# A Study of the Impact of Pitch Misalignment on Wind Turbine Performance

## Abstract

**:**

## 1. Introduction

- a reliable model for the power output of the wind turbine of interest is formulated;
- the residuals between measurements and model estimates are studied before and after the intervention on the wind turbine of interest.

## 2. The Test Case and the Data Set

- The first data set is denoted as ${\mathrm{D}}_{\mathrm{bef}}$ and contains the data collected from 1st January 2017 to 1st March 2018. It is a period prior to the intervention on turbine T04.
- The second data set is denoted as ${\mathrm{D}}_{\mathrm{aft}}$ and contains the data collected from 1st April 2018 to 1st September 2018. It is a period after the intervention on turbine T04.

## 3. The Methods

- the active power of T01;
- the active power of T02;
- the active power of T03;
- the active power of T05;
- the reactive power of T01.

## 4. The Results

- ${\mathrm{D}}_{\mathrm{bef}}$ was randomly divided in two subsets: D0 ($\frac{2}{3}$ of the data set) and D1 ($\frac{1}{3}$ of the data set). D0 was used for training the model and constructing the weight matrix $\underline{W}$, and D1 was used for validating the model.
- ${\mathrm{D}}_{\mathrm{aft}}$ (also named D2 for simplifying the notation in the following) was used to quantify the performance improvement.

#### 4.1. A Crosscheck of the Results

- The first dataset is denoted as ${\widehat{\mathrm{D}}}_{bef}$ and contains the data collected from 1st January 2017 to 1st January 2018. It is a period prior to the intervention on turbine T04.
- The second dataset is denoted as ${\widehat{\mathrm{D}}}_{aft}$ and contains the data collected from 1st January 2018 to 1st March 2018. This data set is also from a period before the intervention on turbine T04.

- ${\widehat{\mathrm{D}}}_{bef}$ is randomly divided in two subsets: $\widehat{D}0$ ($\frac{2}{3}$ of the data set) and $\widehat{D}1$ ($\frac{1}{3}$ of the data set). $\widehat{D}0$ is used for training the model and constructing the weight matrix $\underline{W}$, and $\widehat{D}1$ is used for validating the model.
- ${\widehat{\mathrm{D}}}_{aft}$ (also named $\widehat{D}2$ for simplifying the notation in the following) is used for evaluating whether there is a remarkable performance difference with respect to $\widehat{D}1$.

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**The average difference R between power measurement y and estimation $\widehat{y}$ (Equation (4)). Data sets: D1 and D2. Sample run of the model.

**Figure 5.**The average difference R between power measurement y and estimation $\widehat{y}$ (Equation (4)). Data sets: $\widehat{D}1$ and $\widehat{D}2$. Sample run of the model.

Wind Turbine | T01 | T02 | T03 | T04 | T05 |
---|---|---|---|---|---|

T01 | 0 | 449 | 1140 | 1870 | 2561 |

T02 | 449 | 0 | 703 | 1433 | 2125 |

T03 | 1140 | 703 | 0 | 730 | 1423 |

T04 | 1870 | 1433 | 730 | 0 | 692 |

T05 | 2561 | 2125 | 1423 | 692 | 0 |

$\mathit{\gamma}$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

${\overline{\delta}}_{\gamma}$ (kW) | 60 | 62 | 61 | 61 | 62 | 62 | 62 | 62 | 62 | 62 |

N. of regressors | 7 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 5 | 5 |

$\eta $ | 66 | 66 | 67 | 70.6 | 70.3 | 75.3 | 78.6 | 85.3 | 87.6 | 88.3 |

**Table 3.**Statistical behavior of the residuals between measurements and estimations for the different random choices of the D0 and D1 data sets.

Residual | ${\mathit{\delta}}_{\mathit{ave}}$ (kW) | ${\overline{\mathit{\delta}}}_{\mathit{ave}}$ (kW) | ${\mathit{\sigma}}_{\mathit{\delta}}$ (kW) |
---|---|---|---|

$R({\mathit{x}}_{1})$ | 0.3 | 61 | 89 |

$R({\mathit{x}}_{2})$ | 35 | 74 | 101 |

**Table 4.**Statistical behavior of the residuals between measurement and estimation for the different random choices of the $\widehat{D}0$ and $\widehat{D}1$ data sets.

Residual | ${\mathit{\delta}}_{\mathit{ave}}$ (kW) | ${\overline{\mathit{\delta}}}_{\mathit{ave}}$ (kW) | ${\mathit{\sigma}}_{\mathit{\delta}}$ (kW) |
---|---|---|---|

$R({\mathit{x}}_{1})$ | 0.05 | 59 | 86 |

$R({\mathit{x}}_{2})$ | 4 | 67 | 93 |

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**MDPI and ACS Style**

Astolfi, D. A Study of the Impact of Pitch Misalignment on Wind Turbine Performance. *Machines* **2019**, *7*, 8.
https://doi.org/10.3390/machines7010008

**AMA Style**

Astolfi D. A Study of the Impact of Pitch Misalignment on Wind Turbine Performance. *Machines*. 2019; 7(1):8.
https://doi.org/10.3390/machines7010008

**Chicago/Turabian Style**

Astolfi, Davide. 2019. "A Study of the Impact of Pitch Misalignment on Wind Turbine Performance" *Machines* 7, no. 1: 8.
https://doi.org/10.3390/machines7010008