# Perspectives on SCADA Data Analysis Methods for Multivariate Wind Turbine Power Curve Modeling

## Abstract

**:**

## 1. Introduction

## 2. Multivariate Wind Turbine Power Curve Models

- The selection of the data sources;
- The selection of the input variables;
- The selection of the model structure.

- There is no particular added value in employing meteorological mast data in addition to SCADA data. Furthermore, it should be noticed that the presence of this kind of data is not guaranteed for most operating wind farms.
- There is an evident added value when including the most important operation variables (like blade pitch or rotor speed) in the multivariate models.
- Linear and polynomial models are likely too simplistic. Highly non-linear models are preferable, but there is no particular evidence of the superiority of one type. In general, artificial neural networks, Support Vector Regression with Gaussian kernel and Gaussian process regressions seem to be adequate.
- The regression problem is likely complicated by increasing rotor size. In [17], the same kind of method is tested on three real-world wind turbines (Senvion MM92, Vestas V90 and Vestas V117) and the highest error (normalized to the rated) occurs for the Vestas V117 wind turbine, which is 3.45 MW against 2 MW of the other test cases.
- The use of sub-component temperatures as regressors of the multivariate model has not been much explored, but it looks promising. It should be noticed that the temperature sensors in a wind turbine are numerous and it is unlikely that they fail simultaneously; therefore, their use for compensating lack of reliable wind speed measurements in case of anemometer bias is interesting.
- The test cases in [17] indicate that different input variables are selected by an Automatic Features Selection, depending on the type of wind turbine control (for example, electric pitch vs. hydraulic pitch).
- Summarizing the above points, the most important ingredients for a good multivariate power curve regression in the author’s opinion are a vast data set, including numerous possible covariates, and the use of a non-linear model, for which the relevant features can be selected automatically.

## 3. Discussion and Perspectives

- From Equation (3), it arises that the power factor is a function of the blade pitch and of the tip speed ratio, which is equivalent to the rotational speed.
- From the discussion of Table 1, it arises that the operation variables, in particular blade pitch and rotor speed, are the most effective additional covariates for a multivariate power curve model.
- It has been decided to include the generator speed in the set of input variables because in [15,35] it has been observed that the aging of generator efficiency can affect remarkably the amount of power which is extracted. Wind turbines of the same model can produce different power for the same generator speed. Therefore, it reasonable to add this covariate to the regression.

- Remove outliers;
- Select a model type;
- Select input variables through Automatic Features Selection algorithms or basing on user’s experience or objectives (as in this case);
- Optimize the set up of the model;
- Train the model;
- Validate the model by predicting the output, given the input variables, on a test data set;
- Analyze the goodness of the regression through appropriate error metrics.

## 4. Summary

- Summarize the rationale for SCADA-based power curve analysis in wind energy practice and support the use of multivariate approaches;
- Review and discuss in detail the literature regarding data-driven multivariate wind turbine power curve analysis;
- Given the above points, analyze a test case in order to furnish innovative perspectives on the topic.

- Use highly non-linear models, like ANN, SVR, GP.
- Start from the vastest set of covariates which is considered potentially meaningful.
- Possibly employ Automatic Features Selection for individuating the most appropriate input variables.

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial Neural Network |

IEC | International Electrotechnical Commission |

GP | Gaussian Process |

NMAE | Normalized Mean Absolute Error |

MAE | Mean Absolute Error |

MAPE | Mean Absolute Percentage Error |

NRMSE | Normalize Root Mean Square Error |

NWP | Numerical Weather Prediction |

RMSE | Root Mean Square Error |

SCADA | Supervisory Control And Data Acquisition |

SVR | Support Vector Regression |

TI | Turbulence Intensity |

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**Figure 2.**Example of power curve for a moderate turbulence and a high turbulence site, Vestas V52 wind turbine.

**Figure 9.**Example of scattered power curve and simulated power curve through a Support Vector Regression (using average wind speed, rotor speed, generator speed, blade pitch).

**Table 1.**Summary of model structures, data sources, input variables selection (in addition to the wind speed) and results for the literature about multivariate wind turbine power curve.

Ref. | Model | Data | Input Variables | Error |
---|---|---|---|---|

[19] | Cluster center fuzzy logic ANN k-nearest neighbors Adaptive neuro-fuzzy interference model | SCADA | Wind direction Ambient temperature | NMAE: 1.9% |

[20] 1 | Additive kernel density | SCADA + Met mast | Wind direction Air density Humidity Turbulence intensity Wind Shear 1 Wind Shear 2 | NRMSE: 34.9% |

[20] 2 | Additive kernel density | SCADA + Met mast | Wind direction Air density Turbulence intensity Wind Shear 1 | NRMSE: 15.9% |

[22] | Random forest Extremely randomized trees Stochastic gradient regression trees k-nearest neighbors Binning method 5-parameters logistic | SCADA | Wind direction Yaw error Blade pitch Rotor speed | MAE: 59 kW |

[27] | ANN | SCADA + Met mast | Wind direction Air density Turbulence intensity Yaw error | MAE: 15.3 kW |

[28] | Gaussian process + ANN | SCADA | Wind direction | NMAE: 1.34% |

[29] 1 | Gaussian process | SCADA | Air density Blade pitch | NMAE: 1.64% |

[29] 2 | Gaussian process | SCADA | Air density Rotor speed | NMAE: 1.13% |

[29] 3 | Gaussian process | SCADA | Air density Blade pitch Rotor speed | NMAE: 1.07% |

[30] | Least squares Cubic spline ANN Response surface | SCADA | Air density Blade pitch Rotor speed | NRMSE: 0.96% |

[5] | ANN | SCADA + Met mast | 12 meteo variables | NRMSE: 2.41% |

[31] | Polynomial LARS | SCADA | Wind direction Turbulence intensity Ambient temperature Rotor speed Blade pitch Yaw error 18 internal temperatures | NRMSE: 1.71% |

[32] | Radial basis ANN + Tabu search | SCADA | Wind direction Ambient temperature Blade pitch | NMAE: 1.28% |

[33] | Principal component linear Support vector Feedforward ANN | SCADA | Ambient temperature Blade pitch Rotor speed 1 internal temperature | NMAE: 1.27% |

[17] | Support vector | SCADA | Blade pitch Rotor speed Generator speed | NMAE: 0.87%–1.39% |

Input Variables | NMAE (%) | NRMSE (%) |
---|---|---|

Wind speed (Avg.) Blade pitch (Avg.) Rotor speed (Avg.) Generator speed (Avg.) | 0.98 | 1.77 |

Blade pitch (Average) Rotor speed (Average) Generator speed (Average) | 1.05 | 1.96 |

Wind speed (Avg., Min., Max., Std. Dev.) Blade pitch (Avg., Min., Max., Std. Dev.) Rotor speed (Avg., Min., Max., Std. Dev.) Generator speed (Avg., Min., Max., Std. Dev.) | 0.59 | 1.08 |

Blade pitch (Avg., Min., Max., Std. Dev.) Rotor speed (Avg., Min., Max., Std. Dev.) Generator speed (Avg., Min., Max., Std. Dev.) | 0.69 | 1.22 |

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Astolfi, D.
Perspectives on SCADA Data Analysis Methods for Multivariate Wind Turbine Power Curve Modeling. *Machines* **2021**, *9*, 100.
https://doi.org/10.3390/machines9050100

**AMA Style**

Astolfi D.
Perspectives on SCADA Data Analysis Methods for Multivariate Wind Turbine Power Curve Modeling. *Machines*. 2021; 9(5):100.
https://doi.org/10.3390/machines9050100

**Chicago/Turabian Style**

Astolfi, Davide.
2021. "Perspectives on SCADA Data Analysis Methods for Multivariate Wind Turbine Power Curve Modeling" *Machines* 9, no. 5: 100.
https://doi.org/10.3390/machines9050100