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Nonstandard High-Voltage Electric Insulation Models
Thomas Christen, ABB Corporate Research, ABB Switzerland Ltd
24 October 2012 | Slide 1
Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan
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Standard procedure (usually AC)
1. Calculate electric field (test conditions, …)
2. Check for dielectric withstand
Electric breakdown (E < breakdown field)
Thermal runaway (electro-thermal simulation)
Nonstandard procedure for
o Direct Current (DC) simulations
o E-Field simulation including electric breakdown
equation for charge carrier avalanche sparks etc.
Simulation for Insulation Design
24 October 2012 | Slide 2
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Quick & Computational resource friendly
o Parameter studies
o Various different (test) scenarios
Flexible with respect to physics /modeling
o Bulk (PDEs, ODEs, …)
o Insulator interfaces / surfaces
o Boundary conditions (electric contacts, …)
o Multi-physics
Simulation requirements for fundamental R&D
24 October 2012 | Slide 3
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Insulator bulk equations (no intrinsic carriers)
Poisson
Continuity
Current density
strongly nonlinear
Physics strongly determined by boundary condition
Example: Space Charge Injection in Insulators
24 October 2012 | Slide 4
Inception field
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Comsol Model
Example: Space Charge Injection
24 October 2012 | Slide 5
Injection Boundary condition
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Plate-plate geometry
Current-time transient after switching on a DC voltage
Example: Space Charge Injection
24 October 2012 | Slide 6
t /
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Norm
aliz
ed tota
l curr
ent density
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Symbols: simulation
Line: analytical solution
Voltage
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Plate-plate geometry
Steady-state current-voltage characteristics: three regions
Example: Space Charge Injection
24 October 2012 | Slide 7
Finite inception field Zero inception field
Finite saturation current I II III
3
2
8
9
L
Uj
Symbols: simulation
Lines: analytical solution
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Non-uniform space charge and electric field distributions
Example: Space Charge Injection
24 October 2012 | Slide 8
x [cm]
0 1 2 3 4 5 6 7 8 9 10
[
C/m
3]
0.00
0.01
0.02
0.03
10 s
0.1 ms 10 ms
Inception field
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Rod-plate geometry
Field limitation of spatial field enhancements
Example: Space Charge Injection
24 October 2012 | Slide 9
U [MV]
0.0 0.2 0.4 0.6 0.8 1.0
E [
kV
/mm
]
0
10
20
30
40
50
60
Space charge
controlled field
Laplace field
I
II
III
Inception field
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Voltage pulse
Injected space charge clouds at different times (in units of “time of
flight”)
Example: Space Charge Injection
24 October 2012 | Slide 10
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Inception
Example: Streamer Inception
24 October 2012 | Slide 11
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Inception
Example: Streamer Inception
24 October 2012 | Slide 12
Main Idea
Reduce the integral along field-lines of a vector field to a first order PDE
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Example: Streamer Inception and Propagation
24 October 2012 | Slide 13
(Particle tracing)
Plug-plate
Simulation Procedure:
1. E-Field
2. f – Field
3. Particle Tracing
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Modeling flexibility of a
simulation tool is crucial for
basic R&D
Conclusion
24 October 2012 | Slide 14
