Conduction and breakdown theories in commercial liquids

Commercial liquid dielectrics such as transformer oil always contain impurities: solid particles (fibres, dust), dissolved gas, moisture and gas bubbles. Their conduction at high stress and their breakdown are explained by two main theories: the suspended particle theory and the cavitation and bubble theory. (Thermal and stressed-oil-volume mechanisms are also mentioned in texts.)

1. Suspended particle theory

Principle. Solid particles with permittivity $\varepsilon_2$ greater than that of the liquid $\varepsilon_1$ become polarized in the field. In a non-uniform field a spherical particle of radius $r$ experiences a force towards the region of maximum stress:

$$F = r^3\,\frac{\varepsilon_2 - \varepsilon_1}{2\varepsilon_1 + \varepsilon_2}\,E\,\frac{dE}{dx}$$

For a highly conducting particle ($\varepsilon_2 \to \infty$) the factor becomes 1, giving the largest force.

Process.

  electrode
  |  o o       particles drift to
  |   o  o     high-stress region
  | o-o-o-o-o-o  chain (bridge)
  |            |
  electrode    heating, vapour -> breakdown

1. Particles move towards high-field regions near the electrodes.
2. They line up along the field lines and form a chain (bridge).
3. The bridge carries a larger current; local heating vaporizes moisture and oil.
4. A vapour/gas channel forms along the bridge and the gap breaks down.

Results explained.

• Breakdown strength falls as particle content and moisture increase.
• Strength depends on time of voltage application: a bridge takes time to form, so strength under impulse is higher than under steady AC.
• Particle movement is opposed by viscosity and diffusion; if the drift force is smaller than these, no chain forms.

2. Cavitation and bubble theory

Sources of bubbles:

• Gas pockets on rough electrode surfaces
• Electrostatic repulsion between space charges at the liquid surface
• Dissociation of liquid molecules by electron collisions
• Vaporization of liquid by corona at sharp points

Process (Kao's theory).

1. A bubble in the liquid has lower permittivity, so the stress in it is higher than in the liquid.
2. Electrostatic forces elongate the bubble along the field (surface tension opposes this).
3. When the voltage drop along the elongated bubble equals the minimum Paschen breakdown voltage of the gas, the gas ionizes.
4. Ionization decomposes more liquid, the bubble grows into a gas channel and bridges the electrodes; breakdown follows.

The critical field for breakdown of a bubble of radius $r$ is

$$E_0 = \frac{1}{\varepsilon_1 - \varepsilon_2}\left\{\frac{2\pi\sigma(2\varepsilon_1 + \varepsilon_2)}{r}\left[\frac{\pi}{4}\sqrt{\frac{V_b}{2rE_0}} - 1\right]\right\}^{1/2}$$

where $\sigma$ is surface tension and $V_b$ the voltage drop in the bubble (Paschen minimum).

Results explained.

• Breakdown strength rises with pressure (bubbles harder to form) and falls with dissolved gas.
• Strength depends on initial bubble size, hydrostatic pressure and temperature.

Comparison