Void discharge behaviours as a function of cavity size and voltage waveform under very low-frequency excitation

Measurement of partial discharge (PD) is a vital method to assess the health of the electrical insulation in highvoltage power equipment. As diagnostic testing at very low frequency (VLF) is increasingly being used, it is important to investigate PD behaviours under such a low-frequency voltage excitation. This study presents the PD characteristics at VLF excitation under different applied voltage waveforms, including sinusoidal and trapezoid-based waves. Also, the effects of cavity size on PD behaviours at VLF are investigated. Experiments were performed to measure PDs in a cylindrical void bounded by solid insulation. The results show that discharge activities at VLF, in general, exhibit lower magnitude and repetition rate when compared with power frequency. Also revealed is the strong dependency of discharge parameters on the rate of voltage rise. Physical mechanisms to explain discharge behaviours are given.


Introduction
Diagnostic tests play an essential role in examining the health of high-voltage power equipment, in particular for those which have been in service for a considerable period of time.Their insulation materials are gradually degraded over time as they are continuously suffered from a combination of electrical, thermal, mechanical, and environmental stresses.During this degradation process, insulation materials are subjected to long-term exposure of internal partial discharge (PD) activities which are commonly considered as the main cause of deterioration.
PD diagnostic tests are usually performed at normal operating voltage level and power frequency (50/60 Hz).PD measurement data are commonly analysed by the phase-resolved partial discharge analysis method [1,2].The same approach can also be used when testing with applied AC voltage at any other frequencies [3,4].In particular, PD testing at very low frequency (VLF), generally at 0.1 Hz, is commonly employed.It does not require much reactive power to energise the test object to the required high voltage.Thus, the test supply is small, compact, and convenient for field testing of high capacitance items such as high-voltage cables.
PD behaviours in cavities bounded by solid insulation under various applied frequency excitation have been studied extensively [5][6][7][8][9].It has been shown that discharge characteristics are strongly dependent on the applied frequency in different ways.According to [7,8], PD magnitudes exhibit larger values at low applied frequency, while in [9], PD measured data showed that the discharge level is similar or lower at 0.1 Hz when compared with 50 Hz.
Moreover, change in PD characteristics with ageing has also been analysed under different waveforms [10][11][12][13].Kim et al. [10] studied the degradation of low-density polyethylene material in an encapsulated cavity at different times during an endurance test.Experimental results showed that variation of discharge characteristics might be explained by change of the gases within the cavity and degradation of the cavity surface with time.Wu et al. [11] also investigated PD characteristics in a cavity within polyethylene (PE) with time under sinusoidal and square voltage waveforms at power frequency.It was reported that transitions of PD activities might be due to physical conditions of the void such as discharge area, surface conductivity, and bulk conductivity of the material.Also, byproducts produced from electrical discharges might contribute to change of the local electrical field distribution which affects PD characteristics.Niasar et al. [12] presented a comparative study of PD behaviours within a cavity in new and thermally aged oil-impregnated papers and showed that no significant difference was observed.Changes of PD activities were mainly due to variations of physical parameters and gas composition within a void.However, these researches are mainly performed at power frequency.There is limited knowledge of PD behaviours within a cavity under VLF excitation at different applied voltage waveforms.Krotov and Cavallini [14] performed PD investigations under cosine-rectangular waveform at VLF but did not specify the rate of voltage rise and presented results only for cosine-rectangular and sinusoidal waveforms.
In this paper, PD behaviours in a cylindrical cavity bounded by solid insulation under applied voltage at a VLF of 0.1 Hz and power frequency (50 Hz) are studied.The investigation includes consideration of the effects of different cavity size and voltage waveforms such as sine wave and trapezoid-based waves.The reason of choosing trapezoid-based waveforms in this research is to improve the distinction of PD characteristics under square-like voltage waveforms at VLF and power frequency via several defining features of the waveforms, i.e. the linearly changing period of voltage, its rate of voltage change, and the period of constant voltage.

Test samples
The test objects are small blocks of solid dielectric materials with a cylindrical void to produce internal discharges.These test objects were precisely fabricated by employing a three-dimensional (3D) printer to achieve the desired geometry and dimensions.The test objects were designed using a 3D layout software tool which is capable of exporting compatible files for printing software.The printing process of designed objects was then executed in the 3D printer (UP Plus 2) which allows building of test objects with very thin layers of 0.15 mm.The material used is acrylonitrile butadiene styrene which is a common thermoplastic polymer.The schematic diagram is shown in Fig. 1.A void with a height of 1 mm is designed to be at the centre of a disc-shape block with thickness of 3 mm and diameter of 50 mm.The diameter of the void is varied and tabulated in Table  transformer oil-filled chamber to prevent unwanted surface discharges during testing.

PD measurement system
A time-resolved PD measurement system fully compliant to IEC 60270 Standard [15] was employed to record in real-time individual discharge events.The circuit set-up is shown in Fig. 2. High-voltage waveforms were produced by a function generator (Agilent 33500B Series) and then amplified by a high-voltage power amplifier (Trek 20/20C-HS).This amplifier is capable to amplify large signal bandwidth up to 5.2 kHz with <1% distortion.The coupling capacitor of 1.1 nF was connected to a commercial PD detection system (Mtronix MPD600) to record discharge activities.

Voltage waveforms
Different testing voltage waveforms such as sinusoidal and trapezoid-based shapes were used in this research.The parameters for characterisation of trapezoid-based waveform are shown in Fig. 3.A symmetric trapezoidal wave with equal linear rising and falling edge period is shown in trace (b), i.e. t 1 = t 3 .Trace (a) is a symmetric triangular wave which can be considered as a special case of a symmetric trapezoid-based waveform when t 2 = 0.

Effects of cavity size
This section presents experimental results on effects of the cavity size on PD characteristics at VLF and power frequency.PD behaviours in insulated disc-shaped cavity with diameter of 2, 4, 6, and 8 mm, respectively, were recorded at applied voltage level of 10 kV.
The maximum and average discharge magnitudes are depicted in Fig. 4. As can be seen in Fig. 4, the maximum discharge gradually increases when the cavity size is larger at both frequencies.This may be due to the availability of free charges generated in the void.With increased void size, the cavity surface which is perpendicular to the electric field is larger, thus it can emit more free charges under the effect of applied voltage.Therefore, PD inception level is decreased when the void size is increased.Consequently, under the same applied voltage, PDs in larger voids are ignited at higher overvoltage ratio compared to inception voltage, which results in larger discharge magnitudes.Note that the cavity depth is unchanged.Therefore, to a certain extent, the relative field distribution between the void and the solid insulation above and below it is not affected and so is the inception voltage.The simulation of electric field distribution in test samples at the positive voltage peak, i.e. at the time of 5 ms, is shown in Fig. 5. Simulation results show that the field distribution in test samples with various void sizes is almost identical along the symmetrical axis parallel to the electric field, i.e. z-axis.
It is interesting to observe that the average discharge magnitude at VLF increases with the void size, while it is slightly reduced when the void diameter is >4 mm as in Fig. 4b.A possible explanation is the effect of surface charges on PD activities.At VLF, more space charges generated after a PD are likely to decay as the time span between two consecutive discharges are considerably large, i.e. in orders of hundreds of milliseconds.Hence, it reduces electron generation rate igniting the following discharge.As a result, the next PD has a higher probability to be incepted at voltage level higher than the inception value which gives larger discharge magnitudes.
There will always be field distortion around the cavity edges.The field in the cavity can only approach uniform when its diameter is significantly larger compared to the height.Owing to the comparable size between the depth and diameter of the cavity, the field in the cavity is not uniform, particularly for sample 1.As the diameter is increased, the cavity field distribution will become   more uniform and so less variation in the field distribution.This may be the reason why the result for sample 1 in Fig. 4b does not follow the same trend as seen with the other samples.
On the other hand, the statistical time lag at 50 Hz is much lower than at VLF, so free charges generated after a discharge are less likely to decay.Therefore, when the local electric field recovers and exceeds the critical inception value, the large electron generation rate available presents a favourable situation for discharges to be incepted.
According to measurements, lots of discharges with low magnitudes were recorded, which implies discharges are incepted when the critical inception value is exceeded as available electrons are plentiful in this moment.As the void size is increased, the discharge area is enlarged and thus the accumulated charge distribution may not be uniform over the whole surface area.Thus, there could be several charge concentration points on the cavity surface which enables multiple discharges to be ignited simultaneously.This also explained the increase in PD repetition rate when the cavity diameter is larger.

Effects of applied voltage waveforms
In this section, test sample 1 with a void diameter of 2 mm was used to investigate PD behaviours under different applied voltage waveforms.Note that the voltage level is stated in rms value for sinusoidal waveform but in peak value for other waveforms.

PD behaviours under sinusoidal waveform:
The test sample was subjected to traditional sinusoidal waveform at frequencies of 0.1 and 50 Hz and applied voltage over the range from 8 to 10 kVrms.Discharge characteristics as a function of applied voltage at both frequencies are depicted in Fig. 6.For both VLF and power frequency, discharge behaviours are clearly dependent on applied voltage levels.As voltage level is increased, maximum discharges rise from 393 to 480 and 488 to 742 pC for 0.1 and 50 Hz, respectively.Also for both frequencies, the PD occurrence rate is progressively intensified at higher voltage levels.On the contrary, average discharges at power frequency and VLF show opposite tendency when the voltage level is increased.At 50 Hz, the average PD magnitude gradually decreases, i.e. 303-155 pC, while it steadily increases at frequency of 0.1 Hz, i.e. 75-121 pC.The former is caused by an intensified number of low magnitude discharge activities at higher voltage level at power frequency.

PD patterns under symmetric triangle waveform:
In this section, the symmetric triangular voltage waveform was used to stress the test object at frequency of 0.1 and 50 Hz [16].As expected, PD activities happened evenly in both half voltage cycles.Therefore, for the sake of analysis and discussion, only the PD characteristics in the positive half-cycle are summarised in Table 2.It can be seen from this table that discharge behaviours are strongly dependent on the applied voltage under both VLF and power frequency.Discharge magnitudes and repetition rate at both frequencies are larger at higher applied voltage.PD characteristics at 0.1 and 50 Hz are fairly similar at voltage level of 12 and 10 kV, respectively.The scatter plots of the PD phase-resolved patterns under these conditions are quite similar as shown in Fig. 7.The rate of rise of voltage, however, is greatly different between these frequencies, hence causing significant dissimilarity of PD magnitudes at same voltage level.Under excitation of power frequency, the discharge repetition rate gradually increased from 8.4 pulses per cycle (ppc) to 8.8 ppc when the applied voltage is raised from 9 to 10 kV.On the contrary, under VLF excitation, discharges were hardly observed at voltage level <11 kV.Under such a low-frequency excitation, discharge magnitudes and occurrence rate increased considerably when the voltage is raised from 11 to 12 kV.

PD patterns under trapezoidal-based voltage waveform:
In this section, symmetric trapezoid-based waveforms with different linear ramping rates of voltage rise were used at VLF and power frequency [16].For comparison purposes, it is desirable to quantify the fraction of voltage varying duration (i.e.t 1 or t 3 ) with respect to one half voltage period.This parameter can be expressed as:   Two values of α (10 and 20%) were selected in this research to investigate effects of the rising rate of trapezoidal voltage on PD characteristics at VLF and power frequency.As anticipated, the PD patterns are fairly symmetrical in both half-cycles of voltage waveform as shown in Figs. 8 and 9. Hence, only the positive halfcycle PD parameters are tabulated in Table 3.This table provides comparison between 50 and 0.1 Hz and at different voltage levels.Interestingly, most of PD activities occur during the voltage changing period at both applied frequencies.From Table 3, it can be seen that PD parameters are strongly dependent on the rise rate of voltage, i.e. α.At both excitation frequencies, discharge magnitudes are higher at smaller value of α, that is shorter time of voltage changing period t 1 .
Under excitation of 50 Hz frequency, larger discharge magnitudes were obtained for shorter time of voltage changing period t 1 .For the case of α of 10%, the maximum discharge magnitudes were 167 and 2074 pC at applied voltage of 9 and 10 kV, correspondingly, while the average discharge magnitude was 81 pC at 9 kV and 1719 pC at 10 kV.At α of 20%, a reduction in discharge magnitudes was observed.The average discharge magnitudes were 61 and 885 pC at applied voltage of 9 and 10 kV, respectively, while the maximum discharge magnitude was 84 pC at 9 kV and 1699 pC at 10 kV.
At VLF of 0.1 Hz, PDs were barely detected at voltage level <11 kV regardless of voltage changing period t 1 .A similar dependent tendency, i.e. shorter time of t 1 causes larger discharge magnitudes, was also experienced at applied voltage >11 kV.For the faster voltage rise rate, i.e. α of 10%, maximum discharges steadily increase from 1493 pC at 11 kV to 1766 pC at 13 kV while the average discharge magnitudes gradually rise from 665 pC at 11 kV to 706 pC at 13 kV.With longer rise time t 1 , i.e. α of 20%, the maximum discharges rise from 1014 to 1504 pC, and the average discharges increase from 469 to 636 pC when the applied voltage was increased from 11 to 13 kV.Measurement data indicate that PD behaviours are strongly dependent on the ramping rate of voltage dU/dt rather than the applied voltage level.In fact, for the same factor α, the rise time of voltage at VLF is much longer than that at power frequency.For instance, with α = 10%, the rise time t 1 is 1 ms at 50 Hz but increases dramatically to 500 ms at 0.1 Hz.As a consequence, an applied voltage of 10 kV at power frequency could induce larger discharges and higher occurrence rate than under a higher applied voltage of 13 kV at VLF due to the much shorter rise time dU/dt at 50 Hz.
To investigate further the influence of voltage rise time on PD activities, a customised 0.1 Hz trapezoidal waveform with comparable rise time to 50 Hz was used.The rise time t 1 of these voltage waveforms is 1 ms (α = 10%) and 2 ms (α = 20%), while the peak voltage period t 2 is 4998 and 4996 ms, respectively.The PD phase-resolved patterns under these particular waveforms at 10 kV are shown in Fig. 10.Discharge characteristics obtained for positive voltage polarity at applied voltage of 10 kV are summarised in Table 4. From Tables 3 and 4 at frequency of 0.1 Hz, it can be seen that voltage waveforms with a shorter rise time can trigger more discharges per cycle and larger discharge magnitudes even at lower applied voltage.Moreover, discharge magnitudes at 0.1 Hz are smaller than those at 50 Hz at the same voltage level of 10 kV when both trapezoid-based voltage waveforms have the same voltage rise time t 1 .With t 1 = 1 ms for instance, maximum and average discharge magnitudes are 1388 and 218 pC, respectively, at 0.1 Hz, while they are 2074 and 1719 pC at 50 Hz, correspondingly.These differences can be explained by the effects of surface charge decay which are described in the following section.
An approximately square voltage waveform was obtained by increasing the constant voltage duration t 2 to T/2 at frequency of 0.1 and 50 Hz [17].Owing to the high-voltage amplifier limitation, the square voltage rise time was measured at 112 μs.As expected, discharges mostly occur at the voltage polarity transition at both frequencies as shown in Fig. 11.Discharge magnitudes, however, are greatly different between the two frequencies.At power frequency, discharge magnitudes are significantly larger than those at VLF by a factor of about five times.As can be seen from the PD patterns, discharge activities tend to intensify at large magnitudes at 50 Hz, whereas at 0.1 Hz, almost all discharge activities are incepted with low magnitudes.This significant difference may be attributed to the duration of constant voltage in the waveform at each frequency.The longer period of the peak applied voltage exhibits a decrease in discharge magnitudes.

Discussion
Measurement results in Section 3 generally indicate that discharge magnitudes at power frequency are larger than those at VLF.Furthermore, the applied frequency also affects the PD occurrence rate in such a way that there are more discharges per cycle at higher applied frequency.These dissimilarities of PD characteristics could be attributed to the charge decay time constant τ decay [7,9,18].If τ decay is smaller than the duration of applied voltage period, i.e. τ decay < 1/ f , it may be assumed that most of free charges have already decayed and thus surface deposited charges are not contributing much in the PD process.On the other hand, if the decay time is longer than the voltage period, i.e. τ decay > 1/ f , charges are not decayed and will exert a significant contribution to the total field in the cavity.In this circumstance, discharge magnitudes are strongly dependent on the applied frequency as evident in Section 3.2.1.At frequency of 50 Hz, free charges are not decayed between two consecutive discharges and hence PD would be incepted at the instant when the local field exceeds the critical value.Consequently, more discharges with low magnitudes are produced at higher applied voltage.It is assumed that the underlying discharge mechanism is based on 'streamer discharge' type.Free charges generated after a discharge are eventually deposited on the cavity surfaces due to the external applied electric field.The presence of accumulated surface charges creates a residual electric field which significantly enhances the local electric field in the cavity [7].However, the accumulated charges will decay over time via several mechanisms such as surface conduction, recombination, and diffusion into deeper traps in the cavity surface [7,19].This surface charge decay reduces the effect of residual field generated by accumulated charges on the cavity electric field.
The effect of charge decay under trapezoid-based applied waveform is illustrated in Fig. 12.Here, it is assumed that residual electric field does not exist initially; the cavity field, i.e.E cav (blue straight line), is equivalent to the external field associated with the applied voltage, E 0 (black dashed line).A discharge will be incepted when E cav is larger than the inception value, E inc , and a starting electron is available.During the discharge process, the cavity field is dropping rapidly and stops at the residual value E res lower than the extinction value, E ext , which determines PD ceased condition.Free charges released after a PD process deposit on the cavity surface and then produce an electric field, E q , which is in the opposite to the external field E 0 .If the constant voltage period is shorter than the decay constant τ decay (e.g. in the case of 50 Hz), E q is fairly stable as charges are not decayed.This phenomenon under square voltage was also discussed in previous research [20].When E 0 reverses its polarity, E 0 and E q have the same direction and thus, the total cavity field is enhanced significantly as seen in Fig. 12a.Therefore, the following PD would be incepted at a higher electric field and thus result in a larger discharge magnitude.On the contrary, free charges do not contribute much in the enhancement of cavity electric field at 0.1 Hz as charge decay is significant due to relatively long period of constant peak voltage as in Fig. 12b.Consequently, next PD pulse would be ignited at a lower electric field and smaller discharge magnitude.
The dependence of PD magnitudes on the linear ramping rate of voltage may be due to charge polarisation under trapezoid-based voltage as referred in [21].During the peak voltage period t 2 , the whole insulation material is polarised with the appearance of both dipoles and free charges.Under a sudden polarity change during voltage reversal, only the high-frequency relaxation dipoles could manage to reverse their orientation in time.The remaining dipoles with low relaxation frequency need more time to react to the field change.Consequently, these long relaxation time dipoles also produce their own field which has the same polarity as the external electric field at the instant the applied voltage reverses polarity.Thus, this residual field caused by these dipoles contributes to the enhancement of the cavity field which could initiate discharges with larger magnitudes.

Conclusion
This paper presents a comparative study of internal discharges in a cylindrical void bounded by solid insulation material as a function of cavity size and applied voltage at VLF and 50 Hz.Different voltage waveforms including sinusoidal and trapezoid-based type were employed to stress the test objects.Various PD characteristics (magnitude, repetition rate, phase-resolved patterns) are analysed.It is concluded that PD behaviours are strongly dependent on the applied frequency and the rise rate of voltage.PD magnitudes at VLF are generally lower than those at power frequency excitation irrespective of voltage waveforms.Moreover, a larger cavity could lead to more discharges with low magnitudes as the discharge surface area is increased.Surface charge contributes to field enhancement in the cavity and thus influences the PD characteristics.In particular, charge decay has significant impact on PD characteristics at 0.1 Hz.These findings help to gain better understanding of PD behaviours at VLF excitation and provide directions for future investigations.For practical applications of VLF diagnostics on extruded high-voltage power cables, further experimental study with appropriate polymeric materials is required.

Fig. 5 Fig. 6
Fig. 5 Electric field distribution in test samples along the z-axis

( a )
Maximum PD magnitudes, (b) Average PD magnitudes and repetition rate

Fig. 12
Fig. 12 Electric field behaviour due to discharges under applied trapezoid-based waveform (a) Charge decay ignored, (b) Charge decay considered . The whole set-up including two brass electrodes and the test object was completely immersed in a High Volt., 2018, Vol. 3 Iss.2, pp.96-102 This is an open access article published by the IET and CEPRI under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)

Table 2 PD
characteristics under triangular voltage waveform with different applied frequency f, Hz U, kV Q max , pC Q ave , pC Repetition rate, ppc 98 High Volt., 2018, Vol. 3 Iss.2, pp.96-102 This is an open access article published by the IET and CEPRI under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)

Table 3 PD
characteristics under trapezoidal voltage waveform at 50 and 0.1 Hz with different rise time factor

Table 4 PD
characteristics under 0.1 Hz trapezoid-based waveform with customized rise time at 10 kV f, Hz t 1 , ms Q max , pC Q ave , pC Repetition rate, ppc High Volt., 2018, Vol. 3 Iss.2, pp.96-102 This is an open access article published by the IET and CEPRI under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)