This paper has the purpose to derive an analytical model ("continuum" model) able to describe the behavior of partial discharge (PD) repetition rate and amplitude, occurring in a cavity embedded in polymeric insulation, as a function of the frequency of the supply voltage, going from AC power supply frequency, 50–60 Hz, to DC. In the range between DC and 50–60 Hz focus is made on data coming from tests under AC sinewave with very low frequency (VLF) such as 0.1 Hz and 0.01 Hz, which are commonly used for cable testing. It is shown that the proposed "continuum" model can provide reasonably good fit to the experimental results obtained in the range DC to 60 Hz, regarding PD repetition rate and amplitude. To reach such result, the equivalent circuit is modified from that commonly used and made by fully-capacitive or resistive components, in order to take into account the change of polarization mechanisms which, depending on dielectric material, may play a non-negligible role to establish the repetition rate from low frequency to DC power supply. In addition, the residual voltage after a PD event has to vary with frequency to reach good fitting. Also, it is shown that PD amplitude under DC and VLF can be lower than under AC 50–60 Hz due to the delay time of the firing electron, thus experimental PD amplitude varies with frequency depending on material and defect typology and location.

中文翻译：

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室温下电源电压频率对局部放电重复率和从交流到直流的充电幅度的影响建模

本文旨在推导出一个分析模型（“连续体”模型），该模型能够描述局部放电 (PD) 重复率和振幅的行为，发生在嵌入聚合物绝缘材料的空腔中，作为电源频率的函数电压，从交流电源频率 50–60 Hz 到直流。在 DC 和 50–60 Hz 之间的范围内，重点关注来自具有极低频 (VLF)（例如 0.1 Hz 和 0.01 Hz）的 AC 正弦波下测试的数据，这些频率通常用于电缆测试。结果表明，在 PD 重复率和幅度方面，所提出的“连续体”模型可以为在 DC 到 60 Hz 范围内获得的实验结果提供相当好的拟合。要达到这样的结果，等效电路是从常用的电路修改而来的，由全电容或电阻元件制成，以考虑极化机制的变化，这取决于介电材料，可能起到不可忽略的作用，以建立重复率低频转直流电源。此外，局部放电事件后的残余电压必须随频率变化才能达到良好的拟合。此外，由于发射电子的延迟时间，DC 和 VLF 下的 PD 幅度可能低于 AC 50-60 Hz，因此实验 PD 幅度随频率而变化，具体取决于材料和缺陷类型和位置。可能对建立从低频到直流电源的重复率起到不可忽视的作用。此外，局部放电事件后的残余电压必须随频率变化才能达到良好的拟合。此外，由于发射电子的延迟时间，DC 和 VLF 下的 PD 幅度可能低于 AC 50-60 Hz，因此实验 PD 幅度随频率而变化，具体取决于材料和缺陷类型和位置。可能对建立从低频到直流电源的重复率起到不可忽视的作用。此外，局部放电事件后的残余电压必须随频率变化才能达到良好的拟合。此外，由于发射电子的延迟时间，DC 和 VLF 下的 PD 幅度可能低于 AC 50-60 Hz，因此实验 PD 幅度随频率而变化，具体取决于材料和缺陷类型和位置。