A) Effect on Space Charge Limited Field
Elevated temperature has two effects: thermal expansion and
increased conductivity. Taking the latter first, conductivity is often
modeled as the product of a field-dependent term and a temperature-dependent
term. The temperature-dependent term is of the
form exp(φ/kBT), where φ is an activation energy which, for XLPE,
is generally in the range of 0.8 eV, kB is Boltzmann’s constant,
and T is the absolute temperature. This results in the conductivity
increasing by roughly three orders of magnitude from 300 to
400°K. Examining Figure 1, we see that this would decrease the
space charge limited field to the range of 150 kV/mm. At this
space charge limited field, the background field required to generate
a space charge limited field extent of 1.5 µm is reduced
appreciably from room temperature, as seen in Figure 9. Thus,
when operation at elevated temperature is considered, the maximum
defect length is in the range of 100 µm for an operating
field in the range of 15 kV/mm, which is roughly a factor of two
less than at room temperature.