A deterministic model for the growth of non-conducting electrical tree structures

Abstract

Electrical treeing is of interest to the electrical generation, transmission and distribution industries as it is one of the causes of insulation failure in electrical machines, switchgear and transformer bushings. In this paper a deterministic electrical tree growth model is described. The model is based on electrostatics and local electron avalanches to model partial discharge activity within the growing tree structure. Damage to the resin surrounding the tree structure is dependent on the local electrostatic energy dissipation by partial discharges within the tree structure and weighted by the magnitudes of the local electric fields in the resin surrounding the tree structure. The model is successful in simulating the formation of branched structures without the need of a random variable, a requirement of previous stochastic models. Instability in the spatial development of partial discharges within the tree structure takes the role of the stochastic element as used in previous models to produce branched tree structures. The simulated electrical trees conform to the experimentally observed behaviour; tree length versus time and electrical tree growth rate as a function of applied voltage for non-conducting electrical trees. The phase synchronous partial discharge activity and the spatial distribution of emitted light from the tree structure are also in agreement with experimental data for non-conducting trees as grown in a flexible epoxy resin and in polyethylene. The fact that similar tree growth behaviour is found using pure amorphous (epoxy resin) and semicrystalline (polyethylene) materials demonstrate that neither annealed or quenched noise, representing material inhomogeneity, is required for the formation of irregular branched structures (electrical trees). Instead, as shown in this paper, branched growth can occur due to the instability of individual discharges within the tree structure.

Electrical Trees and Their Growth in Silicone Rubber at Various Voltage Frequencies

“…Electrical trees are pre-breakdown phenomena that accelerate the occurrence of insulation failure [1][2][3][4][5][6][7]. Owing to the harsh working conditions of power electrical equipment, there have been many investigations to determine the influence of temperature, voltage type, voltage frequency, thermal aging, and moisture on electrical treeing characteristics [8][9][10][11][12][13][14][15].…”

Partial discharge energy and electrical tree volume degraded in epoxy resin

“…Another model [10], assumed that the damage is proportional to the amount of energy released by the PDs and the channel formation occurs when both the local damage and the local field exceed critical values [11]. In the model proposed in [12], the material damage produced by PDs was determined by the local electrical energy dissipated by the discharges and by the local electrical fields in the dielectric surrounding the tree. The tree would extend when the accumulated damage (quantified as energy) exceeded the energy to form a new channel, which was calculated considering the vaporization energy of the material and the volume of the new segment channel.…”

Electrical treeing characteristics in XLPE power cable insulation in frequency range between 20 and 500 Hz

“…The addition of physical process helps to reproduce many of known characteristics of tree growth [15]. A deterministic treeing model has been proposed [16] and used successfully by Dodd [17] to study the growth of non-conductive electrical tree structures in epoxy resin. The model produces formation of branched structure of tree without the need of random variables.…”

“…The model produces formation of branched structure of tree without the need of random variables. The more detailed description of these models can be found in literature [17]. Recently, cellular automata (CA) model has been reported to simulate tree growth [18].…”