In this chapter, chemical and physical structure and morphology of polymers were summarized and to identify the structure of polymers which are commonly used as electrical insulators. XRD and SEM were used in characterizing polymer crystallinity and morphology.

In this chapter we introduce the basic electrical terminology and account for the wide variation of observed electrical conductivities and charge transport processes. Our treatment is introductory and necessarily simplified; the reader is referred to more advanced texts during the discussion.

In this chapter, the description of physical and chemical aging and their effect on electrical degradation and breakdown is discussed. The dielectric response measurement results for polymers are calculated. It shows the structural relaxation via segmental motion in the amorphous region which thereby increases in density. This time-dependent change as the system moves towards thermal equilibrium is known as physical aging. Chemical aging usually proceeds via the formation of polymer free radicals.

Water trees in crosslinked and uncrosslinked polyethylene are easily visible under the microscope, and often appear to show some structure. Thus regions of greater water density have sometimes been termed channels. However this terminology cannot be taken to indicate the presence of hollow tubes since no cracks or crazes have been revealed by scanning electron microscopy (SEM). Even though some isolated cracks have been observed by transmission electron microscopy (TEM) the typical physical feature marking the path of a water tree is the presence of a large density (approximately 10⁶mm^-3) of spherical microvoids whose radius (a) is 1 μm-5 μm.

Electrical trees found in polymeric insulation grow in regions of high electrical stress, such as metallic asperities, conducting contaminants and structural irregularities. Partial discharges in voids can also generate degradation structures from the void surface which are essentially electrical trees. Those trees initiated at an electrode are termed vented trees, while trees generated in the body of the insulation have a branched channel structure roughly oriented along the field lines and are referred to as bow-tie trees. In this case the term vented tree is an apt one as electrical trees are composed of inter-connected hollow tubules with the channel at the base forming a vent for the whole system which may in some cases allow access to the external environment, or to the atmosphere of the void for partial discharge initiated trees.

A considerable amount of evidence has now been accumulated showing that water trees reduce the breakdown strength of polymer insulation (see Shaw and Shaw and references therein). In this respect bow-tie trees perform a different role to that of vented water trees, causing a reduction of breakdown strength even when the bow-tie water tree length is small (~20 μm), in contrast to vented water trees where a strong decrease in breakdown voltage only occurs when the trees become long, fig. 6.1. This difference has been associated with the alternative manner in which insulation deterioration is accumulated in the two cases. Thus in the case of bow-tie water trees it is their number density which is important in determining the average size of tree sufficient to give the global deterioration which will reduce the breakdown strength. In contrast vented water trees rarely amalgamate in cables and the criterion for the deterioration they generate is the length of the individual tree compared to the insulation thickness. Considered in this light the crucial factor in the reduction of breakdown strength is the extent to which water trees provide a degraded route across the insulation, which may be approximately measured by the degree of water treeing. Measurements of the breakdown strength across tree sections have shown that the treed region does not act as a conductor which decreases the dielectric thickness, but rather as a region with a much lower breakdown strength the smallest value of which is found at the base of the tree.

This chapter talks about the factors affecting treeing which are the morphology effect, chemical composition, and temperature.

This chapter tells about the general aspect of material design, processing, inhibition and suppression of electrical trees.

Charge injection and transport in insulating polymers is reported. Hole transfer is possible however since electron-hole recombination would then occur at the electrode. High fields can reduce both the height and width of this potential barrier. The band structure may be less well defined. In this case there are very few carriers in the higher-energy states which are sufficiently close for carriers to easily move from one to another and there are many carriers trapped in the lower-energy states which are too far apart for carriers to easily move between them.

Spatial and temporal evolution of temperature in thin (25 μm thick) films of polyethylene as a DC field was applied; no circumferential cooling was used. In this case, as the field was increased, hot spots appeared on the film and gradually one of these dominated and led to breakdown. Although this was clearly Joule heating it is not clear that the breakdown mechanism was purely thermal.

Stark and Garton noticed that the breakdown strength of many thermo plastics dropped when their temperature was increased such that they started to soften. They speculated that this was due to a mechanism which is often termed electromechanical breakdown. Electromechanical breakdown occurs when the mechanical compressive stress on the dielectric caused by the electrostatic attraction of the electrodes (or, more accurately, by electrostric tion) exceeds a critical value which cannot be balanced by the dielectric's elasticity. The electromechanical breakdown voltage can be evaluated by equating these two stresses for the equilibrium situation before breakdown in a parallel-plate dielectric slab.

In this chapter the electric breakdown mechanism in polymers is discussed. In electronic breakdown the field causes either the number or the energy of the electrons to reach unstable magnitudes such that they rise catastrophically. Polymers generally shows intrinsic and Avalanche breakdown. Another type of breakdown generally shown by semiconductor p-n junctions is Zener or field-emission breakdown in which electrons are excited at high rate from valence to conduction band thereby enhancing conductivity.

In these breakdown mechanisms charge carriers are accelerated by the electric field through spaces in the dielectric. In partial discharge breakdown sparks occur within voids in the insulation causing degradation of the void walls and progressive deterioration of the dielectric. In free volume break down carriers are accelerated through spaces within low-density amorphous regions; the energy thereby gained is lost through collisions and various mechanisms have been proposed as to how this may lead to breakdown. The voids necessary for partial discharges may be thought of as extrinsic since they are artifacts of the process used for manufacturing the insulating system. On the other hand free volume is an intrinsic feature of polymeric insulation in which there are always variations of density between crystalline and uncrystallised regions. Free path lengths of up to a few tens of nanometers may be possible through free volume at room temperature. Voids may range almost up to a millimeter in poorly made material and are generally not recognised below a few tens of nanometers. The latter dimension may therefore be used as a 'rule of thumb' dividing line between voids and free volume. In this chapter we will describe these two breakdown mechanisms.

Statistical features of electrical breakdown is reported. Conclusive results of constant-stress tests (variously known as 'life', 'voltage endurance' or 'static' tests) on polymeric insulation are not abundant in the literature. Indeed when reviewing the literature it is surprising how little is reported of such tests considering the implications for lifetime prediction.

The aim of this chapter to discuss those models of breakdown which attempt to develop a physical origin for the breakdown statistics. The analysis presented in this section shows that the basic condition for the applicability of Weibull statistics to breakdown is that of self-similarity in an initial distribution of potential breakdowns bounded at its upper end.

This chapter describes standard tests in which the breakdown stress or time to breakdown is evaluated for a polymeric material or insulating system; the interpretation of these tests is also discussed. Examples of some of the breakdown tests adopted by American and other cable manufacturers are given. In all these tests conditions are carefully specified to ensure reproducibility between test laboratories.

Comparison of AC and DC breakdown behaviour is reported. Spatial variation in permittivity, gradients in the polarisation and hence electric field will exist when the material is electrically stressed. The applied field is 'uniform', and without allowing for space-charge injection, polymeric materials will contain local space charge concentration giving field gradients and a range of local field strengths.

This chapter discusses power cable assessment procedures.The most common cable validation tests are voltage-withstand tests and partial discharge tests.

The coverage of this book will be concerned only with a selection of the methods proposed for the detection of the degradation process. The water trees, partial discharge and electrical trees are not intended to be exhaustive but rather to illustrate the types of approach adopted and to assess their effectiveness.

The first 43 lines deal with inputting the data, sorting it into order, and finding its logarithms which are used later on. Lines 44-67 use a least squares technique to find a first estimate for the shape parameter. Lines 68-103 use the Newton-Raphson technique to find maximum-likelihood estimates of the distribution parameters. The program will run if only the first 103 lines are entered and produce correct maximum likelihood esti mates. The remainder of the program estimates confidence limits in a rather unusual way. The graphs used for the graphical methods for confidence limit estimation described in. References 723 and 820 are represented as several-order equations (polynomials, hyperbolas etc.). Values calculated from these are then used in the same way as in the graphical techniques. The equations are faithful representations of the graphs for values of n between 5 and 120 and the technique is reasonable provided the data is not highly censored. Also shown is a typical output from the program.

Calculating the threshold value of a 3-parameter Weibull distribution using MathCAD⁸²⁶, Parameter findings of 3-parameter Weibull distribution using least squares.

This chapter presents the proof of an integral equation.