## Yanling Wang* , Xing Zhou* , Likai Liang* , Mingjun Zhang** , Qiang Zhang*** and Zhiqiang Niu****## |

Category | Date of wind speed |

I | day6, day7 |

II | day1, day5, day9, p |

III | day2, day3, day4, day8, day10 |

We use number day1,day2,...,day10 to represent 10-day historical wind speed data respectively, and p stands for input data used to forecast. As seen in the Table 1, the input data is assigned to class, that is to say, when we use the input data to realize the forecast of short-term wind speed, the historical data whose label is day1, day5, day9 should be used as the training sample of LSSVR. Practical prediction used 30 groups historical data, but only 10 groups of historical data was used to display Ward clustering analysis method just for convenience. The trends in wind speed data for categories I, II, and III are shown in Fig. 3, Fig. 4, and Fig. 5 respectively.

We can see that the change trend of data of day1, day5, day9, p is consistent enough through observing the change trend of wind speed data of classes I, II, and III. So the Ward clustering analysis method can realize the accurate classification of historical data, and the classification results are satisfactory.

4.2 Parameter Optimization Based on Particle Swarm OptimizationThe parameters of the least squares support vector regression machine will change the performance of SVM, and then affect the prediction accuracy of the model. However, the SVM itself cannot determine the optimal parameters. In order to optimize the selection of parameters, PSO algorithm is adopted to improve the prediction accuracy of the model.

During the learning of least squares support vector regression machine, part of data is selected as training data, another part of the data is used to test. Then the model is evaluated according to the test results. Finally, the model chooses the best parameters. The measurement criterion is the fitness function. We select the average relative error as the fitness function, such as Eq. (17).

In Eq. (17), *f _{MSE}* is on behalf of the fitness function value,

The parameters of this model which need to be optimized are: the regularization parameter γ and kernel parameter σ. First, a group of random particles should be initialized. Each particle represents a set of values of the regularization parameter and kernel parameter. The initial position is an arbitrary particle, and the arbitrary particle is trained by LSSVR. We calculate the value of fitness function. A set of optimal regularization parameter and kernel parameter can be found by iterative trained, thus the optimization of LSSVR parameters can be realized.

4.3 Selection of Input DataWhen predicting the wind speed at a certain time, it is necessary to select a certain amount of historical data as input variables. The number of input independent variables will also have a certain impact on the accuracy of the forecast. Inadequate input variables cause the relationship between the predicted output data and the input data cannot be fully reflected. However, adequate input variables lead to data redundancy, which makes the inherent relationship between the data cannot be adequately represented. In order to select the input independent variables, the average wind speed data for 3 hours, 5 hours, and 8 hours in succession are selected as the input. The selection of the input independent variables is determined by observing the prediction error and the analysis results are shown in Table 2.

Table 2.

Input variable | Average relative error |

3 hours before the wind speed | 0.3749 |

5 hours before the wind speed | 0.1622 |

8 hours before the wind speed | 0.2874 |

It can be seen that the prediction accuracy is the highest when the wind speed data is selected as the input independent variable for 5 hours before the prediction time, that is to say, when the wind speed data for t moment was predicted, t-1, t-2, t-3, t-4, t-5 time wind speed data as input, can realize the prediction of short-term wind speed.

4.4 Model TestNow we forecast short-term wind speed of 24 hours for a certain farm (short-term prediction means predicting every 15 minutes). We select eight days whose wind speed is similar to data for prediction by Ward clustering analysis as the training sample of LSSVR, so it is total 8×24×4 sets of training data and 24×4 sets of predicted data. Related parameters of PSO algorithm are shown in Table 3.

The value of forecasted wind speed and actual wind speed is shown in Fig. 6.

Table 3.

Population size n | Maximum iterations | Acceleration constant c_{1} | Acceleration constant c_{2} |

20 | 200 | 1.5 | 1.7 |

In Fig. 6, the predicted result of wind speed is close to the actual value, and the model can accurately predict the wind speed. The relative error of each prediction point is calculated, and the relative error of each prediction point is shown in Fig. 7.

As seen from Fig. 7, the prediction error of the model is stable. The average relative error of the estimates is 5.11% and the maximum relative error is not more than 14%. For forecasting of short-term wind speed, the industry standard of relative error issued by the State Grid should be less than 20% [20], and the prediction data we get meets the industry standard. It proves that the prediction of the model performances is good and the model is reliable.

In this paper, we have proposed short-term wind speed forecast based on LSSVM. Compared with the traditional short-term wind speed forecasting methods, the proposed model is applied in regression field to find the regression relationship between historical data and forecast data. When choosing the training sample, the model uses cluster analysis innovatively to select appropriate historical data rather than chooses a large number of historical data casually as sample.

The model observably improves the quality of the training samples, hence the accuracy and reliability of the model can be improved. Now, the view of SVM cannot select the optimal parameters by itself, so it is combined with PSO algorithm to optimize the parameters. Hence, the model’s prediction error can be limited at about 5%, and the result of the model can get great improvement compared with the traditional methods.

She is a postgraduate in School of Mechanical Electrical and Information Engineering at Shandong University, China. She is major in circuit and system. Her main research interests include current-carrying transmission and automation of electric power systems. Yanling Wang, Xing Zhou, Likai Liang, Mingjun Zhang, Qiang Zhang, and Zhiqiang Niu

She received her Ph.D. degree from School of Electrical Engineering from Shandong University, China in 2013. She teaches as an associate professor in School of Mechanical Electrical and Information Engineering at Shandong University, China. Her current research interests include power system operation and control.

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