# Modified Power Curves for Prediction of Power Output of Wind Farms

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## Abstract

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## 1. Introduction

- (1)
- A physics-based approach in which the effect of atmospheric variables are added to standard power curves. Wagner et al. [2,3] studied the effect of wind shear by proposing an equivalent wind speed using multiple measurements of wind speed distributed vertically. Additionally, methods to incorporate the effect of turbulence intensity [4,5,6,7] and yaw error [8] have been explored. The effect of atmospheric stability on the performance of power curves has also been examined [9,10]. Moreover, the applicability of equivalent wind speed extends beyond power curves. It can also be implemented in wind farm parameterization models such as Weather Research and Forecast (WRF) model [11].
- (2)
- A data-driven approach for modeling power production. Clifton et al. [1] used a machine learning algorithm called random forests (RF) to predict wind power and found that RFs are a very promising alternative to standard power curves. Neural networks [12,13], conditional kernel density [14] and support vector machines [15] are other data-driven models that have been investigated for power prediction.

## 2. Model Development

#### 2.1. Standard Power Curve

#### 2.2. Modified Power Curves

#### 2.2.1. Modified Power Curve Based on One-Second Data

^{−3}). The adjustment for density variation can be implemented as follows [16]:

#### 2.2.2. Modified Power Curve Based on Ten-Minute Data

## 3. Data Description

#### 3.1. Turbine Data

^{−1}and reaches its rated power at 13.5 m·s

^{−1}(Figure 1). The SCADA system of the turbine provides the standard ten-minute averaged wind speed, temperature, pressure, turbine orientation, power generation and wind turbine operational data. A unique feature of this site is storage of SCADA data from the turbine at 1 Hz rate, a feature that allows us to implement both variations of the model and study the effect of averaging timescale on the performance of the model.

#### 3.2. Meteorological Tower Data

#### 3.3. Data Quality Control

#### 3.3.1. Meteorological Tower Data

^{−1}difference in wind speed measurement and an average of 6.6 degrees in wind direction measurement.

#### 3.3.2. SCADA Data

## 4. Discussion of Results

^{−1}for the four month period of study. It should be noted that average wind speed during the period of study is higher than annual average wind speed at the site [19]. Turbulence is also important for predicting wind turbine power. A typical measure of turbulence at the turbine inflow is turbulence intensity ($TI$), defined as follows [17]:

^{−3}) is used to normalize air density variations. Ambient pressure, temperature, and relative humidity measurements were used for calculating air density at hub height. The distribution is shown in Figure 7e. As it can be seen, air density at this site varies considerably with a mean value of 1.19 kg·m

^{−3}during the four-month period of study, which is close to the reference density.

^{−3}to 2 kg·m

^{−3}, which is an exaggerated range of density variation, and did not happen during the period analyzed. The smaller is the value of reference density, the wider is the peak of the distribution. A chosen value of ${\rho}_{0}$ = 0.5 kg·m

^{−3}results in the widest peak, while a chosen value of ${\rho}_{0}$ = 2 kg m

^{−3}results in the narrowest peak in the distribution. The mean value of density at this site for the four month period of study is 1.19 kg·m

^{−3}, and the resulting distribution falls somewhere in between the widest and narrowest distributions.

^{−3}, which coincides with the mean value of density over the whole four-month period of study and it is in agreement with IEC recommendation for generating power curves [16]. This value for reference density results in the lowest values of $RMSE$ = 86 kW and $MAE$ = 63 kW.

^{−3}, we found the best performance of the model, as shown in Figure 12, compared to the standard power curve. Using the optimum value for reference density, the ten-minute version of the model achieves a 26% improvement in prediction in terms of both $RMSE$ and $MAE$ compared to standard power curve.

#### Power Surface

^{−1}according to IEC [16]. To have roughly equal number of bins along the $\rho $ axis, the bin width along this axis is set to be 0.01 kg·m

^{−3}. Available data are transferred onto two-dimensional bins and generated power is averaged over each bin as shown in Figure 13a. Because the available data do not cover the whole area of feature space, wind power is linearly interpolated along the $\rho $ axis to fill the whole feature space, as shown in Figure 13b. Then, interpolated two-dimensional binned date are used to create a three-dimensional power surface, as shown in Figure 14.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Power curve for the 2.5 MW study turbine, derived using ten-minute data from 20 February to 18 June 2018 and bins of 1 m·s

^{−1}. Cut-in region, operational region and rated region are shown.

**Figure 2.**Wind veer and shear at inflow results in different values of yaw error ($\theta $) and wind speed at different heights. Turbulence also causes fluctuations over mean values of wind speed, yaw error and density. All of these variables are used for predicting power generation by the wind turbine.

**Figure 3.**Location of wind turbine of study in relation to 106 m met tower. Kirkwood community college campus is located in between. Image: Google.

**Figure 4.**Mounting position of instruments and boom levels on the met tower. Booms 1–6 extend towards the west while boom 7 extends towards the east.

**Figure 5.**Wind rose at the site of the wind turbine from: (

**a**) SCADA data; and (

**b**) met tower data. Wind rose were generated after quality checks were applied to the data for the period of study.

**Figure 6.**Ten-minute averaged Hub height (

**a**) wind speed and (

**b**) wind direction measurements from SCADA and met tower data after preliminary quality checks. The dashed diagonal line shows a 1:1 relationship. It should be noted that wind direction at hub height from met tower was not available during the period of study due to sensor failure, and it was interpolated from wind direction at 32 m and 105 m.

**Figure 7.**The observed distribution of meteorological variables based on ten-minute averaged data: (

**a**) hub height wind speed (m·s

^{−1}); (

**b**) turbulence intensity (TI) at hub height; (

**c**) shear exponent; (

**d**) wind veer (degrees); and (

**e**) air density at hub height (kg·m

^{−3}).

**Figure 8.**Standard power curve versus ten-minute and one-second versions of the model based on bins of 0.5 m·s

^{−1}and ${\rho}_{0}$ = 1.225 kg·m

^{−3}.

**Figure 9.**Performance of: (

**a**) standard power curve; (

**b**) ten-minute version of the model; and (

**c**) one-second version of the model, when a reference density of ${\rho}_{0}$ = 1.225 kg·m

^{−3}is considered.

**Figure 10.**Distribution of rotor equivalent wind speed for three different values of ${\rho}_{0}$. Smaller value of ${\rho}_{0}$ results in wider distribution of ${U}_{req}$.

**Figure 12.**Performance of: (

**a**) standard power curve; and (

**b**) ten-minute version of the model, considering an optimum value for reference density (${\rho}_{0}$ = 1.19 kg·m

^{−3}).

**Figure 13.**(

**a**) Two dimensional binning of wind power in terms of rotor equivalent wind speed and density using available data; and (

**b**) linear interpolation of available data for filling empty bins. The bins’ dimensions are 0.5 m·s

^{−1}× 0.01 kg·m

^{−3}.

**Figure 15.**Performance of: (

**a**) standard power curve with (${\rho}_{0}$ = 1.19 kg·m

^{−3}); (

**b**) ten-minute modified power curve with (${\rho}_{0}$ = 1.19 kg·m

^{−3}); and (

**c**) power surface.

Sensor | Make/Model | Quantity | Heights | Resolution |
---|---|---|---|---|

Barometric Pressure | Setra 278 | 2 | 6, 106 m | 1 Hz |

Temperature Sensor | NRG 110S | 2 | 6, 20 m | 1 Hz |

Wind Vane | NRG 200P | 7 | 6, 10, 20, 32, 80, 106 m | 1 Hz |

Cup Anemometer | A100LK | 7 | 6, 10, 20, 32, 80, 106 m | 1 Hz |

T/RH Sensor | Vaisala-HMP 155 | 4 | 10, 32, 80, 106 m | 1 Hz |

Sonic Anemometer | Campbell Scientific-CSAT3B | 4 | 10, 32, 80, 106 m | 20 Hz |

Gas Analyzer | LICOR-LI 7500-RS | 1 | 106 m | 20 Hz |

Gas Analyzer | Campbell Scientific-Irgason | 1 | 106 m | 20 Hz |

Radiometer | Kipp&Zonen-CNR4 | 1 | 106 m | 1 Hz |

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**MDPI and ACS Style**

Vahidzadeh, M.; Markfort, C.D. Modified Power Curves for Prediction of Power Output of Wind Farms. *Energies* **2019**, *12*, 1805.
https://doi.org/10.3390/en12091805

**AMA Style**

Vahidzadeh M, Markfort CD. Modified Power Curves for Prediction of Power Output of Wind Farms. *Energies*. 2019; 12(9):1805.
https://doi.org/10.3390/en12091805

**Chicago/Turabian Style**

Vahidzadeh, Mohsen, and Corey D. Markfort. 2019. "Modified Power Curves for Prediction of Power Output of Wind Farms" *Energies* 12, no. 9: 1805.
https://doi.org/10.3390/en12091805