As a key concern in a power system, a deteriorated insulation is likely to bring about a partial discharge phenomenon and hence degrades the power supply quality. Thus, a partial discharge test has been turned into an approach of significance to protect a power system from an unexpected malfunction. An improved Hilbert–Huang Transformation (HHT) is proposed in this work as an effective way to address the issues of an optimal shifting number and illusive components, both suffered in a conventional HHT approach, and is then applied to a defect mode recognition for a partial discharge signal analysis in the case of a cross-linked polyethylene insulated power cable. As the first step, the partial discharge signal detected is converted through the proposed improved HHT to a time-frequency-energy 3D spectrum. Then as the second step, the fractal features contained therein are extracted by way of a fractal theory, and in the end the defect modes are recognized as intended by use of an extension method.

As technology development progresses and improved living standards are promoted, there is a corresponding and growing demand for power quality in human society. As an essential facility in all sections of industries, a power system influences economic growth or human’s daily life, from something as little as a power outage, to something far more serious, such as severe damage to power generation and transmission equipment, or even an entire power network shut down, which would be a tremendous thread to the power system [

According to the literature [

Subject to the defect types of an insulator, a partial discharge process is a highly complicated phenomenon, that is, distinct defect models bring about distinct discharge spectrums as expected. In a bid to accurately recognize insulation conditions of a power cable, a data base is built for diagnosis purposes by successively measuring partial discharge signals from a sequence of defect models. This work aims to analyze a detected discharge signal through the Hilbert–Huang transform, an approach with a high resolution to a nonlinear as well as non-stationary signal. Yet, there exist two inherent problems, degrading the accuracy in signal analysis and hence a barrier to an automatic defect mode identification. The first problem is lacking a decision criterion to precisely specify the optimal shifting number. In the case of an excessive shifting number, the intrinsic physical meaning carried in extracted intrinsic mode function (IMFs) will be unintentionally removed, that is, any instant frequency cannot be viewed out of all the IMFs accordingly. The second is that illusive components may be seen in the course of empirical mode decomposition (EMD) process as a result of the use of the extrema interpolation, i.e., a cause for a mode confusion problem.

For this sake, combined with a K-S test and an energy ratio sorting, an improved HHT, abbreviated as IHHT hereafter, is proposed as an effective approach to specify the optimal shifting number and as a decision criterion in the identification of illusive components. With the optimal shifting number, each IMF is purified, then illusive components are filtered out according to the decision criterion, and in the end, the accuracy of the Hilbert spectrum is thus improved. For the reason that feature extraction cannot be performed with little effort out of a Hilbert spectrum, the automatic identification of partial discharge defect modes is performed on a time–frequency–energy 3D spectrum, a spectrum converted from the Hilbert spectrum. Consequently, four features, namely fractal dimension, mean energy and mean discharged energy, are extracted as a prerequisite of the identification task. As put forward in a prior work of ours [

EMD is an approach in which a complicated signal can be expressed as the sum of

It is postulated in an EMD analysis that an arbitrary signal

An EMD decomposition is made through the following steps. As the first step, all the local extremum points must be located, then concatenated via cubic splines so as to form the upper and the lower envelopes respectively [_{10} between such two envelopes is evaluated as

In case _{10} does satisfy the IMF definition, _{10} is treated as the first IMF. If not, the above step is iterated with _{10} as the initial value until the maximum shifting number

Empirically, it is very unlikely to make _{1k} satisfy the IMF definition in the course of decomposition, meaning that it takes the maximum number,

Subsequently, letting _{1}=_{1k}, _{1} is extracted out of _{1}, the updated signal, is given as

Performing

Such iteration terminates in the event that no more IMF can be found for a monotonic function _{n}

Based on the local characteristic timescale of the signal, EMD decomposes a signal into _{i}

Construct an analytical signal

And then an amplitude function is given as

An instantaneous phase function is as

The instantaneous frequency is represented as

And the Hilbert spectrum is denoted as

Without taking the residual _{n}

In an attempt to definitely specify the optimal shifting number and rid illusive components, an improved version of HTT is proposed as follows.

A Kolmogorov-Smirnov (K-S) test is conducted as a way to view the difference of probability distributions between two distinct sets of data. Assuming _{1}, _{2}, _{3}, … , _{n}}, a cumulative distribution function (CDF) is defined as [_{n}_{0}

Furthermore, the similarity probability

A near zero

For the purpose of an accurate decomposition of a practical discharge signal in HTT, there is an optimal shifting number required to preserve the intrinsic physical meaning. Treated as the fundamentals of the decision criterion, the signal power ratio between IMFs is defined as
_{n}

As illustrated in

As a consequence of both the upper and lower envelopes identified by means of extrema interpolation, illusive components are seen in IMFs in the course of an EMD decomposition. It is hence postulated that the HTT accuracy can be upgraded in case all the illusive components can be identified and filtered out in an effective manner. Underlain by a K-S test, an iterative decision criterion is proposed in this work to address the threshold value problem as put forward by the authors of [

As illustrated in

Numerous underground cables exist for the power distribution level in urban areas. Defects in cable may cause PD phenomena and infect power supply reliability. Therefore, this study establishes four defect types of cable joints frequently encountered in the on-site construction phase. The proposed inspection method should be able to determine the insulation quality of a cable joint, and can be used by the construction unit to verify the quality of the cable joint and provide training materials for construction taskforces. Ideally, this approach can help prevent similar construction defects in the future.

Statistics in the literature indicate that a high proportion of the cross-linked polyethylene (XLPE) power cable breakdowns occur in cable joints [

In the voltage step-up procedure of the PD experiment, a 25 kV cable should have 14.4 kV(U_{0}) rated phase to ground voltage. However, according to IEC 60502-2 for a power cable from 6 kV to up to 30 kV, the test after installation voltage should be 1.7 U_{0} for 5 min [

Researchers have successfully used fractal theory to address the problem of modeling and describe complex shapes. This technique has potential for the classification of textures and objects present in images and natural scenes, and for modeling complex physical processes [

The definition of fractal dimension by self-similarity is straightforward, where self-similar means they are the same from near as from far, it is often difficult to be either estimated or computed for a given image data. However, a relevant measure of fractal dimension, the box dimension, can be more efficiently computed instead. In this work, suggested by Voss, the method has been followed for the computation of fractal dimension D from the image data. Define _{b}

This value is found to be proportional to ^{−D}, according to which the box dimension can be estimated by calculating

The ideal fractal is likely to confirm to statistical similarity for all scales, that is, fractal dimensions are all independent scales. However, fractal dimension alone is found insufficient for discrimination purposes, since two distinct surfaces could share the same value of

^{2}(

Extension theory contains the concepts of matter-elements and extension sets and its main application is in solving contradiction and incompatibility problems [

_{i}

_{i}

_{j}

_{ij}

_{ij}

The classical domain

_{1}_{2}_{3}

_{k}

The proposed power cable joints recognition, based on IHHT with fractal feature extraction, was performed based on the electrical signal measured in the experiment models. A total of 240 sets of measurement data were associated with the six types of experiment models. Subsequently, 20 tests are randomly selected for the identification training purpose, while the rest is used for the test purpose. Here, a detected partial discharge signal is analyzed by HHT and IHHT respectively, and various features are extracted out of a time–frequency–energy 3D spectrum, following which the intended defect mode identifications are made using an extension method. A random noise between ±10% to ±30% is introduced into such features to test the ability against noise interference.

In this section, a partial discharge signal is analyzed by the conventional HHT, which decomposes extracted IMFs at the same time as signals, since extrema interpolation is adopted during the EMD process. This is an approach well applied to the analysis of a nonlinear as well as non-stationary signal, and the cost is that illusive components are very likely to be evoked. Accordingly, the improved HHT is proposed as an effective approach to enhance the reliability of signal analysis conducted by the conventional HHT. Underpinned by an extension theorem, all the identification processes are made automatic for an easy comparison in terms of identification ratio. Such identification results are about to be discussed in the following section.

With the

An original detected signal is analyzed here by the IHHT approach as referred to in

Even though the identification ratio and the ability against noise interference are improved as a consequence of the removal of illusive components and mode confusions, the identification ratio still remains relatively low between similar defect modes. For this sake, the energy level (E), denoted by the

For further improving the recognition rates of IHHT, additional PD features extracted from phase-resolved 3D patterns are taken into account. The detailed procedure of feature extraction from a phase-resolved 3D pattern can refer to authors’ previous research [

As illustrated in

Propose in this work is an improve HHT, which employs a Kolmogorov–Smirnov test and a sorting result by signal energy ratio in the determination of an optimal shifting number. In a bid to rid illusive components, a cumulative K-S test is presented as well, such that all the IMFs can be extracted accurately as expected, the intrinsic physical meaning can be reserved over each spectral band, and then partial mode confusion problems are successfully addressed. This improved HHT approach is then applied to defect mode recognition of partial discharge signals detected from cross-linked polyethylene insulated power cables. It converts the detected discharge signal to a time–frequency–energy 3D spectrum, extracts features, namely fractal dimension, lacunarity and average energy, through a fractal theory, and in the end successfully recognizes defect modes by use of an extension method. By an analysis on a field detected signal, it is concluded that the IHHT combined with phase-resolved PD pattern is demonstrated to be superior to the HTT in terms of identification results and the ability against noise interference.

The research was supported by the National Science Council of the Republic of China, under Grant No. MOST 106-2221-E-167-017.

FengChang Gu a conceived and designed the study; HungCheng Chen performed the experiments in the laboratory; MengHung Chao studied and tested the algorithm; All the coauthors collaborated with respect to the interpretation of the results and in the preparation of the manuscript.

The authors declare no conflict of interest.

Flowchart for the determination of an optimal shifting number.

Judgment criterion of illusive components for a cumulative test.

Analysis flow of improved Hilbert–Huang Transformation (HHT).

Experimental defect models in XLPE power cable.

Block diagram of partial discharge (PD) measurement experiment.

Procedure for computing fractal dimension and lacunarity.

Extension membership function.

Flow chart of the extension recognition method.

Partial discharge signal. (

Time–frequency–energy 3D spectrums by HHT for (

Feature distributions for time–frequency–energy 3D spectrums by HHT.

Time–frequency–energy 3D spectrums by IHHT for (

Feature distributions for time–frequency–energy 3D spectrums by IHHT.

Feature distributions for time-frequency-energy 3D spectrums by IHHT with the

Phase-resolved 3D patterns for (

Feature distributions for phase-resolved

Mean identification results for various preprocessing approaches.

Identification results by HHT versus features fractal dimension (FD)- lacunarity (Λ)- mean-discharged (M).

Noise | 0% | ±10% | ±20% | ±30% | |
---|---|---|---|---|---|

Model | |||||

Type I | 100 | 100 | 80 | 50 | |

Type II | 95 | 90 | 90 | 85 | |

Type III | 0 | 5 | 10 | 20 | |

Type IV | 80 | 70 | 65 | 60 | |

Type V | 100 | 95 | 95 | 85 | |

Type VI | 95 | 80 | 80 | 45 | |

Average | 78.3 | 73.3 | 70 | 57.5 |

Identification results by IHHT versus features FD-Λ-M.

Noise | 0% | ±10% | ±20% | ±30% | |
---|---|---|---|---|---|

Model | |||||

Type I | 100 | 100 | 80 | 32 | |

Type II | 100 | 65 | 60 | 35 | |

Type III | 50 | 40 | 25 | 15 | |

Type IV | 80 | 80 | 65 | 45 | |

Type V | 100 | 95 | 85 | 80 | |

Type VI | 100 | 80 | 60 | 50 | |

Average | 88.3 | 76.6 | 62.5 | 42.8 |

Identification results by IHHT versus features FD-Λ-MD-E.

Noise | 0% | ±10% | ±20% | ±30% | |
---|---|---|---|---|---|

Model | |||||

Type I | 100 | 100 | 100 | 100 | |

Type II | 100 | 95 | 95 | 90 | |

Type III | 100 | 90 | 65 | 70 | |

Type IV | 100 | 95 | 85 | 65 | |

Type V | 100 | 95 | 90 | 90 | |

Type VI | 95 | 65 | 75 | 55 | |

Average | 99.2 | 90 | 85 | 78.3 |

Identification results improved by combining IHHT with phase-resolved patterns.

Noise | 0% | ±10% | ±20% | ±30% | |
---|---|---|---|---|---|

Model | |||||

Type I | 100 | 100 | 100 | 100 | |

Type II | 100 | 95 | 95 | 90 | |

Type III | 100 | 90 | 80 | 75 | |

Type IV | 100 | 95 | 90 | 70 | |

Type V | 100 | 95 | 90 | 90 | |

Type VI | 100 | 85 | 80 | 75 | |

Average | 100 | 93.3 | 89.2 | 83.3 |