2.1 Time-domain Parameters

PD signals in the time-domain can be described by pulse parameters such as rising time, falling time, and pulse width in Fig. 1. The rising time is defined as the duration from 10 % to 90 %, while the falling time represents the duration from 90 % to 10 % of the first half-cycle pulse. The pulse width corresponds to the time interval between 50 % of the start and the end of the pulse. These parameters provide useful information on discharge dynamics and are often different depending on defect types. In this paper, rising time, falling time, and pulse width were extracted from individual PD pulses to be used as classification features.

그림 1 부분방전 단일 펄스의 시간 영역 파라미터

Fig. 1 Time-domain Parameters of PD Single Pulse

2.2 Frequency-domain Parameters

Frequency-domain analysis of PD signals enables the identification of characteristic frequency components. The frequency spectrum of each PD pulse was obtained by fast Fourier transform(FFT) which is an efficient implementation of the discrete Fourier transform(DFT). The DFT of a discrete signal x_n with length N is defined as:

where X_k represents the spectral component at frequency index k. By eliminating redundant calculations, the FFT reduces the computational complexity from O(N²) for the DFT to O(N log₂ N). The dominant frequency component and the distribution of spectral peaks were extracted as features. These parameters indicate how the discharge energy is distributed over the frequency range, and characteristic differences among defects can be observed in the high-frequency ranges.

2.3 Statistical Parameters

Statistical parameters such as skewness and excess kurtosis can be calculated to analyze the distribution characteristics of PD signals. Skewness indicates the asymmetry of the distribution, while excess kurtosis describes the sharpness compared to a normal distribution. These parameters allow the discrimination of PD defects by reflecting the variation of pulse amplitude and the concentration of discharge events. Fig. 2 shows data distributions for skewness and excess kurtosis values.

그림 2 방전 시 왜도 및 첨도 값의 분포: (a) 왜도, (b) 첨도

Fig. 2 Distribution of Skewness and Excess Kurtosis Values (a) Skewness (b) Excess kurtosis

3.1 Artificial Neural Network(ANN)

ANN algorithm is a computational model inspired by the structure of the human brain with an input layer, one or more hidden layers, and an output layer. Each neuron processes input signals through weighted connections and activation functions, enabling nonlinear transformations. The learning process is carried out by adjusting the weights to minimize the error between predicted and target outputs. Fig. 3 shows the structure of ANN algorithm for PD classification in this paper^{[17- 18]}.

그림 3 부분방전 분류를 위한 인공신경망(ANN) 알고리즘

Fig. 3 The ANN Algorithm for PD Classification

3.2 Support Vector Machine(SVM)

SVM algorithm is a supervised learning method known for its robustness and strong generalization performance, particularly when the dataset is limited or contains noise. The main concept of SVM is to find an optimal hyperplane that maximizes the margin between different classes in a high-dimensional feature space as shown in Fig. 4. For PD classification, a SVM has been applied successfully to various types of input features including frequency-domain parameters, statistical indicators, and time-domain waveform characteristics. With the use of kernel functions, a SVM can handle nonlinear boundaries by mapping the input data into higher-dimensional spaces where separation becomes more feasible^{[19- 20]}.

그림 4 부분방전 분류를 위한 서포트 벡터 머신(SVM) 알고리즘

Fig. 4 The SVM Algorithm for PD Classification

3.3 k-Nearest Neighbor(KNN)

KNN algorithm is a simple and intuitive classification method based on measuring the similarity between data points. It does not require a training phase in the traditional sense. Instead, when a new data point is introduced, it is classified based on the majority class among its K nearest neighbors in the feature space in Fig. 5. In the field of PD diagnosis, a KNN can be applied using various distance measures such as Euclidean or Mahalanobis distance on features extracted from PD signals. Its simplicity makes it well-suited for real-time or low resource environments, and it offers flexibility in adapting to changing data patterns^{[18, 20- 21]}.

그림 5 부분방전 분류를 위한 최근접 분포(KNN)알고리즘

Fig. 5 The KNN Algorithm for PD Classification

4.1 Experimental Setup for PD Test

To analyze the PD characteristics of different defect types in eco-friendly GIS, an experimental setup was configured as shown in Fig. 6. A high-voltage oil-immersed transformer rated at 20 kV and 100 mA was used as the power source. The AC transformer was a HIPOTRONICS 710-5 model with a rated output of 20 kV and 100 mA. The output voltage was gradually increased in 1 kV steps using a voltage regulator until PDs were initiated. The electrode systems were fabricated to simulate typical PD conditions observed in GIS and were installed in a test chamber with a length of 1 000 mm and a diameter of 500 mm. The electrode system was filled with gas at a pressure of 0.5 MPa. As an eco-friendly alternative to SF₆, g³ gas was used in this study. The g³ gas consisted of a mixture of NOVEC 4710, CO₂, and O₂, with NOVEC 4710 comprising 4 % of the total gas volume. To prevent gas cross-contamination, the chamber was purged and refilled at least five times before each test.

For PD detection, both electrical and non-electrical measurement methods were used. In the electrical method, a coupling capacitor and a PD measurement system based on IEC 60270 were used to measure the apparent charge of PDs and to analyze PRPD patterns as reference data for each PD defect. The coupling capacitor was an OMICRON MCC 210 model with a rating of 100 kV and 1 nF, and the PD measurement system was an OMICRON MPD 600 model with an accuracy within ±2 %. In parallel, a UHF sensor was employed as the non-electrical method and connected to an oscilloscope to capture the electromagnetic signals generated by PD defects. The UHF sensor was fabricated by WOOSUNG PLATEC with an operating frequency range of 500 MHz to 1.5 GHz. The oscilloscope was a Tektronix 5204B with a bandwidth of 2 GHz and a sampling rate of 10 GS/s. The distance between the UHF sensor and the PD electrode system was set to 500 mm.

그림 6 부분방전 시험을 위한 실험 구성도

Fig. 6 Experimental Setup for PD Test

4.2 PD Electrode Systems

Four types of electrode systems were fabricated to simulate representative defects in eco-friendly GIS: free moving particle(FMP), protrusion, delamination, and floating. The FMP defect represents metallic particles introduced during manufacturing or operation, which can move under an electric field and cause breakdown. The FMP defect was simulated using a spherical and concave plate electrode with aluminum balls of 2 mm placed in a gap of 20 mm. The protrusion defect corresponds to a sharp protrusion on enclosure, often caused by contamination or mechanical damage. It was designed using a plane electrode and a tungsten–copper needle electrode with a tip radius of 5 μm, separated by a gap of 2 mm. The delamination defect reflects separation in laminated dielectric structures. It was reproduced by inserting a thin epoxy film with a central hole of 5 mm between planar electrodes as a localized cavity. The floating defect represents ungrounded conductive materials unintentionally embedded in insulation. It was simulated by mounting a thin conductive plate on an epoxy substrate with a floating conductor placed a few millimeters above the plane electrode. All plate electrodes were rounded at the edges to avoid field enhancement, and a brass terminal was attached to the high-voltage electrode for stable operation. Fig. 7 shows the four electrode systems to simulate typical GIS defects.

그림 7 부분방전 전극계 : (a) 자유 이동 금속입자(FMP), (b) 돌출, (c) 박리, (d) 부유전극

Fig. 7 PD Electrode Systems (a) FMP (b) Protrusion (c) Delamination (d) Floating

5.1 PD Measurement and Parameter Extraction

Fig. 8 presents the PD pulse waveforms measured by a UHF sensor for the four defect types. In general, the waveforms obtained in g³ showed similar shapes to those in SF₆, but the amplitudes were consistently higher in g³. For the FMP defect, the pulse shapes were almost identical in both gases. However, the amplitude was higher in g³, and the pulse width was slightly shorter, while the rising time remained nearly the same. For the protrusion defect, the amplitude was also higher in g³, but the rising time, falling time, and pulse width exhibited only minor differences. For the delamination defect, the waveform shapes in g³ differed more noticeably from those in SF₆ compared to other defects. Although the amplitudes in the two gases were similar, the rising time and pulse width in g³ were shorter, while the falling time was longer, making the delamination defect more distinguishable between the two gases. For the floating defect, the amplitude in g³ was significantly higher and this difference in the rising time, falling time, and pulse width showed small variations. In g³, the rising time, falling time, and pulse width varied depending on the defect type. The FMP and floating defects showed relatively short rising times, while the protrusion defect exhibited the longest pulse width. The delamination defect showed a relatively long rising time compared with the other defects.

These results are consistent with the extracted parameters listed in Table 1 and indicate that defect identification is feasible based on pulse parameters in g³.

그림 8 부분방전 결함에 따른 부분방전 펄스파형:(a) SF₆, (b) g³

Fig. 8 PD Pulse Waveforms According to PD Defects (a) SF6 (b) g3

The frequency-domain analysis was performed using the FFT function in Origin software. A rectangular window was used with amplitude correction, and the power spectrum was normalized to mean square amplitude. No additional digital filtering was applied before FFT analysis. The frequency spectrum of PD defects in g³ showed overall similarities with those in SF₆ because the fundamental discharge mechanism is the same in both gases. However, differences were observed in the distribution and intensity of spectrum components depending on defect type in Fig. 9. In particular, protrusion and floating defects in g³ exhibited shifts or attenuation in certain frequency ranges compared with SF₆, while delamination defects showed distinctive peaks that can serve as discriminative features. These results indicate that the frequency characteristics of g³ are not identical to those of SF₆ and should be considered separately in diagnostic applications, although the general spectrum patterns are similar. In g³, the FMP defect showed wide frequency components, while the protrusion defect had relatively stronger frequency components below 1 GHz. The delamination defect produced distinctive peaks across the spectrum, and the floating defect was mainly concentrated below 1.0 GHz but its overall intensity was relatively weak compared to other defects over 1.0 GHz. These differences in frequency characteristics can be effectively used for defect identification in g³.

그림 9 부분방전 결함에 따른 주파수 스펙트럼: (a) SF₆, (b) g³

Fig. 9 Frequency Spectrum According to PD Defects (a) SF6 (b) g3

In terms of statistical parameters for kurtosis and skewness, all types of PD defects showed overall similar trends in SF₆ and g³. Specifically, all defects indicated negative excess kurtosis which means platykurtic distributions that are flatter and have lighter tails than a normal distribution. Furthermore, the skewness was positive for all defects except protrusion defect with negative skewness. A positive skewness indicates that most pulse amplitudes are concentrated at lower values with a long tail extending to the right. In g³, the FMP defect showed a platykurtic distribution with relatively stronger positive skewness which means the presence of larger amplitude pulses despite its flat distribution. The protrusion defect was clearly distinguished by its negative skewness, indicating a longer tail toward lower amplitudes and a greater concentration of samples at relatively higher amplitudes. The delamination defect demonstrates the most stable distribution with a kurtosis value close to the normal distribution compared to other defects. The extracted parameters are shown in Table 1.

To clarify the frequency-domain parameters, the frequency spectrum was divided into four frequency ranges: 0 to 0.5 GHz, 0.5 to 1.0 GHz, 1.0 to 1.5 GHz, and 1.5 to 2.0 GHz. For each frequency range, the peak frequency was defined as the frequency corresponding to the maximum spectral magnitude within that range. Therefore, the peak frequency values represent the frequencies at which the maximum spectral peaks occur in each frequency range.

5.2 Results for PD Classification

To confirm the optimal diagnostic algorithm for PD classification for eco-friendly gas-insulated power equipment, three representative machine learning algorithms such as ANN, SVM, and KNN were evaluated using 9 extracted feature parameters in g³.

The ANN structure consisted of an input layer with 9 neurons, a hidden layer with 32 neurons, and an output layer with 4 neurons corresponding to the four defect types. To adjust the activation thresholds of each layer, one bias node was connected to every layer. During training, the target output of the corresponding output neuron was set to 1 for defect classification. The learning rate was set to 0.01, and the network was trained for 60 epochs until the mean square error reached 0.001. The proposed ANN algorithm achieved a mean accuracy of 92.7 % using five-fold cross-validation. The SVM algorithm was designed and optimized through parameter tuning. The penalty parameter C was varied from 0.01 to 1 000, and four kernel functions, namely linear, radial basis function (RBF), polynomial, and sigmoid, were examined. The kernel coefficient γ was tuned only for the nonlinear kernels, such as RBF, polynomial, and sigmoid, because γ is not used in the linear kernel. During optimization, the SVM model achieved the highest mean accuracy of 92.2 % when the linear kernel was used with C = 10. Therefore, γ was not applied to the final linear-kernel SVM model. These results indicate that the extracted PD features were largely linearly separable under the present experimental conditions. The KNN algorithm was designed and optimized through parameter tuning. The major hyperparameter was the number of neighbors k, which determines how many nearest samples contribute to classification. The KNN model achieved the highest accuracy of 91.1 % with k=1, where classification was determined by the single nearest neighbor using the Euclidean distance metric. These results indicate that PD features were sufficiently separable in the dataset, although the reliance on a single neighbor highlights sensitivity to noise.

To construct a balanced and reliable PD dataset, PD pulses were repeatedly acquired under identical measurement conditions for each defect type. A total of 1 000 PD pulses were collected, consisting of 250 pulses for each defect type, namely FMP, protrusion, delamination, and floating. To maintain class balance during model evaluation, stratified sampling was applied so that the proportion of each defect class was equally reflected in the training and test datasets. The classification performance was evaluated using 5-fold cross-validation. In each fold, 800 samples were used for training and the remaining 200 samples were used for testing. The classification accuracies listed in Table 2 represent the mean values averaged across the five folds. This procedure was applied to reduce the dependence of the results on a specific data split and to evaluate the generalization performance of each algorithm.