S.J. Dodd

Propagation of electrical tree structures in solid polymeric insulation

Two alternative theoretical approaches to electrical tree propagation exist. Stochastic models attribute tree structures to random probabilistic factors, whereas in the discharge-avalanche model mechanism-driven field fluctuations are responsible. Here we review the predictions of these approaches in the light of the available experimental evidence. It is shown that both models give the fractal structures and the form of structure distribution observed experimentally. The width of the distribution functions predicted are, however, less than those found experimentally. The quantitative formulation available to the physical model also enables it to reproduce several other features of tree propagation such as voltage dependence, growth laws, and discharge behavior patterns. This is not possible in the stochastic approach without mechanistic assumptions which are difficult to relate to the stochastic process. The connection between the discharge-avalanche model and deterministic chaos is explored. Experimental evidence is presented supporting the contention that the electrical treeing phenomenon is the result of a deterministic breakdown mechanism operating in a chaotic regime at fields lower than those required for runaway breakdown. Space-charge deposition and re-arrangement is proposed as the physical origin of the chaotic field fluctuations. Tree shapes are shown to be related to the variation in the fluctuation range available as the tree grows in accord with the predictions of the discharge-avalanche model.

On the structure and chemistry of electrical trees in polyethylene

The structure and chemistry of two electrical trees (designated Tree A and Tree B) grown in low density polyethylene have been studied by a combination of confocal Raman microprobe spectroscopy, optical microscopy and scanning electron microscopy. Despite being grown under similar conditions (A, 30 °C and 13.5 kV; B, 20 °C and 13.5 kV), these two trees exhibit very different structures. Tree A exhibits a branched structure while Tree B is more bush-like. In Tree A, the very tips of the structure are made up of hollow tubules, which exhibit just the Raman signature of polyethylene. On moving towards the high voltage needle electrode, fluorescent decomposition products are first detected which, subsequently, are replaced by disordered graphitic carbon. From the relative intensity of the graphitic sp2 G and D Raman bands, the constituent graphitic domains are estimated to be ~4 nm in size, which leads to a local tree channel resistance per unit length of 1–10 Ω µm−1. These structures are therefore sufficiently conducting to prevent local electrical discharge activity. In Tree B, the observed fluorescence increases continuously from the growth tips to the needle. Here, the tree channels are not sufficiently conducting to prevent electrical discharge activity within the body of the tree. These results are discussed in terms of mechanisms of tree growth and, in particular, the chemical processes involved.

Effect of tree channel conductivity on electrical tree shape and breakdown in XLPE cable insulation samples

The results of an investigation into electrical tree growth in XLPE cable insulation using an embedded needle electrode are reported for a range of voltages from 9 kV rms to 27 kV rms. The partial discharge (PD) activity and tree structures were measured simultaneously throughout the tree growth and the trees were recorded from initiation up to and including the final runaway stage. A multifractal analysis was also performed on the tree structures as they propagated, and it was found that their fractal dimension increased and the distribution of embedded structures changed as small side channels were added to the tree as it grew. At 11 kV rms only branch trees were found and only bush (bush-branch) trees at higher voltages, but at 9 kV rms trees of three different shapes were formed. Observation of the tree shapes at 9 kV rms under reflected light followed by a detailed analysis using con-focal Raman spectroscopy, showed that the stagnated and branch-pine (monkey puzzle) tree shapes were due to the formation of a conducting graphitic deposit upon the walls on tree branches in the region of the needle electrode. This was not present in the branch trees produced at 9 kV rms. A simple scheme is presented for the formation of branch-pine trees and their corresponding PD activity based on the concept of conducting branch generation. The trees produced at 13 kV rms and above have a bush shape, which converts into a bush branch shape when a runaway branch grows from their periphery. This is shown to happen when the field at the bush tree periphery exceeded a voltage independent critical value, which was estimated to be 100 MV/m. The consequence of this result for the initiation of the runaway stage in branch trees is commented upon.

The effect of voltage and material age on the electrical tree growth and breakdown characteristics of epoxy resins

Electrical tree growth (a long-term electrical breakdown process) has been investigated in Araldite CT200 and CT1200 epoxy resins as a function of voltage and material age (defined as the time between manufacture and testing of pin-plane samples). Reproducible and predictable electrical tree growth was obtained for both CT200 and CT1200 epoxy resins provided that (i) the essentially random tree initiation time is removed and (ii) the samples tested were of the same age. The tree growth and time to failure (defined as the time to breakdown from a pre-initiated 10 mu m tree) characteristics as a function of both voltage and sample age show large step changes at a critical voltage and critical age. In particular, the resin physical ageing has a large effect on the tree growth behaviour, with the time to failure varying by three orders of magnitude over a time span of 3 years. Measurements of some of the physical properties (residual internal mechanical stress, surface refractive index, glass transition temperature and dielectric loss) of CT200 epoxy resin all indicate the occurrence of physical ageing of the resin, with structural (network) relaxation as the most important ageing process. However, these measurements are unable to account for the step change (critical age effect) found in the time to failure of tree growth. The fractal nature of tree growth and its relationship with voltage and the long-term changes in the properties of the resin are briefly commented upon.

Analysis and modelling of electrical tree growth in synthetic resins over a wide range of stressing voltage

A simple accumulated damage analysis method and an empirical field-driven tree growth model are proposed to characterize and describe the spatial and temporal development of electrical trees. Examples are presented for trees grown in CT200 and CY1311 epoxy resin pin-plane samples subjected to a wide range of 50 Hz alternating current electrical stress. It is shown that a materials resistance to treeing may be described quantitatively, allowing the relative performance of different synthetic resins to be easily compared. For CY1311 epoxy resin, tree structural characteristics change progressively from branch to bush structures as the stressing voltage is increased. It is shown that the time to failure is primarily influenced by the local electric field and the resultant tree geometry and fractal dimension of tree growth and is not simply dependent on the applied voltage.

Systematic and reproducible partial discharge patterns during electrical tree growth in an epoxy resin

The partial discharge activity (the number of discharges per second) during electrical tree growth in the flexible epoxy resin CY1311 was measured using a phase-resolved synchronous counting system. The experimental conditions, voltage and pin-plane spacing were varied to produce a wide range of tree structures from branch to bush. Systematic and repeatable changes in the partial discharge activity occurred, depending on the experimental conditions and these correlated with the type of tree structure (branch density or fractal dimension) formed. The type of tree growth was principally determined by the applied electric field and the occurrence of regular changes (bursts) in the partial discharge activity which are associated with a sudden and temporary phase shift and broadening of the partial discharge phase distributions. The number of bursts an their dynamics determine the type of tree grown.

The correlation between the partial discharge behaviour and the spatial and temporal development of electrical trees grown in an epoxy resin

Combined partial discharge detection and video monitoring of the tree growth have shown a strong correlation between the partial discharge activity and the spatial and temporal development of electrical tree growth in CY1311 epoxy resin. CCD imaging of the spatial distribution of light emitted, due to partial discharges in the tree structure, has shown that the different modes of partial discharge behaviour reflect their different spatial distribution within the existing tree structure, with new growth occurring at those parts of the tree in which the partial discharges are active. The dynamics of the partial discharge behaviour, namely the frequency and duration of two modes of activity, is controlled by the experimental conditions (voltage and pin - plane spacing) and determines the type (fractal dimension) of the resultant tree. During one mode of activity, rapid low-fractal-dimension radial growth of the tree occurs. During the other mode, new growth occurs at a slower rate from the tree structure near the pin electrode, leading to an increase in the overall fractal dimension of the tree structure.

A Deterministic Model for the Growth of Non-conducting Electrical Tree Structures

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.

Simulation of partial discharges in conducting and non-conducting electrical tree structures

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. Previous experimental investigations of electrical treeing in epoxy resins have found evidence that the tree structures formed were either electrically conducting or non-conducting, depending on whether the epoxy resin was in a flexible state (above its glass transition temperature) or in the glassy state (below its glass transition temperature). In this paper we extend an existing model, of partial discharges within an arbitrarily defined non-conducting electrical tree structure, to the case of electrical conducting trees. With the inclusion of tree channel conductivity, the partial discharge model could simulate successfully the experimentally observed partial discharge activity occurring in trees grown in both the flexible and glassy epoxy resins. This modelling highlights a fundamental difference in the mechanism of electrical tree growth in flexible and glassy epoxy resins. The much lower resistivities of the tree channels grown in the glassy epoxy resins may be due to conducting decomposition (carbonized) products condensing on the side walls of the existing channels, whereas, in the case of non-conducting tree channels, subsequent discharges within the main branches lead to side-wall erosion and a consequent widening of the tubules. The differing electrical characteristics of the tree tubules also have consequences for the development of diagnostic tools for the early detection of pre-breakdown phenomena.

The measurement of very low conductivity and dielectric loss in XLPE cables: a possible method to detect degradation due to thermal aging

The dielectric response of crosslinked polyethylene (XLPE) insulated, miniature power cables, extruded with inner and outer semicons, was measured over the frequency range 10-4 to 104 Hz at temperatures from 20 to 100 °C. A dielectric spectrometer was used for the frequency range 10-4 to 10-2 Hz. A bespoke noise-free power supply was constructed and used to measure the dc conductivity and, using a Fourier transform technique, it was also used to measure the very low dielectric tanδ losses encountered at frequencies of 1 to 100 Hz. Tanδ measurements of <;10-5 were found in this frequency range and attributed to a β-mode dielectric relaxation lying above 100 Hz due to motion of chain segments in the amorphous region and an β-mode relaxation lying below 1 Hz window due to twists of chains in the crystal lamellae. The dc conductivity measurements were consistent with those of the dielectric spectrometer and indicate lower dc conductivities in vacuum degassed cables than have been previously reported for XLPE (less than 10-17 S.m-1). The conduction process is thermally activated with an activation energy of approximately 1.1 eV. Higher conductivities were found for non-degassed cables. A transformer ratio bridge was used for measurements in the range 1 to 10 kHz; loss in this region was shown to be due to the series resistance of the semicon layers. Thermal ageing of the cables at 135 °C for 60 days caused significant increases in the conductivity and tanδ and it is considered that such measurements may be a sensitive way of measuring electrical degradation due to thermal aging.