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

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Wind Power Forecasting Error 

Distributions: 

An International Comparison

Preprint

B.-M. Hodge, D. Lew, and M. Milligan

National Renewable Energy Laboratory

H. Holttinen and S. Sillanpää

VTT

E. Gómez-Lázaro

University of Castilla-La Mancha

R. Scharff and L. Söder

KTH Royal Institute of Technology

X. G. Larsén and G. Giebel

Technical University of Denmark

D. Flynn

University College Dublin

J. Dobschinski

Fraunhofer Institute for Wind Energy and Energy System Technology

To be presented at The 11th Annual International Workshop on Large-Scale 

Integration of Wind Power into Power Systems as well as on Transmission 

Networks for Offshore Wind Power Plants Conference

Lisbon, Portugal

November 13–15, 2012

Conference Paper

NREL/CP-5500-56130

September 2012
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1

Wind Power Forecasting Error Distributions

An International Comparison

Bri-Mathias Hodge, Debra Lew, Michael Milligan

National Renewable Energy Laboratory

Golden, CO, USA

Emilio Gómez-Lázaro

University of Castilla-La Mancha

Albacete, Spain

Xiaoli Guo Larsén, Gregor Giebel

Technical University of Denmark

Roskilde, Denmark

Hannele Holttinen, Samuli Sillanpää

VTT

Espoo, Finland

Richard Scharff, Lennart Söder

KTH Royal Institute of Technology

Stockholm, Sweden

Damian Flynn

University College Dublin

Dublin, Ireland

Jan Dobschinski

Fraunhofer Institute for Wind Energy and Energy System Technology

Kassel, Germany

Abstract—Wind power forecasting is essential for greater 

penetration of wind power into electricity systems. Because no 

wind forecasting system is perfect, a thorough understanding of 

the errors that may occur is a critical factor for system 

operation functions, such as the setting of operating reserve 

levels. This paper provides an international comparison of the 

distribution of wind power forecasting errors from operational 

systems, based on real forecast data. The paper concludes with 

an assessment of similarities and differences between the errors 

observed in different locations.

Keywords—wind power forecasting, power system operation,

power system reliability, power systems, wind power generation

I. INTRODUCTION

The amount of wind power being incorporated into power 

systems worldwide has been increasing dramatically during 

the past decade. Wind power has no fuel costs and zero 

emissions, which means that its increased presence in power 

generation portfolios provides great benefits to society.

However, wind power is a variable and uncertain power 

resource, in contrast to traditional thermal power units. This 

has led to concerns from utilities and system operators about 

how increasing amounts of wind power will be handled in 

system operations [1]. One way to reduce the uncertainty 

surrounding wind power output is through wind power 

forecasting systems. Typical systems used in operational 

forecasting consist of one or more Numerical Weather 

Prediction (NWP) models that provide forecasts of wind speed 

on a grid over a geographic area, coupled with statistical 

techniques that translate the forecasts to local wind plant 

conditions and convert forecasted wind speed to power [2].

Although these forecasts provide system operators with an 

expected wind power output level at future times, they are not 

perfect forecasts. Understanding the magnitude and frequency 

of wind power forecasting errors can facilitate the integration 

of wind power through advanced operational techniques, for 

example, setting dynamic reserve levels [3, 4], using 

stochastic unit commitment models [5, 6], or through simply 

increasing operator awareness. Power system operations are 

already designed to handle a certain degree of variability and 

uncertainty because load is itself both variable and uncertain

[7]. Therefore, we are most concerned with the large and 

infrequent wind power forecasting errors. Large forecasting 

events can lead to major economic inefficiencies through nonoptimal commitment schedules.

Wind power forecast errors are often a concern in wind 

integration studies and stochastic unit commitment models.

Many of these studies assume that the forecast error 

distribution follows a normal distribution [3, 8, 9]. However, 

this is an overly simplistic assumption for most forecasting 

methods and timescales examined [10, 11]. Other distributions 

have been examined, including the Weibull [12] and beta [13]

distributions; however, in this work we utilized the hyperbolic 

distribution [10]. We analyzed the forecast error distributions 

observed in a number of different countries and electrical 

systems and at two different timescales that are important in 

the unit commitment and economic dispatch process.

Comparisons were made between the different cases, and 

conclusions on the importance of the differences for power 

systems operations with higher wind power penetrations were 

drawn.

II. METHODS AND DATA

In this study, statistical analysis techniques were applied to 

wind power forecasting data taken from seven countries. Dayahead wind power forecasts were supplied for seven countries 
2

or balancing areas within a country. Hour-ahead wind power

forecasts were utilized for two countrywide systems and for 

one large wind plant in a balancing area. The hyperbolic 

distribution parameters were fitted to the data using a 

maximum likelihood method.

Mean, μ, and variance, σ, the first two standardized 

moments, are frequently used in the characterization of wind 

forecasting error distributions, providing important 

information about the distribution. However, considering the 

third and fourth statistical moments can provide additional 

information [10, 14, 15]. Skewness, γ, is the third moment and 

is a measure of the probability distribution’s asymmetry.

Kurtosis, κ, is the fourth moment and describes the magnitude 

of the distribution’s peak. Conversely, kurtosis can also be 

thought of as a measure of the thickness of the tails of the 

distribution. A distribution with a high kurtosis value is 

leptokurtic; one with a low kurtosis value is platykurtic. 

Leptokurtic distributions have more pronounced peaks, 

slimmer shoulders, and longer tails than normal distributions 

with identical first two moments. In what follows, we refer to 

excess kurtosis, the kurtosis above that of the normal 

distribution, simply as kurtosis.

We utilized some standard statistical tools such as 

histograms, quantile-quantile (Q-Q) plots, and cumulative 

distribution function plots. It is important to note that the 

forecast errors were normalized, based on the wind power 

capacity, for the sake of comparison. Therefore, all of the 

forecast errors lie on the interval from -1 to 1. The Q-Q plots 

shown here are normal Q-Q plots that compare the observed 

distribution to a Gaussian distribution with the same mean and 

standard deviation as the observed distribution. They include a 

line that runs through the first and third quantiles of the 

observed distributions. If the two distributions are identical,

the line should pass through all of the points in the observed 

distribution. The cumulative distribution plots show how 

likely a random error from the distribution will be less than or 

equal to the magnitude selected.

III. SYSTEM OPERATIONS WITH FORECASTS

Wind power forecasting plays an important role in 

reducing the uncertainty of wind generation. Forecasts may be 

included directly in the unit commitment and economic 

dispatch scheduling process used to ensure enough generation 

is available to meet forecast load, or they may simply provide 

situational awareness for the balancing authority. Day-ahead 

forecasts are often required for the unit commitment process

because the starting of large thermal units can often take 24 

hours or more. The forecasted wind power output at this 

timeframe can be used to optimize the availability of other 

generation units during the course of the following day. The 

economic dispatch process sets the final power output for units 

that are online and is performed closer to the time of 

realization, often one hour ahead. Variability and forecast 

errors at smaller timescales are often compensated with 

reserves held for that purpose. Because wind forecasts can be 

helpful to system operations in both the unit commitment and 

economic dispatch phases, we examined the wind power 

forecasting errors that occur at these two timeframes, in this 

paper represented by day-ahead and hour-ahead forecasts.

IV. ERROR DISTRIBUTIONS FROM OPERATIONAL SYSTEMS

In this section, we examine wind power forecast error 

distributions observed in a total of seven countries at the dayahead and hour-ahead timescales. In this work, we follow the 

convention that the error is equal to the forecast minus the 

realized value.

A. Day-Ahead Forecasts

1) United States

Day-ahead forecasts for the United States were taken from 

the Electric Reliability Council of Texas (ERCOT)

interconnection for the year 2010, with an installed wind

capacity of approximately 9,000 MW. As shown in Figure 1, 

the distribution was leptokurtic, with a significant negative 

skew. The distribution also had a fairly large spread, with 

minimum and maximum error values above half of the 

installed capacity. The red line represents a normal 

distribution with the same mean and standard deviation as the 

observed errors. Figure 2 shows that the distribution was 

poorly represented by the normal distribution. The observed 

error distribution had a more pronounced peak, slimmer 

shoulders, and fatter tails than the corresponding normal 

distribution. This is an example of the differences between the 

observed error and normal distributions, and the other data sets

show similar features.

Figure 1. Histogram of the normalized day-ahead forecast errors for the 

ERCOT system. μ = 0.0117; σ = 0.1187; γ = -0.616; κ = 1.0308

Figure 2. Normal Q-Q plot of the ERCOT day-ahead forecast errors. If the 

observed errors were well represented by a normal distribution, all 

observations would lie on the straight line.
3

2) Finland

The Finnish installed wind capacity was the smallest in the 

study, with 102 MW of rated power. However, the capacity 

was spread over 25 sites (77 turbines), with the largest 

distance between the sites being 630 km. Figure 3 shows the 

slightly positively skewed and leptokurtic distribution of 

observed wind power forecasting errors for the Finnish 

system. The distribution included a number of fairly large 

positive forecast errors (over-forecasting), with a few 

exceeding half of the installed capacity. This may have been

the result of the smaller number of turbines included in this 

data set, and possibly erroneous data used in producing the 

forecasts.

Figure 3. Histogram of the normalized day-ahead forecast errors for the 

Finnish system. μ = -0.0155; σ = 0.0751; γ =0.0720; κ = 3.1036

3) Spain

The Spanish installed wind power forecasting error 

histogram is shown in Figure 4. This data was from the year 

2010 and included 19,300 MW of wind power capacity. The 

distribution was leptokurtic and fairly strongly positively 

skewed. The forecasts also displayed a notable bias, 

corresponding to more than 15% of installed wind power 

capacity. The distribution also had distinctly fat tails in both 

the over- and under-forecasting directions.

Figure 4. Histogram of the normalized day-ahead forecast errors for the 

Spanish system. μ = 0.1624; σ = 0.0514; γ =0.3855; κ = 3.0180

4) Sweden

The day-ahead forecasts for the Swedish system (year 

2011) included 2,899 MW of installed wind capacity. The 

forecast errors plotted in Figure 5 showed a slightly 

leptokurtic negatively skewed distribution. The Swedish errors 

were interesting for their fairly small spread, with the largest 

errors being less than 30% of installed wind capacity. This 

was likely because of the large geographic diversity stemming 

from the multiple sites covering a large geographic area. It 

was also interesting to see that the normal distribution would 

under-represent the negative error tail, but over-represent the 

positive error tail, because of the skewness. Figure 6 shows the 

cumulative distribution function of the observed errors, the 

normal distribution based on those errors, and a hyperbolic 

distribution fit to the observed errors. It was readily apparent 

that the hyperbolic distribution provided a superior fit to the 

data than did the normal distribution, with the hyperbolic line 

running on top of the observed errors line for much of the 

cumulative distribution function. The Swedish example was 

chosen to display the cumulative distribution plot because of

the clear example of the improved fit of the hyperbolic 

distribution. However, other cumulative distribution functions 

would have similar characteristics.

Figure 5. Histogram of the normalized day-ahead forecast errors for the 

Swedish system. μ = -0.0052; σ = 0.0603; γ = -0.7252; κ = 0.7757 

Figure 6. Cumulative distribution plot of the normalized Swedish day-ahead 

forecast errors
4

5) Denmark

The Danish system data included 3,871 MW of installed 

wind capacity for the year 2011. The distribution was more 

strongly leptokurtic than many of the other day-ahead forecast 

error distributions examined previously, as shown in Figure 7.

Also, in contrast to the other countries, the distribution was 

fairly symmetric, with only a slightly positive skew. The 

spread of the data was fairly small with relatively few errors 

greater than 25% of the total installed capacity. This was 

likely a result of the geographic diversity acquired from the 

turbines being spread throughout the country. In addition, 

Denmark has a long history of wind power forecasting and 

contains relatively easy terrain.

Figure 7. Histogram of the normalized day-ahead forecast errors for the 

Danish system. μ = -0.0005; σ = 0.0534; γ = 0.1378; κ = 2.3859 

6) Ireland

The Irish data was from the year 2011 and included 1,557 

MW of installed wind capacity. The Irish day-ahead 

forecasting errors had a small positive skew and were 

leptokurtic, as shown in Figure 8. There was a fairly large 

spread to the distribution, with a significant amount of forecast 

errors approaching 50% of installed wind power capacity. This 

was likely because of the small geographic area covered by the 

wind turbines. For reference, the total land area of Ireland is 

roughly 1/6th the land area of Sweden and 1/5th that of 

Germany.

Figure 8. Histogram of the normalized day-ahead forecast errors for the 

Irish system. μ = -0.0123; σ = 0.0827; γ = 0.3063; κ = 3.0311

7) Germany

The German data was from the year 2010 and covered the 

total installed wind capacity in Germany ranging from 25.18 

GW in January 2010 to 26.39 GW in December 2010. The 

power measurement was based on an up-scaling algorithm 

based on spatially distributed reference wind farms that 

included about 25% of the total capacity. The forecasts were 

used and published by the German transmissions system 

operators and were based on combinations of power forecasts 

from different providers and on different NWP models. The

day-ahead forecasting errors had a slightly negative skew, and 

were leptokurtic, as shown in Figure 9. The spread of the data 

was relatively small, with all errors less than 30% of installed 

wind capacity. This was because of the large number of 

turbines included in the analysis, as well as the geographic 

spread of the locations used.

Figure 9. Histogram of the normalized day-ahead forecast errors for the 

German system. μ = 0.0092; σ = 0.0450; γ = -0.2891; κ = 3.5896

B. Hour-Ahead Forecasts

In power system scheduling, short-term wind power 

forecasts are necessary to set the generating unit output levels 

in the dispatch process, which often coincides with intraday 

market timing. These shorter term forecasts are used to reduce 

the uncertainty from day-ahead forecasts; consequently, only 

these forecast errors must be balanced by reserve power [16].

Although the dispatch interval may vary between systems, we 

used a one-hour interval as a representative example.

1) United States

The U.S. hour-ahead forecast error distributions came from 

a single wind plant in the Xcel Colorado service territory with 

approximately 300 MW of capacity. Because this data came 

from a single plant, the benefits of geographic diversity were 

not apparent. This was clear when looking at the extreme 

values shown in Figure 10. The maximum errors for the single 

plant were approximately 80% of the total capacity. It must be 

noted that these large values were likely because of the manual 

curtailment of wind plant output. These hour-ahead forecasts 

also had a much greater kurtosis value than the day-ahead 

forecasts observed in the previous section. The practical 

implication of this is that the forecasts were often more 

accurate, but had occasional instances when they were very 

inaccurate.
5

Figure 10. Histogram of the normalized day-ahead forecast errors for the

Xcel Colorado wind plant. μ = -0.01; σ = 0.08; γ = - 0.01; κ =17.62 

2) Spain

The hour-ahead forecasts for the Spanish system included

20,091 MW of wind power capacity, the second largest 

amount in this study. Figure 11 shows the histogram of the 

forecast errors. One important aspect to note is the smaller 

range of values shown in the Spanish data, with forecast errors 

above 10% of capacity being very rare. Part of the explanation 

is that the forecasts were hour-ahead instead of day-ahead 

data; the smaller forecasting interval reduced the uncertainty 

in the forecast considerably. The fat tails shown in Figure 11

resulted in a poor fit to the normal distribution. Further 

verification of this finding was provided by the dramatic 

deviations in the tails in the normal Q-Q plot shown in Figure 

12.

Figure 11. Histogram of the normalized hour-ahead forecast errors for the 

Spanish system. μ = -0.0018; σ = 0.0133; γ = - 1.6585; κ =20.2385

Figure 12. Normal Q-Q plot of the Spanish hour-ahead forecast errors. If the 

observed errors were well represented by a normal distribution, all 

observations would lie on the straight line.

3) Germany

The hour-ahead forecasts for the German system were for 

the same set of wind plants described in the day-ahead section.

The histogram of the hour-ahead forecast errors is shown in 

Figure 13. The spread of the errors was very small, with no 

errors above 10% of installed capacity. As mentioned for the 

Spanish system, the large amount of wind turbines considered 

(~25 GW), with the resulting geographic diversity, was an 

important factor in the smaller spread of the error distribution, 

as was the usage of online power measurements that underlay

a high-quality data check. The distribution was leptokurtic and 

slightly negatively skewed.

Figure 13. Histogram of the normalized hour-ahead forecast errors for the 

German system. μ = 0.0004; σ = 0.0116 γ = - 0.2194; κ =3.7389 
6

V. COMPARISON

The wind power forecasting errors shown in this study 

followed at least one common theme, regardless of country, 

forecasting period, or installed wind capacity considered: they 

were all leptokurtic distributions that were poorly represented 

by normal distribution. However, the distributions shown 

varied considerably based on each of the aforementioned 

criteria. As might be expected, the hour-ahead forecasts had

much higher kurtosis values than those made at the day-ahead 

timescale. This would be expected from the reduction in 

uncertainty that occurs between making a forecast in the dayahead time frame versus a single hour ahead. These 

distributions had many more very small forecast errors but still 

had large forecast errors in extreme cases with high power 

ramps, as represented by the relatively fat tails of the 

distributions. Generally speaking, the larger the installed wind 

power capacity, the smaller the spread of the distribution. This 

was related to the geographic diversity of having more 

turbines experiencing different weather conditions at the same 

time, though one exception of this is the ERCOT day-ahead 

data set. Most of the wind capacity installed in Texas is found 

in a narrow corridor in the northwest panhandle of the state.

Additionally, wind turbines in the United States tend to be 

built in clustered plants, with a high density of turbines in a 

small area. In some of the European countries considered, the 

turbines are built in smaller groups, with less dense clusters of 

wind power. This geographic distance means that the 

forecasting errors between individual turbines are not as well 

correlated.

TABLE I. DAY-AHEAD FORECAST SUMMARY

U.S. Finland Spain Sweden Denmark Ireland Germany

Installed 

Capacity 

(MW)

9,000 102 19,300 2,899 3,871 1,557 26,000

Data Set 

Length 

(Hours)

9,504 8,760 8,760 7,370 8,760 8,760 8,760

Forecast 

Horizon 

(Hours 

Ahead)

8–32 12–36 1–48 16–40 12–36 6–144 12–48

VI. CONCLUSION

This study examined the day-ahead and hour-ahead wind 

power forecasting errors seen in operating practice in seven 

countries. The distribution of forecasting errors was shown to 

be poorly represented by the normal distribution often 

assumed in wind integration studies. The distributions were 

found to be more leptokurtic, with an important distinction 

being the heavier tails seen in the operational forecast error 

distributions. Extreme errors that are not represented by 

normal distribution can have a large economic impact on 

integration planning studies and system operations. We

recommend that future integration studies use representative

wind power forecasting error distributions to guide the process 

instead of making the normal distribution assumption. In this 

study, the hyperbolic distribution was found to better represent 

the entire wind power forecasting error distribution. Further 

investigation is planned on the significance of the differences 

found in the country-to-country variations of wind power 

forecasting error distributions. Likely causes of such 

differences—such as country-specific geographic features, 

forecasting methods, model input parameters, and long-term 

wind resource quality—will be analyzed. The use of this 

information can be important in system operations, impacting 

operational and planning policies. An examination of how 

these country-specific error distributions could impact issues 

such as wind power curtailment policies and thermal generator 

flexibility is planned. Additional work is also planned on 

disaggregating forecast error distributions based on time of 

day and prevailing weather patterns to extract more useful 

information for system operations.

ACKNOWLEDGMENT

B.H., D.L., and M.M. thank David Maggio at ERCOT and 

Keith Parks at Xcel Energy for supplying data used in this 

study. R.S. and L.S. thank Mikael Kröckel and Oskar Sämfors 

at Svenska Kraftnät for supplying data on Sweden. X.L. and 

G.G would like to thank the Nordic Energy Research project 

IceWind for funding under TFI PK-int01.

This work was also supported by the U.S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with the 

National Renewable Energy Laboratory.

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