Simulation of electric field distribution in the XLPE insulation of a 320 kV DC cable under steady and time-varying states

For HVDC cables, the electric field distribution is determined by the conductivity of insulation material, which is a function of temperature and field. As the result, the conductivity-dependent field in the DC insulation is an electro-thermal coupled field. A modified 2D model is set up in this paper to simulate the thermal field distribution of a 320 kV DC cable, and based on that, the electric field distribution in the XLPE insulation is studied by the finite element method without consideration of space charge effect. Electric field distribution of steady state is computed under thermal equilibrium and rated DC voltage, and it is found to be a quasi-linear function of the radius, with the field strength remaining nearly unchanged in the central part of the insulation, whose value is approximately equal to the average field. The field reversal is determined by the thermal activation energy in XLPE conductivity expression, with a larger activation energy corresponding to a lower temperature difference across the insulation when the field reversal happens, and the increase of electric field coefficient is beneficial for improving the field distribution. Simulation of the time-varying states is performed under thermal equilibrium and three typical transient waveforms, including the continuous rising DC voltage, polarity reversal DC voltage and the DC superimposed switching impulse. It is shown that the rise speed of the continuous rising voltage is a key parameter for the maximum field strength, with a high speed leading to a high field at the inner border of insulation, and a time duration of 2r to 3r is recommended for the voltage rise edge. By the consideration of the transition relaxation progress from the initial capacitive field to the steady-state resistive field, a formula is set up to calculate the field strength of the insulation after the application of a time-varying voltage, and the calculated results are highly consistent with those obtained by numerical simulation.