Failure type and failure level detection of insulators according to monitored leakage current

Abstract

Due to the ever-increasing growth of electric energy consumption, the production of high-quality, reliable and high-reliability electricity is very important. Therefore, it is essential to have distribution and sub-transmission networks with a good reliability factor. In power distribution and sub-transmission lines, it is necessary to somehow isolate the conductors under voltage from the towers, and insulators are used for this purpose. These insulators have two main tasks. One of the main tasks of insulators is to isolate (insulate) the line conductor from the body of the tower. The insulators must be able to isolate the high voltages of the lines from the body of the tower without having a leakage current, and on the other hand, the insulators must be able to withstand the mechanical forces resulting from the weight of the conductors and the applied forces caused by wind and ice. Also, leakage current is one of the important parameters for condition monitoring of insulators in power grid lines. Failure to inspect the insulation for contamination and health conditions will lead to insulator failure and will cause faults in the electrical system. Therefore, it is very important to monitor the condition of the insulator. Based on this, in this paper, according to the data related to leakage current and also according to the introduced wear out function, a procedure for measuring the condition of insulators has been obtained. Finally, the condition of each insulator will be determined according to the defined indicators. Also, the failure level of each monitored data will be obtained using sensitivity analysis.

1. Introduction

The conductors of the distribution and super distribution lines have a high potential difference compared to the mast body and to each other. For this reason, in power systems, they isolate them using high pressure insulators. Insulators are designed and produced in different models and dimensions according to the voltage level used and the environmental conditions of the region. Insulators, which are called electrical network insulators, generally have two important mechanical and electrical functions. Among the mechanical duties of an insulator, it can be mentioned that it has good mechanical endurance and can withstand the worst weather conditions. Regarding the electrical duties of the insulator, it can be pointed out that it must have good insulating properties to become a suitable separator for the conductors. On the other hand, the insulators, in addition to the need to withstand the working point voltage of the system, must have their electrical endurance against unstable atmospheric conditions, especially be resilient when struck by lightning or during network switching maneuvers [1].

In the study and testing of insulators, it is very important to find out the aging and wear of the insulator. The authors [2] have discussed this phenomenon in detail. Among the wear characteristics of insulators, the following can be mentioned.

• •Expansion of cement,
• •Corrosion of parts and components,
• •Electrical and mechanical stresses,
• •Drying of the bitumen covering layer (bitumen paint),
• •Increasing the amount of leakage current in the insulator

In the continuation of this article, the analysis of leakage current (LC) in insulators will be discussed. In a simple definition, any current that flows from a hot conductor to the ground on the external surface of a device is called leakage current. The amount of leakage current of the insulator is one of the very important factors that must be taken into account in the design of the insulator and its installation in the lines. Although this current cannot enter the insulator, it affects the performance of the insulator. This current flows in a path with low relative resistance on the surface of the insulator. This path with low resistance is actually the interface between the insulator and the surrounding air. This path shows less resistance than the air around the insulator, so it is also called the surface leakage current path of the insulator. It is possible to reduce the amount of this leakage current with measures, but the amount of this current never reaches zero, therefore, there is always a small amount of leakage current flowing in this path.

In [3], the effect of uneven distribution of pollution in conditions of different humidity on insulator has been measured. Also, according to this reference, an Artificial Neural Network (ANN) has been used to predict the flashover voltage.

In wet and windy conditions, conductive contaminants begin to dissolve in water on the surface of the insulator, which increases the leakage current and affects the performance of the insulator. According to Ref. [4], it uses a data collection system to measure the insulator leakage current and weather parameters around the insulator. Artificial intelligence is then used to create a predictive model for leakage flow based on weather parameters. Then this information is transferred to maintenance users. Also, in Ref. [5], the formulation of the resistance of the residual pollution layer on the insulator is proposed and a typical insulator is taken as an example to analyze and calculate its resistance. Also, the theoretical resistance has been confirmed by numerical simulation using COMSOL Multiphysics software.

In the literature, leakage current monitoring is used to test different types of insulators, including single hanging insulators, terminal insulators, insulators installed in posts, insulators Anti-pollution and fog, insulators with an umbrella or on an insulator chain, etc. Have been implemented [6].

Among the various insulator monitoring algorithms, leakage current stands out as one of the most meaningful indicators of contamination performance, as it indicates how close the string of insulators is to flashover. Reference [7] presents a new method for predicting the leakage current in insulator strings by considering the weather information of the insulators. The analysis is based on a combination of a newly developed Cumulative Pollution Index (CPI), which estimates the deposition of dissolved pollution in the insulator strings, and a machine learning technique such as the Random Forest algorithm.

One of the main problems in monitoring the insulator based on its leakage current is the analysis of the results of the measured leakage current under varying harmonic content in the system voltage. Based on this, reference [8] states the possibility of using the instantaneous value of the time integral of the leakage current as a parameter with low sensitivity to monitor the leakage current in the presence of voltage harmonics in insulators.

Also, in Ref. [9], an innovation has been proposed to identify the health condition of composite insulators by examining leakage current along with electric field stress (EFS) and electric potential (EP) profiles. It should also be noted that the deposition of pollution on the surface of polymer insulator is a serious issue because it often leads to flashover and even insulator failure. Accordingly, in Ref. [10], to estimate the intensity of the contamination level, the surface leakage current (SLC) signals of a polymer insulator with a contaminated surface have been analyzed in the time-frequency domain through the hyperbolic stack transform (HST).

Due to high voltage in substations, manual inspection of insulators can be very dangerous. Therefore, in Ref. [11], a non-invasive computer vision system based on an infrared thermal camera (IRT) is presented for automatic monitoring and visual inspection of overhead electrical insulator. Also, reference [12] has also used deep learning to condition monitoring on the insulator.

An insulating chain can be between 4 and 60 discs depending on the voltage level used, and the line to ground voltage is distributed between these discs along the insulating chain. In the chain of ceramic insulators, unlike the glass type (in which any type of defect and perforation can be seen with the eye), its puncture cannot be detected with the naked eye. But the voltage during the cap and the punched insulating pin decreases significantly. Therefore, by measuring the electric field in the ceramic insulator, it is possible to understand its performance and health status [13].

Positron Company is a multinational company that was established in 1970 AD. It is headquartered in Canada and has sales offices in Europe and Asia. In Ref. [14], this company mentions a device called “positron” whose work is based on measuring the electric field around the insulator. By using this device, you can get valuable information about the health status of the insulator. It should be noted that the user brings the positron close to the insulator using a special wand. This is called Hot Sticks and it is a special combination of foam. Other types of this cane are available from reinforced plastic and fiberglass. Hot Sticks must be manufactured and designed according to ASTM F711 [15,16].

Deep learning algorithms can also be applied to unsupervised activities. In the studies of various topics, this issue is important because the unlabeled data is more than the labeled data [17,18]. Researchers conducted in the last decade about monitoring the condition of insulators pay special attention to the use of image processing methods and deep learning topics. Reference [19] considers the correct identification of the insulator from other details in the images prepared of the lines and towers as an important principle in identifying the presence of cracks and physical defects in the insulators. This index becomes important due to the fact that the insulators have different dimensions according to the application and the voltage level used, and during the preparation of images, the lines are recorded at different angles in the image, which makes it difficult to identify errors. It is difficult. The R–CNN (Regions with Convolutional Neural Networks) method achieves high-accuracy object detection by using a deep convolutional neural network to classify object proposals [20,21].

In [22,23], a new approach based on active infrared thermography is proposed to evaluate and measure the condition of ceramic insulators. In this method, an external source of energy is used to heat the neck of the sample insulator. Heat spreads inside the insulator, and finally, due to the difference between the defective and healthy parts of the insulator, its condition can be detected by a thermographic camera. The data obtained after image processing is analyzed and gives the user the required information about the depth and size of the crack or gap inside the insulator. According to the claim of the authors [23], the validity of this measurement method has been proven by performing a series of tests on different samples, both healthy and defective (defects of different sizes). This method has been noticed due to the lack of contact with the insulator, speed, complete imaging and quantitative estimation of insulator defects. The use of these cameras, in addition to the insulators used in the lines, is also used to check and test the porcelain insulators in the substations.

According to Ref. [24], it has been determined that condition monitoring of leakage current and voltage characteristics in insulators shows well the health and failure condition of the insulator. Also, according to this reference, it has been stated that the contamination severity by the y soluble deposit density, wetting level, non-soluble deposit density as well as the uneven distribution pollution as environmental factors affect insulator. To check the condition of the insulator, valid data has also been collected in this reference.

Also, authors in Refs. [25,26] have introduced a procedure to determine the failure of the monitored data of the circuit breakers, which is general and can be used for other electrical network equipment. A similar procedure has been used in Ref. [27] to diagnose the failure and functional age of gas pipeline equipment.

In [28], an acoustic emission method for condition monitoring and PD detection of defective ceramic insulators is investigated. Based on this, a sequence of data processing using an artificial neural network (ANN) has been carried out for easy and accurate classification of defective insulators to extract and select the most important signatures for the classification of defects in insulators.

In [29], a combined finite element method (FEM) together with the method of moment (MOM) is proposed to calculate the leakage current with lower error values than the FEM simulation method compared to the actual values obtained from the experimental test. In this study, experimental tests have been used to validate the data obtained for training using a neural network. Also, to perform the classification of contaminated insulators, reference [30] has presented computer vision techniques to extract contamination features and a neural network (NN) model to classify these conditions.

The non-uniform distribution of the electric field and potential along the insulator causes problems such as erosion and flashover. Also, due to the wind direction in cold regions, the non-uniform pollution layer accumulates on the surface of the insulator. Reference [31] investigated the effect of the ice layer with different configurations in combination with ring-shaped contamination, which is more common in cold regions, on the insulation surface to obtain the electric field distribution and leakage current of polymer insulator.

According to the contents and literature review, Table (1) shows the aspects and innovations expressed in the relevant references as well as the present paper. According to this table, failure type and failure level detection are the innovations of this paper, which are going to be stated below.

Table 1.

Compare the proposed method and previous methods.

No.	Aspect	[3]	[4]	[5]	[7]	[8]	[9]	[10]	[11]	[12]	[24]	This paper
1	Considering contamination	✓	✓	✓	✓		✓	✓			✓	✓
2	Flashover phenomenon	✓									✓
3	Maintenance scheduling									✓		✓
4	Considering LC		✓	✓	✓	✓	✓	✓			✓	✓
5	Failure prediction			✓	✓				✓	✓
6	Harmonic voltage					✔					✓
7	Condition monitoring				✓	✓	✓	✓	✓	✓	✓	✓
8	Classification							✓	✓	✓
9	Machine learning								✓	✓
10	Failure type detection (Failure Tracking)										✓	✓
11	Failure level detection											✓

The rest of this paper is constructed as follows. In Section 2, the leakage current monitoring and characteristics are introduced. Based on this, leakage current monitoring is discussed first and then the leakage current characteristics are introduced. In Section 3, the proposed method will be introduced. Based on this, border areas expression and correction will be introduced first, and then failure level detection will be identified by introducing failure level detection. In Section 4, the results related to the above are discussed and finally, the paper concludes in Section 5.

2. Leakage current

By creating contamination on the surface of the insulator, the conductivity on the surface of the insulator increases and a current is formed on its surface. The higher the amount of contamination, the higher the leakage current will be. This leakage current on the insulator has two components: background current and partial discharge current. As this current increases, a flashover will be created on the insulator and will lead to an outage in the power grid. Therefore, it is generally necessary to monitor and evaluate the health condition of insulator to ensure the integrity of the insulator. Fig. (1) shows the schematic of an insulator with contamination and leakage current.

Fig. 1.

Insulator with contamination and leakage current.

One of the effective methods for developing new techniques for diagnosing the health of insulators is extracting features from the leakage current waveform. The properties of this characteristic may be derived from the frequency and time domain of the LC signal. Six LC features/indices are extracted in both time and frequency domains in this work.

2.1. Leakage current monitoring

Leakage current Monitoring and voltage characteristics in transmission line insulators is considered as a good technique to predict the physical condition of insulators in service. In the present paper, the time and frequency characteristics of LC were extracted in different situations to evaluate the health status of the insulator [24]. The intensity of pollution indicated by.

• •Soluble Deposit Density (SDD),
• •Wet surface (Wt),
• •Non-Soluble Deposit Density (NSDD)
• •Uneven distribution of pollution (Pu/PL)

were selected as environmental factors that affect insulator. Six properties were used to evaluate the physical condition of insulators, four of which are derived from the LC signal in the time domain, namely.

• •LC signal peak (C₁),
• •Phase shift between applied voltage and LC (C₂),
• •LC signal slope between two consecutive peaks (C₃) and
• •Crown factor (C₄)

The remaining two indicators of the set of leakage current characteristics, namely.

• •Total harmonic distribution (C₅)
• •Harmonic ratio index (C₆)

were obtained from the frequency domain of the LC signal.

One of the goals of classifying LC indices based on laboratory results is to reflect the physical state of insulators. The findings showed that the proposed indicators had an important effect in determining the physical condition of insulators [24].

According to the IEC 60507 standard, the SSD index is defined as equation (1) [24]:

$$SDD={\left(5.7\times {\sigma }_{20}\right)}^{1.03}\times \raisebox{1ex}{$V$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$$ (1)

where σ₂₀ represents the conductivity of the pollution solution at 20 °C, V represents the volume of the pollution solution and A is the insulator surface area. Meanwhile, equation (2) is used to determine NSDD:

$$NSDD=\raisebox{1ex}{$\left(\left(w_S-w_i\right)\times {10}^3\right)$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$$ (2)

where w_s is the mass of filter paper under contamination and w_i is the mass of filter paper in dry conditions. As shown in Table (2), in this study three degrees of SDD and NSDD have been evaluated according to light pollution, medium and high based on IEC 60507 standard.

Table 2.

Pollution severity readings.

Parameter	Value
σ20 (S/m)	0.00	0.39	0.79	1.38
SDD (mg/cm2)	0.00	0.05	0.12	0.20
NSDD (mg/cm2)	0.00	0.15	0.25	0.35
Wt (1/h)	0	3	6	9
Contamination Level	Clean	Light	Medium	Heavy

The specifications of the system under test are given in full detail in Ref. [24]. Insulators were tested under non-uniform and uniform pollutant scenarios. In the case of non-uniform contamination, three distinct contamination ratios of top-to-bottom SDD (Pu/PL) were chosen: 1/3, 1/5, and 1/8. The top and bottom surfaces of the insulator were contaminated separately during the non-uniform application of the contamination layer to produce SDD_U and SDD_L, while the overall SDD may be satisfied by equation (3) [24,32]:

$$SDD=\frac{SD{D}_U\times S_U+SD{D}_L\times S_L}{S_U+S_L}$$ (3)

where S_U and S_L are the upper and lower insulator levels, respectively. Based on these specified pollution ratios, the pollution of SDD_U on the upper side and SDD_L on the lower side can be satisfied by equation (4):

$$SD{D}_U=\frac{2\times SDD}{1-\left(P_u/P_L\right)},SD{D}_L=\frac{2\times SDD}{1+\left(P_u/P_L\right)}$$ (4)

2.2. Leakage current characteristics

Next, the characteristics of the leakage current are analyzed in the domains of time and frequency.

2.2.1. Time domain LC characteristics

LC peak (I_m) and phase shift between the applied voltage and LC (ϕ) are obtained from the general AC formula and according to equation (5):

$$I=I_m\cdot \mathit{sin}\left(\omega t+\phi \right)$$ (5)

where ω is the angular frequency calculated with ω = 2πf and the frequency value of f in this study is 50 Hz. Now, the characteristics of C₁ and C₂ can be obtained as relations (6) and (7):

$$C_1=I_m$$ (6)

$$C_2=\phi =\frac{\Delta t}{T}\times 360°$$ (7)

The phase difference between the applied voltage and LC (ϕ) has been obtained in full detail in Ref. [24] and its data has also been collected.

Calculating the slope of the line between two consecutive peaks of the leakage current signal has obtained the third characteristic of C₃. As a result, equation (8) is used to represent C₃:

$$C_3=\frac{\sum _{n=1}^m\left|y_n-y_{n-1}\right|}{x_n-x_{n-1}}=\frac{\sum _{n=1}^m\left|\Delta y_n\right|}{\Delta x_n}$$ (8)

where Δy_n is the leakage current difference between neighboring peaks in n and Δx_n is the time period between these peaks. The fourth feature is the crest coefficient (C₄), which is calculated by dividing the peak value by the RMS value of the leakage current. As a result, equation (9) expresses the characteristic of C₄:

$$C_4=\frac{I_{Peak}}{I_{RMS}}$$ (9)

2.2.2. Frequency domain LC characteristics

The LC frequency range below 500 Hz has characteristic properties for contaminated insulators. Therefore, in this paper, the odd harmonics and total harmonic distortion (THD) of LC below 500 Hz are used to provide indicators to evaluate the condition of insulators. LC frequency characteristics are expressed by C₅ (THD) and C₆ (harmonic ratio) indices and according to equations (10), (11):

$$C_5=THD=\frac{\sqrt{\sum _{n=2}^{\infty }{I}_n}}{I_1}$$ (10)

$$C_6=\frac{\sum _n{I}_n}{I_3},n=5,7,9$$ (11)

where n represents the odd harmonic order.

3. Methodology

In this section, the methodology of paper will be discussed. The process of this proposed methodology is shown in Fig. (2).

Fig. 2.

Proposed methodology.

Based on this, the following steps will be taken.

• •
  At first, the desired data gathering will be done. So,

  • ✓
    Leakage current data will be collected.
  • ✓
    C₁–C₆ indicators will be formed by equations (6), (7), (8), (9), (10), (11).
• •
  The border detecting of C₁–C₆ will be done.

  • ✓
    The border ranges of each indicator will be obtained.
  • ✓
    The correction of normal, abnormal, critical and pre-flashover border ranges of each index will be done.
• •The insulator wear out function of C₁–C₆ will be obtained according to the introduced border ranges by equation (14).
• •
  At the end, a procedure for sensitivity analysis will be obtained and based on that, the failure level of insulator will be obtained by equation (16), (17), (18). So,

  • ✓
    If FL_FO<0.3679, insulator is in (pre-flashover condition);
  • ✓
    Otherwise (FL_FO > 0.3679), If FL_Cr<0.3679, insulator is in (critical condition);
  • ✓
    Otherwise (FL_Cr > 0.3679), If FL_AN<0.3679, insulator is in (abnormal condition),
  • ✓
    Otherwise (FL_AN > 0.3679), insulator is in (normal condition),

In the following, each of these steps will be explained in detail.

3.1. Border areas expression and correction

In this section, the expression and correction of the border ranges of each of the criteria C₁–C₆ will be discussed. Normal, Abnormal, Critical and Pre-flashover border ranges of each criteria C₁–C₆ are shown according to Table (3) [24]. It is important to mention that the limitations of the present study depend on the type of pollution and the type of insulator. However, in this study, the mentioned data have been used to implement the proposed procedure and also to compare with the considered reference.

Table 3.

Insulator border range [24].

Index	Range
	Normal	Abnormal	Critical	Pre-Flashover
C1	<1.165	>1.165 & <2.86	>2.86 & <10	>10
C2	>59.3	>18.7 & <59.3	>0 & <18.7	∼0
C3	<1.53	>1.53 & <5.1	>5.1 & <28	>28
C4	<1.6	>1.6 & <2	>2 & <2.8	>2.8
C5	<15	>15 & <45	>45 & <65	>65
C6	>3	>1 & <3	>0.4 & <1	<0.4

In order to integrate these six indices, it is necessary to have similar behavior. As can be seen.

• •C₁, C₃, C₄ and C₅ indices are in normal condition at values close to 0 and with an increase in each criterion, it will tend towards Pre-flashover condition.
• •C₂ and C₆ indicators work in the opposite way and with the decrease in the value of each criterion, it tends towards the normal situation.

Now, using equations (12), (13), two indices C₂ and C₆ will be rewritten and converted into relations C₂^new and C₆^new.

$$C_2^{new}=\left[1-\frac{C_{2i}}{C_{2,\max }}\right]\times C_{2,\max }$$ (12)

$$C_6^{new}=\left[1-\frac{C_{6i}}{C_{6,\max }}\right]\times C_{6,\max }$$ (13)

So, C_2i and C_6i are the values of each of the second and sixth criteria, respectively, and C_2,max and C_6,max are the highest values of the second and sixth criteria, respectively.

Now, by applying these changes, all six criteria will have similar behavior. This same behavior is shown in Fig. (3).

Fig. 3.

The general behavior of six indices.

According to this figure, C_j of each of the six indicators, L_AN is the lower range of the abnormal condition, L_C is the lower range of the critical condition, and L_FL is the lower range of the Pre-flashover condition. The behavior of the six indices will be defined as Table (4).

Table 5.

Faulty condition number of C₁–C₆ in abnormal analysis.

	Pu/PL	WI1	WI2	WI3	WI4	WI5	WI6
Faulty Condition Num.	1/3	24	24	21	33	21	24
	1/5	21	22	21	33	21	23
	1/8	18	22	21	33	21	22

Table 4.

Definition of six indices behavior.

Index	Range
	Normal	Abnormal	Critical	Pre-Flashover
Cj	<L_AN	>L_AN & <L_C	>L_C & <L_FL	>L_FL

3.2 (see Table 5). WEAR OUT FUNCTION.

In this part, the wear out index will be introduced to express the amount of wear out of the insulator using the leakage current. Based on this, according to the values obtained from the leakage current and six indices C₁–C₆, and also each of the ranges determined for these six indices, equation (14) can be with the aim of determining the wear out rate of the insulator.

$$WI=e^{-\frac{C_i}{UL}},i=observation$$ (14)

where WI is the wear out index, C_i is the observed values in each of the six indices, and UL is the upper limit of each index. If the observed value is equal to the defined upper limit, the wear out index borderline according to equation (15) will be equal to 0.3679.

$$W{I}_{\text{borderline}}=e^{-\frac{C_i}{UR}}{|}_{C_i=UR}=e^{-1}=0.3679$$ (15)

Fig. (4) shows the schematic expression of this wear out index.

Fig. 4.

Schematic expression of insulator wear out index.

According to this figure, by moving away from the value of 0, the value of the wear out index will be smaller, and by crossing the boundary value of UL, the wear index will be less than the value of 0.3679 and will reach the value of 0. According to this figure.

• •Values greater than 0.3679, healthy condition
• •Values less than 0.3679, faulty condition

3.2. Failure level detection

Now, in this part, the failure level of each of the insulator indicators will be determined. According to what was shown in Fig. (3), three boundary ranges are defined to determine the insulator failure behavior. Now, according to the wear out index defined in relation (14), Abnormal, Critical and Pre-flashover failure level is introduced as relation (16)–(18):

$$F{L}_{AN}=e^{-\frac{C_i}{L\_AN}},i=observation$$ (16)

$$F{L}_{Cr}=e^{-\frac{C_i}{L\_\mathrm{C}}},i=observation$$ (17)

$$F{L}_{FO}=e^{-\frac{C_i}{L\_\text{FL}}},i=observation$$ (18)

So that FL_AN, FL_Cr and FL_FO are Abnormal, Critical and Pre-flashover failure levels, respectively and L_AN, L_C and L_FL are Abnormal, Critical and Pre-flashover lower limits, respectively as shown in Fig. (3).

Now, according to equations (16), (17), (18), the following results can be discussed.

• ❖If FL_FO<0.3679, insulator is in (pre-flashover condition);
• ❖
  Otherwise (FL_FO > 0.3679)

  • ➢
    If FL_Cr<0.3679, insulator is in (critical condition);
  • ➢
    Otherwise (FL_Cr > 0.3679)

    • •
      If FL_AN<0.3679, insulator is in (abnormal condition),
    • •
      Otherwise (FL_AN > 0.3679), insulator is in (normal condition),

4. Results

In this section, the results related to the condition monitoring of insulator using leakage current data will be analyzed and finally discussed.

4.1. Border areas scaling results

According to the schematic presented in Fig. (3), the scaling of C₁–C₆ will be expressed according to Fig. (5). So, C₁–C₆ ranges are shown in Fig. (5-a) to Fig. (5-f), respectively.

Fig. 5.

Border area scaling of C₂–C₆ (a) C₁ range (a) C₂ range (a) C₃ range (a) C₄ range (a) C₅ range (a) C₆ range.

Now, by changing the scaling in indices C₂ and C₆ and according to equations (12), (13), the scaling of C₂ and C₆ will be obtained as Fig. (6). So, C₂^new and C₆^new ranges are shown in Fig. (6-a) and Fig. (6-b), respectively. This scaling will be obtained differently according to the different values of Pu/PL = 1/3, 1/5 and 1/8, which are shown in detail in all three situations.

Fig. 6.

New border area scaling of C₂ and C₆ (a) C₂^new range (b) C₆^new range.

4.2. Insulator failure detection

In this section, the wear out of each observation of C₁–C₆ indicators is measured. Fig. 7, Fig. 8, Fig. 9 as well as Tables (5)–(7) show the results related to this section. These figures show the wear out values of C₁–C₆ indicators according to equation (14) and the data available in Ref. [24] and in three ranges of abnormal, critical and pre-flashover, respectively.

Fig. 7.

Wear out indices on abnormal upper limitation of (a) C₁ (b) C₂ (c) C₃ (d) C₄ (e) C₅ (f) C₆.

Fig. 8.

Wear out indices on critical upper limitation of (a) C₁ (b) C₂ (c) C₃ (d) C₄ (e) C₅ (f) C₆.

Fig. 9.

Wear out indices on pre-flashover upper limitation of (a) C₁ (b) C₂ (c) C₃ (d) C₄ (e) C₅ (f) C₆.

So.

• •Fig. (7-a), Fig. (7-b), Fig. (7-c), Fig. (7-d), Fig. (7-e), and Fig. (7-f) show the wear out of C₁, C₂, C₃, C₄, C₅, and C₆ indicators according to the abnormal range, respectively. When this index is lower than the drawn black line (0.3679), the situation is worse than normal condition. According to this figure, the C₄ index shows the worst condition. Also, according to Table (5), it can be seen that the highest number of abnormal conditions is observed in C₄ index with the number of 33.
• •Fig. (8-a), Fig. (8-b), Fig. (8-c), Fig. (8-d), Fig. (8-e), and Fig. (8-f) show the wear out of C₁, C₂, C₃, C₄, C₅, and C₆ indicators according to the critical range, respectively. When this index is less than the drawn black line (0.3679), the situation is worse than abnormal condition. According to this figure, the C₄ index shows a worse condition. However, by comparing this figure with Fig. (7), it can be seen that the wear out have found a better condition, which is natural due to the comparison with worse conditions. Also, according to Table (6), the highest number of critical conditions has been observed in C₃ and C₄ index with the number of 17 (see Table 6).
• •Finally, Fig. (9-a), Fig. (9-b), Fig. (9-c), Fig. (9-d), Fig. (9-e), and Fig. (9-f) show the wear out of C₁, C₂, C₃, C₄, C₅, and C₆ indicators according to the pre-flashover range, respectively. When this index is less than the drawn black line (0.3679), the situation is worse than the critical condition. According to this figure, the C₄ index shows a worse condition, although by comparing this figure with Fig. 7, Fig. 8, it can be seen that the wear out have found a better situation, which is due to comparison with worse conditions (pre -flashover). Also, according to Table (7), the highest number of critical condition has been observed in C₄ index with the number of 1.

Table 6.

Faulty condition number of C₁–C₆ in critical analysis.

	Pu/PL	WI1	WI2	WI3	WI4	WI5	WI6
Faulty Condition Num.	1/3	4	7	17	17	6	10
	1/5	4	7	17	17	6	9
	1/8	1	7	17	17	6	9

Table 7.

Faulty condition number of C₁–C₆ in pre-flashover analysis.

	Pu/PL	WI1	WI2	WI3	WI4	WI5	WI6
Faulty Condition Num.	1/3	0	0	0	1	0	0
	1/5	0	0	0	1	0	0
	1/8	0	0	0	0	0	0

4.3. Insulator failure level discussion

In this part, according to the results obtained from the previous part and according to the sensitivity analysis presented in section 3-3, the failure level of each data of the insulator leakage current will be discussed. According to this.

• •
  Only two data from index C₄ (data no. 29 of 1/3 and 1/5) have pre-flashover condition. Because the FL_FO of this data is lower than 0.3679 (according to Fig. (9-d)), while the rest of the data in Fig. (9) are higher than 0.3679. according to this, in each index, the following values have pre-flashover condition:

  • ✓
    0 data from C₁,
  • ✓
    0 data from C₂,
  • ✓
    0 data from C₃,
  • ✓
    1 + 1 = 2 data from C₄,
  • ✓
    0 data from C₅, and
  • ✓
    0 data from C₆,
• •
  Apart from the above data, any other data that is less than 0.3679 in Fig. (8) will have a critical condition. According to this, in each index, the following values have critical condition:

  • ✓
    4 + 4+1 = 9 data from C₁,
  • ✓
    7 + 7+7 = 21 data from C₂,
  • ✓
    17 + 17+17 = 51 data C₃,
  • ✓
    17 + 17+17-(1 + 1) = 49 data from C₄ (two data with pre-flashover condition are subtracted from it),
  • ✓
    6 + 6+6 = 18 data from C₅, and
  • ✓
    10 + 9+9 = 28 data from C₆
• •
  Apart from the data mentioned above, any other data that is less than 0.3679 in Fig. (7) will have an abnormal condition. According to this, in each index, the following values have abnormal condition:

  • ✓
    18 + 21+24-(9) = 54 data from C₁ (9 data with critical condition are subtracted from it),
  • ✓
    22 + 22+24-(21) = 47 data from C₂ (21 data with critical condition are subtracted from it),
  • ✓
    21 + 21+21-(51) = 12 data from C₃ (51 data with critical condition is subtracted from it),
  • ✓
    33 + 33+33-(49)-(2) = 48 data from C₄ (2 data with pre-flashover condition and 49 data with critical status are subtracted from it),
  • ✓
    21 + 21+21-(18) = 45 data from C₅ (18 data with critical condition are subtracted from it), and
  • ✓
    22 + 23+24-(28) = 41 data from C₆ (28 data with critical condition are subtracted from it)

So, Table (8) can be summarized for data with normal, abnormal, critical and pre-flashover conditions. It should be noted that in each set C_j, 36 data are collected for each of the 1/3, 1/5, and 1/8 modes, which will have a total of 3 × 36 = 108 data.

Table 8.

Failure level condition number of C₁–C₆.

	C1	C2	C3	C4	C5	C6
Sum	108	108	108	108	108	108
Pre-flashover Condition No.	0	0	0	2	0	0
Critical Condition No.	9	21	51	49	18	28
Abnormal Condition No.	54	47	12	48	45	41
Normal Condition No.	45	40	45	9	45	39

Now, as can be seen, the worst condition is for C₄ (dividing the peak value by the RMS value of the leakage current), which has the highest value of pre-flashover condition and the lowest value of normal condition.

By comparing the paper results with [24], the proposed procedure will be validated. According to this.

• •By reducing the amount of Pu/PL from 1/3 to 1/8, the insulation condition has improved in both works.
• •In Ref. [24], C₁–C₆ results are stated cumulatively (while in the present paper, they are analyzed both as each observation and cumulatively), and the cumulative comparison with [24] confirms the proposed method.

Also, the innovations related to this paper compared to Ref. [24] can be stated as follows.

• •According to the proposed procedure in section (3–1), the data are of the same type (per unit and in the same direction) and therefore the comparison is easier.
• •Due to the per unit scale, it is possible to compare indicators with each other.
• •The result of the monitoring of insulation conditions has been analyzed both for each observation and cumulatively.

5. Conclusion

In this paper, the type and level of failure of insulator was investigated using leakage current data. Based on this, after determining the six indicators, the boundary limits for normal, abnormal, critical and pre-flashover conditions are obtained, and then by defining the wear out function for the insulator, the failure of each indicator is calculated. In the following, using sensitivity analysis, the damage levels of each data obtained from the leakage current will be determined. Based on this, by comparing the above two stages, i.e. determining the wear out and of each observation of the insulator, as well as determining the failure level of insulator, in addition to a more detailed analysis of the insulator condition, the introduced method has been validated. The proposed method is completely data-based and its output results will be clear without any human decision for the degree of insulator failure. According to the results of this paper, it is determined how the general condition of the insulator is and whether it needs maintenance or not, and it is also determined which indicator of the insulator is in a worse condition and which factor the maintenance team should pay more attention to. By using the method of this paper, defective insulators can be identified based on the rules and data obtained.

Data availability statement

The data are available on request.

CRediT authorship contribution statement

M. Monemi: Writing – review & editing, Writing – original draft, Validation, Methodology, Formal analysis, Data curation, Conceptualization. S.M. Shahrtash: Supervision, Project administration. M. Kalantar: Visualization, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.