Dielectric Breakdown of Gases - Fachgebiet Hochspannungstechnik

Dielectric Breakdown of Gases 

Disruptive discharges 

Overview 

Non-self sustaining discharge 

• mobility, drift velocity 

• average free traveling distance 

• pre-current density 

• impact ionization by electrons, formation of avalanches 

• ionization coefficient 

Self sustaining discharge 

• secondary emission coefficient 

• generations mechanism (Townsend mechanism) 

• Paschen‘s law 

• streamer mechanism 

• disruptive discharges in the extremely inhomogeneous field 

• disruptive discharges at impulse voltage stress 

• correction with air density, impact of humidity 

• dielectric strength of SF 6 

Fachgebiet 

Hochspannungstechnik 

High-Voltage Technology / Chapter 9, Part 2 - 1 -


Secondary emission coefficient 

Theroleof positive ions: 

• no contribution to ionization of the gas (energy too low!) 

but...... 

release of free electrons from the metallic cathode surface 

necessary energy: 

Work function W a 






Element 

Work Function W a (eV) 

Cs 0.7 ... 1.9 

Al 1.8 ... 4 

Ag 3.0 ... 4.7 

Mo 3.2 ... 4.2 

Ni 3.7 ... 5 

Cu 3.9 ... 4.8 

Fe 3.9 ... 4.8 

Au 4.3 ... 4.9 

Cr 4.4 

W a 

≈ ¼ W i 

Order number Name 

Allocation of shells 

K ... N with electrons 

K L M N 

1 Hydrogen (H) 1 

2 Helium (He) 2 

3 Lithium (Li) 2 1 

4 Beryllium (Be) 2 2 

5 Boron (B) 2 3 

6 Carbon (C) 2 4 

7 Nitrogen (N) 2 5 

8 Oxygen (O) 2 6 

9 Fluor (F) 2 7 

10 Neon (Ne) 2 8 

11 Sodium (Na) 2 8 1 

12 Magnesium (Mg) 2 8 2 

13 Aluminum (Al) 2 8 3 

14 Silicon (Si) 2 8 4 

15 Phosphorus (P) 2 8 5 

16 Sulfur (S) 2 8 6 

17 Chlorine (Cl) 2 8 7 

18 Argon (Ar) 2 8 8 

19 Pottassium (K) 2 8 8 1 

20 Calcium (Ca) 2 8 8 2 

1 st ionization energy 

(eV) 

1 st activation energy 

(eV) 

Remark 

13.6 10.2 

24.59 19 inert gas 

5.39 

9.32 

8.3 

11.26 

14.53 6.3 (for N 2 ) 

13.62 7.9 (for O 2 ) electronegative 

17.42 Fluor (F) electronegative 

21.56 16.6 inert gas 

5.14 

7.65 

5.99 

8.15 

10.49 

10.36 

12.97 electronegative 

15.76 inert gas 

4.34 

6.11 






W = W a 

E 











W = 2*W a 

E 











Precondition for release of a free charge carrier 

by an ion colliding with a metal surface: 

2·W a ≤ W = W i + W kin ≈ W i 

Yield of free charge carriers: 

Secondary emission coefficient (by positive ions) γ i 

or 

Second Townsend ionization coefficient 

γ = i 

number of released free charge carriers by positive ions 

number of positive ions arriving at the electrode surface 






Release of free electrons from the cathode surface by photons 

Necessary energy again: 

Work function W a 

"photo effect" 

or "photo emission" 

Precondition for release of a free charge carrier 

by a photon colliding with a metal surface: 

h·ν ≥ W a 

with ν = c 0 

/λ 

Frequency of 

the photon 

h ... "Planck‘s constant" or "Quantum of action" 

= 6.625·10 -34 Ws 2 = 4.134·10 -15 eVs 

c 0 

... velocity of light = 2.998·10 8 m/s 

λ 

h⋅c 

W 

≤ 

0 

a 






Question: 

What is the required wavelength to release a free electron from the surface 

of a copper electrode? 

h ⋅ c 4. 135 ⋅10 eVs ⋅ 2. 998 ⋅10 

m/s 

λ ≤ = = 

W 

48 . eV 

a, Cu 

−15 8 

258 

nm 

visible light: λ = 380 nm ... 750 nm 

UV-light: λ = 100 nm ... 380 nm 

Exposure of measuring sphere gaps by UV-lamps (see IEC 60052)! 






Number of photons approximately proportional to number of positive ions 

at breakdown electric field strength 

Definition of a common secondary emission coefficient γ possible: 

γ = 

number of released free electrons from the electrode surface 

number of positive ions 

γ = f(E/p, electrode material, surface condition, type of gas) 






Estimations: 

Under atmospheric conditions and gap spacings of several centimeters 

("long-range breakdown"): 

Air: γ ≈ 2·10 -6 

SF 6 

: γ ≈ 2·10 -7 

For the "close-range breakdown" in air: 

Aluminum: γ ≈ 0.035 

Copper: γ ≈ 0.025 

Iron: γ ≈ 0.02 





Generations mechanism 

radiation 

start 

electron 

1 st avalanche 

secondary emission 

start 

electron 

2 nd avalanche 

electric field strength E 

cathode 

anode 






No. of 

avalanche 

number of 

start electrons 

number of elctrons 

in the avalanche 

number of generated ions 

(elementary charges) 

1 1 

α 

2 γ(e s −1) 

3 

4 

γ 

γ 

2 αs 

( e − 

3 

1) 

αs 

( e −1) 

2 

3 

γ 

γ 

γ(e 

2 

3 

(e 

(e 

s 

e α α 

1 

αs 

αs 

αs αs αs 

αs 

αs 

−1) 

⋅e 

−1) 

−1) 

2 

3 

⋅e 

⋅e 

αs 

αs 

γ 

γ 

2 

3 

γ(e 

(e 

(e 

αs 

αs 

−1) 

⋅e 

−1) 

−1) 

2 

3 

⋅e 

⋅e 

αs 

αs 

e s − 

− γ(e −1) 

= γ(e 

− γ 

− γ 

etc. etc. etc. etc. 

2 

3 

(e 

(e 

αs 

αs 

−1) 

−1) 

2 

3 

αs 

2 

= γ (e 

3 

= γ (e 

−1) 

αs 

αs 

2 

−1) 

−1) 

3 

4 

A breakdown can happen only if each avalanche is at least 

as large as its predecessor, i.e.: 

γ 

α 

α n 

αs 

(e −1) ≥γ 

(e −1 ) or γ (e −1) 

≥ 1 

n+ 1 s n+ 

1 n s 






αs 

γ (e −1) 

≥ 1 

Solving to: 

αs ≥ ln (1 + 1/γ) = k 

Townsend condition of ignition for the homogeneous field 

s 

∫ α dx ≥ 

0 

Townsend condition of ignition for the slightly inhomogeneous field 

k 

A breakdown can happen only if the number of ionizing collisions has 

reached a critical value k. 

k = 2.5 ... 18 






Depending on electrode material, type of gas, electric field strength and pressure 

3 to 18 ionizing collisions along the discharge path are required 

in order to initiate a breakdown. 

The development of a breakdown according to the generations mechanism 

is limited to k = α·s



Traveling time in the gas along a distance of 1 to 2 cm: 

v e 

≈ 500 (cm/s)/(V/cm) · 30 000 V/cm = 150 mm/µs 

v i 

≈ (1...2) (cm/s)/(V/cm) · 30 000 V/cm = (0.3 ... 0.6) mm/µs 

for electrons: ca. 100 ns 

for ions: ca. 20 µs 

propagation time of 

electron avalanche 

Expected current: 

electron 

current 

propagation 

time of ions 

ion current 






Actual (measured) current: 

propagation time of 

electron avalanche 

photo effect = decisive mechanism 





Paschen's law 

Derived so far: 

B 

( E p) 

α 

− 

⎛E 

⎞ 

= A⋅ e = f ⎜ ⎟ 

p 

⎝ p⎠ 

αs ≥ ln (1 + 1/γ) 

Approximation of ionization coefficient 

Townsend condition of ignition 

E d 

= U d 

/s 

breakdown field strength – breakdown voltage 

Combining these equations and solving to U d 

.... 

U 

d 

B⋅ p⋅s 

B⋅ p⋅s 

= = = f( p⋅s) 

A⋅ p⋅s 

A⋅ p⋅s 

ln 

ln 

⎛ 1 ⎞ k 

ln ⎜1+ 

γ 

⎟ 

⎝ ⎠ 

Paschen's law 





Paschen's law 

Paschen's law: 

U d exclusively depends 

on the product p·s. 

(for a given temperature) 





Paschen's law 

Calculation of breqakdown voltage of a homogeneous plate electrode 

configuration (Rogowski profile) at: 

s = 1 cm, p = 1013 mbar, ϑ = 20 °C. 

From table hvt_9a, slide 76: A = 645 (bar·mm) -1 , B = 19 kV/(bar·mm). 

From slide 12: γ = 2·10 -6 (long range breakdown) 

U 

d 

B⋅ p⋅s 

19kV/(bar⋅mm)1.013bar ⋅ ⋅10mm = = = 30.945 kV ≈ 31 kV 

A⋅ p⋅s 

−1 

645(bar⋅mm) 

⋅1.013bar⋅10mm 

ln 

ln 

⎛ 1 ⎞ ⎛ 1 

ln 1+ 

+ 

⎞ 

⎜ ⎟ 

ln⎜1 

⎟ 

−6 

γ 

210 ⋅ 

⎝ 

⎠ 

⎝ 

When the gap spacing is halved to s = 0.5 cm and the pressure is doubled to 

p = 2026 mbar, the resulting breakdown voltage is exactly the same! 

⎠ 





Paschen's law 

Paschen curve 

short 

range 

breakdown 

long range 

breakdown 

Paschen curve of air at 20 °C in the homogeneous field 

1) experimentally derived curve 

2) for short range breakdown calculated with γ = 0,025 (see slide 12) 

3) for long range breakdown calculated with γ = 2·10 -6 (k = 13) (see slide 12) 





Paschen's law 

Paschen curve 

Paschen minimum by calculation of extreme value: dU d 

/d(p·s) = 0 

(p·s) min 

= e·k/A 

U d,min 

= B·(p·s) min 

- 





Paschen's law 

Paschen minimum 

(p·s) min 

= e·k/A 

U d,min 

= B·(p·s) min 

Gas U d, min (V) (p·s) min (bar·µm) 

SF 6 507 3.5 

O 2 450 9.3 

CO 2 420 6.8 

Air 330 … 350 7.3 

N 2 240 … 250 7.3 

H 2 230 ...270 14 

Ne 129 ... 245 53.2 

Ar 94 ... 265 

He 155 53.2 

At normal pressure 

(p = 1.013 bar): 

s = 7.3 µm 

At s = 1 cm: 

p = 0.73 mbar 





Paschen's law 

Paschen minimum 

At voltages below the 

Paschen minimum a 

breakdown is impossible! 





Paschen's law 

Paschen curve air 

p·s = 1 bar·cm 

U d 

= 31 kV 





Paschen's law Paschen curve SF 6 


U d 

≈ 89 kV 


U d 

≈ 330 kV 





Paschen's law 

Comparison of Paschen minima for air, SF 6 

, Argon 

Mean value of at least 20 measurements 

peak value of 50 Hz alternating voltage 

direct voltage, positive polarity 

dry air 





Paschen's law 

Increase of breakdown voltage at both sides of the Paschen minimum 

Long range breakdown 

short 

range 

breakdown 

long range 

breakdown 

p ↑ ...... 

s ↑ ...... 

free traveling distance ↓ 

electric field strength ↓ 

Short range breakdown 

number of available molecules ↓ 

infinite increase not possible, though! 





Paschen's law 

Paschen curve of a vacuum breaker tube 





Approximations 

For air in the homogeneous field, under atmospheric standard conditions and 

for gap spacings of few centimeters 

E d 

... breakdown electric field strength in kV 

C2 

Ed ≈ C1+ 

s … gap spacing in cm 

s C 1 

= 24.36 kV/cm 

C 2 

= 6.72 kV/cm ½ 

Ud = Ed⋅ s= C1⋅ s+ C2⋅ 

s 

(s ≈ 1 cm ... 10 cm) 

Ud = 24.5⋅ s+ 7⋅ 

s 





Approximations 

For SF 6 

in the homogeneous field, at normal temperature and 

for gap spacings of few centimeters 

U d = [8.84 kV/(bar·mm)]·p·s + 0.5 kV 





Streamer mechanism 

(according to Raether) 

Generations mechanism only as far as the number of electrons of the 

first avalanche stays below a critical value: 

 

E m 

N kr 

≈ e 18 ≈ 10 8 

 

E s 

space charge field E s 

superimposed to 

main field E m 

resulting increase 

of electric field strength 






E 

N el >= N kr 

• photo radiation, propagation at velocity of light 

• formation of new avalanches in front of, behind and beneath the primary avalanche 

• individual avalanches grow together streamer ("cold discharge") 

• propagation velocity 10 cm/µs ... 100 cm/µs 

• several parallel streamers possible 

• finally bridging of the total spacing by a streamer plasma channel, breakdown 






Important: a complete breakdown can 

develop from a single avalanche! 

Condition of ignition for streamer breakdown: 

α ⋅x kr 

≥18 

for the homogeneous field 

x 

∫ kr 

0 

αdx 

≥18 

for the slightly inhomogeneous field 






The drift velocity of electrons at values of the breakdown dielectric 

field strength (ca. 30 kV/cm) was calculated to be v e 

= 150 mm/µs. 

Assuming an ionization coefficient of α = 10.7 cm -1 (see calculation example 

chapter 9a, slide 79) the avalanche has reached the critical amplification e 18 

after a time t kr 

: 

t 

x α ⋅ x 

18 

= = = = 0.11µs 

10.7 cm ⋅15 cm/µs 

kr 

kr 

kr −1 

ve 

α ⋅ve 

The distance x kr 

passed up to this moment is 

x 

18 18 

= = = 1.68 cm 

α 10.7 cm 

kr −1 

conclusions ... 






conclusions ... 

Dielectric breakdowns may occur within a time of little more than 100 ns even 

at gap spacings in the range of far above one to two centimeters. 

The dielectric breakdown of air at atmospheric standard conditions follows the 

Townsend mechanism only at gap spacings of one to two centimeters. 

At gap spacings of several centimeters the streamer mechanism is 

relevant for dielectric breakdown. 






Overview 




















Characteristics of the slightly inhomogeneous field 

Condition of ignition for generations meachnism (Townsend): 

αs ≥ ln (1 + 1/γ) = k = 2.5 … 18 

homogeneous field 

s 

∫ 

0 

αdx 

≥ k = 

2.5 ...18 

slightly inhomogeneous field 

Condition of ignition for streamer mechanism: 

α ⋅x kr 

≥18 


x 

kr 

∫ 

0 

αdx 

≥18 







Definition of inhomogeneity by the utilization factor according to Schwaiger: 

η = E 0 

/E max 

homogeneous field: η = 1 ... 0.8 

slightly inhomogeneous field: η = 0.8 ... 0.2 

strongly inhomogeneous field: η = < 0.2 

η is also called degree of homogeneity. 






slightly inhomogeneous field: U a 

= U d 

When the condition of ignition is fulfilled ⇒ complete breakdown 

U d of the slightly inhomogeneous field is always 

lower than U d of the homogeneous field! 






Due to its non-linear 

dependence on electric field 

strength, ionization 

coefficient α increases more 

with an increase in field 

strength E than it decreases 

with a decrease of E. 








U 

i 

s 

= ∫ 

E id 

x 

0 

= 

U h = E h·s 

s 

∫ 

0 

α 

d 

x 

> 

α·s 

U d,i 

< 

U d,h 






For the same reason: U d, symmetrical 

> U d, asymmetrical 

U 

s 

U 

s 

E 

E 

x 

x 






slightly inhomogeneous 

symmetrical field 

slightly inhomogeneous 

asymmetrical field 

sym 

s 

s 

= ∫ symd 

= asym 

= ∫ 

asym 

0 

0 

U E x 

U E d 

x 

s 

∫ α 

d 

x 

< 

0 

s 

∫ 

0 

α 

d 

x 

U d,sym > U d,asym 






U d = 24.5·s + 7·√s 

symmetrical 

configuration 

asymmetrical 

configuration 






p 

= 

s 

+ 

r 

r 

q 

= 

R 

r 

η ⇒ 

next slide 

D = 100 cm, s = 10 cm 

p = 1.2; q = 1; η = 0.93 

U d = 24.5·s + 7·√s 

symmetrical 

configuration 

D = 25 cm, s = 10 cm 

p = 1.8; q = 1; η = 0.77 

D = 25 cm, s = 10 cm 

p = 1.8; q = ∞; η = 0.62 

D = 10 cm, s = 10 cm 

p = 3; q = 1; η = 0.56 

asymmetrical 

configuration 

D = 10 cm, s = 10 cm 

p = 3; q = ∞; η = 0.375 






spheres 





Development of breakdown in the strongly inhomogeneous field 

η < 0.2 0.2 

Fulfilling the thecondition of of ignition ignitionnot notsufficient to to initiate initiatea complete breakdown 

Formation of of space spacecharges, which whichsuperimpose the themain mainfield 

Pre-discharges, partial partial discharges, corona discharges 

when whenthe theinception voltage U e 

has 

e 

has been beenreached 

Partial Partial breakdowns, stabilized by byregions regionsof of low lowelectric field fieldstrength 

(with (withthe theeffect effectof of a resistive-capacitive series seriesimpedance) 

Breakdown when whenU d 

> 

d or or >> >> U e 

has 

e 

has been beenreached 





Development of breakdown in the strongly inhomogeneous field 

breakdown 

voltage 

corona 

inception 

voltage 

Distinct dependence on polarity 

for U e and U d 

strongly 


Degree of homogeneity η 





Strongly inhomogeneous field, positive tip 

Start electrons must be generated 

in the region where α > 0. 

Primary avalanche develops towards a region 

of increasing field strength. 

Space charge density 

Due to photo ionization: after initial individual 

discharges (streamer type): glow 

Electrons propagate to the anode, positive ions 

form a positiveley charged cloud (space charge) 

Decrease of electric field strength at the tip, 

increase of electric field in the space, 

border of α > 0 shifted to the right 

Strong streamers reaching far out into the space 





Strongly inhomogeneous field, positive tip 

Type of discharge Oscillogram of discharge current 

Streamers 

Glow 

Streamers 





Strongly inhomogeneous field, negative tip 

Start electrons must be generated directly at 

the tip to be able to produce avalanches; 

delay of ignition by statistical scattering 

Primary avalanche propagates towards a region 

of decreasing field strength; individual corona impulses 

Electrons propagate to the anode, positive ions 

form a positively charged cloud (space charge) 

Space charge density 

Attachment of electrons in the region of low electric 

field strength: negative ions, negative space charge 

Increase of electric field strength at the tip, decrease 

of electric field strength in the space, border of α > 0 

shifted to the left 

Trichel impulses, re-ignition whenever the negative 

space charge has disappeared 






Type of discharge Oscillogram of discharge current 

Trichel pulses 

increase Steigerung in frequency der (repetition Frequenzrate) 

with voltage mit der Spannung 

Streamers 

Streamers 

pulseless glow, 

negative glow 





Corona discharges 






• Breakdown voltage of positive tip is always lower 

than that of a negative tip 

U d, d, positive positive 



memory hook: "positive is negative" 

• At alternating voltage stress the breakdown of a strongly inhomogeneous 

asymmetrical electrode configuration generally occurs in the positive half cycle 





Stark inhomogenes Feld 

Ionenschirm 





Strongly inhomogeneous field 

Development of breakdown from pre-discharges 

Range of existence for different types of discharge 

Type of discharge 

Demand in 

voltage per 

unit length 

Leader 

ca. 1 m … several m 

> 20 cm 

< 20 cm 

Streamer 

Glow 

Gap spacing 

(for air under 

standard 

atmospheric 

conditions) 

Limit of homogeneous field 






Leader mechanism 

Pre-requisites: 

• Leader 

• Thermo ionization 

• Negative resistance 

• gap spacing > 1 m 

• sufficiently long time duration of stress 

• sufficiently high voltage rate of change (du/dt) 

• Leader corona (streamer) 

Fulfilled for positive SI voltage and alternating voltage (positive half cycle) 

Not fulfilled for direct voltage and LI voltage 






Leader mechanism at positive SI voltage 






Leader mechanism at positive SI voltage 

For insulation of alternating voltage of û = 1000 kV: s = 2 m 

For insulation of alternating voltage of û = 2000 kV: s = 8 m 

System System voltage voltageof of U s 

> 

s 1200 1200 kV kV not noteconomical 

due dueto to extreme requirements of of insulation! 

Electrical stength stengthto to positive SI SI voltage is is 

dimensioning for forequipment of of EHV EHV systems! 






Inception and breakdown voltages 

≈ 

≈ 

8 

8 

kV/cm 

kV/cm 

≈ 

≈ 

4.5 

4.5 

kV/cm 

kV/cm 

•• direct directvoltage 

•• sphere sphereØ 10 10 cm cm 

•air •air 

•• δ δ = 1 

positive sphere 

negative sphere 







≈ 

≈ 

4.5 

4.5 

kV/cm 

kV/cm 

•• alternating voltage voltage 


•air •air 

•• δ δ = 1 







hom. field 

Tip 

≈ 

≈ 

4...5 

4...5 

kV/cm 

kV/cm 


•air •air 

•• δ δ = 1 

In 

In 

order 

order 

to 

to 

increase 

increase 

inception 

inception 

voltage, 

voltage, 

radii 

radii 

must 

must 

be 

be 

increased. 

increased. 

In 

In 

order 

order 

to 

to 

increase 

increase 

breakdown 

breakdown 

voltage, 

voltage, 

gap 

gap 

spacing 

spacing 

must 

must 

be 

be 

increased. 

increased. 

Tip of 0.5 mm radius 

(voltage strongly depending on implementation of the tip) 







LI voltage 

1.2/50 

≈ 

≈ 

0.8 

0.8 

kV/cm 

kV/cm 

SI voltage 

alternating voltage, 50 Hz 

•• alternating, SI SI and and LI LI voltage voltage 

•air •air 

•• δ δ = 1 

gap spacing s 















•air •air 

•• ϑ ϑ = 20 20 °C °C 

Beyond a certain limit the breakdown develops 

directly when inception voltage has been 

reached, without any pre-discharges, even for 

strongly inhomogeneous configurations! 






Overview 




















Time delay of breakdown 

U 0 

... 

0 

... static staticinception voltage voltage 

U max 

t 0 t ... 

Start electron 

0 

... time time to to reach reachU 0 0 

u 

available 

t S t ... 

S 

... statistical scattering time time 

U 0 

t A t ... 

A 

... time time of of discharge dvpmt dvpmt 

t F t ... 

F 

... time time of of final final breakdown 

+ 

t 0 t S t A t F 

t 

discharge delay delaytime t V t V 

Total Total time time of of breakdown t D t = 

D t 0 t + 

0 t S t + 

S t A t + 

A t F t = 

F t 0 t + 

0 t V t + 

V t F t F 






t S t ... 

S 

... statistical scattering time time 

U max 

u 


available 

- decreases with increasing volume 

- in air at s = 1 mm: several 10 ns 

U 0 

- by UV radiation: t s 

0 

- decrease also by high roughness 

of electrode surface 


t 

- t S 

is higher in electronegative gases than in air 






t A t ... 

A 

... time time of of discharge development 

U max 

u 

U 0 


available 

Generations mechanism limited 

to low values of (p·s) and u ≈ U 0 

Streamer mechanism effective 

Velocity of avalanche propagation: 

v(t) ~ (u(t) - U 0 

) 


t 

d 

t + t + t 

0 S A 

0 S A 

= ∫ v() 

t dt { } 

t 

+ t 

0 S 

~ 

t + t + t 

t 

∫ 

+ t 

0 S 

ut () − U dt= Ad ⋅ = const. 

0 






t A t ... 

A 


U max 

u 

U 0 

A·d 

(voltage-time-area) 

Generations mechanism limited 

to low values of (p·s) and u ≈ U 0 

Streamer mechanism effective 

Velocity of avalanche propagation: 

v(t) ~ (u(t) - U 0 

) 


t 

d 

t + t + t 

0 S A 

0 S A 

= ∫ v() 

t dt { } 

t 

+ t 

0 S 

~ 

t + t + t 

t 

∫ 

+ t 

0 S 

ut () − U dt= Ad ⋅ = const. 

0 






t A t ... 

A 


U max 

u 

A·d 

(voltage-time-area) 

U 0 


t 

Law of of voltage-time-area (Kind, 1957) 






Law Lawof of voltage-time-area 

Discharge development characteristic 

Scatter characteristic 

A·d 

D 

Average characteristic 

A·d 

D 

A·d 

D 

Scatter of time to breakdown 






Breakdown-voltage-time-characteristic 

Problem: spark sparkgap gapshall shallprotect protectequipment 

Impulse breakdown voltage 

Time to breakdown 









No! 










Better,but 

just bad! 







Insulation coordination 

U-t-characteristics 

Voltage 

Rod-rod gap 1210 mm gap spacing 

GIS: withstand characteristic for chopped 

impulses at minimum operating pressure 

Arrester protective characteristic 

(max protection level) 

Time 







LI 

voltage 

SI 

voltage 

TOV 

continuous 

operating voltage 

Minimum 

Minimum 

at 

at 

front 

front 

time 

time 

of 

of 

≈ 

≈ 

1 

1 

ms 

ms 

Schematische Breakdown-voltage-time-characteristics Darstellung von Stoßkennlinien air at in small Luft bei gap 

kleinen spacings Schlagweiten (1) (streamer (1) mechanism) mit Streamerdurchschlag and large gap spacings und großen 

Schlagweiten (2) (leader mechanism) (2) mit Leaderdurchschlag 







50%-breakdown voltage of a rod-plane 

electrode 50%-Durchschlagspannung configuration in air einer under Stab-Platteatmospheric 

Funkenstrecke standard in Luft unter conditions atmosphärischen for 

positive Normalbedingungen LI and SI voltage: bei positiver Blitz- und 

1) Schaltstoßspannung 

standard LI voltage 1.2/50 

2) 1) standard Blitzstoßspannung SI voltage1,2/50 

250/2500 

3) 2) curve Schaltstoßspannung of minimum dielectric 250/2500 strength 

3) Kurve minimaler Festigkeit 






Overview 




















Correction with air density 

Relation between particle density n, gas pressure p and 

absolute temperature T (universal gas law): 

n 

p 

= 

k ⋅ T 

k ... Boltzmann constant = 1.37·10 -23 Ws/K 

absolute gas density 

ρ ~ p (p in bar or Pa; T in K) 

T 

relative gas density (by reference to standard values) 

δ 

ρ p T p 273+ 

20 

p 

0,289 

ρ p T 1013 273 + ϑ 273 + ϑ 

0 

= = ⋅ = ⋅ = ⋅ 

0 0 

(p in mbar or hPa 

ϑ in °C) 






In case of 

• only minor deviation from standard pressure and temperature 

• homogeneous or slightly inhomogeneous field 

Ud p⋅T0 

≈ = δ 

U p ⋅T 

d0 0 

Therefore: correction with density required! Acc. to IEC 60060-1: 

U 

d0 

U 

= 

k 

d 

d 

with 

k 

d 

m 

⎛ p ⎞ ⎛T0 

⎞ 

= ⎜ ⎟ ⋅ 

p 

⎜ 

0 

T 

⎟ 

⎝ ⎠ ⎝ ⎠ 

n 

m = n = 1 

k d 

= δ 

for homogeneous and slightly inhomogeneous field at any kind of voltage 

for strongly inhomogeneous field at direct and LI voltage 






For alternating and SI voltage and s > 1 m (leader mechanism!) 

m = n < 1 

3 7 9 





Impact of humidity 

see chapter HVT 1, Ch. 5 






Overview 




















Breakdown behaviour in SF 6 

•• about about3 times timeshigher higherdielectric strength compared with withair airat at 0.1 0.1 MPa MPa (α (α eff 

/p!) 

eff 

/p!) 

•• at at 0.2 0.2 MPa MPa to to 0.3 0.3 MPa MPa (2 (2 bar bar to to 3 bar) bar) overpressure diel.strength like likeinsulating oil oil 

•• GIS GIS are areoperated at at overpressures of of 0.3 0.3 MPa MPa to to 0.6 0.6 MPa MPa 





Ionization coefficient 

For formation of avalanches: 

α eff 

must be > 0. 

For air this is the case at 

E/p >= 25 kV/(cm bar), 

for SF 6 

it is the case only for 

E/p >= 88.4 kV/(cm bar) 

Reason for the two- to threefold 

dielectric strength of SF 6 

compared 

with that of air! 

Related effective ionization coefficient of air (1), nitrogen (2) and 

Effektiver bezogener Ionisierungskoeffizient von Luft (1), Stickstoff N 2 (2) und SF 6 (3) 

SF 6 (3), in Abhängigkeit depending von der related bezogenen electric elektrischen field strength Feldstärke 






Saturated vapor pressure curve of SF 6 

critical pressure 

liquid 

gaseous 

critical temperature 

SF Meaning 6 -Dampfdruckkurve of critical pressure and temperature: above these values SF 

Bedeutung des kritischen Drucks und der kritischen Temperatur: oberhalb dieser Werte tritt SF 6 nur noch 6 

gasförmig exists exclusively auf in gaseous form 






clean Al-conductor 

(laboratory conditions) 

50-Hz breakdown voltage 

(peak value) 

free conductive particles 

(length: 1 mm) 

free conductive particles 

(length: 6 mm) 

SF 6 

pressure 






Total pressure 

Plan: Plan: 

GIL GILshall shallbe beoperated at at 

20% 20% SF SF 6 

and 

6 

and 80% 80% N 2 2 

SF SF 6 

-air-mixture 

6 100 SF 6 

fraction 

0 Vol.% air 






SF 6 

Air 

Breakdown alternating voltage vs. (p·s) of a homogeneous field configuration in SF 6 and air 

Durchschlagwechselspannung einer Homogenfeld-Funkenstrecke in SF6 

in Abhängigkeit vom Produkt (p·s) mit Vergleichskurven für Luft 






Inception and breakdown alternating and direct voltage vs. gap spacing of 

Anfangs- und Durchschlagspannung einer Spitze-Platten-Funkenstrecke (Spitzenöffnungswinkel 30°) 

in SF 6 bei 1 bar Druck in Abhängigkeit von der Schlagweite s mit Vergleichskurven für Luft bei 

Gleich- und Wechselspannung 

a tip-plate electrode configuration (tip angle 30°) in SF 6 and air at 0.1 MPa 






Inception 

Air 

and breakdown alternating and direct voltage vs. pressure of a 

Anfangs- und Durchschlagspannung einer Kugel-Platte-Funkenstrecke (Kugeldurchmesser 1 cm) in SF 6 

sphere-plate in Abhängigkeit electrode vom Gasdruck configuration p mit Vergleichskurven (sphere für Luft diameter bei Gleich- und 1 Wechselspannung cm) in SF 6 and air

Dielectric Breakdown of Gases - Fachgebiet Hochspannungstechnik

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?