# Fast Numerical Wind Turbine Candidate Site Evaluation

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## Abstract

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## Featured Application

**The method of shortening the required time of data collection before the construction of a small wind turbine is ready to be tested in actual candidate locations, particularly in complex terrain in temperate regions.**

## Abstract

## 1. Introduction

- Because of time constraints, one month of wind speed measurements from the candidate turbine site is available.
- A fine resolution numerical weather prediction (NWP) model for the area is available and its predictions for the past are available.
- Past measurements from meteorological stations in the area, but not from the site under examination, are available.
- One year of wind speed and direction signals for the candidate site are sought after, so 11 months are predicted.
- A yes/no decision on installing the wind turbine at the exact location is required—the option of adjusting the location is not considered.

- The prediction is not real-time, eliminating the timing constraints—model inputs do not have to be available before the time for which the prediction is made. Reanalyses, which are more accurate, can be used.
- No measurement of the wind parameters on the candidate site is available as a model input. The measurements are available as training data to train the model, but not as an input at times close to the time for which the prediction is made.

- The available data cover a very limited time period.
- The focus is on a single location.
- There is a lack of time for measuring, while the wind resource assessment models are addressing the lack of measurement sites in spatial dimensions.

## 2. Methods

#### 2.1. Description of the Site

#### 2.2. Signals

#### 2.3. Regressors

- the current wind speed at Cerklje Airport meteorological station;
- the current wind speed according to the NWP model;
- the current temperature difference between Lisca and Cerklje Airport meteorological stations; and,
- the air pressure change in the last 2 h at Stolp meteorological station.

#### 2.4. Linear Regression

#### 2.5. Gaussian Process Modelling

#### 2.6. Experimental Modelling

**GP SE**:- Gaussian process model with squared exponential covariance function;
**GP lin**:- Gaussian process model with linear covariance function;
**GP SE+lin**:- Gaussian process model with covariance function that is the sum of a squared exponential function and a linear function; and,
**LS lin**:- linear regression with least squares approximation.

#### 2.7. Model Evaluation

#### 2.7.1. Qualitative

#### 2.7.2. Quantitative

#### 2.8. Spatial Transferability of the Method

## 3. Results

#### 3.1. Time-Series Modelling Results

#### 3.2. Results Related to Wind Speed Distribution

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

NWP | Numerical weather prediction |

MOS | Model output statistics |

GP | Gaussian process |

FIR | Finite impulse response |

MSE | Mean square error |

MSLL | Mean standardised log loss |

## References

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**Figure 3.**Digital elevation model [32] of the study area (30 km by 30 km) with the meteorological stations marked.

**Figure 4.**CORINE Land Cover [32] for the study area (30 km by 30 km) with the meteorological stations marked.

**Figure 5.**Splitting of the data in different ways to train and test several models. Model 1 is trained on January data and tested on the other 11 months, etc.

**Figure 6.**Comparison of measurement and model results for Brežice for the first week of May 2017. The model used is a linear regression with least squares model trained on November 2017 data, referred to as Model 11 in Figure 5. It can be seen that the predicted mean value reasonably follows the measured signal and that the predicted variance is nearly constant and reasonable. The figures of merit for the model are R = 0.6906, R${}^{2}$ = 0.4760, MSE = 0.2345, and MSLL = −0.3155 when computed over the whole 11-month test period.

**Figure 7.**Comparison of measurement and model results Brežice over 50 days of 2017. The model used is a linear regression with least squares model trained on November 2017 data, referred to as Model 11 in Figure 5.

**Figure 8.**Scatter plots and Q–Q plots of wind speeds for the Brežice meteorological station. The measurements are compared to the numerical weather prediction (NWP) model (

**left**) and to the linear regression with least squares model trained on November 2017 data (

**right**). The experimental model used is the same one as in Figure 6. The shown LS lin model predictions are for the test data. The black line is the line of equality, and the red line is the least-squares linear fit of all the data points.

**Figure 9.**Scatter plots and Q–Q plots of wind speeds for Stolp meteorological station. The measurements are compared to the NWP model (

**left**) and the linear regression with least squares model trained on May 2017 data (

**right**). The shown LS lin model predictions are for the test data. The black line is the line of equality, and the red line is the least-squares linear fit of all the data points.

**Figure 10.**Sunflower diagrams [39] for Brežice and Stolp meteorological stations. The measurements (

**left**) are compared to the linear regression with least squares model trained on one month of data (

**right**) and the NWP model (

**top**). The experimental models used are the same as in Figure 8 and Figure 9, the LS lin model predictions are for the test data. In a sunflower diagram, each one of the 24 sectors corresponds to one hour of the day. The values for each hour are sorted into classes that are represented with sections of different colours. The length of each section is proportional to the statistical frequency of the values within the class.

**Table 1.**Requirements for fulfilling different needs in wind power. Wind resource assessment characterizes the resource over an area, is performed on historical data, and has long-term time series data available at most for a limited set of locations in the area. Wind power forecasting addresses a selected site, has to work in real time, and it has real-time measurements from the site available. Evaluating a candidate site is done for a selected site on historical data. Traditionally, it requires long-term time series measurement data from the site, while the proposed method performs it with a shorter-term time series of measurements from the site, supported with other available signals.

Addressed Need | Location? | Real-Time Output or Historic Data? | Local Measurements? |
---|---|---|---|

Wind resource assessment | area | historic | spatially limited |

Wind power forecasting | point | real-time | available |

Candidate site evaluation | point | historic | available * |

*** The proposed solution enables evaluation with temporally limited local measurements.**

Name | WGS84 Coordinates | |
---|---|---|

Latitude | Longitude | |

Brežice | 45.906760 | 15.596502 |

Cerklje Airport | 45.900833 | 15.516111 |

Lisca | 46.067735 | 15.284905 |

Stolp | 45.939900 | 15.513132 |

**Table 3.**Figures of merit for various models of wind speed at Brežice meteorological station and for LS lin model at Stolp meteorological station. The values given are the values obtained on the test data averaged over the 12 models with different train/test data set selections and the Brežice models are ordered in ascending MSE.

Model Name | R | R${}^{2}$ | MSE [m${}^{2}$/s${}^{2}$] | MSLL |
---|---|---|---|---|

LS lin | 0.685 | 0.454 | 0.243 | −0.285 |

GP lin | 0.685 | 0.435 | 0.251 | −0.266 |

GP SE+lin | 0.636 | 0.378 | 0.276 | −0.198 |

GP SE | 0.601 | 0.341 | 0.293 | −0.190 |

NWP | 0.418 | 0.000 | 2.842 | - |

LS lin Stolp | 0.811 | 0.652 | 0.442 | −0.514 |

**Table 4.**Wind speed distribution-related figures of merit for various models of wind speed at Brežice meteorological station and for LS lin model at Stolp meteorological station. The wind speed and the cube of the wind speed are averaged over the 11-month test period for each model to obtain $\overline{v}$ and $\overline{{v}^{3}}$. The difference between $\overline{v}$ or $\overline{{v}^{3}}$ obtained with model prediction and $\overline{v}$ or $\overline{{v}^{3}}$ obtained from the measurement is computed, squared, and the 12 squares that correspond to the 12 train/test data set selections are averaged.

Model Name | MSE($\overline{\mathit{v}}$) [m${}^{2}$/s${}^{2}$] | MSE($\overline{{\mathit{v}}^{3}}$) [m${}^{6}$/s${}^{6}$] |
---|---|---|

LS lin | 0.003 | 1.177 |

GP lin | 0.011 | 1.399 |

GP SE+lin | 0.005 | 1.210 |

GP SE | 0.004 | 1.421 |

NWP | 1.004 | 645.327 |

LS lin Stolp | 0.003 | 14.179 |

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## Share and Cite

**MDPI and ACS Style**

Perne, M.; Mlakar, P.; Grašič, B.; Božnar, M.Z.; Kocijan, J.
Fast Numerical Wind Turbine Candidate Site Evaluation. *Appl. Sci.* **2021**, *11*, 2953.
https://doi.org/10.3390/app11072953

**AMA Style**

Perne M, Mlakar P, Grašič B, Božnar MZ, Kocijan J.
Fast Numerical Wind Turbine Candidate Site Evaluation. *Applied Sciences*. 2021; 11(7):2953.
https://doi.org/10.3390/app11072953

**Chicago/Turabian Style**

Perne, Matija, Primož Mlakar, Boštjan Grašič, Marija Zlata Božnar, and Juš Kocijan.
2021. "Fast Numerical Wind Turbine Candidate Site Evaluation" *Applied Sciences* 11, no. 7: 2953.
https://doi.org/10.3390/app11072953