# On the Use of Dual-Doppler Radar Measurements for Very Short-Term Wind Power Forecasts

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## Abstract

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## 1. Introduction

## 2. Data Description

## 3. Forecasting Methodology

#### 3.1. Predictive Wind Speed Densities

#### 3.1.1. Optimization of the Wind Turbine Area of Influence

#### 3.1.2. Evaluation of Predicted Wind Speeds

#### 3.2. Predictive Wind Power Densities

## 4. Results

#### 4.1. Probabilistic Forecast Evaluation

#### 4.1.1. Individual Wind Turbine Power

#### 4.2. Analysis on Limited Radar Availability

#### 4.2.1. Wind Farm Row Aggregated Power Output

#### 4.3. Evaluation of Single Point Predictions

#### 4.3.1. Individual Wind Turbine Power

#### 4.3.2. Wind Farm Row Aggregated Power Output

## 5. Discussion

#### 5.1. On Further Use of Doppler Radar Measurements for Wind Power Forecasting

#### 5.2. On Extension of the Forecasting Horizon

#### 5.3. On Data Quality

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DD | Dual-Doppler |

R&D | Research and development |

D | Wind turbine rotor diameter |

SCADA | Supervisory Control and Data Acquisition |

${P}_{n}$ | Nominal power |

CRPS | Average Continous Ranked Probability Score |

IEC | International Electrotechnical Commission |

$ecdf$ | Empirical cumulative distribution function |

RF | Remote sensing-based forecast |

${P}_{i}^{RF}$ | Predictive densities of power |

$w{s}_{i}^{RF}$ | Predictive densities of wind speed |

${P}_{agg}$ | Average aggregated power |

RMSE | Root-mean-square error |

NRMSE | Normalised root-mean-square error |

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**Figure 1.**(

**a**) location of the Westermost Rough wind farm ( ), 8 km off the Holderness coast, in the North Sea. The colourbar indicates the height above mean sea level in meters; (

**b**) layout of the wind farm showing the position of the radars (○) and the wind turbines (● and ). Wind turbines used for this analysis ( ) are labeled. The dark and light gray shadowed areas indicate the overlapping dual-Doppler measurement area.

**Figure 3.**Wind rose of one-minute mean wind speeds at the height of 100 m (averaged over the radar domain) observed by the dual-Doppler radar system during the period covered in this analysis.

**Figure 4.**Scheme of the remote sensing probabilistic forecasting model (RF) showing the unmodified wind speed predictive densities ($w{s}_{i}$), the wind speed densities after correcting for induction effects ($w{s}_{i}^{RF}$) and the predictive densities of power (${P}_{i}^{RF}$).

**Figure 5.**Wind speed forecast for $WT4$ (marked in red). (

**a**) Dual-Doppler flow field at the time that the forecast is issued and (

**b**) validated; (

**c**) cloud of wind vectors used to derive the probabilistic forecast for $WT4$ and the respective area of influence (blue circle). Notice the different scales on Figure 5c.

**Figure 6.**Average continuous ranked probability score (CRPS) for the one-minute ahead wind speed predictive densities for different areas of influence ${A}_{i}$ with the remote-sensing forecasting (RF) model (blue dots) and for a probabilistic persistence method (magenta line). The area of influence is expressed in number of rotor diameters (D).

**Figure 7.**(

**a**) predictive histogram distribution of wind speeds for $WT4$ at the time shown in Figure 5b. The blue line represents the mean of the distribution and the magenta line the verifying dual-Doppler wind speed 2.5D upstream of the rotor. N indicates the number of wind field vectors; (

**b**) predictive empirical cumulative distribution function of the normalised power for $WT4$ at the same time. The magenta line indicates the observed power.

**Figure 8.**(

**a**) density scatter plot of the dual-Doppler wind speeds 2.5D upstream of the wind turbine rotor (observed wind speed) and the mean of the five-minute ahead wind speeds distributions without velocity correction due to induction effects, (

**b**) including the velocity correction due to induction effects and (

**c**) for persistence.

**Figure 9.**Normalised wind turbine power curve based on 1656 samples of dual-Doppler wind speeds 2.5D upstream of the rotor, at 100 m height (first row of wind turbines). The line is the binned mean power. The error bars represent the standard deviation in 0.5 m/s wind speed bins.

**Figure 10.**A 60 min episode of five-minute ahead predictions of normalised power for $WT3$ with the remote sensing-based forecasting model (RF). Prediction intervals are shown together with the observed power (red squares).

**Figure 11.**Reliability diagram for all wind turbines (WTs) during available measurements (T) for (

**a**) the remote sensing-based forecasting model (RF) and (

**b**) persistence model, simultaneous periods for (

**c**) the RF and (

**d**) persistence model, a reduced radar availability case for (

**e**) RF and (

**f**) persistence model and (

**g**) the aggregation of $WT1$ to $WT7$ and (

**h**) $WT3$ to $WT5$ for both models. $\overline{N}$ indicates the average number of wind field vectors conforming the wind speed distributions of the RF model. In addition, 95% consistency bars are indicated by the error bars.

**Figure 12.**Wind speeds to be forecasted at the wind turbines (white dots) for a horizon of five minutes, a south-southwesterly wind direction and the radar available distance for (

**a**) full radar availability; (

**b**) limited radar availability.

**Figure 13.**(

**Top**) two radar observed wind fields about five minutes apart; (

**Bottom**) time series of power produced and predicted with the remote sensing-based forecasting (RF) model for the wind turbines $WT1$ and $WT6$. Grey lines indicate the two timestamps above the top panels.

**Table 1.**Average continous ranked probability score (CRPS), in % of the nominal capacity (${P}_{n}$), of the five-minute ahead power forecasts for the seven wind turbines evaluated. Results are shown for the remote sensing-based forecast (RF), persistence and climatology benchmarks. Upper row presents the results for all available measurements (T) of each wind turbine. Lower row provides the results for all simultaneous available measurements. Minimum values are shown in bold.

$\mathit{WT}\mathbf{1}$ | $\mathit{WT}\mathbf{2}$ | $\mathit{WT}\mathbf{3}$ | $\mathit{WT}\mathbf{4}$ | $\mathit{WT}\mathbf{5}$ | $\mathit{WT}\mathbf{6}$ | $\mathit{WT}\mathbf{7}$ | ||
---|---|---|---|---|---|---|---|---|

T | 596 | 903 | 997 | 983 | 960 | 846 | 608 | |

RF | 5.11 | 4.06 | 3.92 | 4.57 | 4.50 | 4.29 | 4.82 | |

CRPS [%] | Persistence | 5.37 | 4.98 | 5.04 | 5.07 | 4.96 | 4.88 | 4.85 |

Climatology | 17.93 | 17.45 | 17.32 | 17.15 | 17.07 | 16.96 | 16.79 | |

T | 343 | 343 | 343 | 343 | 343 | 343 | 343 | |

RF | 6.42 | 5.03 | 4.83 | 5.27 | 4.76 | 4.39 | 4.76 | |

CRPS [%] | Persistence | 6.12 | 5.79 | 5.63 | 5.76 | 5.76 | 5.85 | 5.91 |

Climatology | 16.78 | 16.31 | 15.58 | 15.37 | 15.32 | 15.03 | 14.94 |

**Table 2.**Average continous ranked probability score (CRPS) of five-minute ahead forecasts of power for the seven wind turbines evaluated, in the case of a reduced radar availability (Figure 12b). Results (in % of the nominal capacity (${P}_{n}$)) are shown for the remote sensing-based forecasting (RF) model, persistence and climatology benchmarks.

$\mathit{WT}\mathbf{1}$ | $\mathit{WT}\mathbf{2}$ | $\mathit{WT}\mathbf{3}$ | $\mathit{WT}\mathbf{4}$ | $\mathit{WT}\mathbf{5}$ | $\mathit{WT}\mathbf{6}$ | $\mathit{WT}\mathbf{7}$ | ||
---|---|---|---|---|---|---|---|---|

T | 162 | 162 | 162 | 162 | 162 | 162 | 162 | |

RF | 5.09 | 3.75 | 3.45 | 4.25 | 3.91 | 3.49 | 3.99 | |

CRPS [%] | Persistence | 4.58 | 4.56 | 4.41 | 4.84 | 4.10 | 3.75 | 4.36 |

Climatology | 20.73 | 19.86 | 19.19 | 18.83 | 18.51 | 17.97 | 17.57 |

**Table 3.**Average continous ranked probability score (CRPS), in % of the nominal capacity (${P}_{n}$), for the five-minute ahead predictive densities of aggregated power of different sets of wind turbines. T indicates the sample size evaluated. Minimum values are shown in bold. Results are shown for the remote sensing-based forecasting (RF) model, persistence and climatology benchmarks.

${\overline{\mathit{P}}}_{\mathbf{17}}$ | ${\overline{\mathit{P}}}_{\mathbf{35}}$ | ||
---|---|---|---|

T | 340 | 902 | |

RF | 4.19 | 3.87 | |

CRPS [%] | Persistence | 4.98 | 4.75 |

Climatology | 15.51 | 16.61 |

**Table 4.**Normalised root-mean-square-error (NRMSE), in % of the nominal capacity (${P}_{n}$), of the five-minute ahead forecasts for the seven turbines of the first row. T indicates the number of periods evaluated. Minimum values are shown in bold. Results are shown for the remote sensing-based forecasting (RF) model, persistence and climatology benchmarks.

$\mathit{WT}\mathbf{1}$ | $\mathit{WT}\mathbf{2}$ | $\mathit{WT}\mathbf{3}$ | $\mathit{WT}\mathbf{4}$ | $\mathit{WT}\mathbf{5}$ | $\mathit{WT}\mathbf{6}$ | $\mathit{WT}\mathbf{7}$ | ||
---|---|---|---|---|---|---|---|---|

T | 596 | 903 | 997 | 983 | 960 | 846 | 608 | |

RF | 10.06 | 7.90 | 7.70 | 8.93 | 8.50 | 8.16 | 9.06 | |

NRMSE [%] | Persistence | 9.40 | 8.54 | 8.68 | 8.89 | 8.81 | 8.49 | 8.80 |

Climatology | 31.34 | 30.39 | 30.13 | 29.84 | 29.66 | 29.49 | 29.19 |

**Table 5.**Normalised root-mean-square-error (NRMSE), in % of the nominal capacity (${P}_{n}$), of five-minute ahead forecasts for the seven turbines of the first row, for the case of a reduced radar availability (Figure 12b). Results are shown for the remote sensing-based forecasting (RF) model, persistence and climatology benchmarks.

$\mathit{WT}\mathbf{1}$ | $\mathit{WT}\mathbf{2}$ | $\mathit{WT}\mathbf{3}$ | $\mathit{WT}\mathbf{4}$ | $\mathit{WT}\mathbf{5}$ | $\mathit{WT}\mathbf{6}$ | $\mathit{WT}\mathbf{7}$ | ||
---|---|---|---|---|---|---|---|---|

T | 162 | 162 | 162 | 162 | 162 | 162 | 162 | |

RF | 10.09 | 7.35 | 6.83 | 8.89 | 8.01 | 7.09 | 8.01 | |

NRMSE [%] | Persistence | 8.02 | 7.89 | 7.48 | 8.74 | 7.86 | 6.93 | 8.56 |

Climatology | 35.49 | 34.15 | 33.08 | 32.51 | 32.04 | 31.00 | 30.51 |

**Table 6.**Normalised root-mean-square-error (NRMSE), in % of the nominal capacity (${P}_{n}$), for five-minute ahead forecasts of average aggregated power. Results are shown for the remote sensing-based forecasting (RF) model, persistence and climatology benchmarks.

${\overline{\mathit{P}}}_{\mathbf{17}}$ | ${\overline{\mathit{P}}}_{\mathbf{35}}$ | ||
---|---|---|---|

T | 340 | 902 | |

RF | 8.02 | 8.19 | |

NRMSE [%] | Persistence | 8.50 | 8.22 |

Climatology | 26.24 | 28.88 |

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## Share and Cite

**MDPI and ACS Style**

Valldecabres, L.; Nygaard, N.G.; Vera-Tudela, L.; Von Bremen, L.; Kühn, M. On the Use of Dual-Doppler Radar Measurements for Very Short-Term Wind Power Forecasts. *Remote Sens.* **2018**, *10*, 1701.
https://doi.org/10.3390/rs10111701

**AMA Style**

Valldecabres L, Nygaard NG, Vera-Tudela L, Von Bremen L, Kühn M. On the Use of Dual-Doppler Radar Measurements for Very Short-Term Wind Power Forecasts. *Remote Sensing*. 2018; 10(11):1701.
https://doi.org/10.3390/rs10111701

**Chicago/Turabian Style**

Valldecabres, Laura, Nicolai Gayle Nygaard, Luis Vera-Tudela, Lueder Von Bremen, and Martin Kühn. 2018. "On the Use of Dual-Doppler Radar Measurements for Very Short-Term Wind Power Forecasts" *Remote Sensing* 10, no. 11: 1701.
https://doi.org/10.3390/rs10111701