Pierre Mirebeau

On the intrinsic space charge in a DC power cable

Abstract In a DCHV power cable connected to its standard load, the temperature, and therefore the conductivity of the insulation, increases from sheath to core. Combined with the local field, the radial conductivity gradient-recalled in the introduction (Section 1) of this work-builds up an intrinsic space charge. Section 2 reconsiders the calculation of this steady-state space charge first without, then with a simplified account of a field-dependent conductivity. It shows that the space charge in question should be detectable by the advanced techniques now available. Section 3 treats the accumulation, with time, of the “intrinsic” space charge after the onset of the thermal gradient. This treatment clarifies and extends an old pioneering work by Lau. The calculations make an extensive use of the “mean radius”, geometric average of the internal and external radii, and of the reduced field, ratio of the actual field E ( r ) over the Laplace field in the absence of space charge. The shape of the accumulating charge distribution depends strongly on the magnitude of the temperature gradient. An approximate solution is given for the case where the conductivity varies not only with temperature, but also with the local field, and this provides a sound basis for an accurate numerical solution. By comparing the measured charge and field distributions to the theoretical predictions of this work, “extrinsic” space charges, crucial to the cable life, should be identified.