Extraction and Evolution Analysis of Partial Discharge Characteristic Parameters in Moisture-Affected and Aged Oil–Paper Insulation

Abstract

Oil–paper insulation in oil-immersed transformers undergoes a concealed degradation process that is difficult to detect during operation. To understand its discharge behavior, this study examines partial discharge characteristics under controlled moisture absorption and thermal aging. Experiments on S-PD (Surface Partial Discharge) and N-PD (Needle Partial Discharge) were carried out, and partial discharge patterns, discharge frequency, and breakdown voltage were collected to analyze discharge evolution. The results show that partial discharge develops through three stages: initiation, development, and pre-breakdown. In the initiation stage, pulses are sparse with low amplitudes and appear near the voltage peak. During development, both amplitude and discharge frequency increase, and the phase range expands. As breakdown approaches, pulse amplitude rises sharply, the phase distribution covers almost the full cycle, and conductive channels begin to form. Skewness, Peak Degree, and Maximum Steepness were extracted from statistical discharge maps to compare moisture-affected and aged samples. The findings provide experimental support for developing state-evolution-based failure warning models and diagnostic criteria, contributing to improved operational safety of oil–paper insulation systems.

1. Introduction

Transformers are essential components of power systems, and their operating condition directly affects grid safety and stability. In large oil-immersed transformers, degradation of the insulation system is one of the main causes of failures and may trigger chain reactions that lead to regional outages and significant economic losses [1]. According to data reported by CIGRE, about 37.3% of major transformer failures are closely related to insulation degradation [2]. Partial Discharge (PD) detection is a core technique in transformer condition monitoring and plays a key role in early fault warning and insulation health assessment [3]. Therefore, studying the discharge evolution in oil–paper insulation, identifying discharge types, evaluating the severity of PD, and performing quantitative analysis of characteristic parameters are essential for ensuring the safe operation of transformers and extending their service life.

In recent years, PD detection technologies have been widely applied to high-voltage insulation equipment, particularly for monitoring oil–paper insulation [4]. Common detection methods include the pulse current method, ultrasonic method, ultra-high-frequency method, and optical detection method, which are used to monitor PD faults and locate discharge sources [5,6,7]. These methods typically extract key PD parameters—such as Partial Discharge Phase-Resolved Pattern (PRPD), discharge frequency, average discharge magnitude, and phase distribution—to support comprehensive insulation assessment [8]. Building on this, some studies extract characteristic parameters from PRPD patterns, such as Skewness and Peak Degree, to visually represent PD behavior and evaluate fault evolution and insulation state [9]. Reference [10] experimentally investigated several types of PD faults and achieved accurate fault identification and diagnosis based on measurement data. However, quantitative studies on PD in oil–paper insulation remain limited, especially regarding the identification of fault stages and the evolution of characteristic parameters. Most existing work focuses on fault diagnosis, while systematic data on the parameter changes from early to late stages of discharge development is still lacking. This gap restricts the full potential of PD detection in early warning applications for transformer faults.

Thermal aging and moisture absorption are the main factors contributing to the degradation of oil–paper insulation. Reference [11] reported that different levels of aging have a significant impact on the behavior of partial discharge at various stages. Reference [12] further found that both discharge magnitude and discharge repetition rate increase markedly as aging progresses. Researchers have also explored the relationship between partial discharge characteristics and the aging state of oil–paper insulation. According to Reference [13], as aging advances, the Skewness of the positive half-cycle in the pre-breakdown stage becomes negative under needle–plate electrodes, and a similar trend is observed with column–plate electrodes. However, due to the non-monotonic nature of these parameter variations, it is difficult to identify clear threshold features, and the underlying mechanisms have not been fully discussed. Moisture also plays a crucial role in the behavior of partial discharge. Studies have shown that moisture reduces the electrical strength of oil–paper insulation and intensifies partial discharge activity [14,15]. Reference [16] reported that partial discharge parameters associated with moisture content can be used to assess insulation degradation. Extensive research indicates that degradation alters measured partial discharge data, and thermal aging and moisture promote each other: thermal aging increases moisture content, while accumulated moisture accelerates the aging reactions inside the transformer [17,18,19]. However, few existing studies consider the combined effects of both aging and moisture on partial discharge behavior. Most research focuses on single influencing factors, making it difficult to fully uncover the complex evolution of partial discharge characteristics under multiple interacting conditions. This limitation restricts the ability to accurately assess the evolution and risk of partial discharge in transformers operating under realistic environments.

In summary, although many studies have examined the partial discharge characteristics of oil–paper insulation, quantitative analyses of typical discharge defects—such as N-PD and S-PD—under different moisture contents and aging levels are still limited. Therefore, this study establishes N-PD and S-PD fault models using oil–paper insulation samples with varied moisture and aging conditions, systematically extracts partial discharge characteristic parameters, and investigates their evolution in detail. The results provide essential theoretical support for the safe operation of transformers and offer significant engineering value, serving as a reliable basis for early warning, fault diagnosis, and condition assessment of transformer partial discharge.

2. Materials and Methods

2.1. Sample Preparation

In this study, 1 mm Weidmann cellulose insulation paper (Xucheng Insulation Materials Factory, Beijing, China) and KL-25 mineral insulating oil (China National Petroleum Corporation, Korla City, China) were selected to prepare oil–paper insulation samples with different moisture contents and aging levels. First, the insulation paper and insulating oil were dried separately at 85 °C under a vacuum of less than 50 Pa for 48 h, ensuring that their initial moisture contents were controlled below 0.5% and 10 ppm, respectively. A Karl Fischer moisture analyzer (Precision Instrument Equipment Factory, Shanghai, China) was used to verify the moisture levels and ensure the accuracy of the drying process.

Based on the Oommen oil–paper moisture equilibrium curve shown in Figure 1 [20], the required amount of water addition was calculated using the measured oil temperature, oil mass, and paper mass to achieve the target moisture content. The dried insulation paper was then immersed in insulating oil with adjusted moisture content and thoroughly stirred to ensure uniform impregnation. During the impregnation process, the moisture content of the insulating oil was continuously monitored using a micro-moisture sensor, while the experimental temperature was stably maintained at 60 °C, enabling precise control of the moisture state of the oil–paper insulation system.

With reference to the insulation operation requirements of ultra-high-voltage (UHV) power transformers, five groups of samples were finally prepared with target paper moisture contents of 0.5%, 1.0%, 1.5%, 2.0%, and 2.5%, covering the critical moisture range from dry to severely damp conditions that is highly relevant to UHV transformer insulation performance. Moreover, owing to the relatively short duration of the impregnation process and subsequent partial discharge tests, together with stable temperature control and real-time moisture monitoring, significant moisture migration between oil and paper was unlikely to occur. Therefore, within the limited testing time scale and controlled experimental conditions adopted in this study, the moisture state of the oil–paper insulation system can be reasonably regarded as effectively stable.

In addition, based on the “6 °C rule”, thermal aging of the oil–paper insulation was carried out at 75 °C, 90 °C, 105 °C, and 130 °C for 30 days to simulate different service lifetimes [21]. According to the Arrhenius accelerated aging relationship, these temperatures correspond to aging levels equivalent to approximately 0.17, 2.6, 5.4, and 12.6 years of service at room temperature (about 20 °C), thereby obtaining oil–paper insulation samples with different aging grades.

To verify the aging condition of the prepared samples, Frequency Domain Spectroscopy (FDS) measurements were conducted using a Novocontrol broadband dielectric analysis system. FDS measures the complex permittivity (real part ε′ and imaginary part ε″) and the dielectric loss factor tan δ over a wide frequency range (10⁻³ Hz to 10⁷ Hz), providing insights into polarization behavior, interfacial relaxation, charge transport, and conductivity. This technique offers significant advantages for evaluating the condition of oil–paper composite insulation systems [22,23,24,25]. In this study, FDS was employed primarily as an auxiliary validation method to qualitatively confirm the effectiveness of the thermal aging treatment applied to the oil–paper insulation samples. As shown in Figure 2, the imaginary part of the relative permittivity (ε″) in the low-frequency region exhibits a clear increasing trend with aging degree. Under the condition that aging degree was the only controlled variable, this distinct low-frequency response sufficiently demonstrates that the prepared samples possess distinguishable aging characteristics and meet the experimental requirements.

2.2. Partial Discharge Detection System Setup

In transformer oil–paper insulation systems, Surface Partial Discharge and Needle Partial Discharge are two typical forms of partial discharge, commonly caused by insulation aging, structural defects, or electric field concentration. These discharges induce coupled electrical, thermal, and chemical stresses in localized regions, and their long-term development can lead to insulation deterioration or even puncture breakdown, making them recognized failure modes of power equipment [26,27].

To simulate these typical discharge conditions, two representative discharge models were constructed in this study. As shown in Figure 3, The N-PD model uses a metal needle electrode with a radius of 5 mm and a tip angle of 30°, forming a strong localized electric field to represent discharge caused by internal sharp defects such as metallic burrs or suspended particles. The S-PD model uses a flat electrode with a radius of 20 mm and a thickness of 5 mm, placed in close contact with the paper surface to reproduce surface electric-field distortion, creepage, and discharge phenomena commonly observed in transformers.

In addition, an experimental simulation platform for partial discharge studies was established using the laboratory’s existing AC high-voltage source, high-speed imaging system, and partial discharge detector, as shown in Figure 4 This platform enables electrical monitoring of discharge processes under different discharge structures, visual capture of discharge behavior, and correlation analysis between discharge characteristics and insulation degradation. It provides reliable data support for subsequent research on aging mechanisms and the development of diagnostic models.

Partial discharge measurements were performed using the GDYT-20/200 dielectric partial discharge tester (Xigao Electric, Wuhan, China), which enables real-time acquisition of partial discharge signals within oil–paper insulation, with an angular resolution of 0.0009°. Through waveform analysis, key discharge characteristics—including pulse amplitude, repetition rate, and phase distribution—can be extracted to accurately identify discharge behavior at different fault stages. The AC high-voltage source used in the experiment was the GDYD-P series withstand-voltage test system, equipped with an oil-immersed test transformer capable of providing output levels of 0–50/100/150/200 kV. The system displays high-voltage voltage, high-voltage current, and low-voltage current in real time and includes over-current protection and zero-start protection functions. A Vision Research Phantom T2410 high-speed camera (Vision Research Inc., Rochester, NY, USA) was employed for visual recording, supporting a maximum frame rate of 24,270 fps with a resolution of 1280 × 800 and a minimum exposure time of 1.1 μs. The global electronic shutter effectively eliminates motion blur in high-speed discharge events and supports remote independent operation. These instruments collectively enable high-precision partial discharge detection, visual capture, and stage identification, providing reliable support for subsequent discharge characteristic analysis.

2.3. Method of Voltage Application

The prepared oil–paper insulation samples were placed in the established partial discharge detection platform. For the N-PD model, a 1 mm gap was maintained between the needle electrode and the insulation paper. For the S-PD model, the surface electrode was placed in close contact with the paper surface. The entire electrode–paper system was fully immersed in insulating oil to ensure a stable electric field distribution and minimize external interference. A 50 Hz sinusoidal AC source was used for voltage application following a two-stage ramping method. First, the voltage was increased to 10 kV at a rate of 1 kV/s and held for 10 min to stabilize internal air gaps, charge distribution, and interfacial polarization. The voltage was then further increased to 11 kV at the same rate and held for another 10 min. This “hold–ramp” process was repeated until partial discharge breakdown occurred.

Throughout the voltage application process, the pulse amplitude, discharge repetition rate, and phase distribution of partial discharge were recorded in real time. The breakdown voltage and high-speed images at the breakdown moment were also captured to support subsequent analysis of discharge evolution and breakdown mechanisms.

3. Results and Discussion

To investigate the discharge behavior of typical defects under different moisture contents and aging levels, a systematic quantitative analysis was performed on the acquired partial discharge patterns. For each group of oil–paper insulation samples, the power-frequency voltage phase was used as the time reference, and the full electrical cycle was uniformly divided into 360° phase intervals to record all discharge events.

Based on the pulse-resolved partial discharge (PRPD) data, discharge amplitude maps and discharge frequency maps were constructed to reveal the phase-resolved distribution characteristics and energy concentration of the discharges over the entire cycle. Furthermore, the evolution of partial discharge activity was analyzed by dividing the discharge process into the Initiation Stage (IS), Development Stage (DS), and Pre-breakdown Stage (PBS).

The stage division was completed prior to feature parameter extraction and was determined exclusively using quantitative characteristics directly derived from the PRPD data, including the PD pulse repetition rate and its temporal growth trend, as well as the effective phase coverage and phase bandwidth expansion. Specifically, the Initiation Stage is characterized by sparse PD activity with limited phase involvement (phase coverage < 30%); the Development Stage corresponds to a rapid increase in PD repetition rate accompanied by a pronounced expansion of phase coverage across the phase domain (approximately 30–80%); and the Pre-breakdown Stage is identified by near full-phase coverage (>80%) and highly concentrated PD activity immediately preceding breakdown.

3.1. Partial Discharge Patterns of Oil–Paper Insulation

3.1.1. Instantaneous Partial Discharge Patterns

Instantaneous N-PD and instantaneous S-PD refer to the partial discharge patterns obtained by sampling and recording the discharge activity of the insulation samples at multiple time points during the partial discharge experiment. These instantaneous patterns cover the Initiation Stage (IS), Development Stage (DS), and Pre-breakdown Stage (PBS) of the PD evolution process.

In this study, the division of PD evolution stages is completed prior to feature parameter extraction and is based exclusively on quantitative characteristics directly derived from the pulse-resolved partial discharge (PRPD) data. Specifically, stage identification relies on the following:

(1)

The PD pulse repetition rate and its temporal growth trend;

(2)

The effective phase coverage and phase bandwidth expansion.

Since the sampling frequency in this study was relatively high, a large number of instantaneous discharge patterns were collected. Therefore, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12 present only representative patterns for analysis and discussion, aiming to elucidate typical discharge behavior and its evolution process.

3.1.2. Statistical Discharge Frequency Pattern

Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20: The discharge events in the three stages were statistically analyzed using a time window of 30 seconds. In the figure, “次” represents the number of discharge occurrences.

3.1.3. Analysis of Partial Discharge Patterns

As shown in the figure, under different moisture contents and aging levels, N-PD and S-PD exhibit clear and consistent differences in discharge amplitude, phase distribution, and discharge repetition characteristics.

In the IS of N-PD, the PRPD pattern contains only a few discharge pulses, mainly concentrated near the positive half-cycle peak (110–150°) and the negative half-cycle peak (280–330°). The peak charge is generally below 50 pC. At this stage, the local electric field at the needle tip is only slightly above the PD inception threshold, resulting in limited electron avalanche development and very short discharge channels; therefore, both discharge amplitude and repetition rate remain at low levels. As the local electric field distortion expands, the discharge enters the DS. The PRPD pattern shows a significant increase in pulse density, with peak amplitudes extending beyond 100 pC. The phase distribution also broadens considerably in both the positive half-cycle (0–100°, 110–150°) and the negative half-cycle (250–360°). This behavior is mainly attributed to enhanced local thermal accumulation and micro-carbonization, which lower the local breakdown threshold of the insulation. Consequently, the electric field distortion around the needle becomes more severe, leading to more frequent discharge activity. In the PBS, the PRPD pattern is dominated by a dense concentration of high-amplitude pulses (>500 pC), and the discharge repetition rate increases sharply. The phase distribution covers nearly the entire AC cycle, with only small low-density regions near 100° and 280°. At this stage, the discharge channel around the needle becomes increasingly stable and tends toward full penetration, while accumulated space charge causes severe electric field distortion, placing the insulation system in a critical breakdown condition.

The evolution of S-PD also exhibits distinct stage characteristics; however, due to the fundamentally different discharge channel morphology and electric field distribution compared with N-PD, its discharge behavior demonstrates unique features. In the IS, the PRPD pattern contains only a few scattered low-amplitude pulses, mainly concentrated around 135° in the positive half-cycle and 270–360° in the negative half-cycle. Since S-PD occurs along the paper–oil interface, the tangential electric field initially induces sliding discharges at surface defects, but no stable conductive channel is formed at this stage, resulting in limited energy release. In the DS, both discharge amplitude and repetition rate increase significantly, with charge magnitudes reaching several hundred to over one thousand pc. The phase bandwidth expands noticeably; in addition to the main concentration zones, low-amplitude pulses also appear in regions such as 0–45°, indicating that discharge activity is extending across the entire phase range. During this period, continuous surface erosion leads to the formation of carbonized traces, enhancing surface conductivity and intensifying electric field distortion along the interface. This promotes branching and extension of the discharge path. The PBS exhibits pronounced instability. The PRPD pattern shows densely distributed high-amplitude pulses (>1000 pC, occasionally exceeding 10,000 pC), with discharges nearly covering the entire phase domain. This indicates that the carbonized surface channel has become nearly continuous, and the sliding discharge has evolved into a stable flashover discharge, bringing the insulation system into a critical pre-breakdown condition.

Moisture and thermal aging are two critical factors that significantly exacerbate partial discharge severity and accelerate the failure process of oil–paper insulation through different mechanisms. Regarding moisture influence, high moisture content leads to denser occurrences of high-amplitude pulses (>1000 pC and even up to 10,000 pC) in the PRPD patterns. The discharge repetition rate further increases, and the full-cycle phase coverage becomes more pronounced. This is because moisture reduces the local insulation strength, allowing the discharge channel to extend more easily along the paper–oil interface, while also promoting oil-film breakdown and bubble formation. The accumulation of bubbles not only provides conductive paths but also releases additional energy during bubble breakdown events. The influence of thermal aging is primarily reflected in the accelerated progression of discharge evolution. As aging intensifies, the degree of cellulose carbonization increases and more oil degradation products are generated, facilitating the formation of both surface and needle discharge channels. Although the discharge intensity of aged samples in the Initiation Stage may not be as strong as that of high-moisture samples, the transition into the Development Stage and the Pre-breakdown Stage occurs much faster. The density of high-amplitude pulses quickly reaches critical levels, making the insulation system more prone to failure in the later stages.

In summary, both N-PD and S-PD follow an “Initiation–Development–Pre-breakdown” evolution pattern; however, due to differences in electric field distribution and discharge channel morphology, they exhibit distinct behaviors in discharge amplitude, phase expansion, and energy release. Moisture and thermal aging jointly intensify discharge deterioration by reducing local electric strength, altering interfacial structures, and accelerating the formation of carbonized channels, thereby exerting a synergistic accelerating effect on insulation failure.

3.2. Partial Discharge Breakdown Voltage of Oil–Paper Insulation

To ensure the reliability of the experimental results and to minimize the influence of random factors, multiple breakdown tests were conducted for each sample group. For each experimental condition, at least three valid repeated measurements were performed, and the corresponding partial discharge breakdown voltages were recorded. Tests exhibiting abnormal behavior or clear experimental failure (e.g., unstable discharge caused by accidental disturbances) were excluded, and only valid measurements were retained for analysis. For each condition, the mean value and the corresponding standard deviation (SD) of the valid measurements were calculated. The mean value was used to represent the characteristic breakdown voltage under a given condition, while the standard deviation was employed to quantify the dispersion of repeated measurements and assess experimental repeatability. The breakdown voltages corresponding to N-PD and S-PD, together with their standard deviations, are summarized in

Table 1. Partial discharge breakdown voltage of samples with different moisture contents.

Moisture Content (%)	Test 1 (KV)		Test 2 (KV)		Test 3 (KV)		Mean (KV)		Standard Deviation
	N-PD	S-PD	N-PD	S-PD	N-PD	S-PD	N-PD	S-PD	N-PD	S-PD
0.5%	21	17	21	19	20	18	21	18	0.58	1.00
1.0%	21	17	20	16	19	18	20	17	1.00	1.0
1.5%	20	16	18	16	18	17	18.7	16.3	1.15	0.58
2.0%	19	16	18	16	17	16	18	16	1.00	0
2.5%	18	15	17	15	17	15	17.3	15	0.58	0

and

Table 2. Partial discharge breakdown voltage of samples at different aging stages.

T/°C	Test 1 (KV)		Test 2 (KV)		Test 3 (KV)		Mean (KV)		Standard Deviation
	N-PD	S-PD	N-PD	S-PD	N-PD	S-PD	N-PD	S-PD	N-PD	S-PD
75	21	20	21	18	20	19	20.7	19	0.58	1.00
90	20	19	19	18	19	18	19.3	18.3	0.58	0.58
105	19	17	17	16	17	16	17.7	16.3	1.15	0.58
130	17	16	17	15	16	15	16.7	15.3	0.58	0.58

.

Under different moisture contents, the partial discharge breakdown voltage of oil–paper insulation exhibits a clear decreasing trend, with N-PD showing higher sensitivity to moisture variation. As the moisture content increases from 0.5% to 2.5%, the breakdown voltage of N-PD decreases from approximately 21 kV to 17.3 kV, while that of S-PD decreases from about 18 kV to 15 kV. Overall, increased moisture content enhances interfacial polarization and promotes the formation of moisture-assisted conductive pathways, causing the dominant discharge mode to gradually shift from “point-type breakdown” to “interface creepage”.

In contrast, degradation induced by thermal aging is more cumulative and irreversible. As the aging temperature increases from 75 °C to 130 °C, the breakdown voltage of N-PD decreases from 20.7 kV to 16.7 kV, while that of S-PD decreases from 19 kV to 15.3 kV. Although both discharge types show relatively limited variation at the early aging stage, their breakdown voltages drop rapidly under severe aging conditions (105–130 °C). This behavior indicates that aging by-products gradually migrate toward the insulation interface and form carbonized conductive layers, causing the discharge mechanism of S-PD to evolve from polarization-dominated behavior to conductive creepage.

It is worth noting that the observed partial discharge evolution trends are consistent with the PD acceptance philosophy adopted in transformer standards, which aims to ensure sufficient insulation margin by limiting PD activity under prescribed test voltage conditions.

3.3. Discharge Process Diagram

High-speed imaging of the entire discharge process allows clear differentiation between the initiation locations and channel evolution of N-PD and S-PD (Figure 21 and Figure 22).

For N-PD, discharge first appears inside the insulation near the needle electrode as scattered short channels when the applied voltage begins to rise. This indicates that the local electric field primarily triggers internal breakdown within microvoids and pores of the cellulose. As local heating and bubble formation progress, the internal dielectric structure is further weakened, and the discharge channel gradually extends toward the ground electrode, eventually forming a well-defined, directional penetrating path. In contrast, S-PD originates mainly at the contact interface between the metal electrode and the paper surface. At the initial stage, only slight sliding discharges appear along the interface, constrained by surface moisture and the tangential electric field. When the applied voltage increases further, interface field distortion intensifies, causing the discharge to evolve into a surface-spreading sliding channel and subsequently into a continuous surface discharge band between the paper and the electrode. Unlike the internal penetration observed in N-PD, S-PD exhibits a pronounced surface-dependent propagation behavior.

Overall, moisture primarily influences interfacial electric fields and promotes the formation of moisture-conducting pathways, making S-PD easier to initiate at an earlier stage. Thermal aging, on the other hand, degrades the internal structure of the insulation, causing N-PD to intensify more rapidly in the early stage and eventually inducing sustained surface creepage in the later stage. These results highlight the importance of distinguishing between “reversible moisture degradation” and “irreversible structural aging” when evaluating the condition of oil–paper insulation, and the need to establish failure-mode-specific warning indicators to improve lifetime prediction and defect diagnosis accuracy.

4. Feature Extraction

To further reveal the differences in discharge behavior under various moisture contents and aging levels, characteristic discharge parameters were extracted for the early, middle, and late stages of both N-PD and S-PD. These parameters were calculated and quantitatively analyzed according to the following equations.

First, the mean value of the partial discharge data is calculated to represent the overall energy level of the discharge activity:

$$\overline{PD}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^{N}P}{D}_i$$

(1)

Skewness is used to describe the asymmetry of the partial discharge waveform and reflects the non-uniformity of its statistical distribution:

$$\mathrm{Skewness}={\displaystyle \frac{\frac{1}{N}{\displaystyle \sum _{i=1}^N{(P{D}_i-\overline{PD})}^3}}{{\left(\frac{1}{N}{\displaystyle \sum _{i=1}^N{(P{D}_i-\overline{PD})}^2}\right)}^{3/2}}}$$

(2)

Peak Degree is used to quantitatively characterize the concentration of partial discharge data and reflects the sharpness of its statistical distribution:

$$\mathrm{Peak} \mathrm{Degree}={\displaystyle \frac{\frac{1}{N}{\displaystyle \sum _{i=1}^N{(P{D}_i-\overline{PD})}^4}}{{\left(\frac{1}{N}{\displaystyle \sum _{i=1}^N{(P{D}_i-\overline{PD})}^2}\right)}^2}}$$

(3)

Maximum Steepness represents the maximum change in discharge magnitude between adjacent phase intervals and reflects the instantaneous variation rate of the discharge waveform, serving as an indicator of the rapid growth behavior of the discharge:

$$P{D^{\prime }}_{\max }={\max }_i(P{D}_{i+1}-P{D}_i)$$

(4)

Skewness, Peak Degree, and Maximum Steepness were used to characterize the statistical properties and evolution of partial discharge activity under different aging and moisture conditions. These features were extracted from statistical distributions of PD activity, rather than from individual discharge pulses. For each test condition and PD evolution stage (IS, DS, and PBS), PD data were collected using a fixed 30 s time window, during which a sufficient number of discharge pulses (typically hundreds to several thousand) were recorded to ensure statistical representativeness. The same time window was applied to all conditions to maintain consistency and comparability. Based on the above equations, the characteristic parameters for each stage were calculated as follows (Figure 23, Figure 24, Figure 25 and Figure 26):

For the aging group, the Skewness of N-PD is relatively high in the early stage, decreases significantly in the intermediate stage, and increases again in the late stage. This non-monotonic evolution indicates that discharge activity initially exhibits strong randomness and asymmetry, gradually transitions into a more stable and symmetric state as aging progresses, and finally regains asymmetry in the late stage due to intensified discharge activity. From a physical mechanism perspective, the decrease in Skewness during the intermediate stage can be attributed to the homogenization of discharge sites as insulation degradation develops, whereas the subsequent increase in the late stage is associated with local electric field distortion, micro-carbonization, and structural deterioration of the oil–paper insulation, which promote intensified and uneven discharge behavior. In contrast, the Skewness of S-PD exhibits pronounced fluctuations throughout the aging process. In particular, negative Skewness values (approximately −0.4) observed in the intermediate stage indicate the occurrence of reverse discharges, reflecting complex charge redistribution and polarity alternation on deteriorating insulation surfaces. In the late stage, the clear dispersion of Skewness values among samples suggests a multi-point instability mechanism rather than a single dominant discharge site, which is consistent with the inherently heterogeneous nature of surface discharge on aged oil–paper interfaces.

Regarding Peak Degree, both N-PD and S-PD exhibit high values in the early stage, indicating strong pulse concentration and localized discharge events. During the intermediate stage, Peak Degree decreases to the range of 1–5, implying a transition toward a more uniform energy distribution as discharge activity becomes spatially distributed. In the late stage, N-PD shows a renewed increase in Peak Degree, suggesting the re-emergence of high-energy discharge pulses driven by localized electric field enhancement, whereas S-PD remains at a relatively low level, reflecting its evolution toward continuous weak discharge rather than sporadic high-intensity events.

The evolution of Maximum Steepness further reflects the acceleration of discharge dynamics. Maximum Steepness increases gradually during the intermediate stage, indicating an increasing rate of discharge variation as degradation accumulates. In the late stage, N-PD exhibits a sharp increase, with some samples exceeding 4000 pC, while S-PD shows an even more pronounced rise, with values exceeding 10,000 pC. This behavior demonstrates the more violent and transient nature of surface discharge under severe aging conditions, where rapid charge release and unstable discharge channels dominate.

For the moisture group, the Skewness of N-PD decreases more significantly at medium and high moisture levels and tends to stabilize, indicating that moisture promotes discharge symmetry by weakening localized electric field distortion. S-PD exhibits a continuous decline in Skewness, with some samples approaching zero, further confirming the symmetry-inducing effect of moisture on surface discharge behavior. Peak Degree for both discharge types decreases rapidly from the early to the intermediate stage, reflecting the transition from concentrated pulse discharge to more evenly distributed discharge activity. In the late stage, N-PD shows a slight increase in Peak Degree, while S-PD remains relatively stable, corresponding to its near full-phase, high-magnitude discharge characteristics. Maximum Steepness is particularly sensitive to moisture content. Both N-PD and S-PD show substantial increases in the late stage, indicating that moisture accelerates the formation and expansion of discharge channels by reducing the dielectric strength of the oil–paper insulation. Nevertheless, the observed variability among samples suggests that the influence of moisture on discharge rate is condition-dependent and closely coupled with local insulation structure and degradation state.

Through the systematic analysis of these characteristic parameters and their non-monotonic evolution, the discharge behaviors associated with different degradation and failure mechanisms can be effectively distinguished, providing valuable guidance for insulation condition assessment and lifetime prediction of oil–paper insulation systems.

5. Conclusions

This study conducted systematic experiments to investigate the partial discharge behavior of oil–paper insulation under moisture absorption and thermal aging conditions. By integrating instantaneous discharge mapping, discharge frequency statistics, breakdown voltage measurements, and multi-dimensional feature parameter extraction, the study comprehensively revealed the evolution characteristics of typical partial discharge defects under different degradation states. The results demonstrate that although both needle partial discharge and surface partial discharge follow the general evolution pattern of “initiation–development–pre-breakdown”, their discharge characteristics and degradation pathways differ significantly due to variations in electric-field distribution, interface structure, and discharge-channel morphology.

(1)

Increasing moisture content significantly aggravates partial discharge activity in oil–paper insulation. The severity enhancement is more pronounced for surface discharge (S-PD), whereas needle discharge (N-PD) exhibits higher sensitivity to moisture in terms of breakdown voltage degradation. From the perspective of discharge evolution, moisture intensifies interfacial polarization, promotes oil-film rupture and bubble formation, and accelerates the development of moisture-conductive paths along the paper–oil interface, thereby facilitating the lateral expansion of surface discharge. As a result, S-PD in the late stage exhibits markedly increased discharge amplitude, repetition rate, and near full-cycle phase coverage, with dense high-amplitude pulses exceeding 1000 pC. Correspondingly, the breakdown voltage of S-PD decreases from approximately 18 kV to 15 kV, representing an overall reduction of about 16.6%. In contrast, N-PD under high-moisture conditions mainly shows a pronounced broadening of phase distribution, with localized low-density regions appearing near approximately 100° and 280°, reflecting intensified local electric-field perturbations in the vicinity of the needle tip. Its breakdown voltage decreases from about 21 kV to 17.3 kV, corresponding to an overall reduction of approximately 17.6%. These normalized results quantitatively confirm that moisture reduces both interfacial and internal breakdown thresholds, with N-PD exhibiting higher sensitivity to moisture-induced degradation.

(2)

Thermal aging causes progressive and irreversible deterioration of oil–paper insulation by degrading dielectric properties, promoting cellulose carbonization, and accelerating the accumulation of oil decomposition products. Although the discharge intensity of aged samples in the Initiation Stage is not necessarily higher than that observed under high-moisture conditions, thermal aging significantly accelerates the transition from the Development Stage to the Pre-breakdown Stage. As the aging temperature increases from 75 °C to 130 °C, both N-PD and S-PD exhibit earlier stabilization of discharge channels and a rapid increase in high-amplitude pulse density during the mid-to-late stages. For S-PD, severe aging leads to the formation of a nearly continuous carbonized conductive film along the insulation surface, causing the discharge mechanism to evolve from polarization-dominated behavior to conduction-type creeping discharge, with the breakdown voltage decreasing to approximately 15.3 kV. For N-PD, thermal aging similarly promotes earlier channel penetration and intensified space-charge accumulation, resulting in denser high-amplitude pulses and a breakdown voltage reduction to about 16.7 kV. These results indicate that thermal aging primarily accelerates discharge evolution kinetics and failure progression, exerting a cumulative and irreversible impact on insulation reliability.

(3)

Feature-parameter analysis further reveals the differentiated and synergistic effects of moisture and thermal aging on partial discharge evolution. Skewness reflects discharge symmetry, decreasing under high-moisture conditions as discharge tends toward more bipolar behavior, while increasing again in late-stage aging due to the renewed dominance of strong unipolar discharge associated with channel stabilization. Peak Degree characterizes energy concentration, decreasing in the intermediate stage as discharge transitions from isolated high-energy pulses to multi-point distribution, and increasing again under severe aging as carbonized channels promote localized energy concentration. Among the extracted features, Maximum Steepness is particularly sensitive to late-stage discharge intensification. It increases markedly in moisture-affected surface discharge and grows progressively in thermally aged needle discharge, corresponding, respectively, to interface weakening and internal structural degradation. When compared between the Development Stage and the Pre-breakdown Stage within the same discharge type, Maximum Steepness can serve as a normalized indicator of late-stage discharge strengthening, providing complementary diagnostic insight into insulation deterioration.

Overall, this study establishes a systematic analytical framework for characterizing partial discharge behavior in oil–paper insulation under combined moisture and thermal aging conditions. The mechanistic differences among typical defect types are clarified, and the intrinsic evolution of feature parameters with insulation degradation is revealed. The obtained results lay a solid foundation for the development of early-warning models and fault-diagnosis methods based on feature-parameter evolution, thereby contributing to improved operational reliability and lifetime prediction of power transformers.