The LDPE impregnated with acetophenone, one of cross-linking by-products in XLPE, under a high electrical stress of 150kV/mm caused a breakdown with the consumption electric power of κE
2=2.3W/cm
2 which was measured by using the advanced technique combined with the space charge measurement (PEA system) and the external current measurement. This paper discusses on the thermal breakdown model which is occurred when an intrinsic energy, m
dC
v(T
m-T
o)=220J/cm
3, required to impulse breakdown of LDPE equals to the supplying electric power, kE
2Δt, where m
d is a density of material, C
v a specific heat, T
m a melting point of LDPE and T
o a room temperature, κ a conductivity, E an electric field, Δt a formation time of breakdown. It is found that when the thermal breakdown was occurred, the measured electric power, κE
2=2.3W/cm
2, was consumed in a filamentary higher conductivity path (size; a thickness of specimen of a=100µm, and a cross section of filament of ΔS=100µm×100µm).
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