Dimensional Effects on the Measurement of Permittivity of Semiconducting Materials Used in High Voltage XLPE Cables

The intrinsic permittivity, not apparent permittivity, of semiconducting layers of high voltage cross-linked polyethylene (XLPE) cables imposes a significant influence on the design of partial discharge detecting sensors. It has extremely high permittivity, resulting in a dimensional effect, an embodiment of the difference between the intrinsic permittivity and apparent or measurable permittivity. To investigate this dimensional effect in semiconducting material, a mathematical model is set up in this paper for a capacitor with two rectangular-shaped electrodes in parallel, between which is inserted a semi-conducting sample. First, the expression of the electric field in the semiconducting material is worked out theoretically. Then, the measurable or apparent complex permittivity is expressed as a function of intrinsic permittivity, dimensions of the sample and frequency. Next, five blocks with different dimensions are introduced to study the dimensional effect. The numerical analysis demonstrates that above 10 MHz, samples with different dimensions result in different apparent permittivity or measurable permittivity if experiments are carried out for the samples with the assumed dimensions. This implies that dimensional effects should be considered when accurate intrinsic permittivity of the semiconducting materials is needed.