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Current rating @ field limited conductor temperature

For the rating calculation of HVDC cables two limiting factors are considered.

  1. The first is the maximum permissible temperature in the conductor related to the maximum operating temperature of the insulation.
  2. The second factor is the maximum permissible electric field at the insulation screen when the cable carries the load current.

The electric field at the insulation screen (outer radius of the insulation) is increasing as the load increases. This can be explained by the fact that the field distribution is mainly determined by the conductivity of the insulation for a given voltage. Since the conductivity is temperature dependent, the electric field distribution also becomes temperature dependent. It can be shown that the electric field at the insulation screen can be taken into account as a function of temperature drop across the insulation (\Delta\theta_{ins}$). It should be noted that the temperature drop limit might be reached in a specific condition where the other limit of the conductor temperature is not yet reached. It should be noted that the given temperature drop is verified during type testing and is only valid for the given voltage.

Symbol
$I_{c,ins}$
Unit
A
Formulas
$\sqrt{\frac{\Delta \theta_{i,max}}{\operatorname{max}\left(R_{c,ins}\right) T_{ins}}}$
Related
$\Delta \theta_{i,max}$
Limitation of temperature rise insulation material [K]
$R_{c,ins}$
Electrical resistance @ field limited conductor temperature [$\Omega$/m]
$T_{ins}$
Thermal resistance insulation [K.m/W]