Modelling of Partial Discharge Characteristics in Electrical Tree Channels: Estimating the PD Inception and Extinction

VoltagesZepeng Lv, Simon M. Rowland, Siyuan Chen and Hualong Zheng

The University of Manchester, School of Electrical and Electronic Engineering, Manchester, M13 9PL, UK

Kai WuSchool of Electrical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

ABSTRACTPartial discharge (PD) characteristics are inherently linked to associated electrical tree growth characteristics. This paper employs both phase-resolved patterns and pulse-sequence analysis (PSA) to study PDs in a short branch-tree grown from a metallic needle tip. It is found that the shape of PSA dV-dV patterns vary with applied voltage; in particular the values of characteristic voltage difference increase with applied voltage. At 10 kV the value of characteristic voltage difference decreases with tree growth, the average number of PDs per cycle increases, the PD magnitudes decrease, and the characteristic wing-like phase-resolved pattern evolves into a turtle-like pattern. This paper proposes a physical model relating PD activity to tree development, considering space charge accumulation inside the tree channel. All key features of experimental results are explained by the model. It is shown that the characteristic voltage differences are determined by the local PD inception and extinction electric fields. These key parameters determining the PD events can be calculated giving a clear physical interpretation of PD measurements, which is invaluable to those using PD as a condition monitoring or asset management tool.

Index Terms — trees (insulation), epoxy resin insulation, partial discharge, inception and extinction voltages, modeling.

1 INTRODUCTIONELECTRICAL tree growth is an important degradation

process in high voltage dielectric insulation [1]. Partial discharges (PDs) are found in tree channels and are considered to be the cause of tree growth [1]. The characteristics of PDs reflect the physical nature of a tree. For example, it is found that in non-conductive tree channels, PDs extend throughout the main tree, whereas in conductive tree channels PDs only exist at the tree tips [2-3]. Our previous research has shown that the PD patterns continuously change with the early tree growth, and PDs become extinct when a tree stops growing [4-5]. Several methods have been employed to analyze PD activity. The phase resolved partial discharge (PRPD) pattern shows the PD magnitude distribution at different phase angles [6-11]. In PRPD analysis PDs can be divided into different cluster types, such as wing-like, turtle-like, and rabbit-ear. A wing-like PD pattern is associated with long tree channels while the turtle-like pattern is considered to result from activity in short tree channels [6-8].

Pulse sequence analysis (PSA) is a tool based on the time sequence of the partial discharges in voids or tree channels [9-

15]. It is found that the voltage differences between consecutive PDs stay almost constant within voltage cycles, which indicates that it is the voltage difference which determines the PD sequence rather than the time, phase, phase interval or applied voltage [9]. Patsch and Berton proposed an equivalent circuit model to explain the characteristic voltage difference, and distinguished the PD resulting from different defects by the dV-dV pattern [9]. Some attempts are also made to identify the tree features by dV/dt plots [12-13].

This paper studies PDs in a short branch tree. Both PRPD patterns and dV-dV patterns are employed to study the PD characteristics from tree channels. A model considering the space charge accumulation inside the tree channel is proposed to explain observed PD behavior.

2 EXPERIMENTALA conventional point-to-plane sample configuration was

used. The samples were fabricated using epoxy resin LY/HY 5052. The required volume of the resin/hardener system with mixing ratio 100:38 (parts by weight) was hand-mixed for about a minute followed by magnetic stirring for 5 minutes. The mixture was degassed in a vacuum oven at room

temperature for 60 minutes and then poured into a hollow acrylic cube. The mixture is allowed to cure at room temperature for 24 hours, followed by a further 4 hours at 100°C. Ogura needles of 1 mm diameter and 3 µm tip radius were used as HV voltage electrodes, with gap distances of (1.9 ± 0.1) mm. The plane (bottom) surface of each of the samples was coated with aluminum by vacuum evaporation, to ensure good electrical contact with the ground electrode.

Air gaps, not visible using traditional microscopy, are often present at needle tips, even though the epoxy resin sample is fully degassed before curing. A pre-existing air gap around the needle may greatly influence the PD, especially at the early stages of tree propagation [16]. The air gaps can be identified by laboratory XCT projections. Samples without air gaps were selected and used in the following study.

Electrical tree growth and PDs were measured using the system shown in [4]. An HV amplifier supplied voltage to a test cell filled with silicone oil to ensure no surface discharges. A monochrome CCD camera fitted with a telecentric lens monitored the tree until breakdown. A wideband (9 kHz to 3 MHz) digital system (MPD 600) acquired PD data in compliance with IEC 60270. A balanced circuit was employed to reduce background noise. The sensitivity of the measurement system was ~0.35 pC and a minimum detection setting of 0.4 pC was used to eliminate background noise.

3 RESULTS AND DISCUSSIONThe epoxy resin sample considered here was firstly

stressed under 10 kV peak 50 Hz AC voltage to initiate a tree. A two-branch tree with maximum extent of 115 µm was obtained. Once the tree was observed the voltage was removed. The tree was then stressed at 4 kV for 10 minutes, and thereafter the voltage was increased by 1 kV steps for 10 minutes each, up to 10 kV. There was no apparent tree growth when the applied peak voltage was less than 8 kV. Tree growth at 8 kV and 9 kV was marginal. At 10 kV one branch did not grow while the other grew continuously. The tree structure at the end of the test is shown in Figure 1. The 56 µm growth in the final 10 minutes at 10 kV, is highlighted by the red circle. The final length of the left branch is 141µm.

Figure 1. The final tree structure after application of stepped stresses up to 10 kV. The ringed segment grew in 10 minutes at 10 kV.

3.1 NUMBER OF PDS PER CYCLEPDs start to appear during the 4 kV AC voltage step.

However, these are sporadic and the average number per cycle is less than 1. With the increase of voltage, the average number of PDs per cycle increases, as shown in Table 1.

When the peak voltage is between 6 kV and 9 kV, the number per cycle stays relatively stable during each step, as shown in Figure 2a. At 10 kV the number per cycle increases with time, as shown in Figure 2b. The number per cycle at 10 kV in Table 1 is taken from the first minute at that voltage.

Table 1. The number of PD per cycle at with applied voltage

Peak voltage (kV) 4 5 6 7 8 9 10Ave. number of PD / cycle 0.04 0.2 1.2 2.6 3.3 4.4 5.9

(a) at 9 kV (b) at 10 kV

Figure 2. Average number of PDs per cycle during the 9 kV and 10 kV steps.

Figure 3. Average number of PDs per cycle with applied voltage. The tree did not grow significantly in this period, until 10 kV was applied.

Figure 3 shows that the average rate of PDs increases linearly with the peak voltage; the average value being calculated each second. The linear fit is given in Equation 1, where nc is the average number of PDs per cycle, and Vp is the applied peak voltage.

(1)The PRPD pattern and dV-dV pattern for periods of 10 seconds under applied peak voltages from 4 to 9 kV are shown in Figure 4. The PD characteristics are relatively stable when the peak voltage is below 10 kV. The PD characteristics at 10 kV change with time, and are shown in Figure 5.

3.2 MAXIMUM PD MAGNITUDEFrom Figure 4, it can be seen that the PDs under 6 kV are

not continuous and the PRPD patterns only occur in one small area in each half cycle, and it is hard to distinguish a pattern. Above 6 kV, a wing-like PD pattern begins to emerge. This is more obvious in the negative half cycle than the positive half cycle. The maximum PD magnitudes increase with applied voltage. Figure 5 shows the linear fit between maximum PD

(a) 4 kV

(b) 5 kV

(c) 6 kV

(d) 7 kV

(e) 8 kV

(f) 9 kV

Figure 4. PRPD and dV- dV pattern of PDs at voltages less than 10 kV.

magnitudes and applied peak voltage. The quantitative relation is given in Equation 2, where Qmax is the maximum PD magnitude in a 10 second period. This result is consistent with the conclusion in [6] that in a tree channel, the maximum PD magnitude increases linearly with the applied voltage.

(2)

Figure 5. Maximum PD magnitudes at different applied voltages

3.3 VOLTAGE DIFFERENCEThe dV patterns show significant differences under

different applied voltages. The dark points show the coordinates of (dV(i-1), dV(i)), the grey lines show the straight lines from the previous coordinates to the next. Under 4 kV and 5 kV, the dV pattern is a single line with two symmetric points. The slope of the line is -1. At 6 kV two more points emerge and an associated triangular route. At 7 kV, another two points develop and form a rhombus route – regaining symmetry as the postive and negative cycles become more similar. At 8 kV and 9 kV, a new node forms inside the rhombus, and a line with gradient 1 connects two neighouring points at the rhombus route. Again symmetry is lost between polarities.

Figure 6 shows 10 second periods of PD behaviour at 10 kV peak. In the first period, the single line and triangular route disappear, and another right angle route forms inside the rhombus. Between 120 and 130 s, the rhombus route disappears leaving only a symmetric shape with 6 nodes and 6 sides. This pattern continues shrinking. At the same time the PRPD pattern changes from wing-like to turtle-like: the maximum PD magnitude decreases, and the PD number per cycle increases continuously.

Even though the dV-dV patterns change markedly with applied voltage, there are, at most, four characteristic voltage differences in each condition, as shown in Figure 7. The four characteristic voltage differences can be considered as two pairs, and each of them has similar absolute values but with opposite signs. Here the pair with smaller absolute values are defined as dV1 and –dV1. The pair with larger absolute values are defined as dV2 and –dV2. By checking the phase distribution, it is found that dV1 corrsponds to the voltage difference between PDs in the same rising half cycle; -dV1

corrsponds to the voltage difference between PDs in the same

descending half cycle; dV2 corresponds to the voltage difference between the last PD in the descending half cycle and the first PD in the following rising half cycle; -dV2

corresponds to the voltage difference between the last PD in the rising half cycle and the first PD in the following descending half cycle.

(a) 0 - 10 s

(b) 120 - 130 s

(c) 240 - 250 s

(d) 480 - 490 s

(e) 600 - 610 s

Figure 6. 10 second periods of PRPD and dV- dV patterns at 10 kV peak AC voltage.

At 4 kV and 5 kV, there are only voltage differences between PDs of dV2 and –dV2. At 6 kV values of -dV1 appear.

Above 7 kV, all four characteristic voltage differences are seen in the pattern. However, the frequency of dV2 and –dV2

does not increase with the applied voltage above 7 kV; the frequency of dV1 and –dV1 increase continuously with applied voltage. The range of absolute values of dV1 and dV2

increases with increased applied voltage. After 10 kV was applied to the sample, the absolute values of characteristic voltage differences decrease with time. As a result the dV-dV pattern shrinks in magnitude with time. The values of characteristic voltage differences and the applied voltage determine the number of PDs per cycle, the dV-dV pattern and even the PD magnitudes. They can also reflect the nature of PD events, and will be modelled and discussed in the following section.

(a) 4 kV (b) 5 kV

(c) 6 kV (d) 7 kV

(e) 8 kV (f) 9 kV

(g) 10 kV; 0-10 s (h) 10 kV; 480-490 s

Figure 7. Frequency diagrams of the voltage differences in 10 second periods in the different voltage steps.

4 MODELLING OF PD SEQUENCESPastch and Berton proposed a model of an equivalent

circuit to explain the character of PD sequences [9]. This paper illustrates a physical understanding based on space

charge accumulation caused by PD events, and links experimental observations with underlying parameters of PD events. This follows the basic idea of Wu’s model of PD in narrow channels [8]. In a PD event, an avalanche initiates when the local electric field seen by a free electron exceeds the PD inception electric field, EI. The avalanche is extinguished when the local electric field falls lower than the PD extinction voltage Ex. During a PD event, space charge is generated inside the tree channel, and reduces the electric field until the electric field seen by the PD drops below Ex, at which time the PD is extinguished. With this model, Wu explains the phase resolved PD pattern in narrow channels, indicating that wing-like PD patterns form in long tree channels and turtle-like PD patterns form in short tree channels [8]. Here, three more simplifying assumptions are made to further model the characteristics of PD sequences:1. The tree channel is non-conductive, and there is no

charge flow along the tree channel after a PD event.2. Charge injection at the needle/tree channel interface is

blocked.3. All the partial discharges are initiated at the needle tip.

If the tree channel is conductive and the needle tip is able to inject more space charge, the space charge accumulation and movements inside the tree channel make the distribution of electric field more complex. With the adoption of the first two hypotheses, all the charges in the tree channel are generated by partial discharges, and the space charge distribution inside the tree channel can be regarded as fixed between PD events. In other words, we include all space charge movement as part of the PD event, which is described here as occurring for a period defined by initiating and extinguishing electric fields. Consequently after one PD event and before the next, the Poisson electric field due to the space charge inside the tree channel and its image charge on the electrode stay the same. Using this description, the analysis of PD sequence can be greatly simplified.

4.1 VOLTAGE DIFFERENCES BETWEEN CONSECUTIVE PDS AT THE NEEDLE TIP

For simplicity a single straight tree channel, of length l, is considered as shown in Figure 8. The position of the needle tip is at 0, the tree tip is at position D. We consider a 50 Hz AC voltage with peak value of Vp applied to the needle-plane electrode system. To better explain the PDs in the tree channel, the AC voltage cycle is considered in two parts: the descending half cycle (from 90o to 270o) and the rising half cycle (from -90o to 90o). The Nth PD is assumed to occur in the rising positive half cycle when the applied voltage is V1 at time point t1. The (N+1)th PD occurs when the applied voltage is V2 at time point t2, as shown in Figure 9.

Figure 8. A single straight tree channel of length l emanating from a needle tip.

The applied voltage difference between the two PD events is dV1 according to the description of experimental results in Section 3.3. During the Nth and (N+1)th PDs, the potential and electric field distributions go through three stages of change, as shown in Figure 10. The potential and electric field distributions before the Nth PD are shown as the dashed line in Figure 10a. Both the voltage and electric field decrease from the needle tip at position 0 to the tree tip at position D. The potential and electric fields close to the needle tip are similar to those generated by a metal sphere with the same radius: the voltage decreases as (1/r), and the electric field decreases as (1/r2) [8]. At position 0, the potential always equals the applied voltage. When the electric field at the needle tip is higher than EI, PD is initiated, and creates bipolar charges. Electrons and negative ions accelerate towards the positive needle tip, and are subsequently extracted (electrons) or neutralised at the needle, while positive ions move towards the tree tip. The space charge distribution acts to decrease the electric field around the needle tip, and increase the electric field ahead of the space occupied by the PD, until the electric field is lower than Ex, at which point the partial discharge is no longer propagated. The electric field and potential distribution at that point are shown as the solid lines in Figure 10a. d1 is the physical length that the partial discharge propagated under V1. After the PD event, the electric field between 0 and d1 is Ex, according to the analysis in [6].

Figure 9. Distribution of PD events on the applied voltage waveform.

After the Nth PD event, the applied voltage continuously increases with time. According to assumptions 1 and 2, there is no charge injection, extraction or movement inside the tree channel. The potential (V(x,t1)) and electric field (E(x,t1)) distribution caused by space charge will not change. Thus, according to the superposition principle, when the applied voltage increases to V2, changes to the potential (∆V(x)) and electric field (∆E(x)) are due only to the increased applied voltage dV1. The contribution due solely to dV1 is shown as the red dash-dot lines in Figure 10b. The final voltage (V(x,t2)) and electric field (E(x,t2)) distributions are the summations of the distributions at t1 and the change due to dV1. The highest electric field is still at the needle tip, as the solid line shows in Figure 10b. If a PD occurs at t2, the electric field at the needle tip must have increased from Ex to

EI. The applied voltage difference dV1 then corresponds to the electric field increase of (EI - Ex).

(a) immediately before (dashed line) and after (solid line) the Nth PD at t1

(b) after Nth (dashed line) and before (N+1)th PD (solid line), as the applied voltage increases by dV1. The red dash-dot line shows the contribution from

dV1.

(c) immediately before (dashed line) and after (solid line) the (N+1)th PD at t2

Figure 10. Change of potential and electric field distribution along the channel length, before the Nth and after the (N+1)th PD events, of length d1

and d2 respectively.

The electric field of needle-plane system can be described by:

(3)where E is the electric field at the needle tip, Vap is the applied voltage, r0 is the radius of the needle tip, and d is the distance between the needle and plane electrode. The electric field increases linearly with the applied voltage, so the equation can be rewritten as:

(4)F’(r0,d) only contains the factors of the size of needle-plane structure. As the superposition principle is valid for the electric field and voltage

(5)where dVap is the voltage difference, dE is the electric field difference at needle tip caused by the voltage difference. So when the electric field at the needle tip increases from Ex to EI, the voltage difference is:

(6)From Equation 6, it can be seen that in the same rising

half cycle, the voltage difference between the PDs is determined by the PD inception field, the PD extinction field and the size of needle-plane structure. If the PD inception field and PD extinction field do not change with time, the voltage difference between PDs in the same rising half cycle is constant. The phase, time and magnitude of a PD event do not influence the voltage difference between PDs in the same rising half cycle. This argument also follows for sequential PDs within a descending half cycle. If the absolute values of PD inception electric field and extinction electric field do not have polarity dependence, the voltage differences between PDs in the same descending half cycle should have the same absolute value of dV1, but with the opposite sign.

The transition from rising to falling voltages is now considered. Referring to Figure 9, we assume the Mth PD is the last PD in the rising half cycle when the applied voltage is V3 at t3. The voltage increase to the peak value is not able to support another PD in the rising half cycle because Vp-V3 < dV1. The (M+1)th PD occurs when the applied voltage drops to V4 at t4. The applied voltage difference between the two PD events is -dV2 as shown in Figure 11.

During the Mth and the (M+1)th PDs, the potential and electric field distributions undergo three main changes, shown in Figure 11. After the Mth PD, the field between 0 and d3 (d3 being the length of the discharge event) drops to the extinction value EX (as argued for the Nth PD) as shown in Figure 11a. At t4, with the voltage decrease in the descending half cycle, the applied voltage is decreased to V4, and for the PD to occur the electric field must change from EX to -EI. As the electric field direction changes, the direction of PD propagation also changes. As the Poisson electric field stays the same due to assumptions 2 and 3, the change of electric field at the needle tip due to the voltage decrease dV2. Then:

(7)

(a) immediately before (dashed line) and after (solid line) the Mth PD at t3

(b) after the Mth (dashed line) and before the (M+1)th PD (solid line), as the applied voltage decreases by dV2. The red dash-dot line shows the

contribution from dV2.

(c) immediately before (dashed line) and after (solid line) the (M+1)th PD

Figure 11. Change of potential and electric field distribution before the Mth

and after the (M+1)th PD events.

It can be seen from Equation 7 that the voltage difference again is determined by the PD inception field, the PD extinction field and the radius of the needle tip, and has no relation to the phase, time or PD magnitude. The voltage difference between the last PD in the rising half cycle and the first PD in the descending half cycle is higher than the following PD in the same descending or rising half cycle, as seen in experimental results.

Rainer and Hoof found that it is the voltage difference which determines the appearance of PDs [9]. Equations 6 and 7 thus explain the origin of the characteristic voltage differences, shown in Figure 8, and why the PD sequence is determined by the voltage difference. From the above discussion, it can be seen that the two characteristic voltage differences correspond to different PD events. The smaller characteristic voltage difference corresponds to the PDs within the same rising or descending half cycle. Those PDs have the same propagation direction. The larger characteristic voltage difference is the voltage difference between the last PD in a rising or descending half cycle and the first PD in the following half cycle. These PDs are physically propagated in opposite directions. Based on this observation, several issues are discussed below.

4.2 PD INCEPTION AND EXTINCTION VOLTAGEAccording to Equations 6 and 7, PD inception electric

field EI and extinction electric field Ex can be calculated based on the observed characteristic voltage differences by the following Equations:

(8)The apparent PD inception voltage VI and extinction voltage Vx are thus given by:

(9)From the results shown in Figures 4, 6 and 7, it can be

seen that the values of dV1 and dV2 change with applied voltage and duration of voltage application. If the average values of dV1 and dV2 at different applied peak voltages are extracted from the original data, then VI and Vx can be calculated from Equation 9. Those characteristic values obtained from the different applied voltages are shown in Figure 12. It can be seen that the average values of dV1, dV2

and VI all increase with the applied peak voltage, while the values of Vx are independent of applied voltage. However, from Figure 7e-7h, it can be seen that voltage difference values are distributed rather than having a specific value. The values of dV1 show the barrier to initiate another PD event in the same rising half cycle. At low voltages, from 4 kV to 7 kV, the distributions of dV1 appear to be ‘cut off’, as if the higher values in the distribution are censored. The resulting

absence of high values (those higher than the peak voltage) in an otherwise unchanged distribution, appears to be the cause of the reduction in the average of dV1 at low applied voltages, suggesting the fundamental physics is unchanged.

Figure 6 and 7 also show that the values of dV1 and dV2

change with the duration of voltage application. The average values (per 10 seconds) of dV1, dV2, VI and Vx are shown in Figure 13. It can be seen that dV1, dV2 and VI decrease in time, while the values of Vx are almost constant. This shows that the barrier to the inception of a PD event becomes lower, but the extinction conditions are unchanged. The reason for the change in inception conditions is not clear, but a PD event would be influenced by the gas content and condition (e.g. gas pressure, temperature, and conductivity) inside the tree channel. The change of tree structure and the conductivity of the tree channel may also affect the inception conditions for a PD event.

Figure 12. Characteristic voltage differences and apparent PD inception and extinction voltages at different applied voltages.

Figure 13. Characteristic voltage differences and apparent PD inception and extinction voltage at 10 kV peak voltage.

4.3 PSA PATTERN AND NUMBER OF PD/CYCLEIt can be seen that the number of PDs per cycle and the

shape of dV-dV patterns both change with applied voltage. As the PD events have characteristic voltage differences and the total voltage difference of a rising or descending half cycle is constant at 2∙Vp, the values of dV1, dV2 and the peak voltage Vp determine the number of PDs per cycle. The number of

PDs per cycle is therefore related to the shape of a dV-dV pattern, and the values of dV1 and dV2 determine the value of the key points in a dV-dV pattern.

If the peak voltage is lower than VI, no PD can be initiated. So the values of VI are all equal to or lower than the applied peak voltage, as shown in Figure 13. If 2∙Vp is higher than dV2, but lower than (dV1+dV2), in each rising or descending half cycle there is at most one PD event, and the total number of PDs per cycle is at most 2. The sequence of voltage differences is: dV2, -dV2, dV2, -dV2,… The resulting dV-dV pattern only has two key points with coordinates (dV2, -dV2) and (-dV2, dV2). The straight line between the two points forms a slope of -1, as shown in Figure 14(a).

If 2∙Vp is greater than (dV1+dV2), but lower than (2∙dV1+dV2), in each rising or descending half cycle there are at most two PD events, then the sequence of voltage differences is: dV2, dV1, -dV2, -dV1, dV2, dV1, -dV2, -dV1,… The resulting dV-dV pattern has four key points with coordinates (dV2, dV1), (dV1, -dV2), (-dV2, -dV1), (-dV1, dV2). The lines between the four points form a rhombus route, as shown in Figure 14(b).

If 2∙Vp is higher than (3∙dV1+dV2), in each rising or descending half cycle, there are at least 3 PD events, and the sequence of voltage differences becomes: dV2, dV1, dV1, -dV2, -dV1, -dV1, dV2, dV1, dV1, -dV2, -dV1,… The resulting dV-dV pattern has 6 key points with coordinates (dV2, dV1), (dV1, dV1), (dV1, -dV2), (-dV2, -dV1), (-dV1, -dV1), (-dV1, dV2). The lines between the six points form a hook-like hexagon as shown in Figure 14(c).

As the measured values of dV1 and dV2 are distributed rather than being deterministic, the dV-dV pattern in Figure 4 shows a combination of the patterns identified in Figure 14. The combinations of patterns arise when the voltage does not clearly define the PD events allowed, so the PD number per cycle is between 2 and 4, or 4 and 6. The dissymmetry of the patterns shown in Figure 4 indicates that PDs are more easily incepted in the descending half than in the rising half cycle.

As mentioned in Section 4.1, when the last PD event happens in a rising half cycle, the value of (Vp-V3) is smaller than dV1. So the PD number across the following descending half cycle nhc is in the range:

(10)Here the average value between the two ranges is used to predict the average value of PD number per cycle.

(11)The value of dV1 and dV2 are 3.6 kV and 11.4 kV at 9 kV. Using these values, Equation 11 may be written as Equation 9. The theoretical prediction shown in Equation 12 is remarkably similar to the experimental fit of Equation 1. This is verification of the prediction of Equation 11.

(12)The factors in equation 1 and 12 only fit the PDs in this

tree channel when the voltage is less than 10 kV. Equation 11 is applicative for all the PDs in non-conductive tree channels.

When the applied voltage is 10 kV, the PD number per cycle increases with the duration of voltage application. This is due to the reduction of the PD inception voltage which reduces the value of dV1.

(a) dV2 < 2∙Vp < (dV1+dV2), giving nc = 2

(b) (dV1+dV2) < 2∙Vp < (2∙dV1+dV2), giving nc = 4

(c) (3∙dV1+dV2) < 2∙Vp , giving nc = 6

Figure 14. The dV-dV patterns of PDs resulting from different values of dV1, dV2 and applied voltage.

In each rising or descending half cycle, the PDs end at around 90o or 270o, as after that point the voltage polarity and electric field direction change. The next PD occurs after a voltage difference of -dV2 or dV2. Thus the phases at which PDs start in a rising half cycle Psr and descending half cycle Psd are:

(13)It can be seen from Equation 13 that with the increase of

applied peak voltage, the initiating phase of each half cycle is

reduced, and the total phase range over which PDs occur increases. This prediction also fits experimental results: under 4 or 5 kV, PDs only exist around 90o and 270o; but with the increase of the applied peak voltage, the initiation phase of each half cycle occurs earlier, even before the zero crossing point, and as a result the phase range in which PDs occur increases.

The average number of PDs per cycle in a sequence follows Equation 8 and the dV-dV patterns of PD events in a sequence follow the basic patterns shown in Figure 14. The experimental results in this paper are classic sequences of discharges from a needle tip following all the characteristics discussed above.

4.4 PD MAGNITUDES AND PRPD PATTERNSAs discussed above, PDs at 4, 5 and 6 kV can hardly form

a PRPD pattern, as in each half cycle there is one PD event at most. PDs at voltages of 7 kV and above (including the first minute at 10 kV) show a wing-like pattern. The maximum magnitude of the wing-like PD pattern rises linearly with the applied peak voltage. PDs initiate when the local electric field exceeds EI, and extinguish when the local electric field drops below EX. During the PD event, space charge is generated which decreases the local electric field from EI to EX when the PD extinguishes. So the amount of charge should be responsible for the local electric field’s drop from EI to EX in the length from 0 to dx (where dx is the maximum propagation length of the xth PD event). The higher the applied voltage, the further the PDs can propagate as shown in Figure 10, increasing local electron avalanche size and so generating higher magnitude PD events.

At 10 kV the wing-like PD pattern transforms into a turtle-like PD pattern with time. The average and maximum PD magnitudes also decrease with time. At the same time, the length of tree channel increases. Previous research on artificial channels indicates that the turtle-like PD patterns appear in short tree channels due to the blocking of PD growth at the tree tip, while the wing-like PD patterns appear in long tree channels [6-7]. Our experimental results seem to be contradictory to this previous understanding of wing-like and turtle-like PD patterns. However, one thing to be noted is that with increased time of voltage application, the value of dV1 continuously decreases from 3.45 kV in the first minute to 1.4 kV in the 8th minute. According to Equation 6, the value of dV1 is linear with the value of (EI-EX). As previously discussed, the charge generated by the PD event decreases the local electric field from EI to EX, so at the same applied voltage, the PD magnitude should be linear with the value of (EI-EX). Thus with the decrease of the value of dV1, the PD magnitude decreases. Figure 15 shows the average maximum PD magnitudes and value of dV1 from 0-600 s. It can be seen that the change of dV1 and the PD magnitude show the same trend, as shown in Figure 15a; they are almost linear with each other as shown in Figure 15b. This is consistent with the discussion above.

From Figure 13, it can be seen that the value of VI

decreases with voltage duration up to 480 s. This is also seen for dV1. The decrease of PD inception voltage means the PDs can propagate longer distances. Once the conditions allow a

PD to propagate further than the maximum length of a tree channel, the PD magnitude is limited by the tree channel length. Then a turtle-like PD pattern forms [6, 8].

(a) Maximum PD magnitudes at 10 kV and the value of dV1 as a function of time.

(b) Linear fit between the maximum PD magnitude and the value of dV1.

Figure 15. Relationship between Maximum PD magnitudes at 10 kV and value of dV1.

One comment which should be added here is that in a wing-like PD pattern, the maximum PD propagation length is considered to be equal to or shorter than the maximum tree length. In this case the tree length does not limit the maximum PD magnitude in the wing-like pattern. However, no matter whether it is a wing-like or a turtle-like PD pattern, all the maximum PD magnitudes show a linear relationship with dV1. This indicates that the value of dV1 (and hence (EI-EX)) is a fundamental parameter controlling a PD event.

4.5 PD IN THE TREE BRANCH FROM A NEEDLE TIPIf approximating the electric field at the surface of the

needle tip to that generated at the surface of a metal sphere with the same radius, the PD inception and extinction voltage can be estimated by Equations (14).

(14)The values of VI vary at different applied voltages and

different voltage application times as shown in Figures 12 and 13. However, the values of VX remain consistent at

3.8 kV ± 0.2 kV. As the radius of the needle tip is 3 μm, the electric field at the surface of needle tip when the PDs extinguish can be determined as 1.2 kV/μm.

As discussed in Section 4.1, after a PD event, the electric field in the volume of the PD drops to EX. As the tree grows at 10 kV, it can be deduced that some PDs can extend from the needle to reach the tree tips. So after a PD event, the following relationship can be obtained:

(15)where Er is the residual electric field after the PD passes, and lmax is the maximum length of the tree channel. The peak voltage is 10 kV and the maximum length of the tree channel is 141 μm so that the average residual electric field Er is less than 0.07 kV/μm. This value is much lower than the calculated value of EX. However, Er is an average value and is calculated over the length of the channel, unlike EI and EX.

The highest electric field at the needle tip is determined by the radius of the needle tip. Inside the tree channel, the highest electric field is determined by the space charge distribution and the local micro structure of the tree channel. As the local tree channel is unlikely to be homogeneous, the highest local electric field may be much higher than the average electric field. That is also why the value of Er is much lower than the value of EX.

4.6 CONDUCTIVITY OF THE TREE CHANNEL AND CHARGE INJECTION FROM THE NEEDLE TIPIn Section 4.1, the first two assumptions concern limiting

the conductivity of the tree channel and charge injection from the needle tip. With these two assumptions, the Poisson electric field can be regarded as constant between PD events, and discussions are greatly simplified. However, in real tree channels, the conductivity is found to increase with the treeing process [17-19]. The PD pattern can also change with the increase of tree channel conductivity, or even cease when the tree channel conductivity is high enough [18, 19]. The characteristics of PD sequences considering the tree channel conductivity and charge injection from the needle tip will be systematically discussed in a separate paper.

5. CONCLUSIONSThe nature of partial discharges and associated electrical

trees are intimately connected. This paper studies the characteristics of partial discharge in a short branch tree channel grown from a steel needle. Both phase resolved partial discharge (PRPD) analysis and pulse sequence analysis (PSA) have been utilised and found to be complementary. It is found the average number of PDs per cycle increases linearly with the applied voltage, and the shapes of dV-dV patterns change with the applied peak voltage. At 10 kV the characteristic voltage differences decrease with time, the average number of PDs per cycle increases, the PD magnitude decreases, and the associated wing-like PD pattern evolves into a turtle-like PD pattern while the tree continuously grows.

This paper proposes a model considering the space charge distribution inside the tree channel. This model explains the

characteristic voltage differences of PDs from the needle. Several conclusions are drawn:1. The characteristic voltage differences are determined by the PD inception and extinction voltage and electric field.

2. The PD inception and extinction voltage/electric field can be calculated from the characteristic voltage differences in the PSA.3. The value of characteristic voltage differences and the applied peak voltage determine the average number of PDs per cycle, and the shape of PSA dV-dV patterns.4. The maximum PD magnitude increases linearly with the value of dV1, the difference in point-on-wave voltage between events within a rising or declining half cycle.5. The observed increase in average number of PDs per cycle, the decrease of maximum PD magnitudes and the PRPD wing-like pattern evolving into a turtle-like pattern at 10 kV are all due to the decrease of PD inception voltage reducing the value of dV1.

This paper links the physical nature of PDs in electrical tree channels to PD measurements. It provides an efficient method to evaluate the PD inception and extinction voltage/electric fields. It then provides a tool with which to interpret the dynamics of PD events in electrical trees. This paper also makes a link between the PRPD pattern and PSA which contain different but related information concerning PD. Together PRPD patterns and PSA can reveal the physical nature of PDs in tree channels, or indeed other kinds of defects.

ACKNOWLEDGEMENTThe authors are grateful to the EPSRC for support of this

work through the project 'Novel Composite Dielectric Structures with Enhanced Lifetimes’ EP/M016234/1.

This paper contains data which is openly available from www.manchestertrees.com.

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Zepeng Lv received the B.S. degree in electrical engineering from Xi'an Jiaotong University, Xi’an, China, in 2009; and then he received his doctoral degree from the same university in 2015. Now he works as a post-doctoral research associate in School of Electrical and Electronic Engineering, The University of Manchester. His research interests are in charge transport and aging processes in dielectrics.

Simon M. Rowland (F ‘14) was born in London, England. He completed the B.Sc. degree in physics at The University of East Anglia, and the PhD degree at London University, UK. He has worked for many years on dielectrics and their applications and has also been Technical Director within multinational companies. He joined The School of Electrical and Electronic Engineering in The University of Manchester in 2003, and was appointed Professor of Electrical Materials in 2009,

and Head of School in 2015. He was elected President of the IEEE Dielectric and Electrical Insulation Society in 2011 and again in 2012.

Hualong ZHENG was born in Henan, China in 1988. He received the B.Eng. degree in Electrical Engineering and Automation from the Changsha University of Science & Technology, China in 2010, the M.Sc. degree in Electrical Power Systems Engineering from the University of Manchester, UK in 2011 and the Ph.D. degree

from the University of Leicester, UK in 2015. He is currently a Research Associate at the University of Manchester. His research interests lie in space charge phenomena in polymeric DC insulations and the corresponding measurement techniques, electrical treeing breakdown process in polymeric materials and PD measurements.