## Liquan Zhao* and Yan Long**## |

Disturbance type | Mathematical model | |

Voltage swell | [TeX:] $$X ( t ) = \left( 1 + B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.1 \leq B \leq 0.8$$ | (D1) |

Voltage sag | [TeX:] $$X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.1 \leq B \leq 0.8$$ | (D2) |

Voltage interruption | [TeX:] $$X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.9 \leq B \leq 1$$ | (D3) |

Harmonic | [TeX:] $$\begin{array} { l } { X ( t ) = \sin \omega t + \alpha _ { 3 } \sin ( 3 \omega t ) + \alpha _ { 5 } \sin ( 5 \omega t ) + \alpha _ { 7 } \sin ( 7 \omega t ) } \\ { 0.05 \leq \alpha _ { 3 } \leq 0.15,0.02 \leq \alpha _ { 5 } \leq 0.1,0.02 \leq \alpha _ { 7 } \leq 0.1 } \end{array}$$ | (D4) |

Impulsive transient | [TeX:] $$\begin{array} { l } { X ( t ) = \sin \omega t + B \left[ u \left( t - t _ { 1 } \right) - u \left( t - t _ { 2 } \right) \right] } \\ { 1 \leq B \leq 3,1 m s \leq t _ { 2 } - t _ { 1 } \leq 3 m s } \end{array}$$ | (D5) |

Transient oscillation | [TeX:] $$\begin{array} { l } { X ( t ) = \sin \omega t + B e ^ { - 10 \left( t _ { 2 } - t _ { 1 } \right) } \sin 10 \omega t \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] } \\ { 0.5 T \leq t _ { 2 } - t _ { 1 } \leq 3 T , 0.1 \leq B \leq 0.8 } \end{array}$$ | (D6) |

Voltage flicker | [TeX:] $$X ( t ) = [ 1 + \alpha \sin ( \beta \omega t ) ] \sin \omega t , 0.05 \leq \alpha \leq 0.1,0.1 \leq \beta \leq 0.3$$ | (D7) |

Voltage swell+harmonic | [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 + B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + \sin ( \omega t ) + \alpha _ { 3 } \sin ( 3 \omega t ) + \alpha _ { 5 } \sin ( 5 \omega t ) + \alpha _ { 7 } \sin ( 7 \omega t ) } \\ { 0.1 \leq B \leq 0.8 , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha _ { 3 } \leq 0.15,0.02 \leq \alpha _ { 5 } \leq 0.1,0.02 \leq \alpha _ { 7 } \leq 0.1 } \end{array}$$ | (D8) |

Voltage sag+harmonic | [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + \sin ( \omega t ) + \alpha _ { 3 } \sin ( 3 \omega t ) + \alpha _ { 5 } \sin ( 5 \omega t ) + \alpha _ { 7 } \sin ( 7 \omega t ) } \\ { 0.1 \leq B \leq 0.8 , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha _ { 3 } \leq 0.15,0.02 \leq \alpha _ { 5 } \leq 0.1,0.02 \leq \alpha _ { 7 } \leq 0.1 } \end{array}$$ | (D9) |

Voltage swell+flicker | [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 + B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + [ 1 + \alpha \sin ( \beta \omega t ) ] \sin \omega t } \\ { T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha \leq 0.1,0.1 \leq B \leq 0.8,0.1 \leq \beta \leq 0.3 } \end{array}$$ | (D10) |

Voltage sag+flicker | [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + [ 1 + \alpha \sin ( \beta \omega t ) ] \sin \omega t } \\ { T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha \leq 0.1,0.1 \leq B \leq 0.8,0.1 \leq \beta \leq 0.3 } \end{array}$$ | (D11) |

Table 2 provides the comparison of average accuracy and the total number of support vectors of multiple PQDs using the original PSO and improved PSO with different amplitude modulation factors A. The A is a parameter of inertia weight as shown in Eq. (12). There were 80 training samples for each disturbance and 120 test samples.

From Table 2, we can see that the average classification accuracy of method based on the original PSO is 93.9394% and the total number of support vectors is 478. However, for the method based on the improved PSO method, when A=2.9 , the average classification accuracy is 94.3182% and the total number of support vectors is 369. Furthermore, when A=3.0 , the average accuracy of the method based on the improved PSO method is 94.7727% and the total number of support vectors is 325. When A=3.1 , the average classification accuracy of the improved PSO method is 94.4697% and the total number of support vectors is 386. When A=3.2 , the average classification accuracy of the improved PSO method is 94.3939% and the total number of support vectors is 406. Although the classification accuracy of the method based on the improved PSO method and the number of support vector vary with different A values, all accuracy values were higher for our PSO method compared to the method based on the original PSO method while the number of support vectors is less than the original method. This shows that the performance of classification method based on the improved PSO is better than the original PSO in terms of accuracy and running time.

Table 2.

Algorithm | Average classification accuracy (%) | Total number of support vectors |

Original PSO | 93.9394 | 478 |

Improved PSO | ||

A = 2.9 | 94.3182 | 369 |

A = 3.0 | 94.7727 | 325 |

A = 3.1 | 94.4697 | 386 |

A = 3.2 | 94.3939 | 406 |

When the value of A is greater than 3 or less than 3, the classification accuracy will be reduced and the number of support vectors will increase. This is because the value of A becomes larger and the maximum and minimum values of the inertia weight will be larger. However, literature has shown that the optimal value of the inertia weight is between 0.4 and 0.9 so the value of A was chosen to be 3 in this paper.

Table 3.

Disturbance type | Classification accuracy (%) | ||||

Original PSO | Grid search | Others improved PSO [16] | Others improved PSO [17] | Improved PSO | |

Voltage sag | 100 | 100 | 100 | 100 | 100 |

Voltage swell | 88.3333 | 90.8333 | 89.1667 | 89.1667 | 90.8333 |

Voltage interruption | 86.6667 | 85.8333 | 88.3333 | 86.6667 | 88.3333 |

Harmonic | 100 | 100 | 100 | 100 | 100 |

Impulsive transient | 97.5 | 98.3333 | 97.5 | 97.5 | 98.3333 |

Transient oscillation | 99.1667 | 99.1667 | 100 | 100 | 100 |

Voltage flicker | 95 | 92.5 | 95 | 94.1667 | 94.1667 |

Voltage sag+harmonic | 90 | 91.6667 | 90.8333 | 90.8333 | 91.6667 |

Voltage swell+harmonic | 90 | 90 | 91.6667 | 91.6667 | 91.6667 |

Voltage sag+flicker | 90 | 90.8333 | 89.1667 | 90 | 92.5 |

Voltage swell+flicker | 96.6667 | 96.6667 | 94.1667 | 95 | 95 |

Average classification accuracy | 93.9394 | 94.1667 | 94.1667 | 94.0909 | 94.7727 |

The classification accuracy of power quality disturbances based on different methods is shown in Table 3. There were 80 training samples of each disturbance and 120 test samples. As shown in Table 3, the accuracies of voltage sag and harmonic disturbance are the same for different methods. For the voltage swell disturbance, impulsive transient disturbance, voltage sag+harmonic, the proposed method has the same accuracy as the grid search method, which is higher than others. For the voltage interruption disturbance, the proposed method has the same accuracy of 88.3333% as the SVM method based on the improved PSO [16] method, which is higher than others. For the transient oscillation disturbance and voltage swell+harmonic, the proposed method has the same accuracy as the SVM methods based on the improved PSO [16] and improved PSO [17] method, which is higher than others. For the voltage sag+flicker, the proposed method has higher accuracy than the others. For the voltage flicker and voltage swell+flicker, the proposed method has lower accuracy than other methods. Although our method has lower accuracy for two types of disturbance signals, our method has the same or higher accuracy for the other nine types of disturbance signals and the average classification accuracy of our method is 94.7727%. This is higher than the accuracy of other methods, which is 93.9394%, 94.1667%, 94.1667% and 94.0909%, respectively. This shows that our method has better performance.

In this paper, an improved PSO method is proposed and used to optimize the parameters of the SVM to improve the performance of the power quality disturbances classification. The improved PSO algorithm utilizes a new exponential function formula for determining inertia weight. In the initial stage of the algorithm, a particle has a rapid searching speed. With a gradual decrease in the inertia weight, the speed of the particles will be reduced and in the later stage, the rate of inertia weight gradually decreases. This is advantageous in allowing for a continuous search of a local area and improving the performance of the algorithm. The parameters of the SVM are optimized by the improved PSO algorithm before the multiple power quality disturbances are classified. Compared with other improved PSO algorithms and grid search algorithms, the average classification accuracy is enhanced by using the improved PSO method. In addition, the total number of support vectors is also reduced.

- 1 W. G. Morsi, M. E. El-Hawary, "Power quality evaluation in smart grids considering modern distortion in electric power systems,"
*Electric Power Systems Research*, vol. 81, no. 5, pp. 1117-1123, 2011.doi:[[[10.1016/j.epsr.2010.12.013]]] - 2 Z. G. Liu, Q. G. Zhang, Y. Zhang, "Review of power quality mixed disturbances identification,"
*Power System Protection and Control*, vol. 41, no. 13, pp. 146-153, 2013.custom:[[[http://en.cnki.com.cn/Article_en/CJFDTOTAL-JDQW201313028.htm]]] - 3 M. Valtierra-Rodriguez, R. de Jesus Romero-Troncoso, R. A. Osornio-Rios, A. Garcia-Perez, "Detection and classification of single and combined power quality disturbances using neural networks,"
*IEEE Transactions on Industrial Electronics*, vol. 61, no. 5, pp. 2473-2482, 2013.doi:[[[10.1109/TIE.2013.2272276]]] - 4 M. Biswal, P. K. Dash, "Detection and characterization of multiple power quality disturbances with a fast S-transform and decision tree based classifier,"
*Digital Signal Processing*, vol. 23, no. 4, pp. 1071-1083, 2013.doi:[[[10.1016/j.dsp.2013.02.012]]] - 5 D. De Yong, S. Bhowmik, F. Magnago, "An effective power quality classifier using wavelet transform and support vector machines,"
*Expert Systems with Applications*, vol. 42, no. 15-16, pp. 6075-6081, 2015.doi:[[[10.1016/j.eswa.2015.04.002]]] - 6 N. Huang, D. Xu, X. Liu, "Identification of power quality complex disturbances based on S-transform and SVM,"
*Transactions of China Electrotechnical Society*, vol. 26, no. 10, pp. 23-30, 2011.custom:[[[http://en.cnki.com.cn/Article_en/CJFDTOTAL-DGJS201110003.htm]]] - 7 Y. Mao. C. Xinxin, Z. Qiang, "A review of short-term wind speed prediction based on support vector machine,"
*Journal of Northeast Electric Power University*, vol. 37, no. 4, pp. 1-7, 2017.custom:[[[http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZGDC201204006.htm]]] - 8 H. F. Chen, L. Qiao, S. L. Liu, "Power quality disturbances identification using decision tree and support vector machine,"
*Power System Technology*, vol. 37, no. 5, pp. 1272-12718, 2013.custom:[[[-]]] - 9 J. Zhang, K. Wang, W. Zhu, P. Zhong, "Least squares fuzzy one-class support vector machine for imbalanced data,"
*International Journal of Signal Processing. Image Processing and Pattern Recognition*, vol. 8, no. 8, pp. 299-308, 2015.doi:[[[10.14257/ijsip.2015.8.8.31]]] - 10 A. A. Abdoos, P. K. Mianaei, M. R. Ghadikolaei, "Combined VMD-SVM based feature selection method for classification of power quality events,"
*Applied Soft Computing*, vol. 38, pp. 637-646, 2016.doi:[[[10.1016/j.asoc.2015.10.038]]] - 11 X. Huang, D. Zhang, B. Feng, X. Xu, S. Guo, R. Liu, "Application of an improved PSO algorithm to control parameters auto-tuning for bi-axial servo feed system,"
*Procedia CIRP*, vol. 41, pp. 806-811, 2016.doi:[[[10.1016/j.procir.2015.12.024]]] - 12 N. Ruoxi, C. Houhe, Z. Rufeng, J. Tao, "Calculation of available transfer capability considering economic dispatch of power system,"
*Journal of Northeast Electric Power University*, vol. 36, no. 6, pp. 18-24, 2016.custom:[[[https://scholar.google.co.kr/scholar?hl=ko&as_sdt=0%2C5&q=Calculation+of+available+transfer+capability+considering+economic+dispatch+of+power+system&btnG=]]] - 13 X. Zhaoyang, W. Xiaoyou, X Degui, X. Zhonghui, "Research on dynamic reactive power optimization based on improved PSO,"
*Journal of Northeast Electric Power University*, vol. 37, no. 3, pp. 33-38, 2017.custom:[[[https://scholar.google.co.kr/scholar?hl=ko&as_sdt=0%2C5&q=Research+on+dynamic+reactive+power+optimization+based+on+improved+PSO&btnG=]]] - 14 G. Liu, F. Li, G. Wen, S. Ning, S. Zheng, "Classification of power quality disturbances based on independent component analysis and support vector machine," in
*Proceedings of the 2013 International Conference on Wavelet Analysis and Pattern Recognition*, Tianjin, China, 2013;pp. 115-123. doi:[[[10.1109/ICWAPR.2013.6599302]]] - 15 Jixiu, H. Zhang, Y. Jin, X. Yan, H. Wang, "Based on SVM power quality disturbance classification algorithm," in
*Proceedings of the 2015 27th Chinese Control and Decision Conference*, Qingdao, China, 2015;pp. 3618-3621. doi:[[[10.1109/CCDC.2015.7162551]]] - 16 H. Xu, G. Chen, "An intelligent fault identification method of rolling bearings based on LSSVM optimized by improved PSO,"
*Mechanical Systems and Signal Processing*, vol. 35, no. 1-2, pp. 167-175, 2013.doi:[[[10.1016/j.ymssp.2012.09.005]]] - 17 Y. Wang, L. Zhang, Y. Liu, J. Guo, "Gold price prediction method based on improved PSO-BP,"
*International Journal of u- and e-ServiceScience and Technology*, vol. 8, no. 11, pp. 253-260, 2015.doi:[[[10.14257/ijunesst.2015.8.11.25]]] - 18 D. Wang, X. Wu, Z. Wang, "Fault location for distribution network with distributed power based on improved genetic algorithm,"
*Journal of Northeast Dianli University*, vol. 36, no. 1, pp. 1-7, 2016.custom:[[[https://scholar.google.co.kr/scholar?hl=ko&as_sdt=0%2C5&q=Fault+location+for+distribution+network+with+distributed+power+based+on+improved+genetic+algorithm&btnG=]]] - 19 F. J. Kuang, S. Y. Zhang, "A novel network intrusion detection based on support vector machine and tent chaos artificial bee colony algorithm,"
*Journal of Network Intelligence*, vol. 36, no. 1, pp. 1-7, 2016.custom:[[[https://scholar.google.co.kr/scholar?hl=ko&as_sdt=0%2C5&q=A+novel+network+intrusion+detection+based+on+support+vector+machine+and+tent+chaos+artificial+bee+colony+algorithm&btnG=]]] - 20 J. Zhang, M. Chen, P. W. Tsai, L. M. Tang, X. R. Ji, "A coverage loopholes recovery algorithm in wireless sensor networks,"
*Journal of Information Hiding and Multimedia Signal Processing*, vol. 7, no. 6, pp. 1354-1364, 2016.custom:[[[https://www.researchgate.net/publication/309671633_A_coverage_loopholes_recovery_algorithm_in_wireless_sensor_networks]]] - 21 W. Qian. L, Lina. X. Bei, C. Houhe, "Planning of distributed energy storage system for improving low voltage and network loss in rural network,"
*Journal of Northeast Electric Power University*, vol. 37, no. 5, pp. 19-24, 2017.custom:[[[-]]]