# Forecasting Short- and Long-Term Wind Speed in Limpopo Province Using Machine Learning and Extreme Value Theory

^{*}

## Abstract

**:**

## 1. Introduction

^{2}) gradients all have an impact on wind speed prediction [3,4]. In order to provide reliable forecasts, forecasting models must take into consideration these factors and their interactions. Warm air is preferred by wind turbines for wind power generation in order to pull more kinetic energy from the environment [5,6].

## 2. Related Literature Review

## 3. Advantages Renewable Resources

## 4. Research Highlights

- (a)
- The Augmented Dickey–Fuller (ADF) test indicated that the data distribution does not change over time, indicating that the mean, variance, and autocovarience are constant over time.
- (b)
- The Theil–Sen estimator for nonparametric trend estimation revealed a potential linear relationship over time.
- (c)
- Forecasts generated by the CNN model exhibited excellent predictive performance on both the training and testing datasets, compared to the Vanilla LSTM network.
- (d)
- CNN demonstrated significant potential in predicting future values, as evidenced by various evaluation accuracy metrics.
- (e)
- The $GEV{D}_{r}$ proved to be a suitable distribution for fitting the data and estimating return levels.
- (f)
- To the best of our knowledge, this is the first study to use Vanilla LSTM, CNN, and the $GEV{D}_{r}$ in forecasting wind speed using South African data.

## 5. Materials and Methods

#### 5.1. Data Source and Study Area

#### 5.2. Analytical Techniques

#### 5.2.1. Vanilla Long Short-Term Memory (Vanilla LSTM)

#### 5.2.2. Convolutional Neural Networks (CNNs)

**Convolution Layer + ReLU Activation**

**Max Pooling**

**Fully Connected Layer + ReLU Activation**

#### 5.2.3. Modelling the r-Largest Order Generalised Extreme Value Distribution ($GEV{D}_{r}$)

#### 5.2.4. Parameter Estimation for the $GEV{D}_{r}$

#### 5.2.5. $GEV{D}_{r}$ Return Levels

#### 5.2.6. Theil–Sen Estimator

#### 5.3. Model Evaluation and Validation

#### 5.3.1. Vanilla LSTM Evaluation Metrics

#### 5.3.2. Evaluation Metrics for the $GEV{D}_{r}$

## 6. Empirical Findings and Analysis

#### 6.1. Seasonal Wind Speed Trends for 2023

#### 6.2. Test for Stationarity

**Augmented Dickey–Fuller (ADF)**

#### 6.3. Theil–Sen Non-Parametric Trend Plot

#### 6.4. Machine Learning

#### 6.4.1. Vanilla LSTM and CNN Results

#### 6.4.2. Training and Validation Loss between Vanilla LSTM and CNN Models

#### 6.5. Model Performance Comparison: Vanilla LSTM and CNN Wind Speed Forecasts

#### 6.6. Short-Term Vanilla LSTM and CNN Predictions

#### 6.7. Extreme Value Theory (EVT)

#### Fitting the r-Largest Order Statistics $GEV{D}_{r}$

#### 6.8. $GEV{D}_{r}$ Goodness of Fit

#### 6.9. Diagnostic Plots for $GEV{D}_{r=2}$

#### 6.10. Return Levels for $GEV{D}_{r=2}$

## 7. Conclusions and Recommendation

- Employ advanced machine learning techniques, such as Kolmogorov–Arnold networks (KANs) and temporal convolutional networks (TCNs). These methods can capture complex relationships within meteorological variables and geographical features, thereby enhancing the accuracy and efficiency of wind forecasting.
- Investigate the use of modern EVT techniques, such as blended GEVD (bGEVD) and generalised autoregressive conditional heteroskedasticity-GEVD (GARCH-GEVD), to present a refined approach to analysing extreme events in wind speed data. By incorporating bGEVD and GARCH-GEVD, future research can gain a deeper understanding of the tail behaviour of wind speed distributions, thereby improving the assessment of potential risks associated with extreme wind events.
- Expand the geographical scope to encompass all nine provinces of South Africa for a clear understanding of regional wind patterns. A broader geographical scope will enable the research to capture diverse wind patterns, ensuring a more robust and representative analysis.
- Encourage collaboration and knowledge sharing among research institutions, government entities, and industry stakeholders. By encouraging collaboration among research institutions, government entities, and industry stakeholders, research outcomes and data can be leveraged collectively. The exchange of knowledge and data can facilitate a more comprehensive understanding of the challenges and opportunities in wind power generation.

## 8. Limitations

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geographic location of Polokwane within Limpopo province. Source: https://w.wiki/B2us, accessed on 5 May 2024.

**Figure 2.**Basic architecture of the Vanilla LSTM network. Source: https://www.researchgate.net/figure/The-structure-of-LSTM-memory-cell_fig5_342998863, accessed on 30 June 2024.

**Figure 3.**Basic architecture of a CNN. Source: https://learnopencv.com/wp-content/uploads/2023/01/tensorflow-keras-cnn-vgg-architecture.png, accessed on 18 September 2024.

**Figure 9.**(

**Top left panel**): Vanilla LSTM daily wind speed predictions; (

**Top right panel**): CNN daily wind speed predictions; (

**Bottom left panel**): Vanilla LSTM yearly wind speed predictions; (

**Bottom right panel**): CNN yearly wind speed predictions.

Measure | Min | Median | Mean | Max | Skewness | Kurtosis | Std Dev | ti |
---|---|---|---|---|---|---|---|---|

Wind speed | 0.20 | 7.96 | 8.15 | 22.86 | 0.68 | 4.01 | 2.86 | 0.35 |

Summer | ||||||||

Measure | min | median | mean | std dev | max | skewness | kurtosis | ti |

Wind speed | 2.38 | 7.34 | 7.36 | 2.20 | 13.55 | 0.245 | −0.088 | 0.30 |

Winter | ||||||||

Measure | min | median | mean | std dev | max | skewness | kurtosis | ti |

Wind speed | 0.2 | 7.96 | 8.35 | 3.45 | 22.87 | 0.913 | 1.321 | 0.41 |

Autumn | ||||||||

Measure | min | median | mean | std dev | max | skewness | kurtosis | ti |

Wind speed | 2.06 | 8.90 | 8.78 | 2.91 | 18.21 | 0.312 | −0.149 | 0.33 |

Spring | ||||||||

Measure | min | median | mean | std dev | max | skewness | kurtosis | ti |

Wind speed | 2.38 | 7.65 | 8.09 | 2.52 | 15.73 | 0.326 | 2.502 | 0.31 |

Model | Input Time Steps | MAE | RMSE | MAPE | Accuracy (%) |
---|---|---|---|---|---|

Vanilla LSTM | Yearly (115) | 0.63 | 0.95 | 0.17 | 82.51 |

Monthly (215) | 0.70 | 0.94 | 0.27 | 85.56 | |

CNN | Yearly (115) | 0.57 | 0.81 | 0.11 | 87.25 |

Monthly (215) | 0.53 | 0.75 | 0.09 | 88.66 |

Model | 2024 | 2025 | 2026 | 2027 | 2028 |
---|---|---|---|---|---|

Vanilla LSTM | 9.43 | 7.75 | 7.85 | 6.87 | 9.43 |

CI | (6.92, 11.94) | (5.59, 9.91) | (5.76, 10.15) | (5.48, 8.79) | (6.82, 13.44) |

CNN | 9.91 | 7.64 | 7.81 | 7.13 | 9.59 |

CI | (7.66, 12.04) | (5.43, 8.51) | (5.32, 10.02) | (6.95, 9.51) | (7.63, 12.11) |

r | $\widehat{\mathit{\mu}}$ | $\mathit{SE}\left(\widehat{\mathit{\mu}}\right)$ | $\widehat{\mathit{\sigma}}$ | $\mathit{SE}\left(\widehat{\mathit{\sigma}}\right)$ | $\widehat{\mathit{\xi}}$ | $\mathit{SE}\left(\widehat{\mathit{\xi}}\right)$ | 95% CI ($\widehat{\mathit{\xi}}$) |
---|---|---|---|---|---|---|---|

1 | 8.910 | 0.382 | 1.387 | 3.964 | −0.453 | 0.633 | (−0.374, 0.129) |

2 | 9.285 | 0.219 | 2.566 | 0.154 | −0.037 | 0.048 | (−0.131, 0.057) |

3 | 9.152 | 0.176 | 2.526 | 0.124 | −0.045 | 0.039 | (−0.122, 0.031) |

4 | 9.025 | 0.151 | 2.509 | 0.107 | −0.055 | 0.034 | (−0.121, 0.011) |

5 | 8.918 | 0.134 | 2.496 | 0.094 | −0.062 | 0.029 | (−0.120, −0.004) |

r | $-\mathrm{log}\left(\mathbf{Likelihood}\right)$ | AIC | BIC |
---|---|---|---|

1 | 1184.656 | 2375.312 | 2382.605 |

2 | 419.271 | 844.542 | 853.914 |

3 | 623.655 | 1253.311 | 1263.899 |

4 | 827.407 | 1660.813 | 1672.264 |

5 | 1030.059 | 2066.118 | 2078.239 |

Model | 5 Years | 20 Years | 50 Years | 100 Years | 200 Years | 250 Years | 300 Years |
---|---|---|---|---|---|---|---|

$GEV{D}_{r=2}$ | 13.03 | 16.51 | 18.61 | 20.14 | 21.63 | 22.10 | 22.89 |

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## Share and Cite

**MDPI and ACS Style**

Makubyane, K.; Maposa, D.
Forecasting Short- and Long-Term Wind Speed in Limpopo Province Using Machine Learning and Extreme Value Theory. *Forecasting* **2024**, *6*, 885-907.
https://doi.org/10.3390/forecast6040044

**AMA Style**

Makubyane K, Maposa D.
Forecasting Short- and Long-Term Wind Speed in Limpopo Province Using Machine Learning and Extreme Value Theory. *Forecasting*. 2024; 6(4):885-907.
https://doi.org/10.3390/forecast6040044

**Chicago/Turabian Style**

Makubyane, Kgothatso, and Daniel Maposa.
2024. "Forecasting Short- and Long-Term Wind Speed in Limpopo Province Using Machine Learning and Extreme Value Theory" *Forecasting* 6, no. 4: 885-907.
https://doi.org/10.3390/forecast6040044