# A New Wind Turbine Power Performance Assessment Approach: SCADA to Power Model Based with Regression-Kriging

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Factors of Wind Turbine Power Output

_{p}is the power coefficient (related to the aerodynamic efficiency of the wind turbine blades, mechanical losses such as shafting, and electrical losses such as generators).

_{i}is the original wind speed; θ is the inflow angle; and ϕ is the tilt angle of the hub.

_{eq}is the rotor equivalent wind speed corrected with wind shear, n is the number of available measurement heights, v

_{h}is the wind speed at the reference height H, Z

_{i}is the middle height of the i-th segment, and the segment separation line is H − R < Z

_{i}< H + R. R is the radius of the rotor. A is the rotor swept area. A

_{i}is the area at the target height Z

_{i}. The area can be calculated as:

_{i}is the measured wind speed, ρ

_{i}is the measured air density, and ρ

_{0}is the reference air density.

## 3. Regression-Kriging Algorithm

^{T}β is a generalized linear model composed of functional basis f = (f

_{j}, j = 1, 2, …, p) and its weights β = (β

_{j}, j = 1, 2, …, p). Z(X) is a Gaussian process function with a mean value of 0. Its covariance equation is defined as [25]:

^{2}> 0 is the variance. R is the covariance equation, which depends on the distance of X − X′ and scale parameters θ.

_{j}(x

_{i}), i = 1, 2, …, m, j = 1, 2, …, p) is the regression matrix. R = [R(x

_{i}− x

_{j}, θ), i, j = 1, 2, …, m] is the correlation coefficient matrix between the training samples. r(x) = [R(x − x

_{i}, θ), i = 1, 2, …, m] is the cross-correlation coefficient matrix between the predicted value input and the training sample.

^{2})* are the maximum likelihood estimates of scale parameter θ and variance σ

^{2}.

_{1}, x

_{2}, …, x

_{n}, the functional basis is:

_{1}, x

_{2}, …, x

_{n}, x

_{i}x

_{j}, ∀ i, j ϵ [1, n]

_{i}> 0, i = 1, 2, …, n is the scale parameter.

## 4. A Data-Driven Equivalence Validation of Input Variables

## 5. Case Study

#### 5.1. Test Case Overview

#### 5.2. Data Processing

#### 5.3. Regression-Kriging Model of WTG OP

#### 5.4. Model Validation

## 6. Conclusions

^{2}between the predicted value and the measured value of both is greater than 99%. To a certain extent, it is completely universal. Therefore, for the modeling of the WTG OP, SCADA data can be selected as an alternative of the wind resource parameters data and contribute to reducing the met mast dependent modeling. Hence, the WTG OP assessment based on the SCADA2power model is a cost-saving method with limited equipment and shows the potential for remarkable economic value.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The effect of turbulence intensity on WTG OP at different wind speeds (Iref is reference value of the turbulence intensity defined by IEC 61400-1:2019 [23], color axis = normalized power at different wind speeds).

**Figure 2.**The effect of wind shear on WTG OP (color axis = normalized power at different wind speeds).

**Figure 3.**The effect of air density on WTG OP (color axis = normalized power at different wind speeds).

**Figure 4.**Scatter plot of wind resource parameters from mast data vs. WTG OP, 2D matrix with so-called partial dependence plots of the WTG OP, this shows the influence of each varies from met mast (turbulence intensity, air density, wind shear, and inflow angle) on the WTG OP. The diagonal shows the effect of a single wind resource parameter on the WTG OP, while the plots below the diagonal show the effect on the WTG OP when varying two dimensions (color axis = normalized power at rated power).

**Figure 5.**Scatter plot of SCADA data vs. WTG OP, 2D matrix with so-called partial dependence plots of the WTG OP, this shows the influence of each varies from SCADA on the WTG OP. The diagonal shows the effect of a single SCADA parameter (blade pitch angle, rotor speed and nacelle accelerated velocity) on the WTG OP, while the plots below the diagonal show the effect on the WTG OP when varying two dimensions (color axis = normalized power at rated power).

**Figure 6.**The comparison result of the actual value and the predicted value of wind2power model and SCADA2power model.

**Figure 15.**Frequency statistics of residuals between predicted and measured values of the three models.

Model Name | Input Factor | Number of Functional Basis | Model | Functional Basis | Covariance Equation |
---|---|---|---|---|---|

SCADA2power model | Pitch angle, Rotor rotational speed, Nacelle acceleration-X, Nacelle acceleration-Y, Nacelle wind speed | 21 | Regression-Kriging | Quadratic Regular functional basis | Exponential Autocorrelation Function |

wind2power model | Wind speed, Turbulence intensity, Air density, Wind shear | 15 | |||

Nacelle Power Curve | Nacelle speed | - | Defined in IEC61400 Standard | - | - |

Model Name | MAE | MSE | MAE | Explained Variance Score | R^{2} |
---|---|---|---|---|---|

SCADA2power model | 0.0110 | 0.0003 | 0.0057 | 0.9949 | 0.99497 |

wind2power model | 0.0136 | 0.0005 | 0.0070 | 0.9922 | 0.99213 |

Nacelle Power Curve | 0.0249 | 0.0014 | 0.0168 | 0.9784 | 0.97666 |

**Table 3.**Statistical results of the residuals of the predicted values of the three models at different quantiles.

Model Name | P10 | P30 | P50 | P70 | P90 |
---|---|---|---|---|---|

SCADA2power model | −0.03141 | −0.01527 | −0.00876 | −0.00258 | 0.009902 |

wind2power model | −0.04417 | −0.01866 | −0.01059 | −0.00357 | 0.015647 |

Nacelle Power Curve | −0.08048 | −0.0389 | −0.0116 | 0.009568 | 0.035237 |

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**MDPI and ACS Style**

Zhang, P.; Xing, Z.; Guo, S.; Chen, M.; Zhao, Q.
A New Wind Turbine Power Performance Assessment Approach: SCADA to Power Model Based with Regression-Kriging. *Energies* **2022**, *15*, 4820.
https://doi.org/10.3390/en15134820

**AMA Style**

Zhang P, Xing Z, Guo S, Chen M, Zhao Q.
A New Wind Turbine Power Performance Assessment Approach: SCADA to Power Model Based with Regression-Kriging. *Energies*. 2022; 15(13):4820.
https://doi.org/10.3390/en15134820

**Chicago/Turabian Style**

Zhang, Pengfei, Zuoxia Xing, Shanshan Guo, Mingyang Chen, and Qingqi Zhao.
2022. "A New Wind Turbine Power Performance Assessment Approach: SCADA to Power Model Based with Regression-Kriging" *Energies* 15, no. 13: 4820.
https://doi.org/10.3390/en15134820