1. Prebreakdown phenomena in liquids and solids:
The effect of additives and phase
Øystein Leif Gurandsrud Hestad
oystein.hestad@sintef.no
Department of Chemistry
December 13th, 2010
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4. 3
Motivation
— All high-voltage equipment depends on insulating materials.
— The processes responsible for dielectric breakdown of liquid
and solid insulators are still unknown.
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5. 4
Why study prebreakdown and
breakdown phenomena?
— For improved reliability.
— Increase the design electric field (reduce cost).
— Push towards new environmentally friendly materials.
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6. 5
Properties of liquid and solid insulation
Liquid insulation
— Complex geometries
— Partially self healing
— Effective coolant
Solid insulation
— Typically higher dielectric strength than liquids
— Not self healing
— Poor thermal conductors
— Needed in all power apparatus (mechanical strength)
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7. 6
Hypotesis
— Hot electrons/electron avalanches are responsible for
prebreakdown phenomena in solids and liquids.
— Electrons accelerated by an electric field will have similar
effect on liquids and amorphous solids.
— Pre breakdown phenomena are similar for the two phases.
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8. 6
Hypotesis
— Hot electrons/electron avalanches are responsible for
prebreakdown phenomena in solids and liquids.
— Electrons accelerated by an electric field will have similar
effect on liquids and amorphous solids.
— Pre breakdown phenomena are similar for the two phases.
— Setup for prebreakdown experiments in liquids and frozen
liquids.
— Additive with known electron scavanger property.
— Additive with low ionization potential (IP).
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10. 8
Field-dependent conduction
Conductivity, σ(E) = µ(E) · n(E) · e
— Carrier density
• Injection of charge from electrodes
• Dissociation of molecules
• Ionization of molecules
— Mobility
• Increase with field, hopping
• Electrohydrodynamic motion (EHD)
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11. 9
Field-dependent conduction
Models for charge injection from electrodes/bulk conductivity
Schottky injection J(E) =
4πemk2
B(1−R)T2
h3 · e
− Φ
kBT
· e
e
2kBT
eE
π 0 r
Fowler-Nordheim J(E) = e3E2
8πhφ · e
−4
3
2m
2
φ3/2
eE
Hopping conduction σ(E) = 2νaen
E · e
− W
kBT
· sinh( eEa
2kBT )
Poole-Frenkel σ(E) = Neff NDeµ · e
− Φ
2kBT
· e
e3/2·
√
E√
4π 0 r kBT
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12. 10
Poole-Frenkel
— Poole-Frenkel is one of a series of high
field conductivity models.
• Bulk limited analogue of the Schottky
effect
• Insulator must have a wide band gap and
contain donors or acceptors
• Barriers localizing the carriers within the
dielectric are lowered by the field
• V(r) = −e2
4π 0 r r − eEr
• rm = ( e
4π 0 r E )
1
2
• ∆Vm = −2( e3
·E
4π r 0
)
1
2
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13. — σ(E) = σ0 · e(k·E
1
n )
— Dielectric time constant, space charge perturbed field
— 1
w = r 0
σ(Fc) ⇒ σ(Fc) = r 0w
— Fc = 1
k · ln r 0w
σ0
n
11
Space charge limited field
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14. — SCLF can be substantially lower than the Laplacian
field
— SCLF extends over a larger volume
— Intense energy disipation, σE2.
— Mechanical and thermal stressing.
12
Space charge limited field
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15. Liquid: Streamers Solid: Electrical trees
No theories exists that can explain all features.
Hot electrons are important for both.
13
Streamers and electrical trees -
prebreakdown phenomena
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16. 14
Inception
— Electron avalanche in liquid or low density region
• High field
• Sufficient extent
• Seed electron
— Discharge in bubble
— SCLF may be important
atom / molecule
high-energetic
electron
«Electron avalanche»
−+−
+→+ eAXeAX 2
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17. 15
1st mode streamer model
N. J. Felici 1988
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18. 16
2nd mode streamer model
Neg: H. M. Jones and E. E. Kunhardt 1985 Pos: W. G. Chadband, 1980
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31. 0 20 40 60 80 100 120 140 160
−20
−15
−10
−5
0
5
10
15
20
25
Time [min]
Temperature [C]
20 C
-15 C
-6.5 C
-1 C/min
10 min
10 min
Impulse
1. Freeze
21
Temperature control
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32. 0 20 40 60 80 100 120 140 160
−20
−15
−10
−5
0
5
10
15
20
25
Time [min]
Temperature [C]
20 C
-15 C
-6.5 C
-1 C/min
10 min
10 min
Impulse
1. Freeze
2. Constant T
21
Temperature control
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33. 0 20 40 60 80 100 120 140 160
−20
−15
−10
−5
0
5
10
15
20
25
Time [min]
Temperature[C]
20 C
-15 C
-6.5 C
-1 C/min
10 min
10 min
Impulse
1. Freeze
2. Constant T
3. Voltage impulse -
possible
degradation/treeing
21
Temperature control
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34. 0 20 40 60 80 100 120 140 160
−20
−15
−10
−5
0
5
10
15
20
25
Time [min]
Temperature [C]
20 C
-15 C
-6.5 C
-1 C/min
10 min
10 min
Impulse
1. Freeze
2. Constant T
3. Voltage impulse -
possible
degradation/treeing
4. Heat
21
Temperature control
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35. 0 20 40 60 80 100 120 140 160
−20
−15
−10
−5
0
5
10
15
20
25
Time [min]
Temperature [C]
20 C
-15 C
-6.5 C
-1 C/min
10 min
10 min
Impulse
1. Freeze
2. Constant T
3. Voltage impulse -
possible
degradation/treeing
4. Heat
5. Constant T
Sample can be healed
between each impulse.
21
Temperature control
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36. Chemicals
— Cyclohexane
• Benchmark liquid
— n-tridecane
• Energy band similar to polyethylene
• Crystalline structure similar to polyethylene
• High melting point (-5.5 ◦
C)
— N,N-dimethylaneline (DMA)
• Low IP (7.12 eV in gas phase)
• Low first excitation energy
— Trichloroethene(TCE)
• Electron scavenger
Model system
Frozen n-tridecane is a convenient model
system for polyethylene. Additives can easily be
added, and testing can be automated.
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38. 24
Cyclohexane (paper 1)
— Verification of experimental setup
— Temperature dependence of 1st mode positive streamers.
Related to energy required for bubble growth.
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39. 25
Neat n-tridecane/cyclohexane (paper 2)
— Pre-inception current
• Cyclohexane: σ(E) ∝ ek
√
E
, Poole Frenkel?
• n-tridecane: σ(E) ∝ ek
3√
E
, XLPE
• Higher SCLF for cyclohexane than for n-tridecane
— Large difference between inception voltage for cyclohexane
and n-tridecane
• Sufficient SCLF for electron avalanche?
• Low density region?
Comparison between liquid and frozen liquid
Similar charge measurements for both phases.
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40. — Pre-inception currents
• FEA (Comsol)
• Gauss law, calculate charge
induced on needle
• Requires accurate formula for field
dependent conductivity.
— Compare results from Comsol with
experiments.
Q = EdA
26
Comparison between FEA and
experiments
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41. 27
Effect of additives (0.1 M DMA and
0.1 M TCE) (paper 3)
DMA (low IP, low excitation energy)
— Increased prop. speed and size of pos. streamers
— Reduces size/charge of neg. streamers but increased light
emission
— Energy emitted as light, reduced energy for phase transition
TCE (electron scavanger)
— Increased pre-inception current
— Reduced inception voltage
— No effect on pos. or neg. streamers
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42. Ionization potential
— Impact ionization
— Photoionization
— Field ionization
Classical result: IP(E) = IP(0) − k ·
√
E
Excitation energies
— Field dependent at low fields for
n-tridecane
— May explain difference in high field
conductivity
Cyclohexane
n-tridecane
IP
Excitation
28
Field dependence of IP and excitation
energy (paper 4)
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43. σ(E) = σ0e
∆(E)
2kBt
(1)
∆(E) = IP(E) − 1(E) (2)
∆(E) = ∆(0) − βPF γE (3)
∆(E) = ∆(0) − β1/3
3
γE (4)
cyclohexane
Energy difference can be fitted to eq. (3),
Poole-Frenkel.
n-tridecane
Energy difference can be fitted to eq. (4),
σ(E) ∝ ek
3√
E .
Cyclohexane
n-tridecane
IP
Excitation
(3)
(4)
n-tridecane
29
High field conductivity (paper 4)
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44. 30
Approximation of field/charge and extent
of SCLF from spheroid in uniform
background field (paper 5)
Critical SCLF extent in XLPE ≈ 2 µm
— FEA (time consuming)
— Exact solution (difficult/impossible)
— Laplace equation solved for prolate
spheroidal coordinates (Zhou and Boggs)
— Solution for concentric sphere geometry and
field dependent conductivity
(Hibma and Zeller)
Approximation
Field on spheroid surface, extent of SCLF along axis, and charge
on the spheroid.
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45. — Laplacian and SCLF region
— Laplacian and SCLF time
region
0 0.2 0.4 0.6 0.8 1
0
5
10
15
0
5
10
15
Time [µs]
Electricfield[MV/m]
31
Approximation of field/charge and extent
of SCLF from spheroid in uniform
background field
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46. 32
Concluding remarks
— Clear correlation between prebreakdown phenomena in liquid
and solid phase.
• Similar processes responsible for inception and propagation
• Electrical trees propagate in amorphous regions
• Inhomogeneity in solid phase, increased scatter.
— Space charge limited field important for inception.
Model system
Frozen n-tridecane is a convenient model system for polyethylene.
Additives can easily be added, and testing can be automated.
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47. 33
Concluding remarks
— Low IP additive enhanced positive streamers/el. trees in
n-tridecane. Increased size of el. avalanches.
— Additives with low excitation energies may retard streamers
through emission of energy as light.
— Ionization potentials and excitation energies are field
dependent.
• Important for all pre-breakdown phenomena.
• May explain high-field conduction in cyclohexane and
n-tridecane.
• Fast mode (photoionization).
Quantum chemistry
Information about molecular ionization potential and excitation
energy levels are essential.
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