materials Article Monitoring Porcelain Insulator Condition Based on Leakage Current Characteristics Ali Ahmed Salem 1 , Kwan Yiew Lau 1, * , Mohd Taufiq Ishak 2, * , Zulkurnain Abdul-Malek 1 , Samir A. Al-Gailani 3 , Salem Mgammal Al-Ameri 1 , Ammar Mohammed 4 , Abdulaziz Ali Saleh Alashbi 4 and Sherif S. M. Ghoneim 5 1 2 3 4 5 * Citation: Salem, A.A.; Lau, K.Y.; Ishak, M.T.; Abdul-Malek, Z.; Al-Gailani, S.A.; Al-Ameri, S.M.; Mohammed, A.; Alashbi, A.A.S.; Ghoneim, S.S.M. Monitoring Porcelain Insulator Condition Based on Leakage Current Characteristics. Institute of High Voltage and High Current, School of Electrical Engineering, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia Faculty of Engineering, National Defence University of Malaysia (UPNM), Kuala Lumpur 57000, Malaysia School of Electrical and Electronic Engineering, Universiti Sains Malaysia, Nibong Tebal 14300, Malaysia School of Computing, Faculty of Engineering, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia Electrical Engineering Department, College of Engineering, Taif University, Taif 21944, Saudi Arabia Correspondence: mtaufiq@upnm.edu.my (M.T.I.); kwanyiew@utm.my (K.Y.L.) Abstract: Insulator monitoring using leakage current characteristics is essential for predicting an insulator’s health. To evaluate the risk of flashover on the porcelain insulator using leakage current, experimental investigation of leakage current indices was carried out. In the first stage of the experiment, the effect of contamination, insoluble deposit density, wetting rate, and uneven distribution pollution were determined on the porcelain insulator under test. Then, based on the laboratory test results, leakage current information in time and frequency characteristics was extracted and employed as assessment indicators for the insulator’s health. Six indicators, namely, peak current indicator, phase shift indicator, slope indicator, crest factor indicator, total harmonic distortion indicator, and odd harmonics indicator, are introduced in this work. The obtained results indicated that the proposed indicators had a significant role in evaluating the insulator’s health. To evaluate the insulator’s health levels based on the extracted indicator values, this work presents the naïve Bayes technique for the classification and prediction of the insulator’s health. Finally, the confusion matrix for the experimental and prediction results for each indicator was established to determine the appropriateness of each indicator in determining the insulator’s health status. Materials 2022, 15, 6370. https:// doi.org/10.3390/ma15186370 Keywords: porcelain insulator; contamination; leakage current characteristics; classification Academic Editors: Hone-Zern Chen and Albena Paskaleva Received: 28 July 2022 Accepted: 28 August 2022 Published: 14 September 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1. Introduction Outdoor insulators are important in electrical power transmission systems. However, the efficiency and health of the insulators are greatly impacted by numerous environmental factors, including wetness and contamination. Outdoor environmental factors, such as contamination and moisture, have a significant impact on insulator effectiveness. Moisture, such as rain and fog, in the presence of pollution reduces the surface resistance of insulators. Surface resistance lowering may result in higher leakage current flowing on the surface and dry band arcing. A large magnitude of leakage currents flowing on the surface over an extended length of time may produce insulator surface deterioration, which might eventually lead to flashover [1–6]. The unwanted discharge may result in a flashover phenomenon that leads to electrical grid disruption or even failure [7–9]. It is, therefore, crucial to monitor the status of the insulators to ensure that they are fit for purpose [10,11]. This would further strengthen the efficiency of the power grid and decrease its failure probability. The evaluation of the performance of outdoor insulators continues to be a significant topic in the high-voltage community [12–15]. The use of the leakage current (LC) parameter in observing the performance of outdoor insulators has been popular and offers many advantages. This is because LC monitoring considers various environmental conditions, Materials 2022, 15, 6370. https://doi.org/10.3390/ma15186370 https://www.mdpi.com/journal/materials Materials 2022, 15, 6370 2 of 22 such as temperature, humidity, pollution, and rain [16]. Moreover, LC monitoring can be done online on a continuing basis. Examples of LC monitoring techniques include the use of the microwave reflectometer system, which has been used to monitor LC for dry insulator surfaces [17]. However, this type of monitoring system is less cost-effective. The authors in [18] offer an alternative method that uses an antenna to monitor LC on polluted insulators by capturing electromagnetic radiation resulting from partial discharge on the insulator. The advantage of this system is that the components used are not damaged by flashover voltage, as is the case of other systems. To the best of our knowledge, however, this system has yet to be tested under large electromagnetic interference caused by coronas and other effects of high-voltage conductors. Another issue of interest in the monitoring technique of polluted insulator LC refers to the competence to establish a strong link between the LC and the condition of the insulator under service. Many researchers have offered various approaches to evaluate the physical state of insulators [16,19–21]. Improvement in LC-based monitoring is achieved by extracting information from the LC components. The LC statistical results, such as average, maximum, and standard deviation, recommended by [22] were used for evaluating the level of contamination. These researchers suggested that these parameters allow the quantification of the dimensions and density of the contamination layer over the surface of the insulator. Another study [19] assessed the contaminated insulator conditions by evaluating the phase angle between current and voltage signals. According to the results in [19], phase angle differences are a helpful indication for assessing contaminants and humidity fluctuations in a clean environment. The assessment of the LC signal in the frequency domain through fast Fourier transform (FFT) and wavelet transformations is also a relevant technique used to predict insulators’ pollution status [23–25]. Overall, the results have indicated that contaminants on the insulator amplify the harmonic of leakage current components, especially the harmonics in an odd order. The results imply that the contamination leads to the rise of the first and third harmonics and the total harmonic distortion (THD) [26]. The concerned harmonics are the first and third component harmonics under an AC voltage. Accordingly, the study found that increasing these harmonics causes a rise in THD, which changes according to the change in the level of contamination and harmonics of the supplied voltage [27]. Some publications in the literature have proposed several numerical indices to identify the performance of overhead line insulators. As far as we are aware, none of them evaluated the performance of insulators using one specific indicator. In direct connection, acoustic and thermal-based diagnostic methods, such as ultrasonic wave [28] and acoustic fault diagnosis [29], have been used to evaluate the health of overhead lines insulator. However, the performance of these techniques is affected by the acoustic frequency noise generated from the electromagnetic field of the overhead line. Infrared thermal imaging [30] and temperature analysis of infrared insulator images [31] are utilized to diagnose polluted insulators as well. However, these techniques rely only on the thermal behavior of the insulator, which is limited in revealing an accurate insulator state. Although the wirelessbased system [32] and network sensors [18] show good performance in monitoring insulator conditions, their high sensitivity to environmental weather, such as dust and rain, influences the accuracy of the results. It is essential to have an indicator reflecting the condition of the insulators [16,20]. The extraction of the LC components based on the frequency domain to calculate the relevant indicators were performed. For example, the ratio of leakage current’s third to fifth harmonic indicator (fifth/third) was extracted to estimate flashover incidences [27]. The published findings for silicon rubber and glass insulators show good correlation between the magnitude of the contamination and the reading of this indicator. In addition, the literature review demonstrated that no attempt has been made to investigate the insulators’ conditions using indices considering the slope of the signal in the time domain and the odd harmonic components between 0 and 500 Hz for LC. This technique is supposed to yield a more reliable prediction when compared with the other leakage current indicators. Materials 2022, 15, 6370 3 of 22 Regarding the classification and prediction of insulator health, the previous work in [33] introduces the support vector machine (SVM) for classifying the condition of the insulator under the effect of the different coating damage modes. The assessment of the contaminated insulators was performed using computer vision in [34] and k-nearest neighbors (k-NN) [35]. The results of these studies indicated that these techniques provide adequate efficiency and accuracy and that they are promising approaches since they are quick and easy to perform. Some researchers have evaluated the conditions of insulators using different artificial intelligence methods, as reported above. However, the application of the naïve Bayes method to estimate the insulator conditions based on the leakage current characteristics has not been investigated, and this will be discussed in our current work. Our current work contributes to estimating the conditions of porcelain insulators, as follows: • • • Six indicators based on the measured LC characteristics in the time domain and frequency domain, namely, the peak current indicator, phase shift indicator, slope indicator, crest factor indicator, total harmonic distortion indicator, and odd harmonic indicator, were extracted by taking into consideration the significant effect of environmental factors on the performance of the overhead line insulators. Environmental factors, including the soluble deposit density, wetting rate, insoluble deposit density, and contamination ratio of the upper to the lower side of the insulator were taken into consideration while simulating the nature of insulators in service. The classification of the state of insulators based on the proposed indicator values using the naïve Bayes approach was conducted. The comparison of the performance of the proposed indicators using the confusion matrix for the actual insulator conditions and naïve Bayes prediction results was carried out. The rest of this paper is structured as follows. Section 2 reviews the process of pollution of the insulators and discusses how LC is measured. Section 3 illustrates the proposed leakage current indicator expressions. Section 4 presents the experimental and modeling results. Finally, the conclusion is presented in Section 5. The advantages of this study are: • • • • The proposed indicators are useful to monitor the condition of overhead line insulators in real time. Insulator condition estimation using LC indicators is simple, low cost, and accurate. Applicable for any insulator type and any voltage level. Monitoring insulator conditions on the transmission line (without removing the insulator and without interrupting the power line). 2. Materials and Methods 2.1. Test Sample The porcelain insulators to be tested were collected from the transmission division of the national network in Malaysia. The selected insulators’ main shape is portrayed in Figure 1. The insulators’ actual specifications are tabulated as in Table 1. In this paper, a single disk of porcelain insulators and a string of three units of porcelain insulators were tested. Materials 2022, 15, 6370 4 of 22 Figure 1. Insulator sample. Table 1. Test insulator structure characteristics. Parameter Symbol Length (cm) Creepage distance L 32 Insulator height H 14.6 Insulator diameter D 25.5 Rib diameters d1 d2 d3 dc 19.5 14.5 10.5 5 2.2. Test Facilities and Procedures The IEC-507 standard, namely, “Artificial pollution tests on high-voltage ceramic and glass insulators to be used on AC systems” [36] was referred to while performing the experimental setup. All experiments were carried out in an artificial test chamber with dimensions 50 cm × 50 cm × 75 cm in which the walls were polycarbonate sheets. The chamber was installed with four inlet valves used for spraying insulators under test for the purpose of wetting. Figure 2a shows a schematic diagram for the high-voltage polluted insulator experimental setup. A photograph of the test setup and the equipment used in the high-voltage laboratory is given in Figure 2b. The experimental circuit setup was composed of the following components: A is a transformer (220 V/100 kV, 5 kVA, 50 Hz), B is a capacitive voltage divider, C is the test sample inside the chamber, D is a monitoring system to measure the leakage current, E is a resistive step-down divider (100:1) employed for the measurement of the LC and protection of the DAQ device, and F is a fog generator with a rate controller for wetting. Materials 2022, 15, 6370 5 of 22 (a) (b) Figure 2. (a) Diagram of insulators’ test arrangement; (b) photograph of the insulat Figure 2. (a) Diagram of insulators’ test arrangement; (b) photograph of the insulators under test. 2.3. Wetting and Polluting Prior to commencing the experiment, traces of grease and dirt were removed carefully for all specimens using alcohol liquid. Next, the insulators were dried for 24 h naturally. The contamination was then applied to the insulator surface based on the solid layer method [37–40]. The pollution was made up of two types of deposits: soluble deposit density (SDD), which is represented by sodium chloride salt (NaCl), and insoluble deposit density (NSDD), which was represented by kaolin. To prepare the SDD, the required amount of NaCl salt was mixed with 1000 mg of water to establish the pollution solution. Then, a conductivity meter was used to measure the conductivity of the polluted solution σσ at room temperature for three amounts of salt (10 g, 20 g, and 30 g) to compute three σσ levels of SDD. Also, three amounts of kaolin (20 g, 40 g, and 60 g) were used to produce the NSDD levels listed in Table 2. Next, the conductivity of the pollution solution at 20 ◦ C was calculated using Equation (1): σ20 =20σσ × [1[1− b((θ −20)] 20)] (1) Materials 2022, 15, 6370 6 of 22 where σ20 and σσ , represent the solution conductivity at 20 ◦ C, and the solution conductivity at the room temperature. θ is the temperature of the solution and b is a temperaturedependent factor that is determined to be 0.02 at = 27.5 ◦ C using Equation (2) [36]. b = −3.2 × 10−8 θ 3 + 1.032 × 10−5 θ 2 − 8.272 × 10−4 θ + 3.544 × 10−2 (2) Table 2. Pollution layer characteristics. σ20 (S/m) SDD (mg/cm2 ) NSDD (mg/cm2 ) Wt (mL/h) Pollution Level 0 0.39 0.72 1.38 0 0.05 0.1 0.2 0 0.15 0.25 0.35 0 3 6 9 Clean Low Medium High The SDD was calculated based on the IEC 60507 [36] and IEC 60815 [41] standards using Equation (3): (5.7 × σ20 )1.03 × V (3) SDD = S where V and S represent the volume of pollution solution, and the insulator surface area, respectively. Meanwhile, Equation (4) was used to calculate NSDD according to the IEC-507 standard [36]: [(ws − wi ) × 103 ] (4) NSDD = S where ws and wi are the mass of the filter paper under contamination and under dry conditions, respectively. As shown in Table 2, three levels were determined for both SSD and NSDD: light, moderate, and high contamination. The sample was then polluted and hung in the test room and left drying for around 1 day to ensure that the polluted insulator was dried. The test room pressure remained constant throughout the experiment, matching the laboratory’s ambient pressure. The temperature in the testing room was roughly 27.9 ◦ C, which was about the same as the indoor temperature in the laboratory. The relative humidity inside the test room was set to 75% and monitored during the testing with the help of a humidity sensor. The spray technique was used to wet the insulator, with six nozzles regularly spaced around the test room wall. A control panel outside the test room was used to automatically calculate the fog flow rate. To achieve the moisture of insulators at different levels, three degrees of wetting rates Wt were applied, i.e., 3 mL/h, 6 mL/h, and 9 mL/h. Under both uniform and uneven contamination distributions, the porcelain was investigated. Also, three contamination ratios of the upper to the lower side of the insulator ( PL /Pu ), i.e., 1/3, 1/5, and 1/8, were selected in the uneven contamination case. The upper and lower surfaces of the insulator were polluted separately in the nonuniform pollution case to yield SDDu and SDDL , whereas the overall SDD can be met by Equation (5) [5,40]: SDD = SDDu × Su + SDDL × S L Su + S L (5) where Su and S L are the area of the upper and lower surface of insulator, respectively. According to these selected pollution ratios, the SDD of the upper and lower sides (SDDu and SDDu ) can be satisfied by Equation (6): SDDPu = 2 × SDD 2 × SDD , SDDPL = 1 + ( PL /Pu ) 1 + ( Pu /PL ) (6) Materials 2022, 15, 6370 7 of 22 2.4. Data Monitoring As illustrated in the experimental setup in Figure 2, the input voltage values were obtained using a divider consisting of two capacitors with a ratio (C1 to C2 ) of 10,000:1. On the other side of the test chamber, the monitoring system consisted of a data acquisition (DAQ) card, oscilloscope, and a PC, which was used to measure LC. A resistive divider (100:1) was employed, since the DAQ’s input voltage range is just 10 V. During the measurement, the LC data were captured from the divider and then transferred using a DAQ card to the PC. The captured data were saved in a CSV file after being displayed on a graphical user interface of the LabVIEW software. For measurement validation, the oscilloscope was utilized to compare with DAQ data reading. Finally, with the help of MATLAB software, the LC data saved were converted into the frequency domain using FFT. 3. Characteristic Parameter of Leakage Current In this paper, six characteristics/indices were extracted in both the time and frequency domains of LC to predict the health of polluted insulators. 3.1. Leakage Current Indicators in Time Domain The time and frequency domain signal of LC was used to derive all the leakage current indicator equations. The formulae presented in this section were used as the indicators of change in LC signal that was affected by the insulator conditions. In the time domain of LC, four indicators were selected. The first and second indicators, which were the peak of leakage current Im (denoted as x1 ), found based on the absolute value of the current signal, and the phase shift φ between the applied voltage and LC (denoted as x2 ) were extracted from the LC general equation, expressed as in Equation (7) [42]: I = Im sin(ωt + φ) (7) where ω is the angular frequency equivalent to 2πf, with the value of frequency f in this study 50 Hz. As such, the first two characteristics can be defined as in Equations (8) and (9): x1 = Im (8) ∆t 360◦ (9) T Figure 3 illustrates how the phase difference φ between the applied voltage and LC can be determined for a clean and a polluted insulator. For a clean insulator, the phase difference φ between the applied voltage and LC appeared to be nearly 90◦ (see Figure 3a). As the amount of pollution on the insulator increased, the phase difference φ between the applied voltage and LC decreased. Under heavily polluted circumstances, the phase difference φ between the applied voltage and LC became nearly zero (see Figure 3b). The third indicator x3 was extracted by calculating the slope of the line between two consecutive peaks of LC signal, expressed as in Equation (10): x2 = φ = m m ∑ | y n − y n −1 | x3 = n =1 x n − x n −1 ∑|∆yn | = 0 ∆xn (10) where ∆yn is the LC difference for adjacent peaks at the nth point for time and ∆xn is the time between these peaks. Figure 4a illustrates how the LC signal slope was calculated. The fourth indicator x4 was obtained from the crest factor, which was calculated by dividing the peak value with the RMS value of the LC waveform, as shown in Figure 4b. As such, x4 is expressed as in Equation (11): I peak (11) x4 = IRMS Materials 2022, 15, 6370 8 of 22 IRMS =  s 1 ii2 n∑ i (12)  where RMS is root mean square,−ii is each measured  value, and n is the number of measurements. = − = − =  − where ∆ nth point for time and ∆ =  = (a) (b) Figure 3. Leakage current and applied voltage phase angle: (a) clean; (b) pollution.  3  1 1 0 1 ∆ ∆ (a) (b) 4 Figure 4. (a) Slope curve extracted from leakage current waveform; (b) crest factor indicator extracted from leakage current waveform. 1 2 3.2. Leakage Current Indicators in Frequency Domain  The frequency-domain signals of LC for polluted insulators have characteristic features at frequencies below 500 Hz. In this paper, the odd harmonic and total harmonic distortion (THD) of LC under 500 Hz were used to propose indicators for insulator condition assessment. The frequency characteristics of the LC are defined by the x5 and x6 indicators, as in Equations (13) and (14), respectively: x5 = THD = s ∞ ∑ In 2 n =2 I1 (13) Materials 2022, 15, 6370 9 of 22 ∑ In x6 = n I3 n = 5, 7, 9 (14) where In represent the nth harmonic and n is the odd-order harmonic number. 4. Classification Model The naïve Bayesian classifier is a classification algorithm based on Bayes’s theorem. Its underlying idea and building approach are more straightforward and simpler than those of support vector machines and neural networks. Furthermore, compared to other algorithms, the naïve Bayesian classifier algorithm suits the approach of this work, and brought great accuracy in classifying the insulator situations. The naïve Bayesian classifier theorem, which is employed in the classification of the suggested LC indicators, is explained in this section. Figure 5 depicts the flowchart of the procedures involved in extracting and categorizing the recommended indicators. Start Select test insulators Insulators Arrangement and performed test Leakage current measurement and saving data as CSV file to PC Change new pollution level Convert leakage current to FFT Extract the useful characteristic of LC Define the LC indicators Determine of indicators values in the pollution levels No Are all sample s diagnosed? Performance assessment End Comparison Insulator condition recognition using NAIVE BAYESIAN CLASSIFIER based on LC indicators Trained NAIVE BAYESIAN CLASSIFIER model NAIVE BAYESIAN CLASSIFIER model establishment Test dataset Classifying LC indicators test data according the condition insulator under test to (Normal, Abnormal, Critical), Training dataset Yes Figure 5. Data extraction and classification of the proposed indicators.  arg max{ ( | )} To understand the naïve Bayesian, method, consider y to be a collection of samples. 1,2,...,  Each sample contains n condition characteristics that represent its special traits, as well as  ( ) ( | )  one class label. All LC features are assumed in this work, while the class  arg maxto be interrelated  , 1,2,...,  ( )  all training  label is assumed to be separated. Assume that examples are classified into m  classifications and that the class labelarg of max each sample changes from {z 1 , z2 , . . . , zm }. As a ( ) ( | )→ , 1,2,..., result, any sample can be shown as an n-dimensional vector. y = (y1 , y2 , . . . , yn ) would be a piece of testing data whose class label has to be determined. A naïve Bayesian classifier may ( ) compute the posterior probabilities and decide the class label for the new sample based ( ) /  ( | )  ( | ) Naïve Bayesian Classifier Materials 2022, 15, 6370 10 of 22 on the previous and class-conditional possibilities of the new sample. A naïve Bayesian classifier uses Equation (15) to characterize the new sample’s class label [43]: n o → z = argmax P(zk y ) zk ,k =1,2,...,m   → ( y|zk ) = argmax P(zk ) P→ (15) P(y) zk ,k =1,2,...,m  → = argmax P(zk ) P( y|zk ) zk ,k =1,2,...,m where P(zk ) represents the previous probability of the zk class that can be found from → P(zk ) = Nk /N, Nk is the number of samples within zk class, N is data set size, and P( y|zk ) represent the class-conditional probability. The main aim of the naïve Bayesian classifier is → to determine P( y|zk ) based on the training samples in the zk class. All features are assumed to be independent by the naïve Bayesian classifier. As a result, the class-conditional probability can be written as in Equation (16): f → P ( y | z k ) = P ( y1 , y2 , . . . , y n | z k ) = ∏ P(y f zk ) (16) i =1 → To find the class label of y , the Naïve Bayesian classifier can substitute the classconditional probability with Equation (16) and yield the decision function in Equation (17). z = argmax zk ,k =1,2,...,m ( f nk P(y f zk ) N i∏ =1 ) (17) where P(y f zk )(1 ≤ f ≤ n) is an essential factor in determining the class label of the new sample. 5. Results and Discussion 5.1. Leakage Current Results The LC findings of uniformly polluted insulators in both time and frequency domains with various SDD levels but fixed NSDD of 0.15 mg/cm2 and Wt of 3 mL/h are shown in Figures 6 and 7. Figure 6 indicates that increased pollution severity causes a considerable rise in LC under specific values of NSDD, Wt, and Pu /PL . The LC increase can be explained by the increase in conductivity of the pollution layer on the insulator’s surface once subjected to wetness. Consequently, the LC flowed from the high voltage terminal to the ground in the form of positively and negatively charged ions. Some spot arcs were observed on occasion under high-contamination conditions, particularly in the existence of moisture. During the flashover, the signal of the LC appeared to be severely distorted, as shown in Figure 6d. Furthermore, when LC increased, the THD and harmonic values increased (see Figure 7), while the phase angle between the current and voltage decreased. The decrease in phase angle between the LC and voltage is due to the resistive current increasing with constant capacitive current. Once the contamination level on the insulator surface was raised, a clear change in the odd harmonics (3rd, 5th, 7th, and 9th) was observed (see Figure 7). As seen in Figure 8, the 3rd harmonic will increase to surpass the 5th, 7th, and 9th harmonics, with a clear increase in the 7th and 9th harmonics. Furthermore, during discharge activity on the insulator’s surface, the 3rd harmonic is often substantially high [44,45]. ϕ Materials 2022, 15, 6370 11 of 22 (a) (b) (c) (d) Leakage current (mA)(mA) Leakage current Figure 6. Leakage current waveform under NSDD = 0.15 mg/cm2 , wt = 3 mL/h and different SDD: (a) SDD = 0.00 mg/cm2 ; (b) SDD = 0.05 mg/cm2 , (c) SDD = 0.12 mg/cm2 , (d) SDD = 0.2 mg/cm2 . 40 4 40 30 30 20 2 0 20 10 10 0 0 5 4 2 0 0 0 3 th 11 kV 33 kV th 11 kV 33thkV 7 5 th 3 th 0 100 0 100 100 7 th 200 200 200 300 300 300 Frequency (Hz) 100 200 300 (a) (Hz) Frequency 400 400 400 400 40 40 30 30 20 th 20 10 3 100 3 th 0 40 11 kV 33 kV 11 kV 33 kV 0 0 100 5 th 5 th 200 100 200 30 20 7 th 300 300 Frequency (b) (Hz) 3 th 20 10 7 th Frequency (Hz) 11 kV 33 kV 11 kV 33 kV 40 30 100 400 0 400 (c) 0 0 100 7 th 5 th 3 th 7 th 5 th 200 300 Frequency (Hz) 100 200 300 Frequency (d) (Hz) 400 400 Figure 7. FFT of leakage current waveform under NSDD = 0.15 mg/cm2 , Wt = 3 mL/h and different SDD: (a) SDD = 0.00 mg/cm2 ; (b) SDD = 0.05 mg/cm2 , (c) SDD = 0.12 mg/cm2 , (d) SDD = 0.2 mg/cm2 . Figure 8. Odd harmonics of leakage current under pollution grading [2]. Table 3 provides the test results of the LC harmonic components’ values (magnitude Im , harmonics, THD, and phase shift angle φ) for different pollution levels under uniform pollution distribution for all investigated conditions. Under the clean condition, the ϕ 5th ϕ and 7th harmonics were greater than the 3rd harmonic. Furthermore, there were no signs ≈ϕ ≈ϕ of flashover. The LC rose marginally as the wetting rate increased when the clean insulators ≈≈ indicates that wetting the insulator surface caused ≈ were tested under a specific NSDD. This ≈ the flow of the charges from the high-voltage terminal to the ground to rise noticeably. Materials 2022, 15, 6370 12 of 22 Table 3. LC characteristics for insulators under different contamination degree for uniform distribution. Single Insulator under 11 kV SDD Wt Im 3rd 5th 7th 9th THD φ Im 3rd 5th 7th 9th THD φ 0 0 0 3 6 9 0 3 6 9 0 3 6 9 1.807 1.975 4.344 7.109 8.886 2.172 6.615 8.590 9.577 4.048 7.306 8.984 10.367 0.005 0.006 0.030 0.039 0.069 0.030 0.099 0.107 0.168 0.057 0.178 0.197 0.326 0.020 0.030 0.149 0.125 0.168 0.138 0.405 0.395 0.592 0.118 0.592 0.627 0.721 0.012 0.010 0.020 0.079 0.099 0.020 0.049 0.079 0.099 0.089 0.049 0.059 0.069 0.020 0.005 0.008 0.007 0.059 0.020 0.059 0.069 0.079 0.089 0.030 0.049 0.089 7.727 7.795 8.492 8.595 9.190 7.944 9.064 9.133 9.578 8.355 9.601 9.853 9.978 ≈90 ≈90 87.026 86.956 85.838 88.802 87.076 87.166 86.277 88.084 85.888 85.269 84.870 1.778 1.944 4.276 6.997 8.746 2.138 6.511 8.454 9.426 3.984 7.191 8.843 10.203 0.005 0.006 0.029 0.039 0.068 0.029 0.097 0.105 0.165 0.056 0.175 0.194 0.321 0.019 0.029 0.147 0.123 0.165 0.136 0.398 0.389 0.583 0.117 0.583 0.617 0.709 0.012 0.010 0.019 0.078 0.097 0.019 0.049 0.078 0.097 0.087 0.049 0.058 0.068 0.019 0.005 0.008 0.007 0.058 0.019 0.058 0.068 0.078 0.087 0.029 0.049 0.087 8.523 8.598 9.367 9.481 10.136 8.762 9.998 10.073 10.565 9.216 10.590 10.867 11.006 ≈ 90 86.370 82.100 82.034 80.980 83.776 82.147 82.232 81.394 83.098 81.027 80.443 80.066 0 3 6 9 0 3 6 9 0 3 6 9 5.134 8.886 11.749 15.501 7.207 12.144 14.711 18.166 8.984 16.093 20.141 25.769 0.089 1.234 1.343 1.777 0.138 1.402 1.649 1.767 0.178 1.876 2.172 2.577 0.425 3.159 2.962 3.554 0.553 2.281 2.271 2.281 0.642 2.488 2.370 3.159 0.089 0.592 0.819 0.908 0.079 0.839 1.382 1.481 0.128 1.007 1.382 1.185 0.039 0.296 0.395 0.760 0.069 0.652 0.691 0.790 0.099 0.553 0.889 1.086 9.384 11.693 12.904 16.482 10.174 12.447 14.688 17.179 11.008 15.248 18.025 21.534 82.036 79.152 67.365 57.495 80.589 66.078 54.142 42.575 78.164 56.098 40.050 33.154 5.053 8.746 11.564 15.257 7.094 11.953 14.479 17.880 8.843 15.840 19.824 25.363 0.087 1.215 1.322 1.749 0.136 1.380 1.623 1.739 0.175 1.846 2.138 2.536 0.418 3.110 2.915 3.498 0.544 2.245 2.235 2.245 0.632 2.449 2.332 3.110 0.087 0.583 0.807 0.894 0.078 0.826 1.360 1.458 0.126 0.991 1.360 1.166 0.039 0.292 0.389 0.748 0.068 0.641 0.680 0.777 0.097 0.544 0.875 1.069 10.351 12.897 14.234 18.180 11.222 13.729 16.200 18.949 12.142 16.818 19.882 23.752 77.392 74.671 63.552 54.241 76.027 62.338 51.077 40.165 73.739 52.922 37.783 31.277 0 3 6 9 0 3 6 9 0 3 6 9 6.319 14.612 16.093 19.055 7.405 16.982 19.351 23.103 9.281 19.549 20.141 25.769 0.217 3.258 4.048 4.542 0.316 3.456 5.233 5.628 0.405 5.529 7.109 6.121 0.711 2.666 3.159 4.048 0.790 3.061 3.653 4.048 0.790 3.554 4.048 4.147 0.109 0.395 0.612 0.938 0.128 1.027 1.086 1.283 0.306 1.283 1.481 1.678 0.079 0.790 1.185 0.790 0.207 0.889 0.968 1.086 0.227 1.580 1.283 1.777 9.384 17.522 21.580 26.575 11.293 24.849 28.861 36.542 11.327 34.873 39.582 48.052 71.058 55.100 38.453 27.106 75.739 52.415 30.160 25.070 70.289 39.581 20.589 14.920 6.553 15.153 16.688 19.760 7.679 17.610 20.067 23.958 9.624 20.272 20.886 26.722 0.225 3.379 4.198 4.710 0.328 3.583 5.426 5.836 0.420 5.733 7.372 6.348 0.737 2.764 3.276 4.198 0.819 3.174 3.788 4.198 0.819 3.686 4.198 4.300 0.113 0.410 0.635 0.973 0.133 1.065 1.126 1.331 0.317 1.331 1.536 1.741 0.082 0.819 1.229 0.819 0.215 0.921 1.003 1.126 0.235 1.638 1.331 1.843 10.444 19.502 24.018 29.578 12.569 27.657 32.122 40.671 12.607 38.814 44.055 53.482 68.988 53.495 37.333 26.316 73.533 50.889 29.281 24.340 68.242 38.428 19.989 14.486 0 3 6 9 0 3 6 9 0 3 6 9 8.313 26.065 29.027 36.036 10.169 28.928 32.482 39.393 10.564 34.950 51.735 64.273 0.523 9.478 9.774 10.732 0.612 9.379 10.762 12.835 0.642 13.743 15.994 17.673 0.948 2.764 2.271 2.271 0.987 2.764 2.666 3.159 1.007 2.962 3.456 2.666 0.444 2.073 2.567 2.666 0.622 2.073 2.271 2.370 0.474 1.185 2.073 1.283 0.316 1.481 1.086 1.283 0.316 1.086 1.185 1.185 0.494 1.481 1.185 1.678 11.339 41.788 47.229 50.029 12.322 52.155 54.681 61.482 12.150 59.059 67.768 69.563 56.727 32.056 17.545 11.537 42.455 26.397 10.709 1.038 32.774 3.912 2.066 0.828 8.621 27.029 30.101 37.370 10.545 29.998 33.684 40.851 10.955 36.244 53.649 66.651 0.543 9.829 10.136 11.129 0.635 9.726 11.160 13.310 0.665 14.252 16.586 18.327 0.983 2.867 2.355 2.355 1.024 2.867 2.764 3.276 1.044 3.071 3.583 2.764 0.461 2.150 2.662 2.764 0.645 2.150 2.355 2.457 0.491 1.229 2.150 1.331 0.328 1.536 1.126 1.331 0.328 1.126 1.229 1.229 0.512 1.536 1.229 1.741 12.620 46.510 52.566 55.682 13.714 58.049 60.860 68.429 13.523 65.732 75.426 77.424 55.074 31.122 17.034 11.201 41.219 25.628 10.397 1.008 31.820 3.798 2.006 0.804 0.15 0.00 0.25 0.35 0.15 0.05 0.25 0.35 0.15 0.1 0.25 0.35 0.15 0.2 3 Unit Insulator String under 33kV NSDD 0.25 0.35 Table 3 also shows the results of the uniformly polluted insulators with the change in SDD, Wt, and NSDD. Table 3 shows that the LC on a clean insulator’s surface is very low, approximately 1.81 mA for single disk and 1.78 for string insulators. This indicates that under clean circumstances, the performance of the insulators is capacitive. Because of the capacitive property of LC, the phase shift angle between current and voltage will be about 90◦ . Under the clean and dry scenario, the 5th harmonic is higher than the 3rd harmonic. Generally, the LC component test results in Table 3 show that: 1. 2. 3. 4. Under dry conditions, surface conductivity was minimal. Therefore, the influence of increasing SDD and NSDD on LC and LC characteristics in this condition was minor. The LC magnitude grew substantially as the contamination severity of SDD, NSDD, and Wt increased. As SDD, NSDD, and Wt increased and Pu /PL decreased, odd harmonic values and THD increased. In contrast, the phase angle decreased. When the Wt was changed for a clean insulator under a specific NSDD, the LC value varies somewhat, as do the temporal and frequency characteristics of the LC. 5.2. Leakage Current Indices Finding Figure 9 shows the LC indices of a clean (0.00 mg/cm2 of SDD) insulator under different Wt and NSDD. Each indicator demonstrates a unique behavior when the wetting rate and NSDD were changed. Of note, there is no significant difference between different NSDD under the same Wt. The x1 , x3 , x4 , and x5 indices increased with the rise in both the Materials 2022, 15, 6370 13 of 22 NSDD and Wt. For example, when the Wt was increased from 3 mL/h to 9 mL/h under 0.15 mg/cm2 of NSDD, the x1 increased from 4.2 to 8.88, x3 increased from 0.065 to 0.11, x4 increased from 1.56 to 1.585, and x5 increased from 7.6 to 10.49. (a) (b) (c) (d) (e) (f) Figure 9. LC indices of a clean insulator under different Wt and NSDD; (a) x1 ; (b) x2 ; (c) x3 ; (d) x4 ; (e) x5 ; (f) x6 . In contrast, the x2 and x6 decreased with the increase in both the Wt and NSDD. For example, when the Wt increased from 3 mL/h to 9 mL/h under NSDD = 0.15 mg/cm2 , the x2 decreased from 87.2 to 86.01 and x6 decreased from 5.9 to 4.7. 5.2.1. Indicators Trends under Different SDD The leakage current indices x1 , x3 , x4 , and x5 under different SDD, NSDD, Wt, and Pu /PL for single and string insulators are presented in Figure 10 and Table 4. The LC indicators of insulators under test increased with the increase in SDD under specific NSDD, Wt, and Pu /PL . On the contrary, the indices x2 and x6 of insulators decreased with the increase in SDD under the same conditions. For example, under NSDD of 0.25 mg/cm2 , Wt of 6 mL/h and Pu /PL of 1/3, when SDD was 0.05, 0.1 and 0.2 mg/cm2 , the x1 for the single disk insulator corresponded to 12.2, 15.4, and 26.6 mA, respectively. The x1 also increased by 26.2% and 118.03% when the SDD increased from 0.05 to 0.1 mg/cm2 and from 0.1 to 0.2 mg/cm2 , respectively. For x6 , when the SDD was 0.05, 0.1 and 0.2 mg/cm2 , x6 corresponded to 2.69, 1.31, and 0.63 mA, respectively. The LC indicators showed a similar trend and performance for the insulator string under 33 kV with minor variations, as illustrated in Table 5. Materials 2022, 15, 6370 14 of 22 x NSDD Wt 0.15 0.25 0.35 0 0.842 0.636 0.522 3 2.64 1.48 0.9 0.44 2.479 6 2.94 1.63 1.19 0.72 9 3.65 1.93 1.57 0.9 0 1.03 0.75 0.73 0.22 0.9493 0.6912 0.6728 0.2028 3 2.93 1.72 1.23 0.67 2.7 6 3.29 1.96 1.49 0.872 9 3.99 2.34 1.84 0.969 1.39 0.8451 0.4131 2.761 1.53 1.117 0.6761 3.427 1.812 1.474 0.8451 1.585 1.134 0.6175 3.032 1.806 1.373 0.8037 3.677 2.157 1.696 0.8931 0 1.07 0.94 0.91 0.413 1.024 0.8995 0.8708 0.3952 3 3.54 1.98 1.63 0.742 3.388 1.895 6 5.24 2.04 1.74 0.911 5.014 2.522 1.952 0.8718 9 6.51 2.61 2.31 1.046 6.23 2.498 2.098 1.001 0.2 0.1 0.05 0 0.2 0.1 0.05 0 11 kV 1 0.196 0.7906 0.5972 0.4901 0.184 1.56 6 5 4 3 2 0.71 1 33 kV 2 SDD (mg/cm ) (a) NSDD Wt 0.15 0.25 0.35 0 0.842 1.27 0.636 0.78 0.522 0.17 3 2.64 7.29 1.48 2.8 0.9 0.45 0.44 0.06 2.479 7.64 1.39 0.8451 2.934 0.472 0.4131 0.063 6 2.94 9.46 1.63 5.82 1.19 0.96 0.72 0.09 2.761 9.914 1.53 6.099 0.196 0.064 0.7906 0.178 0.184 1.331 0.5972 0.817 0.4901 0.067 9 3.65 13.97 1.93 10.03 1.57 1.27 0.9 0.103 3.427 14.64 0 1.03 1.57 0.75 0.97 0.73 0.37 0.22 0.07 0.9493 1.026 0.6728 1.661 0.6912 0.391 0.2028 0.074 3 2.93 11.86 1.72 6.98 1.23 0.85 0.67 0.063 2.7 12.55 1.585 7.385 1.134 0.899 0.6175 0.067 6 3.29 13.85 1.96 8.37 1.49 1.33 0.872 0.104 3.032 14.65 1.806 8.855 1.373 1.407 0.8037 0.11 9 3.99 18.66 2.34 10.64 1.84 3.83 0.969 0.148 3.677 19.74 2.157 11.26 1.696 4.052 0.8931 0.157 1.812 10.51 0.15 20 1.474 1.331 0.8451 0.108 0 1.07 0.78 0.94 0.98 0.91 0.64 0.413 0.082 1.024 1.027 0.8708 0.817 0.8995 0.671 0.3952 0.086 3 3.54 12.85 1.98 6.39 1.63 1.08 0.742 0.113 3.388 13.47 1.895 6.697 1.56 1.132 6 5.24 15.84 2.04 9.11 1.74 3.76 0.911 0.162 5.014 16.6 2.522 9.547 1.952 0.17 3.94 0.8718 9 6.51 24.87 2.61 12.84 2.31 6.98 1.046 0.139 6.23 26.06 2.498 13.46 2.098 7.315 1.001 0.146 0.2 1 0.1 0.05 0 0.2 0.1 0.05 0 11 kV 25 1.117 1.006 0.6761 0.094 15 0.25 10 0.71 0.118 (b) NSDD Wt x3 5 0.35 x4 0.842 0 2.145 1.772 0.636 1.539 0.522 1.917 0.4901 1.665 0.184 1.65 1.525 0.196 0.7906 2.299 0.5972 2.64 2.59 1.48 2.391 1.592 0.9 1.563 0.44 2.776 2.479 1.723 0.4131 1.692 1.39 0.8451 2.587 2.94 6 2.739 1.63 2.521 1.19 2.234 1.575 0.72 2.936 2.761 1.53 2.728 1.704 1.117 0.6761 2.417 3.65 9 2.832 1.93 2.71 1.57 2.43 1.586 0.9 3.036 3.427 1.812 2.932 1.716 1.474 0.8451 2.629 1.03 0 2.216 1.824 0.75 1.609 0.73 1.654 1.937 0.6728 1.709 0.2028 1.557 0.22 0.9493 2.353 0.6912 3 3 2.63 2.93 1.72 2.467 1.23 2.181 1.567 0.67 2.793 2.7 1.585 2.62 1.664 1.134 0.6175 2.316 6 2.762 3.29 1.96 2.485 1.49 2.419 1.582 0.872 2.933 3.032 1.806 2.639 1.68 1.373 0.8037 2.569 9 2.846 3.99 2.34 2.64 1.84 2.596 1.599 0.969 3.022 3.677 2.804 2.157 1.698 1.696 0.8931 2.757 1.07 0 2.312 1.934 0.94 1.623 0.91 1.562 0.413 1.659 1.724 0.3952 1.024 0.8995 2.495 2.087 0.8708 3 2.815 3.54 1.98 2.501 1.63 2.219 1.575 0.742 3.038 3.388 1.895 2.699 1.56 2.357 6 2.862 5.24 2.04 2.558 1.74 2.492 1.591 0.911 3.089 5.014 2.761 2.522 1.69 2.647 1.952 0.8718 9 2.861 6.51 2.61 2.79 2.657 2.31 1.608 1.046 3.088 6.23 3.011 2.498 2.822 2.098 1.708 1.001 0.1 0.05 0 0.2 0.1 0.05 0 0.2 33 kV 2 SDD (mg/cm ) 11 kV 2 SDD (mg/cm ) (c) 0.25 0.35 x 0.196 6.82 0.7906 10.45 0.5972 8.645 0.4901 8.645 0.184 7.181 2.6 2.4 2.2 2 1.673 0.71 1.8 1.6 33 kV 0.842 9.92 0.636 8.21 8.21 0.522 3 2.64 36.56 1.48 15.33 0.9 10.23 0.44 7.43 2.479 38.5 1.39 0.8451 16.14 10.77 0.4131 7.824 6 2.94 41.32 1.63 18.88 1.19 11.29 0.72 7.52 2.761 43.51 1.53 19.88 1.117 11.89 0.6761 7.919 9 3.65 43.77 1.93 23.25 1.57 14.42 0.9 8.04 3.427 46.09 1.812 24.48 1.474 8.466 15.18 0.8451 0 1.03 10.78 0.75 9.88 0.73 8.901 0.22 6.95 0.9493 11.14 0.6912 10.21 0.6728 9.203 0.2028 7.186 3 2.93 45.63 1.72 21.74 1.23 10.89 0.67 7.93 2.7 47.18 1.585 22.48 1.134 8.199 11.26 0.6175 6 3.29 47.84 1.96 25.25 1.49 12.85 0.872 7.99 3.032 49.46 1.806 26.11 1.373 13.29 0.8037 8.261 9 3.99 53.79 2.34 31.97 1.84 15.03 0.969 8.38 3.677 55.61 2.157 33.05 1.696 8.664 15.54 0.8931 30 0 1.07 10.63 0.94 9.91 0.91 9.631 0.413 7.31 1.024 11.31 0.8995 10.24 0.3952 10.54 0.8708 7.776 25 3 3.54 51.67 1.98 30.51 1.63 13.34 0.742 8.4 3.388 54.97 1.895 32.46 1.56 14.19 0.71 8.936 20 6 5.24 59.29 2.04 34.63 1.74 15.77 0.911 8.62 5.014 63.07 2.522 36.84 1.952 16.78 0.8718 9.17 15 9 6.51 60.86 2.61 42.04 2.31 18.84 1.046 8.73 6.23 64.74 2.498 44.72 2.098 20.04 1.001 9.287 10 0.2 0.1 0.05 0 0.2 0.1 0.05 0 2 SDD (mg/cm ) x6 NSDD Wt 5 0 11 kV 2.8 (d) NSDD Wt 0.15 3 60 0.15 55 50 45 40 0.25 35 0.35 0.522 6.222 3.414 0.5972 7.845 4.327 0.4901 6.508 0.184 0.196 7.5 0.7906 0 0.842 3.264 0.636 4.136 3 2.64 0.667 1.48 1.182 0.9 3.28 0.44 5.967 2.479 0.697 1.39 0.8451 1.236 6.241 3.431 0.4131 6 2.94 0.606 1.63 1.224 1.19 3.11 0.72 5.35 2.761 0.634 1.53 1.281 1.117 5.596 3.253 0.6761 9 3.65 0.58 1.93 1.272 1.57 2.939 0.9 4.714 3.427 0.606 1.812 1.33 1.474 4.931 3.074 0.8451 0 1.03 3.145 0.75 3.688 0.73 5.071 0.22 6 0.9493 3.29 0.6912 6.276 5.305 0.2028 3.857 0.6728 3 2.93 0.632 1.72 1.44 1.23 2.69 0.67 5.2 2.7 0.654 1.585 1.492 1.134 5.387 2.787 0.6175 6 3.29 0.569 1.96 1.091 1.49 2.635 0.872 5.093 3.032 0.589 1.806 1.13 1.373 5.276 2.73 0.8037 2.157 1.181 1.696 4.753 2.668 0.8931 9 3.99 0.523 2.34 1.14 1.84 2.575 0.969 4.588 3.677 0.542 0 1.07 3.077 0.94 3.463 0.91 4.889 0.413 5.172 1.024 5.359 5.065 0.3952 3.188 0.8995 3.588 0.8708 3 3.54 0.409 1.98 1.161 1.63 2.158 0.742 3.778 3.388 0.432 1.895 1.226 1.56 2.279 6 5.24 0.42 2.04 0.958 1.74 2.136 0.911 3.725 5.014 0.443 2.522 1.012 1.952 2.256 0.8718 3.934 9 6.51 0.318 2.61 1.242 2.31 2.107 1.046 2.697 6.23 0.336 2.498 1.311 2.098 2.225 1.001 2.848 0.2 0.1 0.05 0 0.2 0.1 33 kV 11 kV 2 SDD (mg/cm ) (e) 7 6 5 4 3 2 0.71 3.989 0.05 1 0 33 kV (f) Figure 10. Leakage current indices of uniform polluted insulators under various wetting rate Wt and NSDD: (a) x1 ; (b) x2 ; (c) x3 ; (d) x4 ; (e) x5 ; (f) x6 . x1 70 60 x1 50 40 x2 x3 x4 x5 x6 x2 18 15 x3 20 2.90 16 2.85 12 2.80 12 9 6 x4 x5 60 55 50 x6 0.8 0.7 0.6 45 2.75 0.5 Materials 2022, 15, 6370 15 of 22 Table 4. LC indices of nonuniformly polluted insulators under different Wt and NSDD for 11 kV insulators. SDD mg/cm2 Pu/PL NSDD mg/cm2 0.15 0.05 0.25 0.35 0.15 0.1 0.25 0.35 0.15 0.2 0.25 0.35 1/3 Wt mL/h 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 1/5 1/8 x1 x2 x3 x4 x5 x6 x1 x2 x3 x4 x5 x6 x1 x2 x3 x4 x5 x6 4.2 7.3 9.6 12.7 6 10.1 12.2 15.1 7.4 13.3 16.6 21.3 5.1 12 13.3 15.7 5.9 13.5 15.4 17.5 7.6 16 16.5 21.1 6.8 21.4 23.8 29.5 8.3 23.7 26.6 32.3 8.7 30.5 46.2 52.7 84.67 81.69 69.53 59.34 83.17 68.20 55.88 43.94 80.67 57.90 41.33 34.22 73.33 56.87 39.69 27.97 78.17 54.10 31.13 25.87 72.54 40.85 21.25 15.40 58.55 33.08 18.11 11.91 43.82 27.24 11.05 1.07 33.83 4.04 2.13 0.00 0.14 0.37 0.78 1.03 0.30 0.69 1.07 3.09 0.52 0.87 3.03 5.63 0.63 2.25 4.69 8.09 0.78 5.63 6.75 8.58 0.79 5.15 7.35 10.35 1.03 5.88 7.63 11.27 1.26 9.56 11.17 15.05 0.63 10.36 12.77 20.06 1.43 1.52 1.56 1.57 1.58 1.55 1.56 1.58 1.59 1.56 1.57 1.58 1.60 1.53 1.59 2.22 2.42 1.60 2.17 2.41 2.58 1.62 2.21 2.48 2.65 1.76 2.38 2.51 2.70 1.82 2.46 2.47 2.63 1.93 2.49 2.55 7.97 9.93 10.96 14.00 8.64 10.57 12.48 14.59 9.35 12.95 15.31 18.29 7.97 14.88 18.33 22.57 9.59 21.11 24.51 31.04 9.62 29.62 33.62 40.82 9.63 35.50 40.12 42.50 10.47 44.30 46.45 52.22 10.32 50.17 57.56 59.09 6.96 3.42 3.18 3.04 6.84 2.82 2.69 2.67 6.25 2.18 2.20 2.12 5.34 1.30 1.33 1.48 5.06 1.44 1.31 1.31 4.16 1.16 1.16 1.20 3.42 0.67 0.63 0.60 3.28 0.71 0.63 0.54 3.21 0.56 0.67 0.46 3.7 6.3 8.4 11.1 5.2 8.8 10.7 13.2 6.5 11.6 14.5 18.5 4.5 10.5 11.6 13.7 5.1 11.8 13.4 15.3 6.6 14 14.4 18.4 5.7 18.6 20.7 25.7 7.3 20.7 23.2 28.1 7.5 27.9 32.9 45.9 86.36 83.32 70.92 60.53 84.84 69.56 57.00 44.82 82.28 59.05 42.16 34.90 74.80 58.00 40.48 28.53 79.73 55.18 31.75 26.39 73.99 41.67 21.67 15.71 59.72 33.75 18.47 12.14 44.69 27.79 11.27 1.09 34.50 4.12 2.17 0.00 0.13 0.36 0.77 1.02 0.30 0.69 1.06 3.07 0.52 0.87 3.02 5.60 0.62 2.24 4.67 8.04 0.78 5.60 6.71 8.53 0.79 5.13 7.31 10.29 1.02 5.85 7.58 11.21 1.26 9.51 11.10 14.96 0.63 10.30 12.70 18.95 1.43 1.52 1.55 1.57 1.58 1.55 1.56 1.57 1.59 1.55 1.57 1.58 1.60 1.53 1.58 2.22 2.42 1.60 2.17 2.41 2.58 1.61 2.21 2.48 2.64 1.76 2.38 2.51 2.69 1.81 2.45 2.47 2.63 1.92 2.49 2.54 7.93 9.88 10.91 13.93 8.60 10.52 12.41 14.52 9.30 12.89 15.23 18.20 7.93 14.81 18.24 22.46 9.54 21.00 24.39 30.89 9.57 29.47 33.45 40.61 9.58 35.32 39.92 42.28 10.41 44.08 46.22 51.96 10.27 49.92 57.28 58.79 8.42 3.53 3.35 3.07 7.88 2.96 2.80 2.83 7.42 2.36 2.41 2.30 6.29 1.62 1.50 1.53 5.73 1.56 1.48 1.56 4.70 1.37 1.28 1.23 3.78 0.76 0.66 0.57 3.58 0.72 0.71 0.58 3.48 0.64 0.57 0.53 3.4 5.9 7.8 10.3 4.9 8.2 10 12.3 6 10.8 13.5 17.3 4.2 9.8 10.8 12.8 4.8 11 12.5 14.3 6.2 13 13.4 17.2 5.4 17.4 19.4 24.1 6.8 19.3 21.7 26.3 7.1 16.7 21.4 42.9 86.62 83.57 71.13 60.71 85.09 69.77 57.17 44.95 82.53 59.23 42.29 35.01 75.03 58.18 40.60 28.62 79.97 55.34 31.84 26.47 74.22 41.79 21.74 15.75 59.90 33.85 18.52 12.18 44.83 27.87 11.31 1.10 34.61 4.13 2.18 0.00 0.13 0.36 0.77 1.01 0.30 0.68 1.05 3.04 0.51 0.86 2.99 5.55 0.62 2.22 4.62 7.97 0.77 5.55 6.65 8.45 0.78 5.08 7.24 10.20 1.01 5.79 7.51 11.10 1.24 9.42 11.00 14.82 0.62 10.20 12.58 16.76 1.42 1.51 1.55 1.56 1.57 1.54 1.55 1.57 1.58 1.55 1.56 1.58 1.59 1.52 1.58 2.21 2.41 1.59 2.16 2.40 2.57 1.61 2.20 2.47 2.63 1.76 2.37 2.50 2.68 1.81 2.44 2.46 2.61 1.92 2.48 2.53 7.85 9.78 10.79 13.78 8.51 10.41 12.28 14.37 9.21 12.75 15.08 18.01 7.85 14.65 18.05 22.23 9.44 20.78 24.14 30.56 9.47 29.17 33.10 40.19 9.48 34.95 39.50 41.84 10.30 43.62 45.73 51.42 10.16 49.39 56.68 58.18 8.99 3.72 3.51 3.45 8.22 3.08 3.02 2.83 8.30 2.48 2.53 2.40 7.88 1.95 1.68 1.71 7.35 1.64 1.55 1.60 5.90 1.45 1.52 1.41 4.72 0.91 0.79 0.72 4.31 0.76 0.71 0.65 4.05 0.78 0.67 0.60 Table 5. LC indices of nonuniformly polluted insulators under different Wt and NSDD for insulator string 33 kV. SDD mg/cm2 Pu/PL NSDD mg/cm2 0.15 0.05 0.25 0.35 0.15 0.12 0.25 0.35 0.15 0.2 0.25 0.35 1/3 Wt mL/h 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 0 3 6 9 1/5 1/8 x1 x2 x3 x4 x5 x6 x1 x2 x3 x4 x5 x6 x1 x2 x3 x4 x5 x6 4 7 9.2 12.2 5.8 9.7 11.7 14.5 7.1 12.8 15.9 20.4 4.9 11.5 12.8 15.1 5.7 12.9 14.8 16.8 7.3 15.3 15.8 20.2 6.5 20.5 22.8 28.3 8 22.7 25.5 31 8.3 29.2 44.3 50.5 79.80 76.99 65.53 55.93 78.39 64.28 52.67 41.41 76.03 54.57 38.95 32.25 69.11 53.60 37.41 26.36 73.68 50.99 29.34 24.38 68.37 38.50 20.03 14.51 55.18 31.18 17.07 11.23 41.30 25.67 10.41 1.01 31.89 3.81 2.01 0.79 0.15 0.39 0.83 1.09 0.32 0.73 1.14 3.28 0.55 0.92 3.21 5.97 0.67 2.39 4.98 8.58 0.83 5.97 7.16 9.10 0.84 5.46 7.80 10.98 1.09 6.24 8.10 11.96 1.34 10.14 11.85 15.97 0.67 10.99 13.55 21.28 1.47 1.57 1.61 1.62 1.63 1.60 1.61 1.63 1.64 1.61 1.62 1.63 1.65 1.58 1.64 2.29 2.50 1.65 2.24 2.48 2.66 1.67 2.28 2.56 2.73 1.81 2.45 2.59 2.78 1.88 2.54 2.55 2.71 1.99 2.57 2.63 8.18 10.19 11.24 14.36 8.86 10.84 12.80 14.97 9.59 13.29 15.71 18.77 8.18 15.27 18.81 23.16 9.84 21.66 25.15 31.85 9.87 30.39 34.49 41.88 9.88 36.42 41.16 43.61 10.74 45.45 47.66 53.58 10.59 51.47 59.06 60.63 7.21 3.54 3.29 3.15 7.09 2.92 2.79 2.77 6.48 2.26 2.28 2.20 5.53 1.35 1.38 1.53 5.24 1.49 1.36 1.36 4.31 1.20 1.20 1.24 3.54 0.69 0.65 0.62 3.40 0.74 0.65 0.56 3.33 0.58 0.69 0.48 3.5 6 8.1 10.6 5 8.4 10.3 12.7 6.2 11.1 13.9 17.7 4.3 10.1 11.1 13.1 4.9 11.3 12.8 14.7 6.3 13.4 13.8 17.6 5.5 17.8 19.8 24.6 7 19.8 22.2 26.9 7.2 26.7 31.5 44 81.39 78.53 66.84 57.05 79.96 65.56 53.72 42.24 77.55 55.66 39.74 32.89 70.50 54.67 38.15 26.89 75.15 52.01 29.92 24.87 69.74 39.27 20.42 14.81 56.29 31.81 17.41 11.44 42.12 26.19 10.62 1.03 32.52 3.88 2.05 0.32 0.14 0.38 0.82 1.08 0.32 0.73 1.12 3.26 0.55 0.92 3.20 5.94 0.66 2.38 4.95 8.53 0.83 5.94 7.12 9.05 0.84 5.44 7.76 10.92 1.08 6.21 8.04 11.89 1.34 10.09 11.78 15.87 0.67 10.93 13.47 20.11 1.47 1.57 1.60 1.62 1.63 1.60 1.61 1.62 1.64 1.60 1.62 1.63 1.65 1.58 1.63 2.29 2.50 1.65 2.24 2.48 2.66 1.66 2.28 2.56 2.72 1.81 2.45 2.59 2.77 1.87 2.53 2.55 2.71 1.98 2.57 2.62 8.14 10.14 11.19 14.29 8.82 10.79 12.73 14.90 9.54 13.23 15.63 18.67 8.14 15.20 18.71 23.04 9.79 21.55 25.02 31.69 9.82 30.24 34.32 41.67 9.83 36.24 40.96 43.38 10.68 45.23 47.42 53.31 10.54 51.22 58.77 60.32 8.72 3.66 3.47 3.18 8.16 3.07 2.90 2.93 7.69 2.44 2.50 2.38 6.52 1.68 1.55 1.59 5.94 1.62 1.53 1.62 4.87 1.42 1.33 1.27 3.92 0.79 0.68 0.59 3.71 0.75 0.74 0.60 3.61 0.66 0.59 0.55 3.3 5.7 7.5 9.9 4.7 7.9 9.6 11.8 5.8 10.4 12.9 16.6 4 9.4 10.4 12.3 4.6 10.5 12 13.7 5.9 12.5 12.8 16.5 5.2 16.7 18.6 23.1 6.5 18.5 20.8 25.2 6.8 16 20.5 41.1 81.64 78.77 67.04 57.22 80.20 65.76 53.88 42.37 77.79 55.82 39.86 33.00 70.72 54.84 38.27 26.97 75.37 52.16 30.01 24.95 69.95 39.39 20.49 14.84 56.46 31.90 17.46 11.48 42.25 26.27 10.66 1.04 32.62 3.89 2.05 0.56 0.14 0.38 0.82 1.07 0.32 0.72 1.11 3.23 0.54 0.91 3.17 5.89 0.66 2.36 4.90 8.46 0.82 5.89 7.06 8.97 0.83 5.39 7.68 10.82 1.07 6.14 7.97 11.78 1.32 9.99 11.67 15.72 0.66 10.82 13.35 17.78 1.46 1.56 1.60 1.61 1.62 1.59 1.60 1.62 1.63 1.60 1.61 1.63 1.64 1.57 1.63 2.28 2.48 1.64 2.23 2.47 2.65 1.66 2.27 2.55 2.71 1.81 2.44 2.58 2.76 1.87 2.52 2.54 2.69 1.98 2.56 2.61 8.05 10.03 11.07 14.14 8.73 10.68 12.60 14.74 9.45 13.08 15.47 18.48 8.05 15.03 18.52 22.81 9.69 21.32 24.77 31.35 9.72 29.93 33.96 41.23 9.73 35.86 40.53 42.93 10.57 44.75 46.92 52.76 10.42 50.67 58.15 59.69 9.31 3.85 3.64 3.57 8.52 3.19 3.13 2.93 8.60 2.57 2.62 2.49 8.16 2.02 1.74 1.77 7.61 1.70 1.61 1.66 6.11 1.50 1.57 1.46 4.89 0.94 0.82 0.75 4.47 0.79 0.74 0.67 4.20 0.81 0.69 0.62 5.2.2. Indicator Trends under Different NSDD The differences in the indicators are comparable to the previous case (pollution variation), and changes in the amount of increment/or decrement can be detected. The test Materials 2022, 15, 6370 16 of 22 findings in Table 5 demonstrate that under constant SDD, Wt, and Pu/PL, increasing the NSDD increases the x1 , x3 , x4 , and x5 , but decreases the x2 and x6 . To further understand the relationship between NSDD and the suggested indices, Figure 11 displays the x1 , x3 , x4 , x5 , and x6 vs. NSDD curves with SDD of 0.2 mg/cm2 , Wt of 6 mL/h, and Pu /PL of 1/1. x1 x2 x3 x4 x5 x2 x6 70 18 15 60 x3 20 2.90 16 2.85 12 2.80 12 x1 50 9 40 6 30 3 0.15 0.20 0.25 0.30 x4 8 60 55 50 x6 0.8 0.7 0.6 45 2.75 2.70 0.35 x5 40 35 0.5 0.4 NSDD (mg/cm2) Figure 11. The impact of NSDD on indicator shift. 5.2.3. Indicator Trends under Different Wt The relationship between the proposed indices x1 –x6 and Wt for porcelain insulator under SDD of 0.2 mg/cm2 , NSDD of 0.35 mg/cm2 , and Pu/PL of 1/1 and different Wt is demonstrated in Figure 12. It is worth noting that when Wt increases, the x2 and x6 fall while the x1 , x3 , x4 , and x5 increase. For example, under SDD of 0.2 mg/cm2 , NSDD of 0.35 mg/cm2 , and Pu /PL of 1/1, the x1 increased by 13.4% and 15.4% when Wt increased from 3 to 6 mL/h and from 3 to 9 mL/h, respectively, whereas under the same conditions, the x2 decreased by 72.1% and 57.2% when Wt increased from 3 to 6 mL/h and from 6 to 9 mL/h, respectively. Figure 12. The impact of Wt on indicators shift. 5.2.4. Indicator Trends under Different Nonuniform Pollution Distribution (Pu /PL ) The relationship between proposed indices x1 –x6 and nonuniform pollution distribution Pu/PL for a polluted porcelain insulator under SDD of 0.2 mg/cm2 , NSDD of 0.35 mg/cm2 , and Wt of 9 mL/h and different Pu/PL as an example is shown in Figure 13. It can be observed that an increase in Pu/PL causes an increase in the x2 and x6 and a decrease in the x1 , x3 , x4 , and x5 . This means that the sample under uniform contamination conditions is more dangerous in terms of flashover incidence than the sample under nonuniform pollution levels. x1 x2 x3 x4 x5 x6 x2 2.5 70 2.0 x1 60 1.5 x3 28 26 x4 2.8 24 22 x5 x6 61 0.6 60 0.5 59 0.4 2.6 Materials 2022, 15, 6370 17 of 22 x1 x2 x3 x4 x5 x6 x2 2.5 70 2.0 x1 60 1.5 50 40 1.0 1/1 1/3 1/5 1/8 0.5 x3 28 26 x4 2.8 24 22 x6 61 0.6 60 0.5 59 0.4 58 0.3 2.6 20 18 x5 2.4 16 Pu/PL Figure 13. The impact of Pu /PL on indicator shift. 5.3. Insulator Condition Based on the Test Data of Indices 5.3.1. Insulator Condition Classification Based on Test Preparation In this section, the ranges of the indicators corresponded to the level of SDD, NSDD, Wt, and Pu /PL are classified. The experimental data indicated that the values of x1 , x3 , x4 , and x5 increased in proportion to an increase in SDD, NSDD, and Wt, but a decrease in Pu /PL . Meanwhile, the indicators x2 and x6 decreased with an increase in SDD, NSDD, and Wt, and decrease in Pu /PL . The proposed index values in the normal range were observed under the clean and low-pollution cases with Wt less than 4 mL/h and NSDD less than 0.2 mg/cm2 . In this case, the possibility of discharge occurrence is almost nonexistent. According to indicator results in Table 5, the insulator was in an abnormal state under low contamination (0.05 mg/cm2 ) with heavy wetting Wt (9 mL/h) and medium and high NSDD (0.25 and 0.35 mg/cm2 ) for all contamination distribution (Pu/PL), except when Pu /PL = 1/8. In addition, the insulator under examination displayed an abnormal condition in the presence of moderate pollution (0.12 mg/cm2 ) under moderate wetting Wt of 6 mL/h, NSDD of 0.25 mg/cm2 , and Pu /PL of 1/1 and 1/5. The probability of a discharge occurring in these conditions is low, except in cases of extreme wetting, where the possibility of flashover increases. Meanwhile, the critical condition of the insulator under test was found under two circumstances: first, under medium contamination conditions with Wt of 9 mL/h, NSDD of 0.35 mg/cm2 , and all contamination distribution Pu /PL cases; and second, when SDD is high under medium and heavy levels for Wt, NSDD, and all Pu /PL cases. The flashover possibility occurring in these conditions is high, especially under high wetting and high NSDD. 5.3.2. Insulator Condition Classification Based on Proposed Indicators To develop a statistical technique for identifying diagnostic indicator borders based on the x1 , x2 , x3 , x4 , x5 , and x6 inputs, the naïve Bayes classification algorithm [46] was trained with the experimental data to predict the insulator’s state. In this study, MATLAB’s Deep Learning Toolbox was employed to develop the classification model. In the classification procedure, 952 data sets for each indicator were used in the classification process using the naïve Bayes classifier algorithm, where 70% of the data (666 data) were chosen for the model training, 15% of the data (143 data) were utilized for the model performance verification, and the other 15% of the data (143 data) were selected