^{1}, László Varga

^{2}and Imre M. Jánosi

^{1,a)}

### Abstract

Reanalysis data are rarely used for wind power estimates because of the limited spatial and temporal resolution. Here we report on a detailed comparison of wind speed and electric power time series recorded at a continental location in Hungary and estimates provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-40 and Interim databases at nearby grid points. The results show that the temporal behavior is adequately represented in reanalysis records with damped magnitudes, as expected. However, characteristic shape differences in the wind speed histograms for turbine measurements and reanalysis hinder a perfect match of statistics. A satisfying agreement of histograms for measured and modeled output powers is achieved by scaling up surface wind speeds to have the same long time average value as for the turbine records. The presented calibration permits us to provide wind power estimates for large geographic areas, where the wind field is similarly coherent as around the test site.

We thank the Hungarian Meteorological Service for the access to the ERA-40 data bank. This work was supported by the European Commission’s DG RTD NEST Programme “Tackling Complexity in Science” (Contract No. 043363) and by the Hungarian Science Foundation (OTKA) under Grant No. NK72037.

I. INTRODUCTION

II. DATA SOURCES

III. COMPARISON OF WIND SPEED RECORDS

IV. WIND ENERGY EXPLOITATION: MEASURED DATA

V. WIND ENERGY EXPLOITATION: ESTIMATES FROM WIND SPEED

VI. DISCUSSION

### Key Topics

- Wind energy
- 15.0
- Time series analysis
- 12.0
- Time measurement
- 5.0
- Geographic location
- 4.0
- Spatial resolution
- 4.0

## Figures

Sketch of the geographic setting of the study area and timeline of the records. Heavy diamond indicates the location of the two Enercon E-40 wind turbines and (, ), gray shading signs indicate Hungary, label the nearby ERA-40 grid points (empty circles), and and (empty squares) locate the grid points from the ERA-Interim database used for comparison. The timeline illustrates the overlapping periods 01/01/2000–08/31/2002 for and records and 01/01/2004–12/31/2005 for and time series. (Photograph: Sándor Zátonyi, http://www.panoramio.com)

Sketch of the geographic setting of the study area and timeline of the records. Heavy diamond indicates the location of the two Enercon E-40 wind turbines and (, ), gray shading signs indicate Hungary, label the nearby ERA-40 grid points (empty circles), and and (empty squares) locate the grid points from the ERA-Interim database used for comparison. The timeline illustrates the overlapping periods 01/01/2000–08/31/2002 for and records and 01/01/2004–12/31/2005 for and time series. (Photograph: Sándor Zátonyi, http://www.panoramio.com)

Wind speed records for the , , and grid points (see Fig. 1) in the first 100 days of the overlapping period.

Wind speed records for the , , and grid points (see Fig. 1) in the first 100 days of the overlapping period.

The same as Fig. 2 for the and (red) and (green) records.

The same as Fig. 2 for the and (red) and (green) records.

Normalized histogram of wind speed for the time series and fitted generalized gamma [see Eq. (2)] probability density functions (thin black lines). The empirical parameters are summarized in Table II.

Normalized histogram of wind speed for the time series and fitted generalized gamma [see Eq. (2)] probability density functions (thin black lines). The empirical parameters are summarized in Table II.

(a) Scatter plot for the equal time wind speeds measured at sites and . The regression line has the slope of 1.529. (b) Normalized empirical wind speed histograms for the turbine measurements (dark, blue) and the transformed record (light, orange): . (c) The same as (b) for the fitted probability distributions.

(a) Scatter plot for the equal time wind speeds measured at sites and . The regression line has the slope of 1.529. (b) Normalized empirical wind speed histograms for the turbine measurements (dark, blue) and the transformed record (light, orange): . (c) The same as (b) for the fitted probability distributions.

Electric power output measured at the turbines (thin black line) and (dashed black line) in three consecutive years; high frequency (10 min) data are smoothed by 1008 point (1 week) running average. Horizontal (blue) lines indicate the annual averages. (Percentage values with respect to the rated power are , , and for and , , and for , respectively.)

Electric power output measured at the turbines (thin black line) and (dashed black line) in three consecutive years; high frequency (10 min) data are smoothed by 1008 point (1 week) running average. Horizontal (blue) lines indicate the annual averages. (Percentage values with respect to the rated power are , , and for and , , and for , respectively.)

Power curve fit Eq. (3) of high frequency (10 min) measured nacelle anemometer data for .

Power curve fit Eq. (3) of high frequency (10 min) measured nacelle anemometer data for .

Comparison of estimated electric output based on (see Fig. 5) and the power curve Eq. (3) from 6 h wind speed data for sites and (red) with direct measurements at the turbines and (green). Note that the latter two curves are 6 h averages of 10 min records.

Comparison of estimated electric output based on (see Fig. 5) and the power curve Eq. (3) from 6 h wind speed data for sites and (red) with direct measurements at the turbines and (green). Note that the latter two curves are 6 h averages of 10 min records.

Normalized histograms of electric power for the time series . The last two (green) are based on direct measurements; the others are estimated by the power curve Eq. (3) from the rescaled surface wind speeds , where the numerical value of is given in the second column of Table II. (The vertical scale is logarithmic.)

Normalized histograms of electric power for the time series . The last two (green) are based on direct measurements; the others are estimated by the power curve Eq. (3) from the rescaled surface wind speeds , where the numerical value of is given in the second column of Table II. (The vertical scale is logarithmic.)

(a) The difference between the histograms for sites and shown in Fig. 9. (b) Histogram of annual average output power estimated from the record by and the power curve Eq. (3). The black arrow indicates the range of measured averages at and .

(a) The difference between the histograms for sites and shown in Fig. 9. (b) Histogram of annual average output power estimated from the record by and the power curve Eq. (3). The black arrow indicates the range of measured averages at and .

## Tables

Equal time two-point correlation [see Eq. (1)] matrix for the time series in the overlapping periods (upper diagonal) and geographic distance in units of km (lower diagonal, in parentheses).

Equal time two-point correlation [see Eq. (1)] matrix for the time series in the overlapping periods (upper diagonal) and geographic distance in units of km (lower diagonal, in parentheses).

Fitted parameters of the normalized wind speed probability distributions for the time series , see Fig. 4. The mean value and standard deviation are taken over the entire available record lengths (see Fig. 1), the parameters of the generalized gamma distribution [see Eq. (2)] are denoted by , , and , and the mode (most probable value) is . The second column is the ratio of average wind speed at the turbine and at the given site .

Fitted parameters of the normalized wind speed probability distributions for the time series , see Fig. 4. The mean value and standard deviation are taken over the entire available record lengths (see Fig. 1), the parameters of the generalized gamma distribution [see Eq. (2)] are denoted by , , and , and the mode (most probable value) is . The second column is the ratio of average wind speed at the turbine and at the given site .

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