The role of local space charge concentrations in producing branched tree structures

Electrical trees are branched damage structures produced in polymeric insulation subject to high divergent fields. The density of branching ranges from a sparse form like a tree in winter to a dense compact form like a bush. This variation in form is significant as the bush structure occurs at higher voltages but grows slower. We present here a deterministic model for the formation of electrical trees based on damage produced by charges injected into the polymer from discharges taking place within the gas-filled tubules of the tree. A number of processes within the mechanism cause the space charge fields to fluctuate chaotically, and this is held to be responsible for the branching that is observed. Different tree shapes are found depending on whether or not injected/extracted charges reach a kinetic energy high enough for damage only at a few tree tips or everywhere around the tree periphery

Electric field requirements for charge packet generation and movement in XLPE

The formation of space charge packets in XLPE (Cross-linked polyethylene) tapes from unaged cable insulation has been studied utilising the pulsed electro-acoustic (PEA) technique. The 150 m thick sheets were studied under constant applied dc field of 120 kV/mm at a temperature of 20 C for a period of 48 hours. After an inception period of about 3.5 hours, during which heterocharge accumulates at the anode and increases the local field there, a sequence of positive charge packets were observed to transit the sample starting from near the anode. Calculation of the internal field showed that the packets required a field of 140 kV/mm for their initiation. Reduction of the applied field step-wise from 120 kV/mm to 80 kV/mm indicated that the charge packet would keep moving as long as the local field at its front exceeded 100 kV/mm, but with a reducing magnitude. A return to an applied field of 120 kV/mm confirmed that the local field required to initiate a new packet was in excess of 135 kV/mm. The results are discussed in terms of current theories of charge packet formation. The first packet appears to be a moving front of field ionisation. The generation of subsequent packets is governed by the field at the anode and the balance of charge injection and extraction process, which occur there. The nature of the negative charges produced at the ionisation front is not clear, but they are unlikely to be electrons

Electrical tree structures generated by the ab-initio discharge-avalanche model

Initially the discharge-avalanche model for electrical tree formation treated the local Poisson fields as being derived from the applied Laplace field via a modification factor that was regarded as a random variable in time and space. Recently we have removed this approximation by calculating the local Poisson fields from the space charge arrangement produced by discharges in the tree tubules and avalanches in the surrounding polymer. This “ab-initio” version of the model has now been fully implemented. The ac-cycle is divided into 16 time segments. In each time segment tube-discharges are allowed to occur if the potential difference along a tube is greater than an onset threshold. Positive space charge is regarded as being deposited on the tube walls in the form of positive ions. Negative charge is allowed to penetrate the polymer where it can be used to initiate avalanches and thereby generate damage. The avalanches compete with a field dependant mobility in rearranging the charge around the tree tips

Application of thermoelectric aging models to polymeric insulation in cable geometry

The life expressions of models of insulation ageing are functions of temperature and field as well as material parameters. A methodology is presented that allows these models to be applied to a cable geometry in which there is a radial variation of both field and temperature. In this way material parameters can be extracted from cable data. The methodology is illustrated using one such model and the parameters deduced from cable failure distributions are compared with those obtained for thin films. This comparison allows conclusions to be drawn about how the ageing process affects specimens of the same material with different volumes

Anomalous dielectric response of very small quantities of virgin, aged and failed silicone oil

A technique is described for making dielectric spectroscopy measurements of very small quantities (<1μl) of oil. The technique utilises surface tension to hold the oil between the plates of a capacitor, the inter-electrode distance being controlled by a micrometer. Breakdown strength can also be estimated using this technique. Three samples of silicone oil, used in cable sealing ends, were tested: virgin, used and failed. A major component in the frequency dependent impedance had the form Z(ω)=B(1-b)(iω)/sup.1-p/). This component was interpreted in terms of a fractal percolation model, and the anomalous thickness dependence predicted by the model verified by varying the inter-electrode distance. The difference observed for the three different samples indicate that conducting contaminants are responsible for the percolation system

Temperature dependance of charge packet velocity in XLPE Cable peelings

The generation and transit of charge packets in 150μm thick peelings from the insulation of Medium Voltage Cables manufactured using the same XLPE batch have been investigated at a number of different temperatures. Charge packet motion was investigated in peelings taken from cables that have been electro-thermally stressed at T= 90 degrees C for 5000 hours with a Laplacian field E ≈ 20kV/mm at the location of the samples. It was found that charge packets were generated by an applied field of 120kV/mm when the internal space charge field reached 140-150kV/mm. Measurements were made in three controlled temperature environments and it was found that the transit time fitted an Arrhenius behaviour with an activation energy of ~1.2 eV. This value is similar to estimates made for the deepest traps (>1.1eV) made from the decay of space charge accumulated at lower fields of 46.67kVmm. It is also close to the activation energy for the conductivity (~1.25 eV) obtained from the dielectric spectroscopy of unpeeled cable sections at Erms ≈ 0.41 V/mm, and ~1.15eV from the dielectric spectroscopy of the peelings (E = 40V/mm). It is therefore concluded that the transit of the charge packet is associated with the trap-to-trap transport of charge carriers located in the deepest traps available. The implications of these results for the mechanism of charge packet generation is discussed

Discharge-generated electrical fields and electrical tree structures

The discharge-avalanche (D-A) model for electrical tree propagation in polymers is founded entirely upon basic physical concepts. Electrical discharges in an existing tree structure are taken to raise the electrical field in the polymer both along the discharge path and particularly at the tree tips. As a result of the field increase, electron multiplication avalanches occur within the polymer causing damage, possibly through ionisation of polymer molecules, which is accumulated over a period of thousands (or more) cycles and eventually leads to a tree extension of limited size. The assumption that the damage produced in an avalanche is proportional to the number of ionisations allows the model to be expressed quantitatively in terms of material properties: such as the ionisation potential, I; the impact-ionisation length parameter λ; the critical number of ionisations for tree extension Nc; discharge features such as the number of 1-electron initiated avalanches per half cycle, Nb ; and the potential difference ΔV between the start and end of the avalanche over a distance Lb

Application of polymer ageing models to power cables

Ageing models have been developed to predict the lifetime of polymeric insulation subject to electro-thermal stresses. We present here a method for applying the models to situations in which the field is not constant over the whole specimen, as for cable geometry. The method has been applied to characteristic lifetime data from AC ageing experiments on cables. The results are presented, and the effect of insulation volume upon the model parameters is discussed

Molecular dynamics simulation of high frequency (1010 to 10 12 Hz) dielectric absorption in the Hollandite Nax(Ti 8-xCrx)O16

The charge-compensating sodium ions that reside interstitially in the one-dimensional tunnels of the hollandite Nax(Ti8-xCrx)O16 are used as a simple model for a fluid. Molecular dynamics are used to calculate the motions of the ions at a range of temperatures between 200 K and 373 K. The polarization response of the system to a step-up electric field is calculated for field strengths between 7.43 MV/m and 74.3 GV/m, and converted to an ac susceptibility. A resonance absorption is found,peaking at frequencies between 4.5x1010 and 8.8x1010 Hz at 297K. The origin of the response is shown to be the anharmonically coupled ion vibrations damped by ion hopping to neighbouring sites. The relationship of the result to the experimentally observed Poley absorption is explored, and a brief comparison of the calculated dynamics to previous theoretical models is made

Towards an understanding of nanometric dielectrics

Dielectric studies are described aimed at providing an understanding of the charge storage and transport of an epoxy resin containing TiO2 nanoparticles. Comparative results for conventionally filled composites are given, and the results discussed in terms of the underlying physics. It is shown that nanometric fillers mitigate the interfacial polarization characteristic of conventional materials with a reduction in the internal field accumulations