Journal of Electrical and Computer Engineering

Volume 2015, Article ID 174538, 11 pages

http://dx.doi.org/10.1155/2015/174538

## An Advanced Partial Discharge Recognition Strategy of Power Cable

Shandong Provincial Key Laboratory of UHV Transmission Technology & Equipment, School of Electrical Engineering, Shandong University, Jinan 250061, China

Received 17 April 2015; Revised 16 July 2015; Accepted 29 July 2015

Academic Editor: John N. Sahalos

Copyright © 2015 Xiaotian Bi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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, multi-SVM recognizer made up of six Support Vector Machines (SVM) is proposed in this paper. The result of the multi-SVM recognizer is determined by the vote of the six SVM. Finally, the BP neural networks and ELM are compared with multi-SVM. The accuracy comparison shows that the multi-SVM recognizer has the best accuracy and stability, and it can recognize the discharge type efficiently.

#### 1. Introduction

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 [1, 2].

In recognizing the types of partial discharge, the extraction of discharge signal features is the key [3]. Because of the large amounts of data from the measured graphics or waveform, they are too difficult to recognize directly. So they need to be transformed from original data to signal features. So far, researchers from home and abroad use statistical characteristic parameters, pulse characteristic parameters, moment features, or fractal characteristics to recognize discharge types. Because of their accuracy and less characteristic parameters, fractal characteristics are becoming more and more popular [4].

Back propagation (BP) network is a kind of widely used pattern recognizer [5]. It has some disadvantages such as network structure, local minimum, and over- or underlearning. Support Vector Machine (SVM) is a new kind of pattern recognition method which is proposed and developed in the recent decades. It can solve the small sample learning problems and solve the local minimum and over-study-learning or under-study-learning problems. Now the SVM has been widely used in the power system [6].

#### 2. Support Vector Machine

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 [7].

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 [8]. In theory, SVM can achieve optimal classification.

Assuming that the given samples are and , . The number of samples is . SVM defines a nonlinear feature space mapping function by inner product function .

The samples are mapped into a high-dimensional space . In the high-dimensional space, the linear regression function is constructed based on the principle of structural risk minimization [9]: where and are the weight coefficient and the deviation, which can be obtained by minimizing the objective function as follows:where is the generalization constant.

When using SVM, solving regression problem, introduce linear insensitive loss function . Cost function is Vapnik insensitive loss function [10]:

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 (1) is transformed into a constrained minimization problem as follows:

Constraints are

Then, build Lagrange function and transform inequality constraints into equality constraints as follows:where , , , is Lagrange multipliers and it satisfies the nonnegative constraints as well:

The optimization problem as (6) can be solved in its dual form. According to the Karush-Kuhn-Tucker (KKT) conditions, the original problem can be transformed into the optimization objective function as follows [11]:

Constraints are

Maximize (8) aswhere is the introduced nonnegative Lagrange multiplier, is the kernel function based on Mercer condition, and the inner product kernel function is as follows [12]:

The introduction of kernel function takes the place of dot product in the high-dimensional space, avoiding the problem of nonlinear mapping function which reduces the computation and complexity significantly. Then the result is as follows:

#### 3. Fractal Method

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 [13].

To the Point Set , if it can be covered by -dimensional hypercube whose side length is , then the box dimension of the Point Set is

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 [14]. If the possibility of the Set Point falling into the th hypercubes is , define the number of information as entropy, which can accurate the system status to level , then

So, the information dimension of Point Set is

#### 4. Simulations

##### 4.1. Finite Difference Time Domain (FDTD)

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 second-order. FDTD can simulate any kind of electromagnetic structure according to the electromagnetic parameters and medium parameters of the model [15]. In isotropic media, two curl equations of Maxwell equations arewhere is the permittivity, F·m^{−1}; is the magnetic permeability, H·m^{−1}; is the conductivity, S·m^{−1}; and is the magnetoconductivity, Ω·m^{−1}.

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 [16].

##### 4.2. Model of XLPE Cables

XLPE cables have the typical coaxial structure. To find out the characteristics of this structure, FDTD simulation program is applied. Figure 2 shows the model of the real 30 kV XLPE cable. The partial discharges source located in the cavity 1 mm from the left side of the port is a discharge voltage pulse along the radial distribution of the cavity. In the coaxial cavity, we placed sensors every 250 mm (red points in Figure 1).