A Dual Interface Analytical Model for Time-Domain Reflectometry of Water Tree Defects in Power Cables
Ye Yuan1,2, Hu Xiao2,2,4
1. State Grid Sanming Power Supply Company Sanming 365000 China; 2. Electrical Engineering College Guizhou University Guiyang 550025 China; 3. College of Electrical Engineering Zhejiang University Hangzhou 310027 China; 4. Zhejiang Horizon Instrument Transformer Co. Ltd Jiangshan 324100 China
Abstract Due to the poor operating environment, medium voltage cables in distribution networks are prone to water tree aging under the combined effect of moisture and voltage, which can degrade the insulation performance. The time-domain reflectometry (TDR) method can be used to detect cable faults, and some recent studies have used it to detect the aging of the local insulation of cables. However, the relationship between the detection results and the aging condition of the insulation is not clear. To address this problem, an equivalent permittivity for the coaxial insulation with water tree defects is derived. Moreover, a time-domain analytical model considering the reflection of dual interfaces is developed to analyze and predict the results of TDR experiments on cables with local water tree defects. First, the equivalent permittivity of the coaxial insulation with water trees was derived based on circuit theory, and the effectiveness of using the equivalent permittivity to characterize the reflection characteristics of water tree defects in cable insulation was verified through finite element simulation. Then, a time-domain dual-interface reflection model considering the interfaces at both ends of the defect was established based on transmission line theory and the equivalent permittivity. This model was used to analyze the relationship between the reflection of water tree defects and the condition of water treeing as well as the characteristics of the input signal (such as amplitude and waveform). Finally, by making cable samples with mimic water tree defects and conducting TDR tests, the effects of factors such as water content, length, and conductivity of the defects on TDR test results were investigated. The results showed that the TDR test results of the mimic water tree defects agreed well with the calculated results of the proposed analytical model, preliminarily validating the effectiveness of the proposed model for analyzing and predicting the reflection characteristics of local water tree defects in cable insulation. The following conclusions can be drawn from this study: (1) The equivalent permittivity can characterize the wave reflection characteristics of local defects in cable insulation. The proposed analytical model considering multiple reflections at both ends of the defect can more accurately predict the reflected waveform generated by local insulation defects. (2) The TDR experiments on the mimic water tree defects showed that the reflection magnitude and waveform were closely related to the water content (quantity of the mimic water trees) and length of the defective section. For example, in this experiment, adding 5 small holes to the defective section increased the amplitude of the reflected wave to 2.6 times the original value, while doubling the length of the defective section increased the amplitude of the reflected wave to 1.6 times the original value. This preliminary result indicates that TDR measurements can provide a basis for assessing the extent and range of similar insulation defects (such as localized moisture and water treeing). The analytical model established in this study helps to link the water treeing condition of cable insulation with TDR test results, and it is expected to provide a reference for the application of TDR testing in detecting water treeing in cable insulation.
Ye Yuan,Hu Xiao. A Dual Interface Analytical Model for Time-Domain Reflectometry of Water Tree Defects in Power Cables[J]. Transactions of China Electrotechnical Society, 2024, 39(1): 55-64.
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2024, Vol. 39 
