# Short-Term Prediction of the Wind Speed Based on a Learning Process Control Algorithm in Isolated Power Systems

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## Abstract

**:**

## 1. Introduction

- Construction of physical meteorological,
- Statistical methods;
- Methods based on machine learning.

## 2. Materials and Methods

#### 2.1. The Study Object—Gorno-Badakhshan Autonomous Oblast

#### 2.2. The Forecasting Model and Learning Process Control Algorithm

- (1)
- Inputs are the previous hours that coincide with the forecast hour during the month (30 values);
- (2)
- Inputs are all previous hours considered during the week (168 values).

- Min-max normalizer layer (it scales wind speeds to values from 0 to 1).
- Input layer: 30 or 168 wind speed values.
- Hidden layer with an adjustable number of neurons:
- weighted summators;
- activation function: sigmoid or ReLU.

- Output neuron.
- Inverse min-max normalizer (it scales the last neuron output to wind speed).

- (1)
- The number of hidden layer neurons that varies from 3 to 21 with a step of 3;
- (2)
- The activation functions of the hidden layer such as ReLU and sigmoidal;
- (3)
- The learning method such as SGD and Adam:
- (4)
- The learning rate such as 10
^{−4}, 10^{−3}, and 10^{−2}.

#### 2.3. Neural Network Learning Algorithms

_{dw}—a matrix characterizing the inertial properties of the parameters of the ANN, in fact, the matrix of the rate of change of parameters; β

_{1}—parameter that sets the balance between considering the previous direction of the gradient and the direction of the gradient obtained on the next training epoch and the next packet, usually the value of this parameter is close to 1 (~0.9); S

_{dw}—a matrix characterizing the degree (“energy”, since the gradient is squared) of the change in the ANN parameters, without taking into account the direction of change; β

_{2}—a parameter that sets the balance between taking into account the previous energy of changing the direction of the gradient and the direction of the gradient obtained at the next training epoch and the next packet, usually the value of this parameter is close to 1 (~0.999); ε—a positive number close to zero to prevent division by zero; α—the size of the learning step; t—package number during training.

- (1)
- The number of hidden layer neurons that varies from 3 to 21 with a step of 3;
- (2)
- The activation functions of the hidden layer such as ReLU and sigmoidal;
- (3)
- The learning method such as SGD and Adam:
- (4)
- The learning rate such as 10
^{−4}, 10^{−3}, and 10^{−2}.

## 3. Obtained Validation Results and Discussion

^{−3}, while when using SGD the optimal step value varies from 10

^{−2}(Table 2 and Table 4) to 10

^{−4}(Table 3) depending on the season and the number of neurons. It was found that the best combination of ReLU +Adam requires from 600 to 800 epochs. Changing the activation function to Sigmoid or the learning method to SGD slows down the learning process and does not improve its quality. Therefore, the obtained results of simulations have shown the advantage of the Adam learning method and the ReLU activation function for all seasons. Moreover, the sharp changes in wind speed characterize the autumn period in the examined area (Table 4) which increases the difficulties of the forecasting process.

^{−2}), the process does not converge. The error does not decrease in the learning process. With a correctly selected rate (10

^{−3}), the accuracy quickly increases both on the training and validation sets. If the learning rate is too low (10

^{−4}), then the learning process is very slow, so the time to achieve acceptable accuracy is an order of magnitude longer than with a correctly chosen step. Table 6 demonstrates the effect of the number of neurons on the results of model learning. It can be seen that 15 is the optimal neuron number for the ReLU+Adam option. Since the data set is quite small, an increase in the number of neurons can lead to the identification of false dependencies. Figure 2 provides examples of the model learning process. For instance, it can be seen that when using ReLU+Adam, the number of neurons has a much stronger influence on the learning process than when using ReLU+SGD.

^{−3}, and the number of neurons was selected separately (Table 7). The obtained results show that this option is significantly inferior to the option when only the corresponding hours of the previous day are used for the forecast (the first option). It also indicates a very high variability of wind speed in the GBAO of the Republic of Tajikistan. The obtained results of the day ahead wind speed predictions are presented in Figure 3. It presents the variability of wind speed and shows that the forecast repeats the daily profile in general but in some hours the deviations can be very large.

## 4. Conclusions

- Non-use of additional meteorological features such as humidity, pressure, and temperature;
- Absence of wind direction in the forecasting model;
- Manual determination of the point in time when the neural network training process should be completed.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The learning process for the winter period, (ReLU, Adam) with a learning step of 10

^{−3}when the number of neurons changes, the training set (

**a**) and the validation set (

**b**); the learning process for the winter period, (ReLU, SGD) with a learning step of 10

^{−3}when the number of neurons changes, the training set (

**c**) and the validation set (

**d**).

Hyperparameters | Neurons | Learning Rate | Epochs | MAPE, Train Set | MAPE, val. Set |
---|---|---|---|---|---|

ReLU, Adam | 15 | 10^{−3} | 800 | 15.34 | 19.57 |

ReLU, SGD | 9 | 10^{−3} | 1200 | 31.6 | 31.08 |

Sigm., Adam | 12 | 10^{−3} | 1800 | 30.73 | 30.21 |

Sigm., SGD | 15 | 10^{−2} | 600 | 34.09 | 32.75 |

**Table 2.**Comparison of the results of different methods of the day ahead predicting wind speed in spring.

Hyperparameters | Neurons | Learning Rate | Epochs | MAPE, Train Set | MAPE, val. Set |
---|---|---|---|---|---|

ReLU, Adam | 15 | 10^{−3} | 600 | 24.58 | 22.11 |

ReLU, SGD | 6 | 10^{−3} | 1200 | 34.97 | 33.19 |

Sigm., Adam | 6 | 10^{−3} | 1200 | 36.05 | 33.65 |

Sigm., SGD | 15 | 10^{−2} | 600 | 36.48 | 33.78 |

**Table 3.**Comparison of the results of different methods of the day ahead predicting wind speed in summer.

Hyperparameters | Neurons | Learning Rate | Epochs | MAPE, Train Set | MAPE, val. Set |
---|---|---|---|---|---|

ReLU, Adam | 12 | 10^{−3} | 600 | 21.58 | 22.58 |

ReLU, SGD | 12 | 10^{−4} | 1000 | 26.49 | 25.20 |

Sigm., Adam | 12 | 10^{−3} | 1200 | 27.06 | 25.24 |

Sigm., SGD | 3 | 10^{−4} | 1000 | 27.01 | 25.20 |

**Table 4.**Comparison of the results of different methods of the day ahead predicting wind speed in autumn.

Hyperparameters | Neurons | Learning Rate | Epochs | MAPE, Train Set | MAPE, val. Set |
---|---|---|---|---|---|

ReLU, Adam | 15 | 10^{−3} | 600 | 19.44 | 27.78 |

ReLU, SGD | 18 | 10^{−3} | 400 | 36.31 | 36.71 |

Sigm., Adam | 12 | 10^{−3} | 600 | 38.84 | 38.92 |

Sigm., SGD | 18 | 10^{−2} | 600 | 38.90 | 38.98 |

**Table 5.**Simulation results based on the selection of a learning step for the ReLU and Adam, 15 neurons.

Learning Rate | Epochs | MAPE, Train Set | MAPE, val. Set |
---|---|---|---|

10^{−2} | 200 | 31.98 | 31.07 |

10^{−2} | 400 | 32.08 | 31.53 |

10^{−3} | 200 | 27.10 | 27.32 |

10^{−3} | 400 | 20.09 | 22.49 |

10^{−3} | 800 | 15.38 | 19.57 |

10^{−4} | 200 | 34.42 | 35.38 |

10^{−4} | 400 | 33.47 | 32.40 |

10^{−4} | 800 | 32.37 | 31.54 |

10^{−4} | 3000 | 23.11 | 24.55 |

**Table 6.**The results of experiments on the selection of a learning rate for the ReLU activation function, the Adam training method, learning rate 10

^{−3}, 800 epochs.

Neurons | MAPE, Train Set | MAPE, val. Set |
---|---|---|

9 | 26.53 | 26.64 |

12 | 20.39 | 24.44 |

15 | 15.38 | 19.57 |

18 | 17.07 | 20.93 |

21 | 18.02 | 21.72 |

Season | Neurons | MAPE, Train Set | MAPE, val. Set | MAPE, val. Set, 24 h ahead |
---|---|---|---|---|

Winter | 18 | 29.40 | 35.39 | 19.57 |

Spring | 15 | 28.26 | 39.50 | 22.11 |

Summer | 18 | 25.43 | 31.91 | 22.58 |

Autumn | 18 | 25.24 | 36.52 | 27.78 |

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## Share and Cite

**MDPI and ACS Style**

Manusov, V.; Matrenin, P.; Nazarov, M.; Beryozkina, S.; Safaraliev, M.; Zicmane, I.; Ghulomzoda, A.
Short-Term Prediction of the Wind Speed Based on a Learning Process Control Algorithm in Isolated Power Systems. *Sustainability* **2023**, *15*, 1730.
https://doi.org/10.3390/su15021730

**AMA Style**

Manusov V, Matrenin P, Nazarov M, Beryozkina S, Safaraliev M, Zicmane I, Ghulomzoda A.
Short-Term Prediction of the Wind Speed Based on a Learning Process Control Algorithm in Isolated Power Systems. *Sustainability*. 2023; 15(2):1730.
https://doi.org/10.3390/su15021730

**Chicago/Turabian Style**

Manusov, Vadim, Pavel Matrenin, Muso Nazarov, Svetlana Beryozkina, Murodbek Safaraliev, Inga Zicmane, and Anvari Ghulomzoda.
2023. "Short-Term Prediction of the Wind Speed Based on a Learning Process Control Algorithm in Isolated Power Systems" *Sustainability* 15, no. 2: 1730.
https://doi.org/10.3390/su15021730