Detection and localization of partial discharge are very important in condition monitoring of power cables, so it is necessary to build an accurate recognizer to recognize the discharge types. In this paper, firstly, a power cable model based on FDTD simulation is built to get the typical discharge signals as training samples. Secondly, because the extraction of discharge signal features is crucial, fractal characteristics of the training samples are extracted and inputted into the recognizer. To make the results more accurate, multiSVM recognizer made up of six Support Vector Machines (SVM) is proposed in this paper. The result of the multiSVM recognizer is determined by the vote of the six SVM. Finally, the BP neural networks and ELM are compared with multiSVM. The accuracy comparison shows that the multiSVM recognizer has the best accuracy and stability, and it can recognize the discharge type efficiently.
With the development of the power industry and urbanization in China, the power cable is used everywhere. As a result, the detection and localization of partial discharge are becoming more and more important in condition monitoring of power cables. Building an accurate model of cables helps analyzing the propagation characteristics of electromagnetic pulse and recognizing its type accurately when partial discharge happens in the cable. So, accurate model is necessary [
In recognizing the types of partial discharge, the extraction of discharge signal features is the key [
Back propagation (BP) network is a kind of widely used pattern recognizer [
SVM is a kind of data mining method based on statistical learning theory. It can handle the regression problems (time series analysis) and pattern recognition (classification problem and discriminant analysis) successfully [
The principle of SVM is to find an optimized classified hyperplane based on classification requirements. The hyperplane can maximize blank area on both its sides and, at the same time, guarantee the classification accuracy [
Assuming that the given samples are
The samples
When using SVM, solving regression problem, introduce linear insensitive loss function
Considering the tolerated fitting deviation, the original problem can be transformed into structural risk minimization objective function problem by introducing two groups of nonnegative slack variables and using the principle of structural risk minimization. The optimization problem as (
Constraints are
Then, build Lagrange function and transform inequality constraints into equality constraints as follows:
The optimization problem as (
Constraints are
Maximize (
The introduction of kernel function takes the place of dot product in the highdimensional space, avoiding the problem of nonlinear mapping function which reduces the computation and complexity significantly. Then the result is as follows:
Most objects in nature are very complex and irregular. When the object has some similarities between the local and global, it can be viewed as fractal. The fractal dimension, as quantitative characterization and basic parameter of the fractal, is an important principle of the fractal theory. According to different definitions and calculation methods, box dimension and information dimension are often used in the fractal calculation [
To the Point Set
Because the box dimension is not able to reflect the unevenness of geometric objects, a box with one or several points may have the same weights. The information dimension has some advantages in this situation [
So, the information dimension of Point Set
Finite Difference Time Domain (FDTD) is a numerical calculation method in solving the time domain electromagnetic problem. It finishes finite difference discretization in time and space domain based on Maxwell equations and then builds the central finite difference equations whose accuracy is secondorder. FDTD can simulate any kind of electromagnetic structure according to the electromagnetic parameters and medium parameters of the model [
In suitable boundary conditions and initial conditions, FDTD can give the time domain characteristic of electromagnetic wave by solving the differential Maxwell equations, which makes it easier for us to analyze the discharge problems in the XLPE power cables [
XLPE cables have the typical coaxial structure. To find out the characteristics of this structure, FDTD simulation program is applied. Figure
XLPE cable simulation model and the distribution of the sensors.
Structure of the model.
The structure and the materials electrical characteristics of the model are shown as in Figure
Materials electrical characteristics of the model.
Structure parts  Outer diameter/mm  Material  Relative permittivity  Conductivity 

Conductor  20.4  Copper  — 

Conductor shield  21.8  Semiconductor  30.0  2 
Insulation  30.1  Silicone rubber  3.2  0 
Insulation shield  31.5  Conductive silicon rubber  90.0  0.5 
Copper joint shield  34.9  Copper  — 

Composite tape  35.5  PVC  3.0 

Polyethylene sheath  40.0  XLPE  2.3  0 
Gaussian pulse is used to simulate the partial discharge voltage pulse:
Waveform of partial discharge voltage pulse.
In order to study propagation characteristics of the electromagnetic signal in the coaxial waveguide, signals are taken from sensor 1 to sensor 8. Field signal which only contains TEM wave measured by sensor 1 is shown in Figure
Waveform of sensor 1.
Results show that the propagation of the signal from sensor 1 to sensor 8 has caused its amplitude to weaken from 9799.4 mV/m to 7485.6 mV/m, reduced by 2.34 dB, and the signal waveform is changed significantly. However, the amplitude and waveform of the signal components below 400 MHz which only contain TEM wave are not changed. It indicates that when propagating in the coaxial waveguide, the attenuation of TEM wave is small and its waveform will remain basically unchanged, while the amplitude of electromagnetic wave decays a lot and the waveform changes because of the dispersion effect of higherorder mode waves.
The simulation data may have some deviation. In order to make the result more accurate, a list of discharge signals from a real power cable line are monitored and recorded. The data recording system is shown as Figure
Real data of discharge signal recording system.
The band of the measuring impedance is 45~250 kHz, and the setting of the monitor is 500 kS/s with 1 MB memory capacity and threshold trigger. So the monitor can store up to 100 cycles of discharge waveform. Their information dimension and box dimension are calculated and recorded, as shown in Table
Real data of discharge signals recorded.
Information dimension  Box dimension  Discharge type  

Discharge 1  (0.51, 1.52)  (0.35, 1.86)  Creeping discharge 
Discharge 2  (1.42, 1.15)  (1.67, 0.85)  External corona discharge 
Discharge 3  (1.63, 1.63)  (1.44, 1.35)  Floating electrode discharge 
Discharge 4  (1.69, 1.06)  (1.81, 0.77)  External corona discharge 
Discharge 5  (0.46, 1.78)  (0.45, 1.55)  Creeping discharge 
Discharge 6  (0.55, 1.65)  (0.37, 1.61)  Creeping discharge 
Discharge 7  (0.61, 1.14)  (0.77, 1.27)  Internal air discharge 
Discharge 8  (0.75, 1.02)  (0.65, 1.18)  Internal air discharge 
Discharge 9  (1.77, 1.67)  (1.27, 1.54)  Floating electrode discharge 
Discharge 10  (0.47, 1.68)  (0.28, 1.61)  Creeping discharge 
In order to make the multiSVM recognizer more accurate, the simulation data are used as training samples to train the SVM and the measured data are used as testing samples to verify its accuracy.
When training SVM recognizer, SVM model and its Lagrange multipliers can be determined by training the samples and solving the quadratic programming equations. The flowchart of multiSVM recognizer is shown as Figure
Flowchart of SVM recognizer.
Studies show that there are approximately four types of PD in XLPE cables: creeping discharge, floating electrode discharge, internal air discharge, and external corona discharge. According to their different characteristics, four PD faults are set in the simulation model.
Gather 80 groups of data (20 groups of each discharge type) from cable partial discharge simulations and process them according to the minimum box counting method. Four fractal characteristics are found from grayscale images: box dimension of the positive half cycle
Fractal characteristics of partial discharge.
Information dimension
Box dimension
Figure
As we know, it is difficult for SVM to solve partial discharge problems. So in this paper the algorithm proposed is multiSVM which is made up of six SVM. The principle to build multiSVM recognizer proposed in this paper is to combine six onetoone SVM together.
Use RBF as multiSVM method’s kernel function:
Comparatively speaking, there are two different kinds of branching algorithms: onetoone algorithms and onetomany algorithms [
Six onetoone SVM are proposed in this paper to recognize four types of discharges. They are defined as SVM1, SVM2, SVM3, SVM4, SVM5, and SVM6. The multiSVM recognizer proposed in this paper is made up of these six SVM. The discharge type is determined by the vote shown in Table
Determine the discharge type by vote.
Recognizer  Creeping discharge  Floating electrode discharge  Internal air discharge  External corona discharge 

SVM1  0  0  1 

SVM2  1  0 


SVM3  1  0 


SVM4  0  1 


SVM5  0  1  0 

SVM6  1 

0  0 
Vote results of four discharge types.
Discharge type  Vote results 

Creeping discharge  SVM1 + SVM2 + SVM3 + SVM4 + SVM5 + SVM6 
Floating electrode discharge  SVM1 + SVM2 + SVM3 + SVM4 + SVM5 − SVM6 
Internal air discharge  SVM1 − SVM2 + SVM3 − SVM4 + SVM5 + SVM6 
External corona discharge  −SVM1 + SVM2 − SVM3 + SVM4 − SVM5 + SVM6 
Use the 80 groups of data (20 groups of each discharge type) from cable partial discharge simulations to train the SVM recognizer. After training, the number of support vectors of each SVM is shown as in Table
The number of support vectors.
SVM1  SVM2  SVM3  SVM4  SVM5  SVM6 

40  18  23  19  35  24 
Take SVM2 as an example. The structure of SVM2 is shown as in Figure
Weights of support vectors of SVM2.










1.32  0.52  0.48  0.74  0.14  0.96  1.25  0.36  0.24 













0.26  0.44  0.61  1.73  0.81  0.41  0.52  1.16  0.85 
The structure of SVM2.
Use the 10 groups of real data recorded in 30 kV power cable as testing samples to verify the effectiveness of the multiSVM recognizer proposed in this paper. After normalizing the data, the fractal characteristics of testing samples are shown as in Figure
Fractal characteristics of testing samples.
Information dimension
Box dimension
After inputting the fractal characteristics of the testing samples into the multiSVM, the vote results are shown as in Table
Vote results of testing samples.
Creeping discharge  Floating electrode discharge  Internal air discharge  External corona discharge  Discharge type result  

Discharge 1 

0  0  0  Creeping discharge 
Discharge 2  0  0  0 

External corona discharge 
Discharge 3  0 

0  0  Floating electrode discharge 
Discharge 4  0  0  0 

External corona discharge 
Discharge 5 

0  0  0  Creeping discharge 
Discharge 6 

0  0  0  Creeping discharge 
Discharge 7  0  0 

0  Internal air discharge 
Discharge 8  0  0 

0  Internal air discharge 
Discharge 9  0 

0  0  Floating electrode discharge 
Discharge 10 

0  0  0  Creeping discharge 
Compared with Table
There are many kinds of intelligent algorithm such as BP neural networks and ELM. In order to prove the accuracy of multiSVM, systematical and comprehensive comparisons are made in this paper. BP neural networks and ELM are applied into the recognizer instead of multiSVM to recognize the discharge type.
BP neural networks are widely used in many aspects. In this paper, calculate the fractal calculation parameters (
The number of input layer neurons is
Detailed expression of BP neural networks.
Input layer neurons  Hidden layer neurons  Output layer neurons  

Input 





Output 





Neurons model 





Neurons expression 



Structure of BP neural networks.
In the setting, the target error is 10^{−4}; after 400 times of training, the BP neural network finishes. The dropping of deviation by training is shown as in Figure
Dropping of deviation by training.
Use 100 groups of simulation data to test the accuracy of BP neural network; the results are shown as in Table
Results of BP neural networks.
Discharge type  

Creeping discharge  Floating electrode discharge  Internal air discharge  External corona discharge  
Test sample number  100  100  100  100 
Correct results number  78  76  80  75 
Accuracy  78%  76%  80%  75% 
In the BP neural networks, the parameters of hidden layer are determined by large numbers of iterations which will take a lot of time and the results may be unsatisfying as well. In order to improve the performance of the network, ELM is proposed by Huang G.B. Etc [
Input: training samples made up of fractal calculation parameters (
Parameters of hidden layer generated randomly
Calculating hidden layer output matrix
Output: optimized weight of network
Results of ELM.
Discharge type  

Creeping discharge  Floating electrode discharge  Internal air discharge  External corona discharge  
Test sample number  100  100  100  100 
Correct results number  90  88  91  86 
Accuracy  90%  88%  91%  86% 
In order to test the accuracy of the multiSVM recognizer proposed in this paper, use 100 groups of simulation data to test the accuracy of multiSVM; the results are shown as in Table
Results of multiSVM.
Discharge type  

Creeping discharge  Floating electrode discharge  Internal air discharge  External corona discharge  
Test sample number  100  100  100  100 
Correct results number  91  92  96  91 
Accuracy  91%  92%  96%  91% 
The accuracy comparison between BP neural networks, SLM, and SVM is shown as in Table
Accuracy comparison.
Algorithm  Discharge type  

Creeping discharge  Floating electrode discharge  Internal air discharge  External corona discharge  
BP neural networks  78%  76%  80%  75% 
ELM  90%  88%  91%  86% 
MultiSVM  91%  92%  96%  91% 
The effectiveness of multiSVM recognizer is satisfied. The accuracy of multiSVM recognizer of all types is over 90%, especially the recognition of internal air discharge (96%). The result shows that the fractal characteristics of partial discharge signals have a strong ability to describe pattern and the recognizer is effective.
Power cable is a very important part of the modern power system. Monitoring of power cables is directly related to the safety and stability of power system. So, it is necessary to build an accurate recognizer to recognize the discharge types correctly. The power cable model based on FDTD simulation is built to get the typical discharge signals as training samples, and fractal characteristics of the training samples are extracted and inputted into the recognizer. To make the results more accurate, multiSVM recognizer is proposed in this paper. Finally, the BP neural networks recognizer and ELM recognizer are compared with multiSVM recognizer proposed in this paper. The accuracy comparison shows that multiSVM recognizer performs best (accuracy of each type over 90%), especially the recognition of internal air discharge (96%). The result shows that the fractal characteristics of partial discharge signals have a strong ability to describe pattern and the multiSVM recognizer is effective.
The authors declare that there is no conflict of interests regarding the republication of this paper.