Improvement of FDR Methods for Identifying Defects of Jointed HV Cable

This paper considers frequency domain reflectometry (FDR) as an effective way to locate high voltage (HV) cable defects. The formula relating FDR to cable local equivalents impedance value is presented, and critical methods such as window function, frequency step, and bandwidth to process FDR data before Inverse fast fourier transform (IFFT) are also demonstrated. Finally, a multi-periods reflection analysis from the IFFT curve is introduced with illustrations from fields measurement to improve the identification of defects for cables with multiple joints.


Principle of FDR
FDR can be considered one type of wide band frequency measurement of cable impedance or reflection coefficients based on which to derive time domain property for analyzing cable impedance noncontinuity along the cable length .

Types of data
There is more than one type of data that could be employed.Reflective coefficient S 11 and wideband impedance Z(ω) are two typical adopted types of data.As S 11 and input impedance Zin() can be transformable with each other, they can also be seen as the same type of data source.
Cable is equivalent to the integration of sectional serial value (Resistance-R, Inductance-L) and parallel value (Conductance-G, Capacitance-C), which is related to geometry and dielectrics such as deformation, loss, void, and water tree.Also from [1,2], they link with the propagation constant at Equation ( 2) and Characteristic impedance from Equation (3).
From Equations ( 4) and ( 5), it can be seen that measured values  and  are well-combined unit impedance values.
As  is commonly measured by vector network analyzer (VNA), it has an advantage at high frequency but suffers from loss of low-frequency data.
From Equation (4), it can be seen that if the cable under test is open-circuited (OP) or short-circuited (SC), Equation (4) becomes: tanh  6    tanh  .7 Unit input impedance is a complex value and is supposed to be continuous along axial length when there is no defect.If some defects exist, it is evident that local unit impedance will change and break the continuity, then total input impedance at both time domain reflection and frequency domain will change accordingly.Latent flaws of insulation show small differences of impedance at earlier periods, and when it is developing to become faults, it exemplifies bigger differences.

Inverse of FDR
A time domain characteristic is derived by inverse fast fourier transform (IFFT) of  or  .With the transformation from the time axis to the distance axis, the uniformity of impedance along cable axial length is analyzed based on IFFT plots.
Typical  and its IFFT plots of lossy cable lines are shown in Figure 1.
As can be seen through IFFT plots from Figure 2, the magnitude and position of cable end terminals and Joints are clearly embodied, and features between different positioned peaks are easy to be contrasted.

Property of FDR and its analytic methods
When performing FDR measurement, it is critical to set some parameters: bandwidth (BW), frequency step (FSTP), and points of sweep (PSWP).
How to select well-suitable BW and FSTP can be a bit tricky as some unknown parameters such as length, size, shape, and loss all influence the outputs.

Resonance periods of impedance and relation to the length
The impedance of the cable is a resonance within the frequency domain [21], so when selecting FSTP, it should guarantee minimum representment of periodic characteristics of resonance.

L 𝑉𝐹 2 * 𝑅𝑃𝐸 8
where RPE stands for resonance periods in the frequency domain, and VF stands for the propagation velocity of electromagnetic wave transmission along the cable. ∆   9 where  and  are neighbor resonance frequencies.From Equation ( 8), the length of the cable can be obtained by sweeping the impedance measurement for at least one full resonance period.According to the Nyquist theorem, at least two sweep frequency points are required within one resonance period to recover the spectral wave and obtain the length of the cable.To guarantee good accuracy, three or more resonance periods (RPE) are suggested.

BW and Sweep points within resonance periods for fault location
Longer cable correlates with more narrow bandwidth.More sweeping points are suggested if multiple faults or defects exist.Resolution for analyzing faults or latent defects with locations can be seen from Equation (10) [23].

Resolution m 𝑉𝐹 2 𝐵𝑊 10
Range m Resoluton NF 11 where NF stands for points of IFFT.As VF is also nonlinear with the dielectric material and aging evolvement condition, normally VF is chosen by averaged estimation or based on the calibrated result from the test sample.
If standard length is well known at referenced humidity and temperature environment, VF can be adjusted to fit the computation which results in equal length.The final obtained VF could be employed for estimating dielectric aging.

IFFT and windowing
When performing IFFT, windowing is a good approach to reduce frequency leakage and help enhance IFFT outputs.The most frequently adopted windowing function are Hanning, True Blacks, and Black-Harries.By comparing (a) to (f), the Black-Harries window is commonly preferred as it contains a better signature to noise than others.But if the cable has more defects with the short length, it is advisable to employ more window functions and make contrasts.

Faults distinguishing with multiple joints
When completing frequency domain measurement and obtaining magnitude to distance curve, the most crucial step is to diagnose the curve and identify defects from lots of peaks.Chances are that there are quite a lot of HV cables with joints that are typical non-uniform impedance and exist as significant signatures on the distance position.Common methods of analyzing defects on the distance curve are seeking the cooperation of adjusting bandwidth and windowing methods are illustrated below.
As can be seen from Figure 3 and Figure 4, it is evident that both bandwidth and windowing functions play an important role in the clearance of hiding signatures on the time domain curve.Also for a certain bandwidth, a good selection of step frequency helps improve the resolution of joints.
Figure 4 IFFT plots with different bandwidth (BW)

Comparison of signatures for the same type of joints
It is easy to compare signatures in both magnitude and distance span on the time domain curve if we know the objective joints are fabricated under the same conditions, such as: 1) Same length of joints: This means joints are made with the same materials, size, and art craft.The difference in local impedance between those joints can be neglected.
2) Same life span: joints are made at the same time, so operating or outage is at the same periods.
3) Same load condition: joints have the same load current.It is necessary to be cautious for cables with by-pass circuits which have different distributed load currents, or even at the same load-loop threephase, cables also possibly have quite significantly different temperatures for unbalanced loads.
It is reasonable to judge that the joints feature a small difference of signature magnitude on the distance axis if the above three conditions are satisfied, and when defects exist at some sections, significant differences can be apparent from peak-to-peak comparisons.

Identifying abnormal peaks for different joints
It is easy to capture abnormal peaks on joints or non-joint locations on the distance curve.When joints are fabricated or repaired at different times or with different art craft, the impedance at the joints may have different complex parameters which contribute to the increment in the magnitude of peaks.
A field test for a multi-joint and Aluminium-Copper combined 970 m long XLPE cable with the same bandwidth of 2.8 MHz and different step frequencies of 3 kHz (pin line), and 5 kHz (red line) is shown in Figure 5.
It is evident that the red curve with 5 kHz step frequency shows more suspective peaks.Identified parameters of the jointed cable are shown in Table 1.

Improvements
Plots of Inversed FDR data as defects concealing on distance curves may show repeated reflections for several periods if the correct bandwidth and frequency step is chosen.Commonly we only analyze timespanned curves within a one-time length of cable.But if some suspected peaks show only small differences, it is difficult to determine upcoming defects without more references.From some experience, neighbor defects may exist at short repaired sections, but on the distance curve, it may only show one peak.
A possible way to see from more than one period of reflection help identify the problem.As shown in Figure 6, the reflections show three significant peaks which are triple times as long as a 700 m cable.Suspected Peaks within the 2 nd and 3 rd periods exemplify one more peak which in the first periods at the same locations contains only one peak.The faults at a distance of about 310 m are finally approved in the fields.From experiments, suitable bandwidth should be chosen to obtain good signal-to-noise and clear reflection peaks in multiple time-length periods.BW<1 M >10 It should be known that optimal bandwidth for a successful test is affected by both length and lossy condition, more attention should be paid to adjust sweep points or bandwidth to help seek defects.When the cable under test has multiple joints, it is expected to have a narrower bandwidth.Also, it is suggested that historic measurement be employed as a reference for tracking defects growth such as local aging or moisture which are expected to be evolved with the operation.Attention also needs to be paid to adopting the same BW, sweep points, or frequency step size when employing references.

Conclusion
FDR has theoretically related to unit equivalent impedance value and is considered effective for HV cable fault and defects locations.Extra attention should be paid to processing captured data and employing techniques to optimize the identification of defects or faults with jointed cables.Bandwidth, frequency steps, and window function play an important role when performing Defects analysis.It is interesting to compare defect peaks from multiple period reflections from the IFFT curve.As defects may evolve with time, comparison with the reference curve is also encouraged for tracking the development of defects.

Table 1 :
Joints parameters of 970 m XLPE cable UNDER TEST SuggestionsSuggested data for HV cable measurement and identification of FDR are presented in TableII.TABLE II: SUGGESTIONS FOR FDR MEASUREMENTS AND ANALYSIS