Simulation of Space Charge Dynamic in Polyethylene Under DC Continuous Electrical Stress

Abstract

The space charge dynamic plays a very important role in the aging and breakdown of polymeric insulation materials under high voltage. This is due to the intensification of the local electric field and the attendant chemicalmechanical effects in the vicinity around the trapped charge. In this paper, we have investigated the space charge dynamic in low-density polyethylene under high direct-current voltage, which is evaluated by experimental conditions. The evaluation is on the basis of simulation using a bipolar charge transport model consisting of charge injection, transports, trapping, detrapping, and recombination phenomena. The theoretical formulation of the physical problem is based on the Poisson, the continuity, and the transport equations. Numerical results provide temporal and local distributions of the electric field, the space charge density for the different kinds of charges (net charge density, mobile and trapped of electron density, mobile hole density), conduction and displacement current densities, and the external current. The result shows the appearance of the negative packet-like space charge with a large amount of the bulk under the dc electric field of 100 kV/mm, and the induced distortion of the electric field is largely near to the anode, about 39% higher than the initial electric field applied.

Space Charge Accumulation at Material Interfaces in HVDC Cable Insulation Part II—Simulations of Charge Transport

“…After some hours, a new equilibrium with a much lower fraction of mobile charge carriers was established, which slowed down the decay rate significantly and limited it through the detrapping process. In our model, the electron detrapping rate values at field strengths from 15 to 60 kV/mm varied from 4.5•10 −4 s −1 to 1.6•10 −3 s −1 , respectively, ( Figure 7), which are rather low magnitudes compared to the literature data [3][4][5][6][7][8][9][10][11]. A different methodology was used in parameter calibration, with most of the literature focusing on polarization; however, this study additionally focused on charge decay in the initial and final stages of the depolarization sequence, which could thus explain these lower rates.…”

“…For deep states, an upper energetic level of 1.03 eV is used, as these states among the deep trap distribution govern the initial decay rate in the model and are present with the highest density. The deep state density is lower compared to the values provided in the reference literature [3][4][5][6][7][8][9][10][11], which could be related to assuming identical lattice/capture parameters for deep and shallow sates, defining the trapping cross-section as A T = a sh 2 . However, this work considers, additionally, depolarization behavior, field dependent trapping and detrapping and makes use of ultra-clean DC-grade XLPE in the measurements, which could make the here found results incomparable to the reference literature [3][4][5][6][7][8][9][10][11].…”

“…The parameters β s and ∆ϕ s are the field parameter and barrier height reduction, respectively, and they account for field enhancement in the rough interfacial geometry. Note that here the sum of the exponential field terms in Equation (10) is reduced with a factor, ƒ s , which can be either zero or one in the literature [3][4][5][6][7][8][9][10][11]. While using ƒ s = 0 results in the unmodified Schottky equation, when it is equal to one, charge injection is reduced below 1-2 kV/mm and no charge is injected when the electric field is zero.…”

“…Following this approach, the purpose of this second part of the paper is to examine and to explain the results of the space charge measurements in XLPE by means of computer simulations of charge transport in the material focusing on surface roughness. For the simulations, the frequently used bipolar modelling approach [3][4][5][6][7][8][9][10][11] is adopted, which considers the field-induced dynamics of mobile and deeply trapped charge carriers within the material. To verify the model, the results of the simulations are compared with those obtained from the space charge measurements, which were carried out using the PEA method at polarizing fields in the range of 15-80 kV/mm and temperatures in the range of 25-70 • C. The experimental procedure including both the polarization stage and, additionally, the charge decay during depolarization was simulated utilizing wide-range field dependencies for all included effects, which were carefully evaluated.…”

“…Recombination parameter range from publications[3][4][5][6][7][8][9][10][11] and used recombination parameters in this model.…”