High-Voltage Insulation Design
Theory: gas discharge and void fields
Overview
Why does insulation with ample withstand voltage sometimes fail after years of use?
The solid insulation may be strong, but small voids or delaminations inside contain air. Air's lower permittivity concentrates the field there, and its dielectric strength is a fraction of the solid's. So even with overall margin, discharge occurs inside the void alone — partial discharge. Each event is small, but it gradually erodes the surrounding insulation, tree-like degradation grows, and eventually the whole insulation fails. Design estimates gas breakdown with Paschen's law and compares it with the voltage across the void.
Paschen's law
p is pressure (Torr), d gap (cm) and γ the secondary-emission coefficient. With these simple constants, a uniform 10 mm gap at 1 atm gives 3.55 kV/mm, slightly above the measured value of about 3 kV/mm.
Voltage across a void
A flat void of thickness t perpendicular to the field is treated as a capacitor in series with the solid (thickness d − t, relative permittivity ε_r). V_PDIV is the partial-discharge inception voltage.
Paschen's 1889 experiments
In 1889 Paschen measured discharge onset voltages in air, carbon dioxide and other gases while varying pressure and electrode gap, showing they depend only on the product of the two. Townsend later explained the relation with electron-avalanche theory, in which electrons striking gas molecules multiply. The existence of a minimum breakdown voltage still matters for electrical design of vacuum equipment, aircraft and spacecraft.
Worked examples
Example 1: breakdown of air gaps
| Gap | 1 atm | 1 atm (field) | 3,000 m altitude | 3,000 m (field) |
|---|---|---|---|---|
| 0.1 mm | 0.87 kV | 8.65 kV/mm | 0.68 kV | 6.75 kV/mm |
| 1 mm | 5.03 kV | 5.03 kV/mm | 3.73 kV | 3.73 kV/mm |
| 10 mm | 35.5 kV | 3.55 kV/mm | 25.8 kV | 2.57 kV/mm |
The Paschen minimum is about 305 V at pd = 0.84 Torr·cm, corresponding to a gap of about 11 μm at 1 atm.
Example 2: PD inception for voids in epoxy (2 mm, εr 4)
| Void thickness | Fraction across void | Void breakdown | PD inception voltage | Mean field |
|---|---|---|---|---|
| 0.05 mm | 9.3% | 552 V | 5.93 kV | 2.97 kV/mm |
| 0.1 mm | 17.4% | 865 V | 4.97 kV | 2.49 kV/mm |
| 0.2 mm | 30.8% | 1,423 V | 4.62 kV | 2.31 kV/mm |
Epoxy itself withstands tens of kV/mm, yet discharge starts at about 2.5 kV/mm mean.
Solid breakdown strength and the field at which partial discharge starts are entirely different things. The void's low permittivity raises the field inside it to about four times its surroundings, and the air there discharges at about 8 kV/mm. Larger voids lower the inception voltage. So for high-voltage parts the first defence is to avoid voids altogether: vacuum casting to remove bubbles and preventing interface delamination. In inverter-driven motors, steep voltage edges concentrate voltage at winding ends and can cause partial discharge in tiny gaps in winding insulation. Inception voltage is fundamentally verified by measurement during product testing.
Insulation design workflow
- Define maximum voltage, overvoltages and operating pressure (altitude).
- Use field analysis to find concentrations at electrode edges and triple points (conductor–solid–air).
- Check clearances and creepage against Paschen's law and standards.
- Estimate PD inception assuming voids and secure margin over operating voltage.
- Measure partial discharge on products, confirming inception and extinction voltages.
“A supply that discharged only at altitude”
A power supply passed sea-level tests, but units installed at high altitude showed discharge marks. High-voltage clearances on the board had been designed for sea-level pressure. Near 3,000 m pressure is about 70%, and calculated breakdown for a 1 mm gap falls about 26%. Combined with field concentration at electrode corners, discharge occurred there. Widening clearances and rounding corners to reduce field solved it.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Judging by solid strength only | Degradation by PD | Evaluate PD inception |
| Designing at sea-level pressure | Discharge at altitude | Use operating pressure |
| Sharp electrode edges | Local field concentration | Rounding and grading |
| Leaving casting bubbles | Discharge in voids | Vacuum casting |
| Overlooking triple points | Surface discharge | Check by field analysis |
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