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Characterization of Cable PD Coupler Transfer Function
PD measurements are undertaken using a wide range of bandwidths, from kHz to
hundreds of MHz. In the case of shielded power cable, the useful bandwidth is limited
by the attenuation of the cable. The typical bandwidth remaining after 100 m of
propagation is ~20 MHz for a medium high voltage shielded power cable.
CHARACTERIZATION WITH PULSE MEASUREMENTS
If we assume that the PD coupler transfer function will be measured using a nearGaussian pulse, the Fourier transform of a Gaussian is a Gaussian. For a Gaussian
current pulse of standard deviation, (s), and peak current Io=Vo/Zc
for which the full width half maximum (FWHM) pulse width (s) is 2.36(s), the -6 dB
bandwidth (Hz) as a function of distance propagated is given by
where  is the cable attenuation in units of Neper-s/m based on the assumption,
which is usually a good approximation, that the cable attenuation constant is
proportional to frequency, i.e., (Nepers/m)(Nepers-s/m)s-1) [1]. Table 1 provides
typical values of  [2].
Table 1. Typical Attenuation Constants
Figure 1 shows the PD pulse bandwidth and PD pulse width as a function of distance
propagated for an attenuation constant of 5x10-11 Nepers-s/m (bottom scale) and
attenuation constant times distance propagated (top scale).
Figure 1. Pulse -6 dB bandwidth as a function of distance propagated for a Gaussian pulse with an initial pulse
width (FWHM) of 1.2 ns (=0.5 ns). At 0 distance, the bandwidth is about 370 MHz. However at 1000 m, the
bandwidth is in the range of 1 MHz for an attenuation constant of 5x10-11 Neper-s/m, well below the typical
detection bandwidth of field PD measurement systems of about 10 MHz. The exact pulse width, as determined
numerically, is shown along with an analytic approximation for the pulse width [1].
To characterize the transfer function of a PD coupler to an upper frequency limit fu,
the signal which reaches the coupler must have a known frequency spectral
distribution to that frequency, which is most easily achieved by having an input pulse
with a bandwidth appreciably greater than that required and sufficiently low
attenuation between the point of injection and the coupler to maintain the necessary
bandwidth to the location of the coupler based on typical cable attenuation.
The cable characteristic impedance is varies appreciably with frequency as a result of
variations in inductance (penetration of the magnetic field into the conductor) and
dielectric properties of the semicons [3]. As a result if a voltage pulse is injected into
the cable, the pulse current on the conductor will be “distorted” by frequency
dependent variations in the characteristic impedance. On the other hand if a current
pulse is injected into the cable, the voltage on the conductor will be “distorted” by
frequency-dependent variations in the cable characteristic impedance. This suggests
that the selection of a current pulse or voltage pulse should depend on whether the PD
coupler is sensitive to current or voltage.
CHARACTERIZATION OF USING A CONTINUOUS SIGNAL
The transfer function of a PD coupler could be measured using a swept sine wave,
although this requires clean injection of the signal (as for the pulse) and termination of
the cable in its characteristic impedance at the other end, which is not necessary for
the pulse based on the assumption that the cable is sufficiently long that the reflection
from the “far end” does not overlap with the injected pulse of interest. As noted above,
the cable impedance is a function of frequency which makes a good termination nearly
impossible and some degree of standing waves inevitable [3]. The effect of such
standing waves on the accuracy of pulse calibration should be evaluated.
REFERENCES
1. Oussalah, N., Y. Zebboudj, and S.A. Boggs. “PD Pulse Propagation in Shielded Power Cable for
Symmetric and Asymmetric PD Pulses”. IEEE Trans DEI. Vol. 14, No. 5, October 2007. pp. 12641270.
2. Oussalah, N., Y. Zebboudj, and S.A. Boggs. “PD Pulse Propagation in Shielded Power Cable and
Implications for Detection Sensitivity”. IEEE Electrical Insulation Magazine, Vol. 23, No. 6,
Nov/Dec 2007. pp. 5-10.
3. Shu, Essay Wen, and Steven A. Boggs. “Dispersion and PD Detection in Shielded Power Cable”.
IEEE Electrical Insulation Magazine. Vol. 24, No. 1, Jan/Feb 2008. pp. 25-29.