# Estimation of the Performance Aging of the Vestas V52 Wind Turbine through Comparative Test Case Analysis

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## Abstract

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## 1. Introduction

- Analyzing the rate of performance decline with age for the wind turbines sited in Italy and comparing against the results in [24];
- Inquiring if the operation curves, and therefore the aging, of the four Italian wind turbines are comparable to those of the test case in [24] when the wind turbines have the same age.

- Four test case wind turbines of the same model as [24] (Vestas V52) are added to the literature;
- The four wind turbines sited in Italy can be compared among themselves and against the reference of [24]: the analysis is therefore vertical (each turbine against itself) and horizontal (each wind turbine against the others in the farm and against the reference in [24]). This investigation provides additional information, with respect to the existing literature, about the extent to which it is possible to individuate recurring patterns in the aging of wind turbines of a certain model.
- The generator of one wind turbine sited in Italy reached its end of life in 2018. Therefore, a devoted analysis is performed in this study in order to understand how the performance of the wind turbine changes after the replacement of the generator with respect to the yearly data set immediately before. This analysis, on the one hand, represents a crosscheck of the proposed methodologies and, on the other hand, provides an estimate of the amount of performance recovery that can be expected by replacing an aged main component, as the generator of a wind turbine.
- It is possible to inquire at least qualitatively if there is a connection between the wind turbine site and aging: the wind turbine in [24] is placed in a peri-urban site (in proximity to the Dundalk Institute of Technology in Ireland), while the other four wind turbines considered in this study are placed in an industrial wind farm in a mountainous area.

## 2. The Test Cases and the Data Sets

## 3. The Method

#### 3.1. Operation Curve Analysis

#### 3.2. Support Vector Regression

- We divide the training data set into two parts: $\frac{2}{3}$ of the data (named D0) are used for training the model; $\frac{1}{3}$ (D1) is used for validating and establishing a reference for the behavior of the residuals between model estimates and measurements.
- The model is subsequently validated on the target data set D2, with the objective of comparing the residuals against the reference for the data set D1.

## 4. Results

#### 4.1. Operation Curve Analysis

#### 4.1.1. Region 2: Curve Analysis

#### 4.1.2. Region 2 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$: Curve Analysis

#### 4.2. Support Vector Regression

- For the vertical analysis, the reference was set by training the regression with the data describing each wind turbine aged seven years. The evolution of the curves was quantified by analyzing how the residuals between model estimates and measurements change in all the posterior data sets for each wind turbine. In practice, this analysis follows the history of each wind turbine and compares each wind turbine against itself. This is equivalent to selecting the D0 and D1 data sets from the seven years age data set for each wind turbine and the D2 data set as each posterior one.
- The objective of the horizontal analysis was inquiring how similar the behaviors of wind turbines of the same model are, which are sited in different environments, when they have the same age. The benchmark was selected as the IRE wind turbine this means that D0 and D1 were selected from the data sets of the IRE wind turbine. A separate model was trained per each age and was validated against the ITA data sets of the same age (which therefore constitute the D2 data set). For example, if one considers the generator speed-power curve, the behavior of the IRE wind turbine is learned through the regression and is replicated by predicting how much power the IRE wind turbine would extract when the generator speeds are those measured at the ITA wind turbines; the comparison between measurement and model estimates allows quantifying the average performance difference between the IRE and ITA wind turbines at a given age.

#### 4.2.1. Region 2: Regression Analysis

#### 4.2.2. Region 2 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$: Regression Analysis

#### 4.2.3. Summary of the Results: Aging Estimate

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Vestas V52 wind turbine at Dundalk Institute of Technology [24].

**Figure 4.**Metso PLH-400V52 gearbox [24].

**Figure 5.**A sample power curve (IRE wind turbine) with the operation regions (2 and $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$) indicated.

**Figure 6.**An example of the binned power curve for the IRE and ITA1 wind turbines having the same age (7 years).

**Figure 7.**The standard deviation of the IEC-based power curve of Figure 6, for the IRE and ITA1 wind turbines having the same age (7 years).

**Figure 8.**An example of the binned generator speed-power curve for the IRE and ITA1 wind turbines having the same age (7 years): Region 2.

**Figure 9.**An example of binned blade pitch-power curve for the IRE and ITA1 wind turbines having the same age (7 years): Region 2 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.

**Figure 11.**Block diagram of the horizontal and vertical analysis based on the support vector regression.

**Figure 12.**Generator speed–power curve: horizontal analysis, consisting of the comparison between the two test cases. For each data set, the difference between the IRE curve and the ITA wind turbines’ curve is represented. (

**a**) Seven years, (

**b**) 8 years, (

**c**) 9 years, (

**d**) 10 years, and (

**e**) 12 years.

**Figure 13.**Generator speed–power curve: vertical analysis, consisting of the comparison of each wind turbine against itself in the earliest data set at our disposal (seven years). The difference with respect to the reference curve for each wind turbine is reported. (

**a**) IRE, (

**b**) ITA1, (

**c**) ITA2, (

**d**) ITA3, and (

**e**) ITA4.

**Figure 14.**Analysis of generator substitution at the ITA4 wind turbine: the generator speed–power curve is reported, in the form of the difference between the data sets ${D}_{2018}^{2}$ and ${D}_{2019}^{2}$ (after the generator replacement at ITA4) and the reference ${D}_{2017}^{2}$ data set (before generator replacement at ITA4). Results are reported for ITA4 and for a sample wind turbine ITA2. (

**a**) ITA2 and (

**b**) ITA4.

**Figure 15.**Blade pitch–power curve: horizontal analysis, consisting of the comparison between the two test cases. For each data set, the difference between the IRE curve and the ITA wind turbines curve is represented. (

**a**) Seven years, (

**b**) 8 years, (

**c**) 9 years, (

**d**) 10 years, and (

**e**) 12 years.

**Figure 16.**Blade pitch–power curve: vertical analysis, consisting of the comparison of each wind turbine against itself in the earliest data set at our disposal (seven years age). The difference with respect to the reference curve for each wind turbine is reported. (

**a**) IRE, (

**b**) ITA1, (

**c**) ITA2, (

**d**) ITA3, and (

**e**) ITA4.

Specification | Data |
---|---|

Model | DVSGF 400/4L SP |

Rated power | 850 kW |

Rated stator voltage | 690 V |

Rated stator frequency | 50 Hz |

No. of poles | 4 |

Weight | 3755 kg |

Moment of inertia | 35.7 kg${\mathrm{m}}^{2}$ |

**Table 2.**Gearbox principal specifications [24].

Specification | Data |
---|---|

Model | PLH-400V52 |

Rated lower | 935 kW |

Rated RPM (low speed shaft) | 26 ${\mathrm{min}}^{-1}$ |

Gearing ratio | 61.799 |

Weight | 5400 kg |

Test Case 1 | Test Case 2 | Age (Years) |
---|---|---|

${D}_{2012}^{1}$ | ${D}_{2014}^{2}$ | 7 |

${D}_{2013}^{1}$ | ${D}_{2015}^{2}$ | 8 |

${D}_{2014}^{1}$ | ${D}_{2016}^{2}$ | 9 |

${D}_{2015}^{1}$ | ${D}_{2017}^{2}$ | 10 |

${D}_{2017}^{1}$ | ${D}_{2019}^{2}$ | 12 |

Parameter | Units | Symbol |
---|---|---|

Wind speed | (m/s) | v |

Wind speed standard deviation | (m/s) | ${\sigma}_{v}$ |

Wind direction | (deg) | $\theta $ |

Ambient temperature | (${}^{\circ}$C) | ${T}_{ext}$ |

Rotor speed | (rpm) | $\omega $ |

Blade pitch angle | (deg) | $\beta $ |

Generator speed | (rpm) | $\Omega $ |

Power | (kW) | P |

Gear oil temperature | (${}^{\circ}$C) | ${T}_{oil}$ |

Region | Condition |
---|---|

2 | $5\le v\le 9$ |

2 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ | $9<v\le 13$ |

Region | Curve | $({\mathit{G}}_{1},{\mathit{G}}_{2})$ | ${\mathit{G}}_{1}$ Range | ${\mathit{G}}_{1}$ Bin |
---|---|---|---|---|

2 | Generator speed-power curve | $(\Omega ,P)$ | [1050, 1550] rpm | 50 rpm |

2 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ | Blade pitch angle-power curve | $(\beta ,P)$ | $[-{2}^{\circ},{4}^{\circ}]$ | $0.{5}^{\circ}$ |

Analysis | D0–D1 | D2 |
---|---|---|

Vertical | Age 7 years (${D}_{2012}^{1}$ IRE–${D}_{2014}^{2}$ ITA) | Subsequent ages for each WT |

Horizontal | IRE data set (from ${D}_{2012}^{1}$, age 7 years) | ITA at same age (from ${D}_{2014}^{2}$, age 7 years) |

Region | Input | Output |
---|---|---|

2 | Generator speed $\Omega $ | Power P |

2 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ | Blade pitch angle $\beta $ | Power P |

**Table 9.**Vertical analysis: estimates of $\Delta $ (%) with respect to the baseline data set (7 years age for each wind turbine).

Age | IRE | ITA1 | ITA2 | ITA3 | ITA4 |
---|---|---|---|---|---|

8 years | −1.6 | +2.0 | +2.1 | 1.3 | 3.9 |

9 years | −3.0 | 0.0 | 0.4 | 0.6 | 1.6 |

10 years | −2.5 | −0.3 | 0.3 | −0.7 | 0.1 |

12 years | −8.8 | 0.0 | −1.3 | −1.2 | 1.6 |

**Table 10.**Horizontal analysis: estimates of $\Delta $ (%) with respect to the corresponding IRE baseline data set for each wind turbine age.

Age | ITA1 | ITA2 | ITA3 | ITA4 |
---|---|---|---|---|

7 years | −1.5 | −2.8 | −1.2 | −3.0 |

8 years | 2.9 | 0.2 | 2.1 | 1.2 |

9 years | 2.4 | 0.0 | 2.8 | 0.2 |

10 years | 1.6 | −0.6 | 1.2 | −1.7 |

12 years | 7.8 | 3.8 | 6.5 | 5.6 |

**Table 11.**Vertical analysis for the generator replacement case study: estimates of $\Delta $ (%) with respect to the baseline data set (10 years age for each wind turbine).

Age | ITA2 | ITA4 |
---|---|---|

11 years | −0.4 | 2.2 |

12 years | −0.8 | 2.4 |

**Table 12.**Vertical analysis: estimates of $\Delta $ (%) with respect to the baseline data set (7 years age for each wind turbine).

Age | IRE | ITA1 | ITA2 | ITA3 | ITA4 |
---|---|---|---|---|---|

8 years | −0.3 | −1.1 | −0.8 | −0.9 | +0.2 |

9 years | 0.0 | −1.4 | −1.0 | −0.9 | +0.2 |

10 years | −0.9 | −1.4 | −1.0 | −0.9 | +0.2 |

12 years | −2.0 | −1.2 | −1.6 | −2.1 | −0.4 |

**Table 13.**Horizontal analysis: estimates of $\Delta $ (%) with respect to the corresponding IRE baseline data set for each wind turbine age.

Age | ITA1 | ITA2 | ITA3 | ITA4 |
---|---|---|---|---|

7 years | 1.2 | 1.1 | 0.8 | −0.8 |

8 years | −2.3 | −1.0 | −1.6 | −3.4 |

9 years | 0.0 | 0.3 | 0.8 | 0.2 |

10 years | 0.0 | 0.5 | 0.6 | −0.4 |

12 years | 0.0 | 0.2 | −0.2 | −1.4 |

**Table 14.**Vertical analysis: estimates of $\Delta $ (%) with respect to the baseline data set (7 years age for each wind turbine): Region 2 and Region 2 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ are considered together.

Age | IRE | ITA1 | ITA2 | ITA3 | ITA4 |
---|---|---|---|---|---|

8 years | −1.3 | 1.2 | 1.3 | 0.7 | 3.1 |

9 years | −2.3 | −0.3 | 0.0 | 0.2 | 1.2 |

10 years | −2.2 | −0.5 | 0.0 | −0.8 | 0.1 |

12 years | −7.4 | −0.2 | −1.4 | −1.4 | 1.2 |

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**MDPI and ACS Style**

Astolfi, D.; Byrne, R.; Castellani, F. Estimation of the Performance Aging of the Vestas V52 Wind Turbine through Comparative Test Case Analysis. *Energies* **2021**, *14*, 915.
https://doi.org/10.3390/en14040915

**AMA Style**

Astolfi D, Byrne R, Castellani F. Estimation of the Performance Aging of the Vestas V52 Wind Turbine through Comparative Test Case Analysis. *Energies*. 2021; 14(4):915.
https://doi.org/10.3390/en14040915

**Chicago/Turabian Style**

Astolfi, Davide, Raymond Byrne, and Francesco Castellani. 2021. "Estimation of the Performance Aging of the Vestas V52 Wind Turbine through Comparative Test Case Analysis" *Energies* 14, no. 4: 915.
https://doi.org/10.3390/en14040915