# Wind Turbine Power Curve Upgrades

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## Abstract

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## 1. Introduction

- Optimization of the pitch angle control system near the cut-in, for an improved start-up;
- Blade retrofitting through the installation of vortex generators and passive flow control devices; and
- Extension of the power curve for very high wind speed, by raising the cut-out and high wind speed cut-in.

## 2. Case 1: Improved Start-Up Through Pitch Angle Optimization

#### 2.1. The Wind Farm and the Data Sets

- ${D}_{bef}$ describes the wind turbines operating before the upgrade and goes from 1 May 2016 to 1 September 2017.
- ${D}_{aft}$ describes T1, T2 and T3 operating after the upgrade and T4 and T5 operating without upgrade and goes from 27 September 2017 (date of installation of the improved start-up system) to 18 January 2018.

#### 2.2. The Method

- The output $y\left(x\right)$ is the power produced by each wind turbine.
- The inputs are nacelle wind speed and wind direction (in the form of sin and cos of the nacelle wind direction $\theta $). Therefore, ${x}_{1}=v$, ${x}_{2}=sin\theta $, ${x}_{3}=cos\theta $.

#### 2.3. The Results

## 3. Case 2: Aerodynamic Retrofitting Through Vortex Generators and Passive Flow Control Devices Installation

#### 3.1. The Wind Farm and the Data Sets

- ${D}_{bef}$ describes the wind turbines operating before the upgrade: it goes from 1 January 2016 to 01/07/2017.
- ${D}_{aft}$ describes T7 operating after the upgrade and the rest of the wind farm operating without upgrade: it goes from 1 September 2017 to 1 April 2016.

#### 3.2. The Methods

#### 3.3. The Results

## 4. Case 3: The Extension of the Wind Turbine Power Curve Above the Cut Out

#### 4.1. The Wind Farm and the Data Sets

#### 4.2. The Methods

- if ${v}_{in}^{bef}\le v\le {v}_{out}^{bef}$ and ${v}_{max}^{bef}\le {v}_{max}\le {v}_{max}^{aft}$: the wind turbine has gained its measured production.
- if $v>{v}_{out}^{bef}$ and ${v}_{max}<{v}_{max}^{aft}$: the wind turbine has gained its measured production.
- if ${v}_{in}^{bef}\le v\le {v}_{out}^{bef}$ and ${v}_{max}<{v}_{max}^{bef}$ and the wind turbine would be in hysteresis according to the pre-upgrade logic: the wind turbine has gained the measured production.
- if ${v}_{in}^{bef}\le v\le {v}_{out}^{bef}$ and ${v}_{max}<{v}_{max}^{bef}$ and the wind turbine would not be in hysteresis according to the pre-upgrade logic: the wind turbine has lost the difference between the rated and the measured production.

- if ${v}_{in}^{bef}\le v\le {v}_{in}^{aft}$ and ${v}_{max}^{bef}\le {v}_{max}\le {v}_{max}^{aft}$: the wind turbine should gain rated power.
- if ${v}_{in}^{aft}\le v\le {v}_{out}^{bef}$ and ${v}_{max}^{bef}\le {v}_{max}\le {v}_{max}^{aft}$: the wind turbine should gain the power indicated by the P model.
- if $v>{v}_{out}^{bef}$ and ${v}_{max}<{v}_{max}^{aft}$: the wind turbine should gain the power indicated by the P model.
- if ${v}_{in}^{aft}\le v\le {v}_{out}^{bef}$ and ${v}_{max}<{v}_{max}^{bef}$ and the wind turbine would not be in hysteresis according to the pre-upgrade logic: the wind turbine has lost the difference between the rated and the power indicated by the P model.
- if ${v}_{in}^{bef}\le v\le {v}_{in}^{aft}$ and ${v}_{max}<{v}_{max}^{bef}$ and the wind turbine would be in hysteresis according to the pre-upgrade logic: the wind turbine should gain rated power.
- if ${v}_{in}^{aft}\le v\le {v}_{out}^{bef}$ and ${v}_{max}<{v}_{max}^{bef}$ and the wind turbine would be in hysteresis according to the pre-upgrade logic: the wind turbine should gain the power indicated by the P model.

#### 4.3. The Results

## 5. Conclusions

- Pitch angle optimization near the cut-in;
- Aerodynamic optimization through the installation of vortex generators and passive flow control devices; and
- Extension of the power curve in the high wind region through a soft cut-out strategy, based on the raising of the cut-out and high wind speed cut-in.

- In this case, the data set at disposal made it possible to study the average power curve according to the IEC guidelines and a certain production improvement near the cut-in was observed. The added value of the proposed ANN method is in the fact that, being driven by the wind statistics at each wind turbine, it is possible to distinguish more finely the behavior of each wind turbine. The order of magnitude of the energy improvement is 1% (1.4% in the most profitable wind turbine, and 0.7% in the least profitable one).
- In this case, the data set at disposal did not make it possible to study the power curve according to the IEC guidelines because the wind speed measurements at the upgraded wind turbine were unreliable after the installation of the flow control devices. The method was therefore based on the use of the power of a certain number of nearby wind turbines as inputs to model the power of the upgraded wind turbine. The result is that the retrofitting had an impact of the order of 2.0% of the AEP. This estimate is of the order of one third lower than the one provided by the wind turbine manufacturer. Since this wind farm is sited on very harsh terrain, this result supports that complex flow conditions have an impact on the efficiency of passive flow control devices.
- The extension of the power curve in the high wind region through a soft cut-out strategy was estimated weighting an order of 0.5% of the AEP of the wind farm since it has been installed. It was observed that this amount is of the order of half the expected, according to the measured wind conditions at the nacelles of the wind turbines. The mismatch between measurement and simulation is explained by the fact that there are frequent shutdowns, due to vibration and control issues, when the wind turbine is expected to work at high wind speed. Since this wind farm is sited on complex terrain, this is more evidence that the production upgrades considerably depend on the conditions at a micro-scale level, especially when rather extreme conditions (wind near the cut-out) come into play.

## Author Contributions

## Conflicts of Interest

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**Figure 4.**Power curve of wind turbine T4 before and after the retrofitting of the T1–T3 wind turbines.

**Figure 5.**The layout of the wind farm for Case 2. In red, the retrofitted wind turbine is indicated (T7).

**Figure 6.**The power coefficient ${C}_{p}$, as computed from the SCADA data, vs. nacelle wind speed: T7 and a sample wind turbine (T2), ${D}_{aft}$ data set.

**Figure 7.**The average differences $R\left({\mathit{x}}_{1}\right)$ and $R\left({\mathit{x}}_{2}\right)$ between T7 power measurements and simulation, for data sets D1 and D2 on a sample model run.

Wind Turbine | $\mathbf{\Delta}$ |
---|---|

T1 | +4.35% |

T2 | +5.95% |

T3 | +3.76% |

Wind Turbine | ${\mathbf{\Delta}}_{\mathit{E}}$ |
---|---|

T1 | +0.51% |

T2 | +0.77% |

T3 | +0.49% |

**Table 3.**Long-term estimate of the energy improvement with respect to the overall production based on the results in Table 1.

Wind Turbine | ${\mathbf{\Delta}}_{\mathit{AEP}}$ |
---|---|

T1 | +0.88% |

T2 | +1.39% |

T3 | +0.74% |

Nomenclature | Wind Speed Regime |
---|---|

${v}_{in}^{bef}$ | high wind speed cut-in before the control system upgrade |

${v}_{out}^{bef}$ | cut-out before the control system upgrade |

${v}_{max}^{bef}$ | shut-down before the control system upgrade |

${v}_{in}^{aft}$ | high wind speed cut-in after the control system upgrade |

${v}_{out}^{aft}$ | cut-out after the control system upgrade |

${v}_{max}^{aft}$ | shut-down after the control system upgrade |

Wind Turbine | Measured Extra Production (% of the Total Actual) | Simulated Extra Production (% of The Total Actual) |
---|---|---|

T1 | 0.55 | 0.78 |

T2 | 0.63 | 0.76 |

T3 | −0.07 | 1.73 |

T4 | 0.51 | 1.76 |

T5 | 0.91 | 2.48 |

T6 | 2.04 | 3.50 |

T7 | 0.65 | 1.49 |

T8 | −0.01 | 0.18 |

T9 | −0.04 | 0.49 |

T10 | 0.06 | 0.62 |

T11 | 0.31 | 0.32 |

T12 | 0.36 | 0.56 |

T13 | 0.50 | 0.57 |

T14 | 0.02 | 0.03 |

T15 | 0.00 | 0.14 |

T16 | −0.02 | 0.67 |

T17 | 0.03 | 0.22 |

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**MDPI and ACS Style**

Astolfi, D.; Castellani, F.; Terzi, L.
Wind Turbine Power Curve Upgrades. *Energies* **2018**, *11*, 1300.
https://doi.org/10.3390/en11051300

**AMA Style**

Astolfi D, Castellani F, Terzi L.
Wind Turbine Power Curve Upgrades. *Energies*. 2018; 11(5):1300.
https://doi.org/10.3390/en11051300

**Chicago/Turabian Style**

Astolfi, Davide, Francesco Castellani, and Ludovico Terzi.
2018. "Wind Turbine Power Curve Upgrades" *Energies* 11, no. 5: 1300.
https://doi.org/10.3390/en11051300