No abstract

Electrical treeing is one of the main mechanisms of degradation in polymeric high voltage insulation, a precursor of power equipment failure. Electrical trees have been previously imaged mostly using two-dimensional imaging techniques; thereby loosing valuable information. Here we review the techniques that have been previously used and present the novel application of X-ray computed tomography (XCT) for electrical tree imaging. This non-destructive technique is able to reveal electrical trees, providing a threedimensional (3-D) view and therefore, a more complete representation of the phenomenon can be achieved. Moreover, taking virtual slices through the replica so created brings the possibility of internal exploration of the electrical tree, without the destruction of the specimen. Here, laboratory created electrical trees have been scanned using XCT with phase contrast enhancement, and 3-D virtual replicas created through which the trees are analyzed. Serial Block-Face scanning electron microscopy (SBFSEM) is shown to be a successful complementary technique. Computed tomography enables quantification of electrical tree characteristics that previously were not available. Characteristics such as the diameter and tortuosity of tree channels, as well as the overall tree volume can be calculated. Through the cross-section analysis, the progression of the number of tree channels and the area covered by them can be investigated. Using this approach it is expected that a better understanding of electrical treeing phenomenon will be developed.

X-ray computed tomography and serial block-face SEM have provided detailed threedimensional reconstructions of electrical trees for the first time. The application of finite element analysis (FEA) to the analysis of electrical fields in an epoxy block containing a tree is considered. Illustrations are provided by way of a number of case studies. It is shown that the limitations of FEA do not arise from the discrete nature of the meshing: rather uncertainties are more concerned with material properties in high fields on the micrometer scale, the limitations imposed by the pixel size of the imaging technique, and the discrete nature of the image reconstruction technique. For a dynamic model of tree growth space charge dynamics on the same physical scale need also to be modelled. A meshing strategy is used, calibrated against the charge simulation method, to ensure accurate but manageable computations in critical parts of a tree such as branch tips.Examples of field values are given using geometric constructs and low-field material characteristics as illustrative values. The field variation around a conducting tree structure, including the maximum field direction as a branch starts to bifurcate, is determined as an example. These yield values in excess of those expected if space charge movement was considered, but consistent with analytical calculations.

Partial discharges (PDs) are one of the most important classes of ageing processes that occur within electrical insulation. PD detection is a standardized technique to qualify the state of the insulation in electric assets such as machines and power cables. Generally, the classical phase-resolved partial discharge (PRPD) patterns are used to perform the identification of the type of PD source when they are related to a specific degradation process and when the electrical noise level is low compared to the magnitudes of the PD signals. However, in practical applications such as measurements carried out in the field or in industrial environments, several PD sources and large noise signals are usually present simultaneously. In this study, three different inductive sensors have been used to evaluate and compare their performance in the detection and separation of multiple PD sources by applying the chromatic technique to each of the measured signals.

Imaging of electrical trees has been an important tool for studying the phenomenon. The authors have previously shown that electrical trees can be three-dimensionally (3D) imaged and virtual replicas generated using X-ray Computed Tomography (XCT) or Serial Block-Face Scanning Electron Microscopy (SBFSEM). Here these techniques are evaluated and compared for 3D analysis of electrical trees along with conventional optical methods. A number of types of laboratory created trees showing range of morphologies were grown and examined to delineate the capabilities of each technique. Cross-sectional images and virtual replicas of the electrical trees from XCT and SBFSEM techniques were compared both qualitatively and quantitatively. SBFSEM provides greater detail than XCT, evidenced by imaging smaller sub-branches and when comparing parameters such as the number of tree channels, tree length or tree volume captured. On average, SBFSEM captures almost double the number of tree channels per slice than XCT, and virtual replicas in most of the cases have larger volumes. However, SBFSEM is a destructive technique, which makes the imaging process less reliable than XCT and not suitable for multi-stage of tree growth experiments. For full analysis, a combination of imaging techniques is proposed. Optical methods are used first to monitor tree growth. Then, micro-XCT which provides pixel size down to ~0.4 µm with a field of view of around 1 mm × 1 mm, can be used to reveal the overall 3D structure of a normal/mature electrical tree. Nano-XCT can be used to explore in more detail regions of interest, with a pixel size of ~65 nm, but a limited field of view of 65 µm. Finally, sections of the tree can be analyzed in even greater detail using SBFSEM, which can provide resolutions below 50 nm. Using this approach, a deeper and more complete analysis of the structure of electrical trees can be achieved.

No abstract

X-ray computed tomography and serial block-face SEM have provided detailed threedimensional reconstructions of electrical trees for the first time. The application of finite element analysis (FEA) to the analysis of electrical fields in an epoxy block containing a tree is considered. Illustrations are provided by way of a number of case studies. It is shown that the limitations of FEA do not arise from the discrete nature of the meshing: rather uncertainties are more concerned with material properties in high fields on the micrometer scale, the limitations imposed by the pixel size of the imaging technique, and the discrete nature of the image reconstruction technique. For a dynamic model of tree growth space charge dynamics on the same physical scale need also to be modelled. A meshing strategy is used, calibrated against the charge simulation method, to ensure accurate but manageable computations in critical parts of a tree such as branch tips. Examples of field values are given using geometric constructs and low-field material characteristics as illustrative values. The field variation around a conducting tree structure, including the maximum field direction as a branch starts to bifurcate, is determined as an example. These yield values in excess of those expected if space charge movement was considered, but consistent with analytical calculations. Index Terms -XCT, x-ray computed tomography, SBFSEM, Serial block-face SEM, FEA, finite element analysis, electrical tree, field, model, charge simulation method, CSM, image-based modeling. This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ Qi Li (aka Steven) was born in Hunan Province, China, in September 1984. He completed the B.Eng. degree in electrical and electronics engineering at

Electrical trees are one of the main mechanisms of degradation in solid polymeric insulation leading to the failure of high voltage equipment. They are interconnected networks of hollow tubules typically characterized from two-dimensional (2D) projections of their physical manifestation. It is shown that complete characterization requires a three-dimensional (3D) imaging technique such as X-ray computed tomography (XCT). We present a comprehensive set of parameters, quantitatively characterizing two types of tree topology, conventionally known as bush-and branchtype. Fractal dimensions are determined from 3D models and from 2D projections, and a simple quantitative relationship is established between the two for all but dense bush trees. Parameters such as number of nodes, segment length, tortuosity and branch angle are determined from tree skeletons. The parameters most strongly indicative of the differences in the structure are the number of branches, individual channel size, channel tortuosity, nodes per unit length and fractal dimension. Studying two stages of a bush tree's development showed that channels grew in width, while macroscopic parameters such as the fractal dimension and tortuosity were unchanged. These parameters provide a basis for tree growth models, and can shed light on growth mechanisms. Index Terms-electrical trees, three-dimensional trees, 3D imaging, fractal analysis, XCT the tree (a slice) is captured in the projected image. Key to the nature of an electrical tree (and its name) is its shape. Quantifying tree-type structures can be traced to Leonardo da Vinci, who introduced the notion of a fixed total thickness for a botanical tree as bifurcation points are passed, and who