -0.68 30.64

30 Minutes -1.36 30.88

1 Hour -0.51 5.97 -0.01 17.62

3 Hour -0.21 1.81 -0.88 1.97

24 Hour -0.03 0.15 -0.65 1.05

72 Hour -0.03 0.06 -0.56 0.84
Distribution Modeling - ERCOT

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The black line represents

a hyperbolic distribution

fit to the data with: 

π = 0.083, ζ = 1.601, 

δ = 0.105, μ = 0.006.

The blue line represents

a normal distribution

with the same mean and

standard deviation.
Distribution Fitting - Xcel 1-Hour-Ahead

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The black line represents a

hyperbolic distribution fit to

the data with: π = 0.087, 

ζ = 3.88 E-5, δ = 1.76 E-6, 

μ = 0.005.

The blue line represents a

normal distribution with the

same mean and standard

deviation.
Forecasting Error Distributions Implications

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Acknowledgements

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• Dr. Debra Lew and Yih-huei Wan– NREL

• David Maggio – ERCOT

• Keith Parks – Xcel Energy

• Dr. Chris Dent – Durham University

• U.S. DOE – Wind and Water Program

Photo by Warren Gretz, NREL/PIX 11188 Photo by Todd Spink, NREL/PIX 14961
Questions?

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Photo from Iberdrola

Renewables, 

NREL/PIX 16105

Photo by Patrick 

Corkery, 

NREL/PIX 17731