Cable Insulation Defect Prediction Based on Harmonic Anomaly Feature Analysis

Abstract

With the increasing demand for power supply reliability, online monitoring techniques for cable health condition assessments are gaining more attention. Most prevailing techniques lack the sensitivity needed to detect minor insulation defects. A new monitoring technique based on the harmonic anomaly feature analysis of the shield-to-ground current is introduced in this paper. The sensor installation and data acquisition are convenient and intrinsically safe, which makes it a preferred online monitoring technique. This study focuses on the single-core 10 kV distribution cable type. The research work includes the theoretical analysis of the cable defect’s impact on the current harmonic features, which are then demonstrated by simulation and lab experiments. It has been found that cable insulation defects cause magnetic field distortion, which introduces various harmonic current components, principally, the third-, fifth-, and seventh-order harmonic. The harmonic anomaly features are load current-, defect type-, and aging time-dependent. The K-means algorithm was selected as the data analysis algorithm and was used to achieve insulation defect prediction. The research outcome establishes a solid basis for the field application of the shield-to-ground harmonic current monitoring technique.

1. Introduction

With the development of the economy and the acceleration of urbanization, the demand for electricity is continuously increasing. The urban distribution network contains a considerable number of power cables. Due to complex routes, diverse operating environments, and the intense density of urban underground cables, there is an escalated power outage risk caused by cable faults [1,2,3]. The aging of cable insulation, accelerated by factors such as environmental conditions and operational stresses, plays a significant role in the degradation of cable performance. Studies have shown that environmental factors like soil moisture and temperature can greatly influence the degradation rate of polyethylene insulation, leading to increased risk of faults [4]. This highlights the importance of developing effective diagnostic methods for the early detection of insulation degradation. The diagnostic methods for distribution cables can be divided into offline testing and online monitoring categories. Offline testing technologies are mostly used when cables fail, as it is often difficult to arrange planned power outages for maintenance [5,6]. The prevailing online monitoring methods encounter technical bottlenecks, such as difficulties in sensor installation, a lack of sensitivity, and false alarming. A substantial amount of investment and human resources is required, but the effectiveness is not satisfactory [7,8].

Harmonic anomaly feature analysis (HAFA) is gaining more attention as a novel condition monitoring method for distribution cables. The HAFA technique essentially measures the shield-to-ground current harmonics using current transformers (CTs) [9,10]. It is a non-invasive and non-destructive technique, with the advantages of convenient sensor installation and low deployment investment. The effectiveness relies on establishing and making use of the relation between the harmonic features and various cable defects, which is the research focus of this paper.

Chen et al. [11,12] performed a finite element modeling (FEM) simulation of a power cable and pointed out that the magnetic field was distorted due to defects. A harmonic current is therefore induced by the magnetic field distortion. The equivalent electric circuit for the water tree defect was proposed based on the harmonic feature obtained from the simulation. Liu [13] analyzed the formation of current harmonics based on the nonlinear conduction theory and demonstrated the proposition through the corona discharge experiment. The nonlinear conduction property might not be prominent, as the conductivity of the Cross-Linked Polyethylene (XLPE) material is very low, typically around 0.01 pS/m [14], if the defect type is not water tree-related. The conductive current magnitude is also difficult to measure, as the magnitude is normally below the μA range. In addition, the strict mathematical model of the current harmonic induction mechanism is not available. The coupling between the electric and magnetic field, the relation of the harmonic content and the defect severity, and the wave propagation behavior have not been fully investigated.

The study of the impact of the water tree on the current harmonic feature [15,16] shows that the distortion of the loss current component is dependent on the water tree content. The current measurement was achieved using a high-voltage bridge circuit. Zhou [17] studied the current harmonic features caused by various defects, such as insulation scratch and corona discharge, and established the relation. However, there are several limitations to this research work: the sample geometry was small compared to practical cables; the sample size was not sufficient; and the monitoring period was relatively short. A simple analysis method was applied to the acquired data, without any proposed mathematical model. As a result, there is room for improvement regarding the testing technology and data analysis method.

In this paper, the current harmonic induction mechanism is firstly deducted based on the Maxwell equations. This includes the magnetic field distortion caused by cable defects and the corresponding current harmonic features. Then, the FEM simulation was performed to verify the assumptions. After that, cable samples with various pre-made defects were operated on a platform simulating practical operation conditions, and data were collected over a relatively long period. Finally, the statistically based analysis approach, K-means clustering, was applied to establish the current harmonic features of various defects. The research outcome can be used as a reference for cable condition diagnosis and fault prediction in the field.

2. Theory and Simulation

2.1. Field Distortion in the Defect Area

An alternating current $I$ flowing through the cable conductor creates a concentric magnetic field in the center conductor, insulation, and shield area. The magnetic field is also an alternating variable. For the single-core power cable, depicted in Figure 1, the relationship between the electric current and magnetic field can be expressed by Ampere’s Law [18,19]:

$${\displaystyle {\oint }_{l}B}\cdot dl=\mu {\displaystyle \sum _{i=1}^n{I}_i}$$

(1)

where $B$ is the magnetic flux density in $T$, $\mu$ is the permeability in $H/m$, and $I$ is the current in $A$.

Inserting the current expression into Equation (1), the flux density at distance $r$ can be calculated by solving the integration, and gives the following:

$$B=\left\{\begin{array}{ll}{\displaystyle \frac{{\mu }_{0}Ir}{2\pi {R_1}^2}}\sin (\omega t+\phi )& 0 \text{<} r<R_1\\ {\displaystyle \frac{{\mu }_{0}I}{2\pi r}}\sin (\omega t+\phi )& R_1\le r<R_3\end{array}\right.$$

(2)

$$r=\sqrt{x^2+y^2}$$

(3)

where $R_1$, $R_2$, and $R_3$ are the external radius of the copper conductor, the insulation, and the metallic shield, respectively. ${\mu }_0$ is the vacuum permeability, $\omega$ is the angular frequency, and $\phi$ is the initial phase angle.

When the cable is free of defects, the flux density $B$ within the center conductor ($0<r<R_1$) increases with the radius, while the flux density $B$ outside ($r>R_1$) decreases with the radius, as illustrated in Figure 2.

The existence of ferromagnetic metal particles, semi-conductive particles, or water changes the insulation permeability considerably, which makes the local permeability different from the surroundings. According to the Maxwell equation and Ampere’s Law, the boundary conditions of the magnetic field $H$ and the magnetic flux density $B$ at the interface between two different media is as follows:

$$\left\{\begin{array}{l}{H}_{1t}=H_{2t}\\ {\mu }_1{H}_{1n}={\mu }_2{H}_{2n}\\ B_{1n}=B_{2n} \\ {\mu }_2{B}_{1t}={\mu }_1{B}_{2t}\end{array}\right.$$

(4)

where ${\mu }_1$ and ${\mu }_2$ are permeabilities of the healthy and deteriorated material, respectively. Variables with the subscript $t$ and $n$ are tangential and normal components.

At the interface of two different media, the tangential component of the magnetic field strength $H_t$ and the normal component of the magnetic flux density $B_n$ are continuous, whereas the normal component of the magnetic field strength $H_n$ and the tangential component of the magnetic flux density $B_t$ are discontinuous. This results in the phenomenon where magnetic field lines refract as they enter from one medium into another. As shown in Figure 3, the refraction laws of $B$ and $H$ at the interface are as follows:

$${\displaystyle \frac{\tan {\alpha }_1}{\tan {\alpha }_2}}={\displaystyle \frac{{\mu }_1}{{\mu }_2}}$$

(5)

When the magnetic field passes through the interface formed by the deteriorated and healthy materials, distortion of the magnetic flux density will occur. This distortion not only leads to an uneven distribution of the magnetic field strength in the defect area, but may also cause the magnetic field lines to concentrate in the deteriorated area, known as the magnetic concentration effect [20,21]. Additionally, the irregularity of the geometric shape and size of the insulation defect, as well as the unevenness of the contact interface between adjacent media, will affect the even distribution of the magnetic field, further amplifying the distortion of the magnetic field in the defect area.

2.2. Current Harmonics in Metallic Shield

The metallic shield is located outside the insulation and outer semi-conductive layer. It provides functions such as the current returning path, electromagnetic interference shielding, and safety grounding. Therefore, the current $I_{SC}$ in the metallic shield mainly includes the induced current $I_{EC}$, the grounding current $I_{GC}$, and the leakage current $I_{LC}$ [22,23]. The flow path is shown in Figure 4 and the expressions of these current components are as follows:

$$I_{SC}=I_{EC}+I_{GC}+I_{LC}$$

(6)

$$I_{EC}={\displaystyle \frac{\epsilon }{R}}=-{\displaystyle \frac{N}{R}}{\displaystyle \frac{d{\Phi }_B}{dt}}$$

(7)

$$I_{GC}={\displaystyle \frac{\Delta V}{R_g}}$$

(8)

$$I_{LC}=V\cdot G$$

(9)

where $\epsilon$ is the induced electromotive force in $V$; ${\mathsf{\Phi }}_B$ is flux passing through the closed metallic enclosure in $Wb$; $N$ is the turn number (equal to 1 for cables); $\mathsf{\Delta }V$ is the electric potential difference in two terminals in $V$; $R_g$ and $R$ are the grounding resistance and conductor resistance in $\mathsf{\Omega }$, respectively; V is the conductor potential in V; and $G$ is the conductance of insulation in $S$.

The grounding and leakage current are mainly determined by electrical parameters such as the voltage rating of the cable system and the conductivity of the cable insulation material. If the cable is in a healthy condition, the principal frequency component of these currents is at a certain power frequency (50 or 60 Hz) because they are introduced by the power supply voltage. When defects are present in the cable insulation, the surrounding magnetic field will exhibit significant distortion. This distortion not only twists the magnetic flux lines passing through the defect area, but also induces currents with higher harmonic components in the cable metallic shield.

Combining Equations (2), (4), and (7), it can be concluded that the magnetic field and its distortion in the defect area is affected by the conductor current I, the permeability $\mu$ in the insulation defect area, and the degree of deterioration. The magnetic field distortion determines the harmonic components of the induced current, particularly its amplitude-frequency characteristics. Therefore, the evaluation of the metallic shield harmonic current feature, which represents the electromagnetic characteristic, is theoretically an effective way of diagnosing the cable insulation condition.

2.3. FEM Analysis

This section studies the magnetic field distortion and the corresponding harmonic current features caused by various defect types in a cable with a 300 A load current. From the simulation results shown in Figure 5, it can be observed that the magnetic flux density increases linearly within the center conductor area and reaches the maximum at the outer surface of the center conductor. Then, it starts to decrease as the distance increases. The flux distortion decreases by 10–15% in the defect area and 5–10% in the adjacent area. The defect type also determines the distortion, as shown in Figure 6. The ferromagnetic metal particle has a larger impact on the distortion than the water.

A harmonic current is introduced in the metallic shield after electromagnetic field coupling. The current waveform does not have a sinusoidal shape, but a ladder shape, indicating the existence of harmonics. The spectrum analysis shows that the harmonic contents contain the 2nd to 11th order, and the 3rd-, 5th-, and 7th-order (150 Hz, 250 Hz, 350 Hz) harmonics are the principal components. The magnitudes of the current harmonics are in close relation with the degree of magnetic field distortion, as summarized by Figure 7.

3. Experiments

To verify the theoretical deduction and FEM simulation results, a platform for the distribution cable experiment was constructed. Cables with various defects were operated on the platform, and the metallic shield currents were recorded for harmonic feature study. Data analysis based on the statistical approach was performed.

3.1. Experimental Setup

The experiment platform consists of a toroidal transformer, a series resonant voltage magnification device, and a harmonic current measurement circuit, as shown in Figure 8. It aims to provide an environment similar to the practical operation conditions for distribution cables.

Cables were pre-conditioned to create the defects that were simulated in the previous section, i.e., contaminated with water, semi-conductive particles, and ferromagnetic metal particles. The defect area is illustrated in Figure 1. Another cable in good condition was also experimented on as a reference. Each cable had a length of 15 m, and the defect dimension was $10 \mathrm{m}\mathrm{m}\times 30 \mathrm{m}\mathrm{m}$. The water drop defect was created by applying a water film to the insulation lamination.

The center conductors of cables with and without defects were firstly connected in series and put through the toroidal transformer. Then, both ends of the metallic shield of the experimented cable were connected together to form a closed loop. The sensors were then used to measure the current of the metallic shield loop. The ambient temperature was controlled to 90 °C so that thermal aging was also investigated.

3.2. Statistical Distribution of the Current Harmonics

To quantify the harmonic current feature in a straightforward way, two variables, $K_n$ and $R_n$, are used to describe the content of the $n$th order harmonic, which is defined as follows:

$$K_{\mathrm{n}}={\displaystyle \frac{I_n}{I_1}}\times 100\%$$

(10)

$$R_{\mathrm{n}}={\displaystyle \frac{K_n}{{K_n}^{\ast }}}$$

(11)

where $K_n$ and $K_n^{*}$ are the harmonic contents of the cable with and without defects, respectively. $R_n$ is the relative harmonic content. $I_n$ is the RMS value of the nth order harmonic current.

Take the box plot (Figure 9) of the harmonics of the cable with ferromagnetic metal particles, with a 300 A load current, as an example. It demonstrates the statistical characteristics of the mean and interquartile range (i.e., the difference between the upper quartile and the lower quartile) of the harmonic contents. It can be observed that the principal components are the third-, fifth-, and seventh-order harmonics, which have higher magnitudes than the other harmonic components. The mean value of the third harmonic is 0.53%, and 50% of the samples are distributed within the range of 0.44% to 0.68%. The mean value of the fifth harmonic is 1.73%, and 50% of the samples are distributed within the range of 1.48% to 1.92%. The mean value of the seventh harmonic is 1.16%, and 50% of the samples are distributed within the range of 0.98% to 1.43%. These values are in good accordance with the FEM simulation results.

4. Results and Discussion

4.1. Current Harmonic Feature Study

As the other defects share the same harmonic distribution characteristic, the analysis will focus on the third-, fifth-, and seventh-order harmonics. The impact of load current, defect type, and aging period are varied to investigate their impacts on the current harmonic feature.

4.1.1. Load Current Impact

The magnitudes of current harmonics increase with the load current for the cable with the ferromagnetic particle defect, as shown in Figure 10. The magnitude increments of the harmonic contents $K_n$ are 0.2‰, 1.05‰, and 0.65‰, respectively. The relative harmonic contents $R_n$, also increase with the load current. The increments are 35.43% for the third harmonic, 4.02% for the fifth harmonic, and 2.03% for the seventh harmonic.

The results indicate that the load current has a significant impact on the current harmonic feature. The increase in load current is helpful for improving the sensitivity of defect detection.

4.1.2. Defect Type Impact

The cables with various defects were aged for 500 h at 300 A, and the average current harmonic results during this period were used for cable defect evaluation.

The ratios of the third, fifth, and seventh current harmonic content are 1.0:3.9:2.8, 1.0:3.7:3.0, 1.0:3.4:2.5, and 1:3.2:2.1 for the good cable and the cable with water, semi-conductive particle, and ferromagnetic metal particle defects, respectively, as shown in Figure 11. The results of different cable defect types exhibit prominent differences. The relative harmonic content of the third harmonic reaches 127.17% for the cable with a ferromagnetic metal particle defect. For the cable with a semi-conductive particle defect, The relative harmonic contents of the third and seventh harmonic reach 107.72% and 109.23%, respectively. The relative harmonic contents are slightly above 100% for the cable with the water ingression defect, which is significantly higher than the cable without any defect.

It can be concluded from the experiment that defects cause an increase in the third, fifth, and seventh current harmonic contents. Different defects exhibit different current harmonic features, in terms of magnitude and ratio.

Figure 12 is the plot of the current harmonic components over time. The aging period is 600 h, and each point represents the average value in every 50 h interval. It can be observed that as the aging goes on, the third-order relative harmonic content continuously increases. It increases by 20% during the first 400 h. Then, the increment accelerates and reaches 40% at the end of the aging period. The relative harmonic contents of the fifth and seventh order increase at the beginning and then start to decrease, reaching a maximum of ca. 115% somewhere between 250 and 400 h.

4.1.3. Aging Impact

The water ingression defect makes the third-order harmonic increase slowly from 100% to 120% over the aging period. The fifth- and seventh-order harmonics rapidly increase at the beginning and reach a maximum of ca. 107.5% somewhere between 100 and 400 h.

In summary, aging increases the magnitudes of the relative harmonic content for the third-, fifth-, and seventh-order harmonics. Different defects have different impacts on the current harmonic feature: the semi-conductive and ferromagnetic metal particle defects exhibit similar behavior, while that of water ingression is prominently different from the other two defects.

4.2. Defect Identification Based on Clustering

Although the current harmonic feature is affected by the three factors discussed in the previous section, interferences from the power apparatus and surrounding environment cause variation in the captured harmonics, as shown in Figure 13. The variation has an adverse impact on the feature observation. The trend in the traces is not clear.

If the current is heavily disturbed by external interferences, the harmonic feature obtained in the lab might be hard to use in practice. Moreover, the interferences and some other unknown factors cannot be compensated by any mathematical model. To solve this challenge, the K-means clustering algorithm is used for current harmonic data analysis [24,25,26]. K-means clustering is an unsupervised machine learning algorithm which groups similar current harmonic data points into clusters. It is relatively easy to use and the results’ presentation is intuitive.

Take the water ingression for example: the current harmonic feature does not differ too much from that of the good cable. The feature identification of the field measurement by humans becomes difficult. The feature becomes more recognizable after clustering, as shown in Figure 14. With the presence of disturbances, the accuracy reaches 75.64%.

Table 1. The recognition accuracy of various types of defects under different conductor currents.

Load Current (A)	Defect Types	Accuracy
100	4	42.78%
200	4	42.78%
300	4	39.44%
400	4	43.33%
500	4	42.78%

is a summary of the identification accuracy of four defect types at different load current levels. The clustering results of the maximum load current, 400 A, are shown in Figure 15, with an accuracy of 43.33%. Therefore, K-means clustering not only presents the current harmonic feature in an understandable way, but also achieves good accuracy.

5. Conclusions

• The current harmonics in the metallic shield are induced by the magnetic flux distortion due to the presence of defects. In the harmonic components from the 2nd to the 11th order, the 3rd-, 5th-, and 7th-order harmonics are the principal components. They are higher in magnitude than the rest, so are selected for further feature study.
• The impact of load current, defect type, and aging time on the current harmonic feature is investigated. Both FEM simulation and the experimental results support that the increase in load current and the extension of the aging period make the third-, fifth-, and seventh-order current harmonic feature more prominent. The metal particles with a higher permeability induce a higher current harmonic magnitude than water, which has a lower permeability.
• K-means clustering can perform fast and efficient data analysis. It successfully identifies four typical cable defect types in a noisy environment with an accuracy of 43.33% when the load current is 400 A.