Newton-Raphson method to determine the intrinsic permittivity of XLPE cable

To identify the location of partial discharge occurring in a XLPE-based power cable, it is essential to obtain the intrinsic values of permittivity of the cross-linked polyethylene (XLPE) material and semiconducting layers. In this paper, a sample is constructed from a segment of XLPE-based power cable. Two capacitors with different configurations of two electrodes are constructed from the sample. Mathematical models are built for each of the two capacitors. Based on the two models, four parameters including the real and imaginary parts of intrinsic complex permittivity of XLPE and semiconducting materials are iteratively derived from the measured results by Newton-Raphson method. It is found that the measured or apparent values of permittivity are different from their intrinsic values. The difference is due to fringing and dimensional effects in the test setup. This shows that the proposed Newton-Raphson based method has to be implemented when determining the intrinsic permittivity of XLPE and semiconducting materials.