Modeling dispersion of partial discharges due to propagation velocity variation in power cables

Effects of Dispersion and Multi-Path Propagation in Partial Discharges Location

“…The transfer function H(ω, L), shown in (1), was proposed in [23] to model the propagation of PDs in medium voltage cables. In (1), α 0 and β(ω) are the real and the imaginary parts, respectively, of the propagation constant.…”

“…In [23], the authors proposed a second order polynomial to model β(ω), to account for the fact that each frequency component travels at a different propagation velocity. β 1 and β 2 are the delay and the dispersion constants, respectively.…”

“…PD pulses, extremely short at their origin, spread in time duration due to dispersion. Assuming that the PD is modeled as a gaussian pulse with initial deviation σ 0 , the resulting pulse deviation σ L after L meters of propagation is shown in (9) [23]. Using the relationship between the time domain deviation (σ) of a gaussian pulse and its bandwidth (B) shown in (10), we derive (11), that shows the bandwidth reduction of a PD pulse because of dispersion.…”

“…Dispersion also produces small variations in the propagation velocity. For example: for β 1 = 5.7 ns/m and β 2 = −0.7 ns 2 m −1 (typical values for a XLPE cable [23]), the group velocity is v p = β…”

“…Although dispersion can be modeled using a classical transmission line approach [21], [22], those models based on transfer function are preferable because no knowledge about the cable geometry or material specification is needed [12], [23]. In this paper we use the model proposed in [23], where propagation is modeled by one single parameter, the dispersion constant, which is easy to measure with a vector network analyzer.…”