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Journal Article

Partial Discharges Characterization in Spherical Voids usingUltra-short X-ray Pulses

Author(s): Adili, Sedat; Franck, Christian

Publication Date: 2014-04

Permanent Link: https://doi.org/10.3929/ethz-b-000081665

Originally published in: IEEE Transactions on Dielectrics and Electrical Insulation 21(2), http://doi.org/10.1109/

TDEI.2013.004180

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Partial Discharges Characterization in Spherical Voids using Ultra-short X-ray Pulses

Sedat Adili and Christian M. FranckPower Systems and High Voltage Laboratories, ETH Zurich

Physikstrasse 3, 8092 Zurich, Switzerland

ABSTRACT This work aims to an improved characterization of partial discharges (PDs) in spherical voids. Start electrons are created by an ultra-short (50 ns) X-ray pulse to eliminate the statistical time lag and the individual PDs are detected with an ultra-wideband detection circuit and a photomultiplier tube. The minimum PD inception field strength is determined by triggering at different phase angles of the applied ac voltage. From this, also the gas pressure inside the void can be calculated. The observed PD characteristic (pulse height, charge magnitude, rise-time, and pulse width) are in agreement with the theory of streamer-like discharges. The measurement setup allows the exact determination of the phase angle of each PD related to the ac phase and an improved modeling of the PD activity can be made. Further unknown parameters (residual field strength, charge decay time constant) can be determined from comparison of the measurements to PD modeling.

Index Terms — partial discharges, insulation testing, time-resolved PD measurements, X-ray applications, PD inception voltage, PD modeling

1 INTRODUCTION

The pulsed X-ray induced partial discharge (PD) measurement (PXIPD) technique uses very short X-ray pulses (~50 ns) to supply start electrons for PD initiation and thus eliminates the statistical time-lag. Gas molecules in a cavity are ionized while the ac voltage is applied and the PD activity is detected immediately after the decay of the X-ray pulse [1-5]. In [4] it was shown how a pulsed X-ray source can be reliably integrated into a conventional PD measurement system. The necessary minimum X-ray dose for PD inception in artificially produced spherical voids was experimentally determined and verified theoretically. It could be shown that the X-ray beam mainly interacts with the gas inside the void and – even with a small number of electrons produced – can successfully lead to a PD development. The X-ray pulse supplies only the start electrons for the first PD, the subsequent PDs are not supported by the X-ray beam.

For all PXIPD measurement series, self-produced spherical voids in transparent epoxy were used as described in Section 3. In a more recent work [5], the effect of the X-ray dose on the triggering and the discharge mechanism was investi-gated by time-resolved PD (TRXPD) current measurements with an ultra-wideband detection circuit and a photo-multiplier tube. The measurements confirmed that pulsed

X-ray inception supplies only initial electrons and that thefurther PD development shows no difference to a naturalPD inception without X-ray application.

The novelty of the measurements presented in this contribution results from the ability of the TRXPD setup to trigger the first PD pulse at arbitrary phase angles of the ac voltage. Main findings from the measurements are reported here: a) the minimum inception field of a spherical void is determined very precisely in and b) the residual electric field strength inside the void directly after a partial discharge pulse as well as the decay time constant of the deployed charges are derived.

The paper is structured as follows: after a brief background of the physics and modeling of PD mechanism in dielectric bounded geometries in section 2, the experi-mental setup, the measurement procedure and the used equipment are described in section 3. The results of measuring the minimum inception field strength Einc are shown in Section 4. Examples of PD modeling and the associated determination of the residual field strength and decay time constants are given in section 5. The paper ends with a discussion of the results in section 6 and a conclusion in section 7.

2 THEORETICAL BACKGROUND 2.1 PD MECHANISM

The physical nature of PDs in cavities surrounded by a dielectric has been the object of study by many researchers for many decades. An overview of the experience and the related phenomena to partial discharges is given in [6-15].

Manuscript received on 3 July 2013, in final form 1 October 2013, accepted XX.

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Figure 1. Charge deployment on the void surface after a PD and associated electrical fields. Evoid is the resulting electric field inside the void, i.e. the sum of the field f·E0 caused by the applied background field E0 and the field Eq caused by the dipolar charges on the void.

The streamer-model [16-20] has shown to describe well the initial stage of PD in spherical or spheroidal voids in our measurements.

For a PD to develop in a void with diameter d, the electric field f·E0 within the void must exceed the inception field strength Estr. In addition, a starting electron must be available. This critical electric field is given as a threshold criterion and is usually called streamer criterion [16]:

(1)

where E0 is the applied background field and d the void diameter. For air (E/p)crit = 25 V/(Pa·m), B = 8.6 m1/2 Pa1/2

and n = 0.5. f is a factor that quantifies the field enhancement in the void and depends on the void shape and the permittivity of the surrounding bulk material [16, 19]. For spherical voids in epoxy ( r=4) f 1.33. p is the pressure in the void and is typically assumed to be in the range of p=50-100 kPa [18].

The PD causes a voltage breakdown in the void and deploys the charges ±q on its walls. This charge displacement can be measured as an apparent charge on the electrodes of the sample [16-17].

The electric field inside the void Evoid at any time consists of two contributions, namely the enhanced background field f·E0 and the field Eq due to the surface charges which have remained from the previous PD (cf. Figure 1).

The surface charge field Eq is directly proportional to the charge deployed by the discharge [19]:

. (2)

The magnitude of the surface charge is directly proportional to the field collapse at the time of PD occurrence and can be written for spherical voids [19]:

(3)

where 0 is the vacuum permittivity and r is the relative permittivity of the bulk epoxy.

When a PD occurs Evoid collapses down to a residual field strength Eres below which the discharge extinguishes. The resulting field collapse can generally be expressed by

(4)

where also the polarity of Eq has to be considered. Eres is characteristic of the streamer-like discharge

mechanism [16] and gives the residual electric field in the void immediately after the total breakdown of the void gap. It is proportional to the critical field strength of the gas:

(5)

is a dimensionless factor and for air it has the value + 0.2 for positive streamers and - 0.5 for negative

polarity streamers [19]. We have found a better agreement of the experimental results and the PD model using ± = 0.2 (see Section 5.2).

The start electron of the very first PD is mainly provided by gas ionization through natural irradiation [19-21]. In our experiments, we create additional electrons by artificial X-ray irradiation and supply start electrons for PD inception [4]. For the following PD pulses the start electrons originate from the deployed charges on the void walls. Besides the amount of deployed charge carriers also the surface properties of the cavity influence the probability of an electron release after the critical field strength is exceeded again. Thus, the PD frequency (average number of pulses per half-wave) depends on the void size and bulk material. The surface conditions inside the void may also change with duration of PD activity.

2.2 PD MODELING Several PD models exist [18, 26-29] which use a stochastic approach to simulate PD behavior in a cavity. They are based on the streamer-like type of PD mechanism as explained above. They reproduce the statistical behavior of PD patterns in a cavity by comparing experimentally gained PRPD patterns to simulation results. The model parameters are determined using Monte Carlo simulation methods which generate the frequency of occurrence, pulse charge and ac phase angle (q, i) of PDs.

When modeling the statistical behavior of partial discharges in cavities the most challenging and influencing part is the generation of PD inception time instants.

The exact knowledge of individual PD occurrence times including the very first one enables to calculate the discharge amplitude and the availability of start electrons for the next PD after a time t, when the electric field in the void has reached the minimum inception field again.

The minimum inception field Einc = Estr for the used cavity is an important parameter in the model. However, so far it was only possible to estimate it theoretically, using equation (1), and with large uncertainty, as in particular the gas pressure is not known.

These models consider surface charge memory effects like the loss of electrons by being trapped into deeper traps of the insulating material so that they cannot be de-trapped

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at Einc or only at sufficient overvoltage. This loss of electrons may be roughly accounted for by an exponential decay term e-

(t/ tr), where tr is a time constant giving the effective lifetime ofan electron in a de-trappable trap [18].

Another phenome-non occurring is that the deployed charges by a PD that are not trapped have a limited lifetime mainly because of conduction along the void walls but also ion drift in the gas volume. This depends on the conductivity of the void surface and studies [10, 20, 25, 29] have shown that the surface conductivity increases significantly at longer (up to some hours) PD activity and during the PD event itself. This surface charge decay happens with a time constant that is dependent not only on the surface conductivity but also on the geometric dimensions of the void [18].

The possibility of triggering the first PD pulse at arbitrary instances enables an advanced PD characterization and allows to determine the model parameters with higher accuracy. On the one hand it is possible to determine the minimum inception field strength direct experimentally and with a very high precision (cf. Figure 3). On the other hand, by the controlled inception of the first-PD and the acquisition of each PD occurrence the time delay between subsequent discharges is known (cf. Figure 5). From this it is possible to judge if the breakdown occurs directly after the critical field strength is exceeded and an estimation of the displaced charges is possible.

Still, it is expected that the parameters show a statistical behavior especially with increasing PD activity in the void. Consequently, we restrict the investigation in the present report to the initial phase of PD activity in a new void.

3 EXPERIMENTAL SETUP The classical PD detection system makes use of a relatively

small bandwidth and records the apparent discharge magnitude and its phase position. To be able to study the discharge mechanism of a PD, its apparent current pulse shape has to be recorded. Considering the time constant of a few ns for a typical PD (streamer-like), the time constant of the measuring circuit has to be small, i.e. a high bandwidth is needed.

In order to achieve a high-bandwidth measurement setup, a new compact ring capacitor was built for our experiments (cf. Figure 2). The coupling capacitor is formed by the grounded electrode together with the high voltage (HV) electrode. The

capacity of the ring coupling capacitor has to be high enough to maintain a high sensitivity of detection [22-24]. A ring epoxy block with r 4 (at AC 50 Hz) was casted to get a higher capacity, but it was observed that even without the epoxy ring, the sensitivity of the system was sufficient. The ground electrode of the sample is the measuring electrode with a diameter Dm = 20 mm. In order to maintain a small stray capacitance, the diameter of the measuring electrode has to be small. On the other hand, a small diameter would induce currents in the coaxial guard electrode. The Ramo-Schockley theo-rem gives the optimal relation between the diameter of the measuring electrode Dm, the separation between the high voltage electrode and the measuring electrode of the sample D and the void diameter d [24]:

(6)

Condition (6) is fulfilled for the samples used in the present measurements with D = 4 mm for samples with d 1.3 mm and D = 3 mm for samples with d 1.2 mm. The resistance RD=10 M (should be high) and is needed to decouple the discharge signal from the high voltage source. By this, the discharge path is restricted to the compact capacitor system. Calculations using an equivalent circuit [8] determined a time constant of the measurement system of ~230 ps. This is well acceptable, since the PD pulses measured show a time constant mostly around 1 ns.

A LeCroy digitizing oscilloscope with a bandwidth of 1 GHz with 10 GS/s was used. The PD current through the 50 resistor Rm is transmitted as a voltage signal by the 50 transmission cable. The terminal connection to the oscilloscope is done across 50 so that reflections are avoided (cf. Figure 2). Consequently, the resulting measurement resistance for the discharge current is 25 .

The X-ray source generates a short pulse of 30-50 ns duration with a maximum photon energy of about 300 keV, see [4]. It can be triggered with a time delay of about 2.5 μs upon receiving a trigger signal. The X-ray beam can irradiate the sample while the ac voltage is applied. The voids were produced by fast gelation of gas bubbles in liquid epoxy. Single blocks containing single voids were then cut and casted again in epoxy. In this way different (exactly known) void sizes in the range from 0.1 mm to > 2 mm could be obtained (see [3] for more details). The results shown in this paper are for a spherical void of 1.3 mm diameter.

Figure 2. Diagram of the TRXPD measurement circuit and the PMT: Cross section of the “short discharge path ring coupling capacitor” CK with the sample in the middle. The epoxy ring with the high voltage electrode and ground electrode builds the coupling capacitor.

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By applying start electrons (X-ray pulse) at different phase angels of the ac voltage and at different rms voltage levels, the inception field strength can be determined.

The AC voltage was first brought to the level where the peak voltage is identical to the theoretically calculated Uinc. A single X-ray pulse that would give ~5 start electrons at Uinc was applied at various phase angles of the positive ac half-wave, beginning at = 0°. In case of an inception at angle inc, the voltage was shut down within a few seconds to avoid long PD activity inside the void in order to minimize aging effects like in [8-9]. A new measurement was then made by applying the same voltage level and by triggering the X-ray pulse at a slightly lower phase angle inc-1° or inc-5°. The procedure was repeated also at angles above inc. In addition, this was done also at falling edge of the positive ac half-wave. In a next step, the voltage level was increased by 1 kV and identical measurement were made. In total, measurements were performed at further increased voltage levels up to Uinc +5 kV. The same procedure was then repeated for a high X-ray dose (~200 start electrons at Uinc). In addition to the first PD pulse, a sequence of 100 subsequent pulses was recorded. PDs reveal themselves also in other forms like emitting radiation from excited particles, ultrasound, heat from particle impact and chemical reactions [25]. The light emitted by the PDs was detected by a photomultiplier tube (PMT, Hamamatsu) module, consisting of a PMT with a build in high voltage power supply. To bundle the light emitted from the void, a convex lens was placed between the light source and the PMT. One part of the light is absorbed by the epoxy of the sample, but still a good sensitivity was possible. At least for the sample measured, the PMT pulse was in the order of some tens of mV.

The PMT signal was used as the trigger signal for the oscilloscope which then acquired both the electrical signal and the PMT signal. The PMT pulses are not used as PD pulse qualification data and will not be analyzed further in this work. The X-ray source and the X-ray beam create electrical noise on the coaxial transmission cable and the setup. To learn about the amplitude and shape of these noise signals, the electrical and optical signals were recorded also when no voltage was applied and, consequently, no PD activity was possible. It is shown that the PMT signal is much less influenced than the electrical signal. Through appropriate shielding of both X-ray source and the coaxial cables, this effect was minimized as much as possible. During the PD measurements, the oscillating current before the rise of the first PD pulse and after its decay corresponds to this noise signal (see Section 5).

3.1 EXPERIMENTAL DETERMINATION OF UINC The experimental determination of the minimum inception

voltage by applying the X-ray pulse at different phase angles of the ac voltage is depicted in Figure 3. It shows different levels of the applied voltage with each marked point as a single TRXPD measurement. The full circles are the points where PD incepted, the open circles show the points where the X-ray pulse was applied (both minimum and high X-ray dose) but no PD inception occurred. From Figure 3 the minimum inception level is clearly visible: Uinc=(7.1 ± 0.5) kV. This corresponds to an operating voltage of 5 kVrms below which no PD activity can occur.

Figure 3. Upper figure: voltage on sample vs. phase angle instant of single X-ray pulse application. Each point in the graph represents a new TRXPDmeasurement. The full circles refer to a successful PD inception and theopen circles give the voltage levels where no PD inception occurs. Lowerfigure: a magnified view of the Uinc level.

The minimum X-ray dose of ~2 μSv at Uinc = 7.1 kV gives Ne 5 start electrons and the maximum X-ray dose of ~70 μSv provides Ne 180.

By using the streamer-criterion of equation (1), the measured inception field strength corresponds to a void pressure of about 50 kPa.

Each point in Figure 3 refers to a new PD test after a previous measurement with X-ray is made and the voltage is shut down to stop the PD activity. The waiting time between the measurements with the same dose was in the range of a few minutes. The waiting time between the test with minimum and maximum X-ray dose was 4 days, where the sample was kept short circuited. Natural inceptions occurred only sporadically between individual PD measurements with X-ray.

4 ADVANCED PD CHARACTERISTICS 4.1 EFFECT OF ELECTRIC FIELD STRENGTH AT

TRIGGERING Generally, the term “first-PD” refers hereafter to the first

PD that is detected at an inception. It is the discharge that is incepted directly by the X-ray pulse. The subsequent-PDs are the ones following the first-PD, meaning PD pulse number 2 to 100.

Figure 4 (left) shows the first-PD pulse that incepted with a minimum X-ray dose at 9.9 kV. It has a peak value of about 55 mA, a rise-time of 0.8 ns, and the pulse-width is 1.3 ns. The corresponding PMT pulse is shown as a dashed line. It has a rise-time of 2.2 ns and pulse-width of 9 ns. The general observation of longer PMT signals compared to the electrical signal was made throughout all measurements. As the PMT signals are only used for reliable triggering, it is only shown as an example. The first five subsequent-PD pulses following the first-PD pulse are depicted on the right-hand side of Figure 4. These subsequent-PD pulses are all similar but differ from the first-PD. They have a

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Figure 4. Example of a single TRXPD sequence (with minimum X-ray dose applied at 9.9 kV which corresponds to 7 kVrms at 90°). Left: first-PD as electrical pulse (solid line) and PMT pulse (dashed line). Right: 5 subsequent-PDs.

Figure 5. Current peak values and time delay between subsequent PDs for the first 40 PDs of the PD sequence in Figure 4.

lower amplitude, slower rise-time and longer pulse-width than the first pulse. Their peak values are nearly constant.

In Figure 5, the peak current of each PD and the time-delay between PDs for the sequence in Figure 4 are shown. The time delay between subsequent pulses is less than 5 ms for the first 3 PDs and then sets to an almost constant time delay of 10 ms for later discharges. A PD pulse repetition rate of 1 pulse per half-wave is evident for this voltage level.

Figure 6 shows the dependence of the peak current of the first-PD on the electric field at the moment of PD inception. Despite a certain scatter, there is a clear indication that the peak current increases with increasing electric field strength. At the same time, the rise-time of the pulses decreases, as depicted in Figure 7. It was also observed that for the first–PD with increasing electric field the pulse-width is tending to decrease (not shown here).

Figure 8 gives the PD charge magnitude of the first-PD and the mean value of the corresponding set of 99 subsequent discharges in dependence of the applied background electric field E0 at the instant of the first PD triggering. The charge magnitude of the first-PD is directly

proportional to the electric field at the time of inception but the subsequent PDs are not affected by the height of the field. They show an almost constant PD magnitude at each applied background electric field.

Figure 6. Dependence of first-PD current peak on the electric field at inception instant.

Figure 7. Dependence of first-PD rise-time on the electric field at inception instant.

Figure 8. Dependence of PD charge magnitude on the electric field at inception instant.

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4.2 TRXPD DEVELOPMENT From the measurements, the minimum inception field

strength and the time instant of the first PD pulse and each subsequent PD are known. These information allow an improved PD modeling.

The total field in the void at any inception time ti (i gives the PD pulse number) is the superposition of the field strength f·E0 (ti) caused by the background field and the field Eq(i-1) caused by the accumulation of the discharges deployed on the void surface during the previous PD events. Two subsequent discharges of the same polarity increase the absolute value of Eq. If a PD has the opposite polarity to its preceding PD the absolute value is decreased.

At the time instant of the first PD, which is incepted by the X-ray pulse application at a known phase angle, the field in the void is only determined by the background field.

When the first-PD occurs at time t1 the electric field caused by the charges deployed on the void surface after the PD is determined by the field collapse in the void and can be expressed as:

(6)

Eres is calculated according to Equation 5. The resulting Eq1 from the first-PD is added to f·E0(t) which gives the total electric field in the void Evoid(t) at any time instant t after the occurrence of the first-PD. Since the time of the next PD event is known, one can easily calculate Evoid(t2) at which the next PD inception can occur. In our model, this is done by keeping Eq(i-1) constant, i.e. tr is very large compared to the characteristics time-scale of 50 Hz.

The following figures show the application of the described PD model on measurements with different applied voltages and different phase angles of X-ray pulse inception. In each figure, the first 3 half-waves of the applied electric field are shown and all the instants of PD occurrences are marked. The field strength f·E0 resulting from the background field is plotted with solid curves and the total field strength inside the void Evoid is plotted as dashed curves. For each PD inception time the resulting Eqi is plotted as a diamond point.

Figure 9 shows the measurement at 5 kVrms with triggering at 90° (minimum inception voltage). In contrast to literature [19] where different values of in equation (5) have been reported for negative and positive discharges,

±=0.2 was taken to calculate the residual field strength for this and all following measurements. It can be seen that the subsequent PDs occur as soon as Evoid reaches Einc again. The inception field strength of subsequent PDs is within the scatter of Einc shown in Figure 3. It is obvious that no statistical time delay occurs for the subsequent-PDs, at least for the initial phase of PD activity.

Figure 10 shows the measurement at 8 kVrms and triggering at 38° (high overvoltage but triggering at instant of minimum inception voltage). The 3 subsequent PDs occur without statistical time delay and incept as soon as Evoid reaches Einc. The slightly lower Einc of PD2 and PD4 are within the scatter of Einc shown in Figure 3. Evoid exceeds

Figure 9. Occurrence time instant of the first-PD and 2 subsequent discharges (crosses) at 5 kVrms. The solid line shows f·E0, the electric field in the void without PD. The dashed line is Evoid with PD. Evoid follows f·E0 in the areas where it is not marked as a dashed line. The diamond points show Eqi after the corresponding PDi. Evoid = f·E0+Eq-Eres.

Figure 10. Occurrence time instant of the first-PD and 3 subsequent discharges (crosses) at 8 kVrms. The solid line shows f·E0, the electric field in the void without PD. The dashed line is Evoid with PD. Evoid follows f·E0 in the areas where it is not marked as a dashed line. The diamond points show Eqi after the corresponding PDi. Evoid = f·E0+Eq-Eres.

Einc for a short period after PD4 where no PD inception occurs.

Figure 11 shows the measurement at 8 kVrms with triggering at 90° (high overvoltage and triggering at high overvoltage). It is shown that the subsequent PDs occur as soon as Evoid reaches Einc. The inception field of subsequentPDs is within the scatter of Einc. It is obvious that almost no statistical time delay occurs for the first 3 subsequent PDs. Evoid exceeds Einc for a short time after PD3 and PD4 but no PD inception occurs.

Figure 12 shows a measurement at 10 kV and triggering at 151° (high overvoltage but triggering at minimum inception voltage at falling slope). The 2nd, 3rd and 4th PD occur as soon as Evoid reaches Einc again. No statistical time delay occurs for the first 3 subsequent PDs. Evoid exceeds Einc for a relatively long time after PD4 where no PD inception occurs.

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Figure 11. Occurrence time instant of the first-PD and 3 subsequent discharges (crosses) at 8 kVrms. The solid line shows f·E0, the electric field in the void without PD. The dashed line is Evoid with PD. Evoid follows f·E0 in the areas where it is not marked as a dashed line. The diamond points show Eqi after the corresponding PDi. Evoid = f·E0+Eq-Eres.

Figure 12. Occurrence time instant of the first-PD and 3 subsequent discharges (crosses) at 10 kVrms. The solid line shows f·E0, the electric field in the void without PD. The dashed line is Evoid with PD. Evoid follows f·E0 in the areas where it is not marked as a dashed line. The diamond points show Eqi after the corresponding PDi. Evoid = f·E0+Eq-Eres.

Figure 13. Occurrence time instant of the first-PD and 7 subsequent discharges (crosses) at 10 kVrms. The solid line shows f·E0, the electric field in the void without PD. The dashed line is Evoid with PD. Evoid follows f·E0 in the areas where it is not marked as a dashed line. The diamond points show Eqi after the corresponding PDi. Evoid = f·E0+Eq-Eres.

Figure 13 shows the measurement at 10 kV and triggering at 30° (very high overvoltage but triggering at minimum inception voltage). The subsequent PDs incept without statistical time delay at Einc or slightly below. It is obvious that no statistical time delay occurs for the first 6 subsequent PDs. Evoid exceeds Einc for a short time after PD4 and PD7 but no PD inception occurs. This example clearly shows the increased pulse repetition rate with increasing applied voltage.

5 DISCUSSION From the experiments, the minimum inception voltage

for PDs in a spherical void embedded completely into solid insulation material was determined very precisely (±7% uncertainty). This has been done by applying ultra-short X-ray pulses at different phase angles of the ac half-wave and for different applied voltages amplitudes. This is a significant improvement compared to previous measurements and calculations. Previous measurements have suffered from the statistical time lag and typically resulted in too high inception field strengths. Calculations suffer from fact that the gas pressure inside the void is not known. Using the precisely measured inception field strength and equation (1), it is now even possible to determine the gas pressure inside the void. In the example of this paper, the gas pressure was p=50 kPa. This is around the lower limit of the pressure range estimated for spherical voids in [16, 18].

It was shown that even a high number of start electrons produced slightly below Uinc is not sufficient to start sustainable PD when only a few hundred microseconds later the minimum inception level is reached. Below Uinc no PD activity of any kind was observed, neither with the electrical signal nor the PMT. This behavior is expected according to the theory presented in section 2. Below the inception field strength, no or only very few ionizing collisions occur. In addition, the charge carriers drift in the field and cross the void within a few nanoseconds and are deployed on the void surface. The number and life-time of free electrons inside the critical volume of the void is thus very limited and, consequently, the gaps breaks down only if the start electron is generated at an instant where the critical field strength is exceeded.

The first-PD pulse shows a strong dependence on the electric field at the instant of inception. The PD charge magnitude and pulse height increase with increasing field strength. This behavior is as expected from the theory presented in section 2. The field inside the void always breaks down to the residual field strength, thus the field collapse increases with increasing background field at the moment of inception. As the amount of charges in the discharge is proportional to the field collapse, cf. equation (3), the charge magnitude and pulse height should also increase. The electron velocity increases with increasing field strength, i.e. the discharge crosses the void faster. Consequently, the discharge duration decreases and the measured pulse width and rise time decrease as well.

The subsequent-PDs have smaller amplitude and their shape (rise-time and width) resembles those first-PD pulses

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Eq4

Eq5

Eq6

Eq7

Eq8

fE0

Evoid

→

Einc

Einc

first PD

PD2

PD3

PD4 PD

5

PD6PD

7

PD8

Eq1

Eq2

Eq3

Eq4

Eq5

Eq6

Eq7

Eq8

fE0

Evoid

→

Einc

Einc

first PD

PD2

PD3

PD4 PD

5

PD6PD

7

PD8

Eq1

Eq2

Eq3

Eq4

Eq5

Eq6

Eq7

Eq8

fE0

Evoid

→

Einc

Einc

first PD

PD2

PD3

PD4 PD

5

PD6PD

7

PD8

Eq1

Eq2

Eq3

Eq4

Eq5

Eq6

Eq7

Eq8

fE0

Evoid

→

Einc

Einc

first PD

PD2

PD3

PD4 PD

5

PD6PD

7

PD8

Eq1

Eq2

Eq3

Eq4

Eq5

Eq6

Eq7

Eq8

fE0

Evoid

→

Einc

Einc

first PD

PD2

PD3

PD4 PD

5

PD6PD

7

PD8

Eq1

Eq2

Eq3

Eq4

Eq5

Eq6

Eq7

Eq8

fE0

Evoid

→

Einc

Einc

first PD

PD2

PD3

PD4 PD

5

PD6PD

7

PD8

Eq1

Eq2

Eq3

Eq4

Eq5

Eq6

Eq7

Eq8

8

that are triggered at the minimum inception level. This is an indication that the subsequent pulses incept as soon as the field strength inside the void exceeds the critical field strength. Charges are deployed on the void surface by preceding PDs, which on polarity reversal serve as start electrons for the subsequent-PDs. The measured PD charge magnitude of subsequent-PDs is constant. In a phase re-solved PD pattern this would correspond to a bar-like structure, a pattern that is indeed observed for larger voids like the one used in the present experiment. This difference between the first-PD and subsequent-PDs was also observed at a natural inception and with a maximum X-ray dose, i.e. at every inception regardless of the inception conditions.

In a further analysis of these experiments, the field stress inside the void is modeled at every instant in time for the first three half-waves after X-ray triggering. Up until to the first PD pulse triggered by X-rays, no charges are deployed on the void surfaces. The field inside the void is thus identical to the background field strength enhanced by the factor f. The field collapse is determined by the difference between the initial field stress and the residual field stress. From this, the exact amount of charges and the corresponding field Eq can be calculated with equation (4). It is thus possible to calculate the field stress inside the void from the superposition of Eq and f·E0. As the exact instant of time of the following subsequent PD pulse is measured, the field collapse, the newly created amount of charges deployed on the surface, and also the new Eq can be calculated. It is thus possible to determine the field stress inside the void for every PD breakdown. A first consistency check can be done by comparing the field stress inside the void for subsequent-PDs with the experimentally determined minimum inception field. No breakdowns occur below the minimum inception field. For the modeling in the present paper, less assumptions have to be made compared to previous reports as some of the parameters are directly measured (Einc) or directly inferred from this (void pressure p). Additional parameters ( ±, tr) can be determined from comparison of the measurements to the simulations. For the measurements of this paper, best results are obtained when the residual field stress for positive and negative discharges is identical ( += -=0.2). Moreover, no substantial time delay between exceeding Einc and discharge inception was observed. This is on the one hand a confirmation of the previously discussed fact of sufficient start electrons for subsequent-PDs originating from the deployed charges on the void surface. This is true for large voids, but could also be an indicator for a tr that is significantly larger than the typical time constant of the 50Hz AC voltage. Going gradually to smaller void sizes in future experiments would enable a better estimation of tr also for different insulation materials.

Nonetheless, the processes are subject to a certain statistical variation. This can be seen from the slight variations of the field stress at subsequent-PD inception and, occasionally, also longer periods with no inception but exceeded field stress occur.

The results presented here clearly show the future potential of this measurement approach. Performing more experiments would enable the determination of further parameters like the statistical time delay caused by tr, the effective work function for electron release, and other material characteristics.

6 CONCLUSION In the present contribution it is shown how the novel

TRXPD setup enables an improved PD characterization. The test setup offers the possibility of providing start electrons by the X-ray pulse at any phase angle of the applied ac voltage.

Firstly, the inception field strength was accurately determined and from it, also the gas pressure inside the void could be calculated. Secondly, the effect of the electric field strength at the moment of inception onto the PD mechanism was studied. It was shown that the detected PDs show an almost linear dependence of the charge magnitude and pulse-height with the electric field. The rise-time and width of the PD pulses decrease with increasing field strength. All these observations are in accordance to the behavior of streamer-like discharges.

Further, these measurements are used for an improved PD modeling. Previous models lacked a number of parameters that had to be inferred indirectly. The relevant parameters influencing the PD activity have been measured (Einc) or were directly calculated from the measurement results (void pressure p). Thus, additional unknown parameters can be derived by comparing the modeling to the measurement results (Eres, , tr). The method and analysis presented here will serve as the basis for further experiments characterizing PD also with other void sizes and in other insulation materials.

ACKNOWLEDGEMENT The project is financially supported by ABB Switzerland

(Corporate Research).

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Sedat Adili received the M.Sc. degree from the Faculty of Electrical Engineering and Information Technology, Vienna University of Technology, Austria in 2009. Since then he has been working on his Ph.D. degree at the Institute for Power Systems and High Voltage Technology, ETH Zürich, Switzerland. His research interests are dielectric phenomena, high voltage test techniques and partial discharges in high voltage insulation in general.

Christian M. Franck (M’04-SM’11) received a diploma in physics from the University of Kiel, Germany in 1999 and the Ph.D. in physics from the University of Greifswald, Germany in 2003. He was with the Swiss corporate research center of ABB from 2003-2009 as a Scientist and Group Leader for gas circuit breakers and high-voltage systems. Currently, he is Assistant Professor for High Voltage Technology at the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland.