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Article

Study on the Unipolar Impulse Aging Characteristics of ZnO Varistors and Their Condition Monitoring Methods

1
Inner Mongolia Ultra-High Voltage Power Supply Company, Inner Mongolia Electric Power (Group) Co., Ltd., Ulanqab 010080, China
2
State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China;2213621605@stu.xjtu.edu.cn (M.X.)
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(17), 9484; https://doi.org/10.3390/app15179484
Submission received: 30 July 2025 / Revised: 21 August 2025 / Accepted: 27 August 2025 / Published: 29 August 2025

Abstract

Metal-oxide surge arresters (MOSAs) are critical devices for overvoltage protection in power systems, and the aging characteristics of their zinc oxide (ZnO) varistors under impulse and power-frequency voltages exhibit significant differences. However, traditional methods for monitoring the aging state of surge arresters suffer from limitations such as insufficient sensitivity and vulnerability to harmonic interference. Therefore, this study conducted accelerated aging experiments on ZnO varistor samples under negative-polarity impulse currents. Key parameters were measured, including the DC reference voltage, the DC leakage current, nonlinear coefficients, and the full current under harmonic-containing power-frequency voltage at a voltage ratio of 0.6. The resistive component was accurately extracted from the full current using a separation method based on the Levenberg–Marquardt (LM) optimization algorithm. Spectral analysis was then performed on both the full current and the extracted resistive current components. The experimental results demonstrate a significant polarity effect in the aging of ZnO varistors under unipolar impulse currents. The LM optimization algorithm enables precise extraction of the resistive current component from the full current. Furthermore, compared to the fundamental and third harmonic components, the amplitude of the DC component within the resistive current exhibits the highest sensitivity to aging, establishing it as a viable aging criterion.

1. Introduction

MOSAs serve as critical safeguards against overvoltage in power systems, providing indispensable protection for transmission, substation, and distribution networks [1]. With the continuous expansion of China’s power grid and increasingly complex operational conditions, lightning strikes and switching overvoltage pose escalating threats to electrical equipment security. MOSAs establish a low-impedance discharge path via internal nonlinear resistive elements (zinc oxide varistors), diverting overvoltage energy to the ground [2]. This effectively limits overvoltage amplitudes and significantly enhances the surge withstand capability of critical equipment, including transformers, circuit breakers, and generators. However, MOSAs face severe aging challenges during long-term operation [3]. Under combined stresses from continuous power-frequency voltage, electrothermal effects of leakage current, lightning and switch impulses, and environmental factors such as ice and snow accretion, the grain-boundary structures of zinc oxide varistors progressively degrade, manifesting as increased leakage current, elevated power loss, shifts in DC reference voltage, and distortions in voltage–current characteristics [4]. Consequently, developing precise arrester aging monitoring techniques is imperative to assess MOSA health status, prevent equipment failures, and ensure power system security—carrying substantial engineering significance [5].
Existing monitoring methods for arresters exhibit significant limitations: the RMS measurement of total leakage current struggles to detect subtle changes in the resistive component during early-stage aging due to capacitive currents exceeding 90% of the total; the DC reference voltage method requires de-energization, compromising timeliness and continuity; and conventional resistive current detection is susceptible to interference from harmonic distortion, voltage fluctuations, and environmental conditions [6,7]. Recent research has focused on high-precision resistive current extraction techniques, such as the open-delta wiring method based on three-phase system symmetry, which significantly enhances monitoring sensitivity by canceling capacitive components, and harmonic analysis, which employs FFT transformations to extract fundamental and characteristic harmonics, such as the third harmonic, of resistive current for constructing nonlinear aging indicators [8,9,10].
Furthermore, compared to power-frequency aging, impulse aging exhibits stronger destructiveness, making it essential to understand the impulse aging characteristics of varistors and accurately assess their aging status [11,12]. Multiple studies report asymmetrical degradation of voltage–current (V-I) characteristics in ZnO varistors under unipolar impulse currents, showing more severe degradation in one polarity direction, whereas bipolar impulses yield symmetrical degradation [11,13]. Yin et al. discovered, during 8/20 μs pulse aging tests, that the DC reference voltage U0.1mA changes more significantly than U1mA, and the nonlinear coefficient reduces rapidly [14]. They proposed the nonlinear coefficient as a superior aging indicator compared to conventional U1mA. Li et al. [15] tested arresters under consecutive 8/20 μs pulses and revealed that the impulse count failure threshold can be determined through U1mA and residual voltage U10kA. Wu et al. [16] investigated the harmonic characteristics of leakage current during impulse aging, observing accelerated growth of higher-order harmonics after multiple impulses followed by abrupt decline prior to failure. This led to their proposal of the third-harmonic ratio as a novel aging criterion. Zhang et al. [17] conducted negative-polarity 15/35 μs impulse aging tests on ZnO varistors, attributing even-order harmonic variations to polarity effects and suggesting their utility as aging indicators. Nevertheless, the universality of these assessment methods requires further validation.
This study employed an impulse aging test system to conduct accelerated unipolar impulse aging experiments on zinc oxide varistors. We obtained DC parameters and AC total leakage currents for varistors at varying aging levels and proposed a resistive component extraction method from total current waveforms using the LM optimization algorithm. Furthermore, fast Fourier transform (FFT) analysis was applied to both total current and resistive current waveforms to investigate aging mechanisms under impulse stress and establish criteria for arrester condition assessment.
The organizational structure of this thesis is arranged as follows: Section 2 proposes a resistive current extraction method based on the Levenberg–Marquardt optimization algorithm, detailing the mathematical model for parameter identification and clarifying the initial value selection strategy and convergence assurance mechanism; Section 3 designs a negative-polarity impulse aging experiment scheme, including test sample parameters, impulse platform setup, and synchronous measurement methods for DC parameters and AC leakage current; Section 4 analyzes experimental results by first revealing polarity effects in DC reference voltage, leakage current, and nonlinearity coefficients, subsequently demonstrating the evolution patterns of AC total current waveforms, and further validating the aging sensitivity and effectiveness of the DC component in resistive current through spectral analysis; Section 5 summarizes core conclusions on polarity-dependent aging mechanisms and DC-component monitoring criteria while discussing verification requirements under complex grid conditions and future research directions.

2. Resistive Leakage Current Extraction Method Based on Levenberg–Marquardt Optimization Algorithm

This study utilizes a resistive current calculation method for zinc oxide arresters based on the LM optimization algorithm [18]. The technical approach proceeds as follows: First, the nonlinear voltage–current (V-I) characteristic curve of the arrester is mathematically modeled using a power-law function to establish its constitutive relationship. Subsequently, based on the reference voltage signals and leakage current time-domain signals, the V-I characteristic parameters (α) and equivalent capacitance (C) are solved via nonlinear least-squares optimization.
To establish an accurate resistive current calculation model, theoretical analysis of the equivalent circuit topology for zinc oxide arresters is essential. As illustrated in the simplified equivalent circuit model in Figure 1 [19], this configuration accurately characterizes the electrical behavior of MOSAs in the low-current region. The topology comprises a nonlinear resistor R and an equivalent capacitance C connected in parallel.
In this model, the nonlinear resistor R represents the voltage-sensitive characteristics of zinc oxide grain-boundary Schottky barriers, while the equivalent capacitance C characterizes the combined effects of geometric capacitance and dielectric polarization at the intergranular layers. Under AC excitation, the total leakage current (IX) of the zinc oxide varistor comprises resistive (IR) and capacitive (IC) components, expressed as
I X = I R + I C
where IR is a function of voltage (u), calculable from C and u, as defined by
I R = f ( u )
I C = C d u d t
where f denotes the nonlinear function relating resistive current to voltage.
For zinc oxide arresters, multiple formulations exist to approximate this nonlinear function. Based on the definition Formula (4) of the nonlinear coefficient, we can derive Formulas (5) and (6).
α = lg I R I 1 / lg U U 1
I R I 1 = U U 1 α
I R = I 1 U U 1 α
Therefore, the resistive current can be expressed as Formula (6), and the formula can be simplified by defining the parameter k:
k = I 1 U 1 α
The final formula is simplified to
I R = k u α
where k is the scaling coefficient and α is the nonlinearity exponent.
To determine the arrester’s model parameters, the resistive current calculation is transformed into a least-squares optimization problem. Firstly, a predefined function is used to fit the nonlinear V-I characteristic curve. For example, given a measured reference voltage signal like Equation (9), the total leakage current can be predicted.
i t * = k u α + C d u d t
The sum of squared errors (SSE) between the predicted and measured values quantifies the model’s goodness-of-fit. A smaller SSE indicates higher parameter accuracy. The SSE is computed as
S S E = n = 1 N ( i t ( n ) i t * ( n ) ) 2
M S E = S S E / N
where N denotes the number of sample points.
Upon obtaining the model parameters k, α, and C, the resistive current and capacitive current can be computed according to Equations (2) and (3). The LM algorithm—a robust method combining the merits of gradient descent and Newton’s methods—is particularly suited for parameter estimation in ZnO arrester models. The LM algorithm minimizes the MSE through matrix operations. The residual vector r, representing deviations between the predicted and measured leakage currents, is defined as
r ( k , α , C ) = k ( u 1 ) α + C d u 1 d t i t 1 k ( u 2 ) α + C d u 2 d t i t 2 k ( u N ) α + C d u N d t i tN
The Jacobian matrix J ( k , α , C ) is
J ( k , α , C ) = u 1 α + k α ln ( u 1 ) u 1 α 1 + d u 1 d t u 2 α + k α ln ( u 2 ) u 2 α 1 + d u 2 d t u N α + k α ln ( u N ) u N α 1 + d u N d t
Let θ be the parameter vector. The approximate Hessian matrix H and gradient vector g are computed from J as follows:
H = J T J + λ I
where λ denotes the damping factor, and I represents the identity matrix.
g = J T r ( θ )
The updated parameter vector is computed via Equation (16):
θ k + 1 = θ k H 1 g
This iterative process repeats until the SSE falls below a predefined tolerance threshold ε, yielding the optimal parameter solution.

3. Experimental Methods

Given that approximately 90% of natural lightning discharges exhibit negative polarity—characterized by more universal charge properties and discharge patterns—this study employed an impulse aging platform depicted in Figure 2a to conduct negative-polarity impulse aging tests on zinc oxide varistor samples. The experimental setup comprised a high-voltage impulse current generator, an intelligent control system, and an integrated measurement instrumentation, which generated negative-polarity impulse currents with amplitudes of approximately 10 kA, as shown in Figure 2b [20,21,22].
The test samples used in this study are shown in Figure 3, featuring a 1 mA reference voltage of 430 V ± 10% and nominal discharge current of 20 kA. Five zinc oxide varistors with similar static parameters were selected as experimental specimens. Prior to testing, all varistor surfaces were cleaned using anhydrous ethanol, followed by thorough drying in a temperature-controlled chamber maintained at 25 °C. During the impulse aging experiments, individual varistors were sequentially placed in nitrogen-purged glass vacuum chambers. The impulse aging test system applied negative-polarity impulses to each specimen, with testing paused every 400 impulses for cooling to ambient temperature and parameter measurement. Experiments were terminated when any varistor exhibited leakage currents exceeding 50 μA or visible physical damage.
As shown in Figure 3b, the marked side of the ZnO varistor block serves as the positive electrode, while the unmarked side functions as the negative electrode. During impulse testing, the impulse current flows from the negative to the positive electrode. When measuring DC parameters, applying the high-voltage terminal of the DC power supply to the marked side yields forward DC parameters, whereas connection to the unmarked side produces reverse DC parameters.
DC parameter measurement constitutes a critical procedure for evaluating the electrical performance of zinc oxide varistors, encompassing determinations of key parameters, including reference voltage (U1mA), leakage current ( I 0.75 U 1 m A ), and nonlinearity coefficient ( α ). To investigate potential polarity effects in unipolar impulse aging, forward and reverse DC parameters were measured for varistors at varying aging stages by alternating the DC voltage application direction. During measurements, a DC voltage source excited the varistor, while an SR570 current amplifier—connected in series—precisely detected and amplified weak leakage currents flowing through the specimen.
In the AC leakage current measurement system, the voltage excitation was powered by mains electricity through a harmonic voltage regulator and step-up transformer to generate harmonic voltage signals meeting experimental requirements. The harmonic components and their amplitudes in the generated voltage with harmonic distortion are listed in Table 1 below. Based on formula calculation (17), the total harmonic distortion (THD) of the power supply in this study was determined to be 24.2%.
T H D = k = 2 N V k 2 V 1 × 100 %
where V1 is the fundamental voltage amplitude, and Vk represents the amplitude of the k-th harmonic component.
A non-inductive 500 Ω resistor was connected in series with the zinc oxide varistor, coupled with a high-precision PicoScope oscilloscope to form the measurement system, ensuring accurate capture of leakage current dynamic characteristics. To guarantee measurement stability and accuracy, each test recorded sufficient data samples via the oscilloscope for subsequent analysis.

4. Experimental Results and Analysis

4.1. DC Parameter Experimental Results

U1mA is defined as the DC voltage at a leakage current of 1 mA. Figure 4 shows the forward and reverse reference voltages of five varistor samples versus the number of impulse cycles during the negative-polarity impulse aging tests.
The results indicate that under unipolar impulse aging, the variation trend of U 1 mA exhibits a polarity effect: the forward reference voltage shows an initial gradual decrease followed by a rapid drop with increasing impulse count, while the reverse reference voltage decreases, then exhibits a slight recovery, and ultimately undergoes a significant drop. This phenomenon is attributed to ion migration theory [23]. Unipolar impulse current injection delivers substantial energy, intensifying ion migration activity within grain boundaries and depletion layers. Consequently, ion migration induces asymmetric distortion of the double Schottky barriers in the ZnO varistor, leading to severe unipolar degradation. This results in distinct variation trends for the forward and reverse DC reference voltages of the sample.
The DC leakage current is defined as the steady-state current value of a ZnO varistor at 0.75 times the reference voltage ( I 0.75 U 1 m A ). As shown in Figure 5, the experimental results demonstrate that during unipolar impulse aging, both types of leakage currents exhibit initial slow growth followed by rapid growth. The growth slope under forward bias is significantly greater than under reverse bias. When the impulse count remains below the critical value, the leakage current increase remains within approximately 15–20% of the initial value, with a relatively gradual change rate. However, once the impulse count exceeds the threshold, the current value rapidly increases, ultimately reaching 2 to 3 times the initial level.
This study employs Equation (4) to calculate the forward and reverse nonlinear coefficients of the samples under different impulse group conditions and plots their characteristic curves versus aging degree, as shown in Figure 6. It is observed that during impulse aging, both forward and reverse nonlinear coefficients exhibit an initial sharp decline, followed by a slow decline and finally a drastic drop. Furthermore, the rate of decrease in the forward nonlinear coefficient is significantly greater than that in the reverse coefficient.
Furthermore, observation of the DC parameter variation trends reveals that the aging rate of varistor sample 3 is significantly greater than that of the other varistors in the multilayer configuration. Therefore, varistor sample 3 is selected as the subject for subsequent analysis of its AC full current variation trend.

4.2. Variation Trend of AC Current Waveform

This paper measures the AC full current waveforms of ZnO varistors with different aging degrees under 50 Hz voltage excitation with harmonics at a typical operating condition with a voltage ratio of 0.6, as shown in Figure 7.
Using the resistive current extraction method based on the LM algorithm described in Section 2, the resistive component is extracted from this full current waveform, yielding the resistive current component within the ZnO varistor’s full current, as illustrated in Figure 8.
Changes in harmonic components are analyzed to reveal the evolution pattern of the full current waveform. The collected full current time-domain waveform and resistive current component undergo FFT analysis. The amplitude variation curves of the fundamental, third harmonic, and DC components are extracted and presented in Figure 9 and Figure 10.
Figure 9 and Figure 10 clearly demonstrate that under harmonic-containing 50 Hz AC excitation at a voltage ratio of 0.6, the amplitudes of the fundamental, third harmonic, and DC components in both the full current and the resistive component of the ZnO varistor continuously increase with the impulse count. A significant surge occurs particularly near the failure threshold.
Based on the experimental data in Figure 9 and Figure 10, we calculated normalized sensitivity factors (NSFs) for each harmonic component in both the full current and resistive current. The results are shown in Table 2.
The DC component’s NSF in resistive current is higher than the fundamental and higher than the basic harmonic and the 3rd harmonic, demonstrating superior sensitivity to aging.
Furthermore, the growth amplitudes of the fundamental, third harmonic, and DC component amplitudes in the resistive component of the ZnO varistor’s full current are more pronounced than those in the full current itself as the impulse count increases. This is especially evident for the DC component of the resistive current. Starting from an almost negligible initial state, it exhibits an approximately linear growth trend during aging, demonstrating higher sensitivity to ZnO varistor degradation.
Therefore, at a voltage ratio of 0.6, the DC component value of the resistive current serves as an indicator of the ZnO varistor’s aging degree. Utilizing the DC component of the resistive current extracted from the full current waveform as an indicator for assessing the aging state of ZnO varistors is feasible.

5. Conclusions and Future Work

The main conclusions obtained from the negative-polarity impulse aging experiments on ZnO varistors in this paper are as follows:
  • Under a negative-polarity impulse current, the aging of ZnO varistors exhibits a significant polarity effect. The forward reference voltage shows an initial gradual decrease, followed by a rapid drop with increasing impulse count, while the reverse reference voltage first decreases, then exhibits a slight recovery, and ultimately undergoes a significant drop. Both forward and reverse leakage currents exhibit increasing trends, with the forward leakage current showing a greater increase than the reverse current. Both forward and reverse nonlinear coefficients demonstrate attenuation trends, with the forward nonlinear coefficient degrading more severely. This phenomenon is attributed to asymmetric aging of the double Schottky barriers in the ZnO varistor during impulse aging, which can be explained by ion migration theory.
  • A high-precision separation of the resistive component from the full current of ZnO varistors under harmonic-containing 50 Hz voltage excitation at a voltage ratio of 0.6 was achieved using the Levenberg–Marquardt optimization algorithm. Signal analysis in MATLAB R2024b enabled spectral analysis of both the full current and its resistive component. The spectral results indicate that the DC component amplitude of the resistive current exhibits the highest sensitivity to aging. Compared to the fundamental and third harmonic components of the resistive current, the DC component amplitude can detect degradation signals earlier during the initial stage of impulse aging, making it an effective criterion for evaluating the aging state of ZnO surge arresters.
This study offers new possibilities for the aging assessment of ZnO surge arresters, though further validation under more complex conditions is required. Future research should focus on verifying whether the LM optimization algorithm maintains accuracy and whether the DC component remains a valid criterion under special grid conditions, such as voltage asymmetry and voltage fluctuations, and on extending experiments to varistors with different material formulations and manufacturing processes to confirm the universality of the conclusions.

Author Contributions

Conceptualization, Y.F. and L.Y.; methodology, W.M.; software, M.X.; validation, X.X., X.T., and Y.Y.; formal analysis, Y.F.; investigation, Y.F.; resources, W.M.; data curation, X.T.; writing—original draft preparation, Y.Y.; writing—review and editing, Z.L.; visualization, M.X.; supervision, X.X.; project administration, L.Y.; funding acquisition, Y.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Inner Mongolia Power (Group) Co., Ltd., grant number 2024-4-34 (Corporate Technology Project: Research on condition assessment and fault prediction techniques for surge arresters) and grant number 2024-4-30 (Corporate Technology Project: Collaborative research on toughening technology and crack detection methods for UHV transmission equipment porcelain housings).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

Author Yongqiang Fan, Wenkai Meng, Xiaoyun Tian, Yonggang Yue and Zhihui Li were employed by the Inner Mongolia Ultra-High Voltage Power Supply Company, Inner Mongolia Electric Power (Group) Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:
ZnOZinc oxide
MOSAMetal-oxide surge arrester
LMLevenberg–Marquardt

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Figure 1. Equivalent circuit model of zinc oxide varistor.
Figure 1. Equivalent circuit model of zinc oxide varistor.
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Figure 2. Impulse aging test platform: (a) photograph of impulse aging platform; (b) negative-polarity current and residual voltage waveforms.
Figure 2. Impulse aging test platform: (a) photograph of impulse aging platform; (b) negative-polarity current and residual voltage waveforms.
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Figure 3. Photograph of ZnO varistor sample: (a) Varistor samples No. 1–5; (b) Schematic diagram of current flow direction.
Figure 3. Photograph of ZnO varistor sample: (a) Varistor samples No. 1–5; (b) Schematic diagram of current flow direction.
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Figure 4. Variation trend of reference voltage during impulse aging: (a) forward side; (b) reverse side.
Figure 4. Variation trend of reference voltage during impulse aging: (a) forward side; (b) reverse side.
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Figure 5. Variation trend of DC leakage current during impulse aging: (a) forward side; (b) reverse side.
Figure 5. Variation trend of DC leakage current during impulse aging: (a) forward side; (b) reverse side.
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Figure 6. Variation trend of nonlinear coefficients during impulse aging: (a) forward side; (b) reverse side.
Figure 6. Variation trend of nonlinear coefficients during impulse aging: (a) forward side; (b) reverse side.
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Figure 7. Full current waveform of Varistor No. 3 under harmonic-containing 50 Hz voltage excitation.
Figure 7. Full current waveform of Varistor No. 3 under harmonic-containing 50 Hz voltage excitation.
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Figure 8. Resistive current component waveform in the full current of Varistor No. 3.
Figure 8. Resistive current component waveform in the full current of Varistor No. 3.
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Figure 9. Variation curve of harmonic amplitudes in varistor full current versus impulse count.
Figure 9. Variation curve of harmonic amplitudes in varistor full current versus impulse count.
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Figure 10. Variation curve of harmonic amplitudes in the resistive component of varistor full current versus impulse count.
Figure 10. Variation curve of harmonic amplitudes in the resistive component of varistor full current versus impulse count.
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Table 1. Harmonic components of power supply voltage.
Table 1. Harmonic components of power supply voltage.
Harmonic OrderFrequency (Hz)Amplitude (V)
Basic harmonic50182.6
Second harmonic10035.2
Third harmonic15024.7
Fifth harmonic25018.9
Seventh harmonic35012.1
Eleventh harmonic5508.4
Table 2. Normalized sensitivity factor of each harmonic component.
Table 2. Normalized sensitivity factor of each harmonic component.
Harmonic OrderFull Current NSFResistive Current NSF
Basic harmonic0.0089%0.025%
Second harmonic0.021%0.048%
Third harmonic0.025%0.056%
Fifth harmonic0.011%0.031%
Seventh harmonic0.015%0.022%
DC component0.072%0.64%
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MDPI and ACS Style

Fan, Y.; Meng, W.; Tian, X.; Yue, Y.; Li, Z.; Xu, M.; Xiao, X.; Yang, L. Study on the Unipolar Impulse Aging Characteristics of ZnO Varistors and Their Condition Monitoring Methods. Appl. Sci. 2025, 15, 9484. https://doi.org/10.3390/app15179484

AMA Style

Fan Y, Meng W, Tian X, Yue Y, Li Z, Xu M, Xiao X, Yang L. Study on the Unipolar Impulse Aging Characteristics of ZnO Varistors and Their Condition Monitoring Methods. Applied Sciences. 2025; 15(17):9484. https://doi.org/10.3390/app15179484

Chicago/Turabian Style

Fan, Yongqiang, Wenkai Meng, Xiaoyun Tian, Yonggang Yue, Zhihui Li, Minxin Xu, Xinyan Xiao, and Lanjun Yang. 2025. "Study on the Unipolar Impulse Aging Characteristics of ZnO Varistors and Their Condition Monitoring Methods" Applied Sciences 15, no. 17: 9484. https://doi.org/10.3390/app15179484

APA Style

Fan, Y., Meng, W., Tian, X., Yue, Y., Li, Z., Xu, M., Xiao, X., & Yang, L. (2025). Study on the Unipolar Impulse Aging Characteristics of ZnO Varistors and Their Condition Monitoring Methods. Applied Sciences, 15(17), 9484. https://doi.org/10.3390/app15179484

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