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Contract No. DE-AC36-08GO28308

Analysis of Variability and 

Uncertainty in Wind Power 

Forecasting: An International 

Comparison

Preprint

J. Zhang,1 B.-M. Hodge,1 E. Gómez-Lázaro,2

A. Line Lovholm,3 E. Berge,3 J. Miettinen,4 H. Holttinen,4 

N. Cutululis,4 M. Litong-Palima,5 P. Sorensen,5 and 

J. Dobschinski6

1 National Renewable Energy Laboratory

2 Univesity of Castilla-La Mancha

3 Kjeller Vindteknikk AS

4 VTT Technical Research Centre of Finland

5 Technical University of Denmark

6 Fraunhofer Institute for Wind Energy and Energy System Technology

To be presented at the 12th International Workshop on Large-Scale 

Integration of Wind Power into Power Systems as well as on 

Transmission Networks for Offshore Wind Power Plants

London, England

October 22 – 24, 2013

Conference Paper

NREL/CP-5D00-60228

October 2013
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1 

This report is available at no cost from the 

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Abstract—One of the critical challenges of wind power 

integration is the variable and uncertain nature of the resource. 

This paper investigates the variability and uncertainty in wind 

forecasting for multiple power systems in six countries. An 

extensive comparison of wind forecasting is performed among the 

six power systems by analyzing the following scenarios: (i) wind 

forecast errors throughout a year; (ii) forecast errors at a specific 

time of day throughout a year; (iii) forecast errors at peak and 

off-peak hours of a day; (iv) forecast errors in different seasons; (v) 

extreme forecasts with large overforecast or underforecast errors; 

and (vi) forecast errors when wind power generation is at 

different percentages of the total wind capacity. The kernel 

density estimation method is adopted to characterize the 

distribution of forecast errors. The results show that the level of 

uncertainty and the forecast error distribution vary among 

different power systems and scenarios. In addition, for most 

power systems, (i) there is a tendency to underforecast in winter; 

and (ii) the forecasts in winter generally have more uncertainty 

than the forecasts in summer. 

Keywords-wind forecasting; reliability; power systems; 

uncertainty; variability 

I. INTRODUCTION

The worldwide nameplate capacity of wind power has 

reached 282,482 MW as of the end of 2012 [1]. Wind energy in 

many countries has already achieved a relatively high level of 

penetration, such as 30% in Denmark, 16% in Spain, and 7.3% 

in Germany [1]. The variable and uncertain characteristics of 

wind power mean that short-term forecasting of wind power 

plays an important role in grid operations at these penetration 

rates. In addition, uncertainties in the wind forecast 

significantly impact the integration costs of wind energy; 

forecast inaccuracies can result in substantial economic losses 

and reliability issues. 

A. Overview of Wind Forecasting 

Wind forecast models can be broadly divided into two 

categories [2]: (i) forecasting based on the analysis of historical 

time series of wind; and (ii) forecasting based on numerical 

weather prediction models. The first type of forecast model 

generally provides reasonable results in the estimation of 

long-term horizons, such as mean monthly, quarterly, and 

annual wind speed. Measure-correlate-predict is one of the 

most popular methods used for long-term wind power 

forecasting [3, 4]. In addition, statistical and machine learning 

techniques that utilize historical data have been shown to work 

well for forecast horizons less than one hour [5, 6]. For 

short-term horizons more than one hour (daily or hourly 

forecasts), the impact of atmospheric dynamics becomes more 

important, and numerical weather prediction models become 

more suitable. Short-term wind power forecasting (between 1 

hour and 72 hours) is uniquely helpful in power system 

planning for the unit commitment and economic dispatch 

process. 

For wind integration studies and stochastic unit 

commitment models, it is important to characterize wind power 

forecast errors, especially for large and infrequent forecast 

errors. A variety of topics on forecast errors have been studied 

in the literature, including distributions of wind power forecast 

errors [7-10], uncertainties in wind forecasting [10-12], the 

economic value of improved wind forecasting [13], and wind 

power ramp forecasting [14, 15]. 

B. Research Motivation and Objectives 

Different wind forecasting strategies are adopted in many 

power systems. Actions taken by power system operators to 

compensate for wind forecast errors are affected by many 

factors, e.g., the location of the power system, wind capacities, 

and time of year. Understanding forecasting errors and 

uncertainties in different power systems and scenarios is 

helpful for (i) developing improved wind forecasting 

technologies for a specified power system and (ii) better 

allocating resources to compensate for wind forecast errors. To 

this end, this paper investigates the uncertainty in wind 

forecasting at different times of year. In addition, an extensive 

comparison of wind forecasting is performed using large-scale 

wind power prediction data from six countries: the United 

States, Finland, Spain, Denmark, Norway, and Germany. In 

this study, day-ahead wind power forecasts were supplied for 

the six countries or balancing areas within a country. 

Jie Zhang, Bri-Mathias Hodge 

National Renewable Energy Laboratory 

Golden, CO, USA 

Emilio Gómez-Lázaro 

University of Castilla-La Mancha 

Albacete, Spain 

Anne Line Lovholm, Erik Berge 

Kjeller Vindteknikk AS 

Kjeller, Norway 

Jari Miettinen, Hannele Holttinen 

VTT Technical Research Centre of Finland 

Espoo, Finland 

Nicolaos Cutululis, Marisciel Litong-Palima, Poul Sorensen 

Technical University of Denmark 

Roskilde, Denmark 

Jan Dobschinski 

Fraunhofer Institute for Wind Energy and Energy System 

Technology, Kassel, Germany 

Analysis of Variability and Uncertainty in Wind 

Power Forecasting: An International Comparison 

Corresponding author, email: bri.mathias.hodge@nrel.gov
2 

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications. 

II. METHODOLOGIES 

To comprehensively understand the variability and 

uncertainty in wind forecasting, the following scenarios were 

analyzed in this study: (i) hourly day-ahead wind power 

forecast errors throughout a year; (ii) forecast errors at a 

specific time of day (hour 14:00 in this paper) throughout a 

year; (iii) forecast errors at peak (7:00 – 22:00) and off-peak 

hours of a day; (iv) forecast errors during different seasons 

(e.g., summer or winter); (v) extreme events with large 

overforecast or underforecast errors (more than 25% wind 

forecast error normalized by total wind capacity); and (vi) 

forecast errors when the wind power generation was at different 

percentages of the total wind capacity: less than 25% of the 

total wind capacity, between 25% and 75% of the capacity, and 

more than 75% of the capacity. 

For each scenario, the distribution of forecast errors and the 

uncertainty in the day-ahead forecasts were estimated. The 95th

percentile of 1-hour-ahead wind forecast errors, an important 

factor for the decision of flexibility reserve requirements, was 

also compared among different countries. 

A. Distribution of Wind Power Forecast Errors 

Multiple distribution types have been analyzed in the 

literature to quantify the distribution of wind power forecast 

errors, including the hyperbolic distribution [8, 9], kernel 

density estimation (KDE) [10], the normal distribution [16, 17], 

and Weibull [18] and beta distributions [7]. KDE was adopted 

in this paper to model the distribution of wind power forecast 

errors for different scenarios. 

KDE is a nonparametric approach to estimate the 

probability density function of a random variable. It has been 

widely used in the wind energy community for wind speed 

distribution characterization [19, 20] and wind power 

forecasting [10, 21]. For an independent and identically 

distributed sample, n ,,, xxx 21  , drawn from some 

distribution with an unknown density f , the KDE is defined 

as [19] 

   





 



   

n

i

i

n

i

ih h

xx K

nh

xxK

n

hxf

1 1

1 )( 1 );(ˆ (1) 

In the equation,  hKhK )/()/1()( has a kernel function K

(often taken to be a symmetric probability density) and a 

bandwidth h (the smoothing parameter). 

B. Uncertainty in Wind Forecasting 

In this paper, the uncertainty in wind forecasting was 

evaluated by the Rényi entropy and standard deviation of 

forecast errors. An information entropy approach was proposed 

in the literature [11, 12] for assessing wind forecasting methods. 

Entropy in information theory is a measure of the uncertainty in 

a random variable; and a smaller information entropy (or 

standard deviation) value indicates less uncertainty in the 

forecasting. In this paper, Rényi entropy was adopted to 

quantify the uncertainty in wind forecasting, which is defined as 

  



n

i

i XH p

1

2 log 1

1 )( 

  (2) 

where α is a parameter that allows for the creation a spectrum of 

Rényi entropies; and i p is the probability density of the th i

discrete section of the distribution. Larger values of α favor 

high probability events, whereas smaller values of α weight all 

of the instances more evenly [11]. The Rényi entropy can 

utilize all of the information present in the forecast error 

distributions to evaluate the uncertainty, whereas the standard 

deviation shows only how much variation or dispersion exists 

from the average or expected value. 

C. Heat Maps of Wind Power Forecast Errors 

One of the most prevalent concerns associated with 

integrating a large amount of wind power into the grid is the 

ability to handle large forecast errors in wind power output. To 

analyze the ramping characteristics in different power systems, 

a heat map of wind forecast errors was developed to present the 

mean forecast error per month and hour of day, which allows 

the operator to simultaneously see the timing and magnitude of 

forecast errors. 

III. VARIABILITY AND UNCERTAINTY ANALYSIS FROM 

OPERATIONAL SYSTEMS

In this work, we followed the convention that the error ( we ) 

is equal to the forecast ( Pwf ) minus the actual ( Pwa ) wind 

power value. 

  PPe wawfw (3) 

The wind power forecast errors from the six countries were 

observed at both the day-ahead and 1-hour-ahead timescale. 

The day-ahead forecasts were estimated using different 

methodologies for the six countries. The 1-hour-ahead 

forecasts for the six countries were synthesized using a 

1-hour-ahead persistence approach. It is important to note the 

1-hour-ahead persistence approach was adopted for analyzing 

power system flexibility but might not be used in some of the 

analyzed power systems. To compare the forecasts in different 

countries, the day-ahead and 1-hour-ahead wind power forecast 

errors were normalized by the total wind capacity in the 

analyzed power system. The following subsections show the 

comparisons in the uncertainties in the forecasting, 

distributions of forecast errors, and heat maps based on 

day-ahead forecasts; the 95th percentiles of forecast errors were 

compared based on 1-hour-ahead forecasts. 

A. 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 a total wind capacity of 

approximately 9,000 MW. The wind power plants are well 

dispersed in the state of Texas. 

The results showed that the level of uncertainty and the 

forecast error distribution vary among different scenarios. For 

the distributions estimated using KDE shown in Fig. 1(a), it 

was observed that the distribution of forecast errors at peak 

hours (7:00 – 22:00) followed a similar trend with the 

distribution estimated using the entire year data. It was 

observed from the comparison between distributions at peak 

and off-peak hours that there were relatively more overforecast 

events at off-peak hours and relatively more underforecast 

events at peak hours. This indicates that the required amount of 

“down” reserves to accommodate wind forecast errors may be 

relatively less than the amount of “up” reserves at off-peak 
3 

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at www.nrel.gov/publications. 

hours, and vice versa at peak hours. By comparing distributions 

among low- medium-, and high-power levels, most 

overforecast events were observed in the low-power scenario, 

followed by medium- and high-power scenarios. This also 

indicated that more “down” reserves are required for the 

high-power scenario, which is more likely to happen at peak 

hours. For extreme events, distributions of overforecast and 

underforecast events were estimated separately. 

Figure 1(b) shows wind forecast errors versus power output 

with 95% confidence interval bands. Confidence intervals, 

represented by red and blue lines, can be used to determine “up” 

and “down” reserve requirements to compensate for a certain 

percentage of occurrences. The range of wind power 

(horizontal axis in Fig. 1(b)) was divided into 10 groups; for 

each group, the average power was calculated as well as the 

confidence intervals that cover 95% of forecast errors. The 

confidence interval bands were then interpolated from the 

group averages. It was observed that more reserves are required 

when wind power generation is approximately 3,500 MW 

4,500 MW. 

The mean hourly day-ahead wind power forecast error per 

month of the ERCOT power system is shown in Fig. 1(c). We 

observed that it tends to underforecast in winter, and tends to 

overforecast at nights in summer. Power system operators 

could mitigate the effects of wind integration on power system 

reliability by adopting appropriate statistical corrections of 

wind forecasting errors based on the pattern of forecasting 

accuracies. It is important to note that the color key in the heat 

map of different countries is represented by different scales, 

with each provided at the bottom of the figure. 

(a) Distributions of day-ahead forecast errors. (b) 95th percentiles of 1-hour-ahead forecast errors. (c) Heat map of day-ahead forecast errors.

Figure 1. Analysis of wind forecast errors of the power system in the United States. 

B. Finland 

The wind capacity analyzed for Finland was the smallest in 

the study, with 130.6 MW of rated power spreading throughout 

23 sites in Finland. The forecasting horizon was 12 hours to 36 

hours, which can be used for day-ahead trading purposes. 

Figure 2 shows the results of wind forecast error analysis for 

the year 2012. As with the U.S. ERCOT power system, the 

distribution of forecast errors at peak hours followed the 

distribution using the entire year’s data. Most forecast errors for 

the high-power scenario were negative, and this tendency can 

help power system operators determine appropriated 

corrections beforehand with high levels of wind power 

generation. The distribution of forecast errors in July was also 

similar with the distribution using the entire year’s data. 

The 95th percentiles of 1-hour-ahead forecast errors in Fig. 

2(b) indicated large reserve requirements with medium levels 

of wind power integration. From the heat map of forecast errors 

in Fig. 2(c), most underforecast errors were observed from 

January to March, and most overforecast events occurred in 

May, and from September to December. 

(a) Distributions of day-ahead forecast errors. (b) 95th percentiles of 1-hour-ahead forecast errors. (c) Heat map of day-ahead forecast errors.

Figure 2. Analysis of wind forecast errors of the power system in Finland. 
4 

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C. Spain 

The Spanish system data included 14,000 MW of total wind 

capacity for the year 2011. The wind power plants are well 

dispersed in the country. Figure 3 shows the results of wind 

forecast error analysis in Spain. 

Distributions of large underforecast and overforecast errors 

were not adequately characterized because of fewer points for 

the two scenarios. As shown in Fig. 3(a), most forecast errors 

for the high-power scenario were negative (as with the analysis 

results in Finland), and this tendency can help power system 

operators determine appropriated corrections beforehand. 

As shown in the figure of 95th percentiles of 1-hour-ahead 

forecast errors, the maximum “down” reserve requirement was 

needed when the wind power reached the total wind capacity. It 

was observed from the heat map that, as with the U.S. ERCOT 

power system, it tended to be underforecast in December and 

January, and overforecast during nights and early morning from 

May to September. 

(a) Distributions of day-ahead forecast errors. (b) 95th percentiles of 1-hour-ahead forecast errors. (c) Heat map of day-ahead forecast errors.

Figure 3. Analysis of wind forecast errors of the power system in Spain. 

D. Denmark 

The Danish system data included 3,265 MW of total wind 

capacity for the year 2012. The wind power plants are well 

dispersed in the country, including all onshore wind power 

plants in Demark. The forecasting horizon was 12 hours to 36 

hours. 

In Fig. 4(a), a multimodal distribution of forecast errors was 

observed in the scenario of a large overforecast. By comparing 

the distributions of forecast errors in January and June, we 

observed that the overall distribution in January was on the left 

side of the distribution in June. This observation indicated 

relatively more underforecast events in January and more 

overforecast events in June for the Danish power system. As 

shown in Fig. 4(b), more underforecast events were observed in 

the medium-power scenario than that in the high-power 

scenario, which differs with power systems in other countries. 

The heat map of forecast errors presents most overforecast 

events at nights and early morning between May and 

September. Most forecasting errors between November and 

March were negative, except during the time period between 

7:00 and 13:00 in December. Overall, the overforecast time 

period in the heat map was more continuous than that in other 

countries, and this observation also applied to underforecast 

time periods. 

(a) Distributions of day-ahead forecast errors. (b) Distributions at different power levels. (c) Heat map of day-ahead forecast errors.

Figure 4. Analysis of wind forecast errors of the power system in Denmark. 
5 

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E. Norway 

The Norwegian system data included 284 MW of total wind 

capacity spreading throughout four sites for the year 2011. The 

forecasting horizon is 12 hours to 36 hours. 

Figure 5 shows the results of wind forecast error analysis. A 

multimodal distribution of forecast errors was also observed in 

the case of large overforecast as with the Danish power system, 

which is not shown in Fig. 5. Similar to most power systems, 

most underforecast events were observed in the high-power 

scenario, followed by medium- and low-power scenarios. 

Figure 5(b) shows wind forecast errors versus power output 

with 95% confidence interval bands for the Norwegian power 

system. Maximum “up” reserves are required with 100 MW to 

150 MW wind power generation, whereas maximum “down” 

reserves are required with a slightly larger wind power 

generation, approximately 140 MW to 190 MW. It was 

observed from the heat map in Fig. 5(c) that there were 

significantly more underforecast events than overforecast 

events throughout the year. 

(a) Distributions of day-ahead forecast errors. (b) 95th percentiles of 1-hour-ahead forecast errors. (c) Heat map of day-ahead forecast errors.

Figure 5. Analysis of wind forecast errors of the power system in Norway. 

F. Germany 

The German system data included 26,000 MW of total wind 

capacity for the year 2010. The wind power plants are well 

dispersed in the country. The forecast of Germany is a sum of 

forecasts for four transmission system operators. The forecast 

of each control zone is a combination of approximately 3 to 6 

different wind power forecast systems based on different 

numerical weather prediction models. The forecasts are used 

for the trading activities on the day-ahead market and are 

consequently generated between 08:00 and 11:00 every 

morning. 

Figure 6 shows the results of wind forecast error analysis. 

The distribution of forecast errors in the German power system 

was narrower than that in other countries, which shows a better 

wind forecasting skill in the German power system. Therefore, 

extreme events in the German power system are defined as 

more than 10% wind forecast error by total wind capacity. As 

shown in Figs. 6(a) and 6(b), (i) the distribution of forecast 

errors for the high-power scenario presented a multimodal 

characteristic and (ii) the overall distribution in July was on the 

left side of the distribution in January, which presents an 

opposite trend with power systems in other countries. The heat 

map in Fig. 6(c) shows that there were relatively more 

overforecast events than underforecast events throughout the 

year. 

(a) Distributions of day-ahead forecast errors. (b) Distributions at different seasons. (c) Heat map of day-ahead forecast errors.

Figure 6. Analysis of wind forecast errors of the power system in Germany.
6 

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at www.nrel.gov/publications. 

G. Comparison of Uncertainty in Wind Forecasting 

The uncertainty in wind forecasting is evaluated by the 

Rényi entropy and standard deviation of forecast errors. Figure 

6 shows the values of Rényi entropy and standard deviation for 

different scenarios. For the calculation of Rényi entropy, the 

number of bins for probability estimation and the value of α are 

set to be 100 and 2, respectively. In Fig. 6, black and red points 

represent the Rényi entropy and standard deviation, 

respectively; the left axis is Rényi entropy and right is standard 

deviation. According to the Rényi entropy metric, the wind 

forecasting in the Danish power system maintains a relatively 

lower level of uncertainty for most scenarios. Based on the 

standard deviation values of wind power forecast errors, there is 

the least uncertainty in the forecasting for the German power 

system, followed by the Danish power systems. The forecast 

error variability is relatively lower for Denmark, Germany, and 

Spain, which all have a significant amount of well-dispersed 

wind power. It was also observed that, for most power systems, 

the forecasts in winter generally had more uncertainty than the 

forecasts in summer. 

The Rényi entropy of power systems in the United States, 

Finland, Spain, Denmark, Norway, and Germany, respectively, 

varied 10.5%, 84.2%, 69.6%, 175.7%, 28.6%, and 37.7% 

among the eleven scenarios. The variation in the standard 

deviation values among the eleven scenarios was more 

significant than that in the Rényi entropy.

Figure 6. Uncertainty in wind forecasting of different scenarios. 

IV. CONCLUSION

This paper compared the variability and uncertainty in wind 

forecasting for multiple power systems from six countries. For 

each power system, eleven scenarios were analyzed to estimate 

distributions of forecast errors. Multimodal characteristics were 

observed in the extreme overforecast scenarios in the Danish 

and Norwegian systems, and in the high-power scenario in the 

German system. The distribution of forecast errors in the 

German power system was relatively narrower than that in other 

countries. For most power systems, there were more 

underforecast events observed in the high-power scenario than 

in the low- and medium-power scenarios. 

The 95th percentiles of 1-hour-ahead forecast errors showed 

that maximum “up” and “down” reserves were required when 

actual wind power generation was at medium to high 

percentages of the total wind capacity. For most systems, the 

forecasts in winter presented an underforecast tendency and 

more uncertainty. There was generally less uncertainty in 

forecasting when wind power plants were dispersed throughout 

a wide geographic area. 

Future work will (i) investigate multiple years of wind 

forecasting data to obtain a general trend of forecast errors, and 

(ii) compare the different methodologies in the forecasting 

systems in different countries and seek to identify the possible 

sources of bias and errors in the forecasts. 

ACKNOWLEDGMENT

This work was 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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