Modelling of Dry-band Discharge Events on Insulation Surfaces

Xin Zhang and Simon M Rowland Electrical Energy and Power Systems (EEPS) Group

School of Electrical and Electronic Engineering The University of Manchester

United Kingdom s.rowland@manchester.ac.uk

Abstract—Discharges on composite insulator insulation surfaces are one cause of long-term ageing. Consequences of such ageing are further acceleration of damage, and ultimately an increased likelihood of flashover. Normally it is an unacceptable flashover probability that requires maintenance or replacement of aged insulators. In some cases however, the surface discharges can lead to deep erosion which can then lead to of the surface being penetrated. This can result in moisture penetration into the core and internal tracking and permanent insulator failure. For these reasons modelling of discharge activity is important to understanding ageing processes. Here we show that the dynamic behaviour of moisture on the surface of an insulator is critical to its ageing. Circumstances are identified in which very rapid ageing can take place. The thermal properties of arcs are also shown to be non-linear. Experimental evidence from testing in salt fog chambers is presented and used to quantify the description of energy available for the degradation process. Using these experimental results, arc power and energy are analyzed as functions of arcing length. Causes for unusual heating of the polymer substrate, which ultimately damages the insulation material more rapidly than otherwise expected, are also identified.

Keywords-double sinusoidal model; triple cylinder model; dry-band arc; arc compression; arc current; arc voltage; arc power; energy radiation;

I. INTRODUCTION The first high-voltage insulator utilized in power

transmission line was invented in 1882. Development resulted in rapid growth over the 19th and 20th centuries [1]. The history of composite insulators dates back to the 1940s, when organic materials were applied in indoor insulator manufacture [2]. For the last thirty years, composite insulators have been increasingly used in modern power transmission systems and are beneficial because of their excellent electrical insulation, good contamination performance, low weight, ease of installation periods and reduced damage from vandalism [3-4].

In practical outdoor situations, influences such as UV radiation, moisture and pollution may reduce the electrical resistance of insulator surfaces. Based on the loss of surface quality, everyday-service electric fields, temporary switching or lightning are able to generate electrical discharges or even dry-band arcing [5]. Dry-band arcing is one of the key

mechanisms responsible for the damage of insulator materials. The degradation process may be summarized as follows: the heat and radiation from arcing may result in chemical changes in the polymer surface, leading to hydrophobicity loss, eroding material, allowing moisture penetration to the fiberglass core and eventually causing the insulator mechanical failure [6-8]. Fig. 1 shows the typical location of a dry-band arc on an insulator surface and its resultant damage.

The currents driving dry-band arcs are normally limited due to the resistance presented by the rest of the insulator surfaces [5]. Besides, commercial materials such as HTV-SIR (high temperature vulcanized silicone rubbers) filled with ATH (alumina trihydrate) are well established and resistant against dry-band arcing [9]. Therefore, the deterioration from arcing discharges is generally considered as a long term hazard on good quality composite insulators.

However, experimental research has confirmed that accelerated degradation on insulation surface could be possible if a dry-band arc is physically compressed in length. Such an arc compression event can result from the movement of moisture with high mobility at the edge of arcing activity. Further energy analysis indicates that the arcing transients with reduced arc length may produce much higher levels of energy dissipation than normal stable arcs which may consequently lead to unexpected failure of dielectric materials [10].

Figure 1. Evidence of damage from dry-band arcing at the bottom core of silicone-rubber based insulator: a) aged insulator sample, b) typical location of

a dry-band arc, c) erosion damage on insulator core from a 1000 hr salt-fog test

978-1-4244-6301-5/10/$26.00 @2010 IEEE

Such mechanisms therefore lead to the need for the

electrical characteristics of such transient arcing together with resultant power and energy radiation need to be further understood. In this paper, a novel double sinusoidal model is proposed to simulate the electrical properties of arcs in terms of arcing current and voltage in time domain. Based on this model, an additional triple cylinder model is applied to analyze the heat flow inside the arc and from the arc to its environment. Modeling parameters are determined from dry-band arcing experiments in salt-fog conditions. A conclusion is drawn that the physically length-compressed arc can lead to transient surges of heat dissipation. This, in turn, may cause more severe damage to insulation material surfaces than normal arcing situations.

II. MODELLING APPROACH

A. Double Sinusoidal Model The Double Sinusoidal Model is developed by using two

sinusoidal waves as a tool for simulation of the I-t (current in the time domain) and V-t (voltage in the time domain) characteristics of dry-band arcing. Fig. 2 shows the model.

Figure 2. Double sinusoidal model based on the experimental I-t and V-t result.

Fig. 2 a) describes the typical I-t and V-t profiles of a dry-band arc experimentally measured. Based on this result, two sinusoidal waves with respective magnitude and angular frequency are chosen to fit the experimental results in Fig. 2 b). For the continuous arcing phenomenon, the simulation approach divides the whole time domain into half power cycles. For each half cycle three sections are identified as: the pre-arcing period, the arcing period and the post-arcing period in Fig. 2 c). Each period is now considered separately:

• Pre-arcing period (0<t<t1) Due to the high impedance presented across the dry-band

area, the current is almost limited to zero. In the meantime, the voltage increases smoothly following the sinusoidal system voltage. In pre-arcing period I-t and V-t are described as:

( ) 0=ai t (1)

( ) 2 sin=a a uu t U tω (2)

Where: ia(t) and ua(t) are simulated current (mA) and voltage (kV) traces in pre-arcing period. Ua and ωu are the rms value (kV) and angular frequency (rad/ms) of the voltage sinusoidal wave (Sine wave I).

• Arcing period (t1<t<t2) In this period, the voltage is sufficient to breakdown the air

gap in dry-band area; the arc striking from t1. Due to the establishment of the arcing channel, the current suddenly increases and then changes smoothly until it returns to zero, while the arcing voltage behaves as an inclined straight line. In the arcing period I-t and V-t are described as:

2( ) 2 sin [ ( )]= − −a a iu

i t I t tπωω

(3)

1 21 1

2 1

( ) ( )−

= − −−

t ta t

U Uu t U t t

t t (4)

Where: ia(t) and ua(t) are the simulated current (mA) and voltage (kV) traces in arcing period. Ia and ωi are the rms value (mA) and angular frequency (rad/ms) of the current sinusoidal wave (Sine wave II). ωu is angular frequency (rad/ms) of the voltage sinusoidal wave, t1 is the arc ignition time (ms), t2 is the arc extinction time (ms), Ut1 is the arc ignition voltage (kV), Ut2 is the arc extinction voltage (kV).

• Post-arcing period (t2<t<T0/2) In this period, the arc is extinguished from t2 due to an

insufficient voltage and current to keep the current flowing. The current is reduced to zero indicating the recovery of surface dielectrics in dry-band area. Consequently, the voltage again follows the sinusoidal system voltage. The I-t and V-t simulations for post-arcing period are described as: ( ) 0=ai t (5)

( ) 2 sin=a a uu t U tω (6)

Where: ia(t) and ua(t) are continuations of the simulated current (mA) and voltage (kV) traces in pre-arcing period. Ua and ωu are the rms value (kV) and angular frequency (rad/ms) of the voltage sinusoidal wave (Sine wave I). T0 is the periodic time of voltage sinusoidal wave. According to the UK power frequency, T0 is set to 40 ms.

The sign function is used to combine the equations from (1) to (6). The I-t and V-t modelling for the half cycle can be obtained as:

1 22

1 [( )( )]( ) 2 sin [ ( )]

2− − −

= − − ×a a iu

sign t t t ti t I t tπω

ω (7)

1 2

1 2 1 21 1

2 1

1 [( )( )]( ) 2 sin *

21 [( )( )]

[ ( )]*2

+ − −=

− − − −+ − −

−

a a u

t tt

sign t t t tu t U t

U U sign t t t tU t t

t t

ω (8)

b)

c) d)

t1 t2

Ut1

Ut2

ia(t)ua(t)

T0/2

a)

Where: 0<t<Tu/2 (ms). Based on the (7) and (8), the simulated I-V traces for the whole time domain is:

00 0

0

00 0

0

( ) ( ) 1( )( ) ( ) 2

( ) ( ) 1( ) ( 1)( ) ( ) 2

⎧ = − ⎫< < +⎬⎪ = −⎪ ⎭

⎨= − ⎫⎪ + < < +⎬⎪ = − ⎭⎩

a a

a a

a a

a a

i t i t kTkT t k T

u t u t kT

i t i t kTk T t k T

u t u t kT

(9)

Where k=0, 1, 2, 3…

B. Triple Cylinder Model [11] The triple Cylinder model is introduced to further analyze

the heat flow inside the arc and from arc to its surroundings. The original model was developed for the investigation of high current (approximate 500 A), low voltage (approximate 20 V), and short length (0-6 mm) arcs in switchgear with metal contacts [11]. In this paper, this model is applied to a dry-band arc with low current (1-5 mA), high voltage (10-25 kV) and between water electrodes. Fig. 3 shows the proposed triple cylinder model.

Figure 3. Triple cylinder thermal model with three zones and corresponding power flow in every direction.

The modelling calculation is based on three cylinder arcing regions respectively near the cathode, anode and in the arc column. In each cylinder zone, a concentrated source of heat (P1, P2 or P3) is situated at the geometrical centre of cylinder. This source dissipates heat energy to both the cylinder lateral surfaces and cylinder faces as demonstrated in fig 4.

Figure 4. Energy flow calculation for one cylinder model

According to Fig. 4 b), total power flowing through the cylinder lateral surface is

2 2=

+b c

dP Pa d

(10)

Where: Pc is the source power.

According to Fig. 4 c), power flowing through one of the cylinder faces is

2 2

1 (1 )2

= −+

p cdP P

a d (11)

Based on the (10) and (11), the energy flows for triple cylinder model in Fig. 3 are summarized as follows:

Total instantaneous power delivered to the cathode is given by

33 2 2

3 311 22 2

1 1 21 2 2 2

2 2

( )1 ( ) 12 ( ) ( )( )1( ) ( ) 1

2 ( ) ( ) ( )1 ( ) 12 ( ) ( )

⎧ ⎫⎧ ⎫⎛ ⎞⎪ ⎪⎪ ⎪⎜ ⎟− +

⎜ ⎟⎪ ⎪⎪ ⎪⎛ ⎞ +⎪ ⎪ ⎪⎪⎝ ⎠⎜ ⎟= − +⎨ ⎨ ⎬⎬⎜ ⎟ ⎛ ⎞+⎪ ⎪ ⎪⎪⎝ ⎠ ⎜ ⎟−⎪ ⎪ ⎪⎪⎜ ⎟+⎪ ⎪ ⎪⎪⎝ ⎠⎩ ⎭⎩ ⎭

K k a

a

d tP t

a t d td tP t k P t k

a t d t d tk P ta t d t

(12)

Where: PK(t) is power delivered to the cathode. kk is a coefficient of heat penetration to cathode. k2a is coefficient of the power flow from the arc column to the cathode spot. k1a is coefficient of the power flow from the anode spot to the arc column.

Total instantaneous power delivered to the anode is given by

33 2 2

3 322 22 2

2 2 11 1 2 2

1 1

( )1 ( ) 12 ( ) ( )( )1( ) ( ) 1

2 ( ) ( ) ( )1 ( ) 12 ( ) ( )

⎧ ⎫⎧ ⎫⎛ ⎞⎪ ⎪⎪ ⎪⎜ ⎟− +

⎜ ⎟⎪ ⎪⎪ ⎪⎛ ⎞ +⎪ ⎪ ⎪⎪⎝ ⎠⎜ ⎟= − +⎨ ⎨ ⎬⎬⎜ ⎟ ⎛ ⎞+⎪ ⎪ ⎪⎪⎝ ⎠ ⎜ ⎟−⎪ ⎪ ⎪⎪⎜ ⎟+⎪ ⎪ ⎪⎪⎝ ⎠⎩ ⎭⎩ ⎭

A a k

k

d tP t

a t d td tP t k P t k

a t d t d tk P ta t d t

(13)

Where PA(t) is power delivered to the anode. ka is a coefficient of heat penetration to anode. k2k is coefficient of the power flow from the arc column to the anode spot. k1k is coefficient of the power flow from the cathode spot to the arc column.

Instantaneous powers from zone 1, zone 2 and zone 3 delivered to the material surface are given by

33 2 2

3 3 11 1 1 2 2 2

1 121 2 2 2

2 2

( )1 ( ) 12 ( ) ( ) ( )( ) ( )

( ) ( )( )1 ( ) 12 ( ) ( )

⎧ ⎫⎧ ⎫⎛ ⎞⎪ ⎪⎪ ⎪⎜ ⎟− +

⎜ ⎟⎪ ⎪⎪ ⎪ ⎛ ⎞+⎪ ⎪ ⎪⎪⎝ ⎠ ⎜ ⎟= +⎨ ⎨ ⎬⎬⎜ ⎟⎛ ⎞ +⎪ ⎪ ⎪⎪⎝ ⎠⎜ ⎟−⎪ ⎪ ⎪⎪⎜ ⎟+⎪ ⎪ ⎪⎪⎝ ⎠⎩ ⎭⎩ ⎭

S s a

a

d tP ta t d t d tP t k P t k

a t d td tk P t

a t d t

33 2 2

3 3 22 2 2 2 2 2

2 211 1 2 2

1 1

( )1 ( ) 12 ( ) ( ) ( )

( ) ( )( ) ( )( )1 ( ) 1

2 ( ) ( )

⎧ ⎫⎧ ⎫⎛ ⎞⎪ ⎪⎪ ⎪⎜ ⎟− +

⎜ ⎟⎪ ⎪⎪ ⎪ ⎛ ⎞+⎪ ⎪ ⎪⎪⎝ ⎠ ⎜ ⎟= +⎨ ⎨ ⎬⎬⎜ ⎟⎛ ⎞ +⎪ ⎪ ⎪⎪⎝ ⎠⎜ ⎟−⎪ ⎪ ⎪⎪⎜ ⎟+⎪ ⎪ ⎪⎪⎝ ⎠⎩ ⎭⎩ ⎭

S s k

k

d tP t

a t d t d tP t k P t k

a t d td tk P t

a t d t

13 1 1 2 2

1 1 33 3 2 2

3 321 2 2 2

2 2

( )1( ) ( ) 12 ( ) ( ) ( )

( )( ) ( )( )1 ( ) 1

2 ( ) ( )

⎧ ⎫⎛ ⎞⎪ ⎪⎜ ⎟+ − +

⎜ ⎟⎪ ⎪⎛ ⎞+⎪ ⎝ ⎠ ⎪⎜ ⎟= ⎨ ⎬⎜ ⎟⎛ ⎞ +⎪ ⎪⎝ ⎠⎜ ⎟−⎪ ⎪⎜ ⎟+⎪ ⎪⎝ ⎠⎩ ⎭

k

S s

a

d tP t k P t

a t d t d tP t k

a t d td tk P ta t d t

Where P1S(t), P2S(t) and P3S(t) are the power delivered to material surface from zone1, zone2 and zone3 respectively. k1S, k2S and k3S are coefficients of heat penetration to material surface from zone1, zone2 and zone3 respectively.

(a) Cylinder model with Pc

(b) Power flowing through cylinder lateral surface

(c) Power flowing through cylinder face

(14)

(15)

(16)

III. EXPERIMENTATION AND MODELLING An experiment was carried out to determine the parameters

for the double sinusoidal model. A brief summary of this experiment is shown in Fig 5: A dry-band arc was created on the inclined silicone-rubber rod in a salt-fog chamber. During the testing period, the moisture above the arc was pulled down by gravity and arc discharges disrupting surface tension, while the lower moisture was stationary. Therefore, the arc was physically compressed in length as the slope of the rod was increased [12]. The variable arc lengths with corresponding I-t and V-t characteristics of arc were recorded. Modelling parameters for the Double Sinusoidal Model were estimated based on these experimental results and are summarized in Table I.

Figure 5. Test arrangement for dry-band arc compression

TABLE I. CALCULATED PARAMETERS FOR DOUBLE SINUSOIDAL MODEL

Double Sinusoidal Model Constant Parameters Variable Parameters

Ua [kV] 17.4 t1 [ms] t1=f(La) =t2+2.99La-11.16

Ia [mA] 1.55 La [cm] 1.1<La<2.3 U0 [kV] 8.7 k 0,1,2,3… Ut1 [kV] 10.30 Ut2 [kV] 6.56

ωu [rad/ms] 0.314 ωi [rad/ms] 0.408

t2 [ms] 8.88 T0 [ms] 40

By substitution of the modelling parameters from Table I into the Double Sinusoidal Model presented in equations (7-9), the I-t and V-t traces of dry-band arcing can be simulated. These are compared with experimental results in Fig. 6. The situation of arc length compression is modelled by the various arc lengths with respectively different I-t and V-t characteristics.

Figure 6. Simulated I-t and V-t traces from Double Sinuoidal Model comparing with experimental results

In Fig. 6, the correlation coefficient r between simulation and experimental results is calculated in each case, showing the r = 0.99 for voltage, r = 0.95 for current with the 2.3 cm arc length; r = 0.996 for voltage, r = 0.986 for current with 1.7 cm arc length; and r = 0.99 for voltage, r = 0.99 for current with the 1.1 cm arc length. The excellent correlation coefficients confirm the validity of Double Sinusoidal Model for simulating the electrical characteristics of dry-band arcing and its compression events.

The simulated I-t and V-t traces from the Double Sinusoidal Model can be used as the input of Triple Cylinder Model. Based on the parameter determination for Triple Cylinder Model in Table II, the final energy radiation from dry-band arc to it surroundings in different directions can be obtained as shown in Table III.

TABLE II. CALCULATED PARAMETERS FOR TRIPLE CYLINDER MODEL

Triple Cylinder Model Constant Parameters Variable Parameters

d1(t)=d2(t) 1 mm ia(t) [mA] Simulation result

from Double Sinuoidal Model

kk 0.3 ua(t) [kV] Simulation result

from Double Sinuoidal Model

k1a 0.2 P1(t) ia(t)×ua(t)/3 k2a 0.2 P2(t) ia(t)×ua(t)/3 ka 0.3 P3(t) ia(t)×ua(t)/3 k1k 0.2 La [cm] 1.1<La<2.3 k2k 0.5 a1(t)=a2(t)=a3(t) kL×ia(t) K1S 0.3 d3(t) La-d1(t)- d2(t) K2S 0.3 K3S 0.3 kL 0.000528

Die

lect

ric ro

pe

Volta

ge d

ivid

er

-50-40-30-20-10

01020304050

0 5 10 15 20 25 30 35 40

(ms)

Volta

ge(k

V)

-5-4-3-2-1012345

Cur

rent

(mA

)

VoltageCurrent

Arc length: 1.7 cm

Simulation Result

-50-40-30-20-10

01020304050

0 5 10 15 20 25 30 35 40

(ms)

Volta

ge(k

V)

-5-4-3-2-1012345

Cur

rent

(mA)

VoltageCurrent

Arc length: 1.1 cm

Simulation Result

-50-40-30-20-10

01020304050

0 5 10 15 20 25 30 35 40

(ms)

Vol

tage

(kV)

-5-4-3-2-1012345

Cur

rent

(mA)

VoltageCurrent

Equilibrium arc length: 2.3 cm

Arcing period

Experiment

-50-40-30-20-10

01020304050

0 5 10 15 20 25 30 35 40

(ms)

Volta

ge(k

V)

-5-4-3-2-1012345

Cur

rent

(mA

)

VoltageCurrent

Equilibrium arc length: 1.7 cm

Experiment Result

Arcing period

-50-40-30-20-10

01020304050

0 5 10 15 20 25 30 35 40

(ms)

Volta

ge(k

V)

-5-4-3-2-1012345

Cur

rent

(mA)

VoltageCurrent

Equilibrium arc length: 1.1 cm

Experiment Result

Arcing period

-50-40-30-20-10

01020304050

0 5 10 15 20 25 30 35 40

(ms)

Vol

tage

(kV)

-5-4-3-2-1012345

Cur

rent

(mA)

VoltageCurrent

Arc length: 2.3 cm

Simulation Result

TABLE III. ENERGY RADIATION FROM DRY-BAND ARCING TO SURROUNDINGS IN A POWER CYCLE

Arc length

Energy to

Cathode

Energy to

Anode

Cathode to

Insulation Surface

Colume to

Insulation Surface

Anode to

Insulation Surface

La [cm] EK [Joule] EA[Joule] E1S [Joule] E2S [Joule] E3S [Joule] 2.32 0.0065 0.0067 0.0309 0.0312 0.0459 2.28 0.0078 0.0080 0.0370 0.0373 0.0550 2.16 0.0082 0.0084 0.0389 0.0393 0.0579 1.94 0.0097 0.0100 0.0462 0.0467 0.0687 1.81 0.0099 0.0102 0.0473 0.0477 0.0702 1.72 0.0108 0.0111 0.0512 0.0517 0.0760 1.45 0.0116 0.0119 0.0551 0.0556 0.0816

IV. DISCUSSION Fig. 7 shows the examples of energy dissipation extracted

from Table III. The results cover the arc lengths of 2.3 cm, 1.7 cm and 1.1 cm. When the dry-band arc is compressed, the energy of the arc (EK, EA, E1S, E2S and E3S) is increased. E3S is the highest energy release to the arc surroundings. E1S and E2S are approximately equal but both provide the lowest energy radiations.

Figure 7. Example results of arcing energy for different radiation directions

V. CONCLUSION The double Sinusoidal model presented in this paper

successfully simulates the I-t and V-t characteristics for dry-band arcing compression. The triple cylinder model, which integrates the double sinusoidal model as the input data, is able to calculate the heat energy flow inside the arc region and from arc to its environment.

The arc modelling work indicates that when the arc is compressed in length due to external motion of the moisture films beside it, the arc energy radiation is enhanced in all the directions from the arc plasma to its surrounding. The worst case may happen when the arc length is extremely short, which

could increase the possibility of damage to the substrate. The instantaneous arc power and accumulated arc energy in the middle of arcing area facing the material surface are highest. Therefore, the material may suffer more damage across that region. The energy dissipation to both water electrodes (edge of two water films) is less. The compression of naturally occurring dry-band arcs may therefore consequently accelerate the material ageing process.

ACKNOWLEDGMENT The authors would like to acknowledge National Gird for

their support of this research.

REFERENCES

[1] J.S.T.Looms, Insulators for High Voltages. London: Peter Peregrinus Ltd, 1990.J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68–73.

[2] J. F. Hall, "History and bibliography of polymeric insulators for outdoor applications," IEEE Transactions on Power Delivery, vol. 8, pp. 376-385, 1993.

[3] R. Hackam, "Outdoor HV composite polymeric insulators," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 6, pp. 557-585, 1999.

[4] M. Kumosa, L. Kumosa, and D. Armentrout, "Failure Analyses of Nonceramic Insulators Part 1: Brittle Fracture Characteristics," in IEEE Electrical Insulation Magazine. vol. 21, May/June, pp. 14-27, 2005.

[5] R. S. Gorur, E. A. Cherney, and J. T. Burnham, Outdoor Insulators. Text book, ISBN 0-9677611-0-7, Phoenix, Arizona, USA, 1999.

[6] Y. Xiong, S. M. Rowland, J. Robertson, and R. J. Day, "Surface analysis of asymmetrically aged 400 kV silicone rubber composite insulators," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 15, pp. 763-770, 2008

[7] S. E. Kim, E. A. Chemey, and R. aackam, "Effect of Dry Band Arcing on the Surface of RTV Silicone Rubber Coatings," in IEEE International Symposium on Electrical Insulation Baltimore, MD USA, 1992.

[8] Y. Zhu, M. Otsubo, N. Anami, C. Honda, O. Takenouchi, Y. Hashimoto, and A. Ohono, "Change of polymeric material exposed to dry band arc discharge [polymer insulator applications]," in Annual Report Conference on Electrical Insulation and Dielectric Phenomena, 2004, pp. 655-658.

[9] S. Kumagai and N. Yoshimura, "Tracking and erosion of HTV silicone rubber and suppression mechanism of ATH," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 8, pp. 203-211, 2001.

[10] X. Zhang and S. M. Rowland, “Dry-band Arc Compression and Resultant Arc Energy Changes,” 11th INSUCON International Electrical Insulation Conference, Birmingham, United Kingdom, pp. 308-313, 2009.

[11] P. Borkowski and E. Walczuk, "Thermal models of short arc between high current contacts," in Proceedings of the Forty-Seventh IEEE Holm Conference on Electrical Contacts, 2001, pp. 259-264.

[12] X. Zhang, S. M. Rowland and V. Terzija, “Modelling of Dry-band Arc Compression”, 16th International Symposium on High Voltage Engineering, Cape Town, South Africa, pp. 284, 2009.

00.010.020.030.040.050.060.070.080.09

1 2 3 4 5

Ener

gy (J

)

Arc Length 2.3 cmArc Length 1.7 cmArc Length 1.1 cm

Ek Ea E1s E2s E3s