The statistical initiation and propagation characteristics of electrical trees in cross-linked polyethylene (XLPE) cables with different voltage ratings from 66 to 500 kV were investigated under a constant test voltage of 50 Hz/7 kV (the 66 kV rating cable is from UK, the others from China). It was found that the characteristics of electrical trees in the inner region of 66 kV cable insulation differed considerably from those in the outer region under the same test conditions; however, no significant differences appeared in the 110 kV rating cable and above . The initiation time of electrical trees in both the inner and the outer regions of the 66 kV cable is much shorter than that in higher voltage rating cables; in addition the growth rate of electrical trees in the 66 kV cable is much larger than that in the higher voltage rating cables. By using x-ray diffraction, differential scanning calorimetry and thermogravimetry methods, it was revealed that besides the extrusion process, the molecular weight of base polymer material and its distribution are the prime factors deciding the crystallization state. The crystallization state and the impurity content are responsible for the resistance to electrical trees. Furthermore, it was proposed that big spherulites will cooperate with high impurity content in enhancing the initiation and growth processes of electrical trees via the 'synergetic effect'. Finally, dense and small spherulites, high crystallinity, high purity level of base polymer material and super-clean production processes are desirable for higher voltage rating cables.

Using a computer-aided image recording monitoring system, extensive measurements have been performed in the inner layer of 66 kV cross-linked polyethylene (XLPE) cables. It has been found that there are three kinds of electrical trees in the samples, the branch-like tree, the bush-like tree and the mixed tree that is a mixture of the above two kinds. When the applied voltage frequency is less than or equal to 250 Hz, only the mixed tree appears in XLPE samples, when the frequency is greater than or equal to 500 Hz, only the dense branch-like tree develops, both of which are attributed to the coexistence of non-uniform crystallization and internal residual stress in semicrystalline XLPE cables during the process of manufacturing. Through the fractal analyses of these electrical trees, it has been found that both the propagation and structure characteristics can be described by fractal dimension directly or indirectly. It is suggested that the propagation and structural characteristics of electrical trees are closely related to the morphology and the residual stress in material at low frequency, i.e., the propagation characteristics of electrical trees depends upon not only the boundaries between big spherulites and amorphous region, but also the impurity, micropore concentration and the relative position of needle electrode tip with respect to spherulites or amorphous region in the low frequency range. However, at high frequency, it has nothing to do with the morphology of material. It is suggested that the injection and extraction process of charge from and to dielectrics via the needle electrode are more intense at high frequency than in low frequency. Thus, it can form relatively uniform dielectric weak region in front of needle electrode, which leads to similar initiation and propagation characteristics of electrical trees at high frequency.

Depending on the morphology of the material and applied voltage frequency, three kinds of electrical trees can exist in cross-linked polyethylene (XLPE) cable insulation, which are conducting, non-conducting, and mixed trees with different growth mechanisms. It is suggested that when the needle is inserted into large spherulites, conducting trees will form in those spherulites; when it is inserted among spherulites, non-conducting trees will appear along the boundaries of spherulites. Frequency will accelerate the growth of non-conducting trees but have little influence on the initiation and growth processes of conducting trees. If the initiation process of non-conducting trees is too difficult, they will grow into mixed trees.Finally, it is concluded that the space charge limited tiny breakdown around the tips of electrical trees is responsible for the propagation process of conducting trees; on the other hand, fast expansion occurs due to local high temperature and pressure along the boundaries, partial discharge in electrical tree paths and charge recombination, etc., which are the main reason for the growth of nonconducting trees.

Due to the limitations of specific insulation structures and the influence of technical process，the growth of electrical trees in high-voltage power equipments with polymer as main insulation materials is more complicated than those in uniform materials，especially in equipment employing semi-crystalline polymer，so it is difficult to characterize by mathematical means. The experiment reported in this paper is the first attempt to focus on the electrical treeing rules in both inner and outer insulation layers of high-voltage XLPE power cable. Through statistical experiments and the SEM observation，large difference in treeing character between the inner and outer layers of cable insulation due to the different crystalline status are found. Electrical trees initiating in the inner layer of insulation has shorter initiation time，higher growth rate and greater variety of shapes compared than in the outer layers. The initiation and propagation mechanisms are also discussed.

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In this paper we investigated the structures and propagation characteristics of electrical trees observed in the high volatage cross-linked polyethylene (XLPE) cable insulation samples under high volatage of 10kV at frequency of 1000—2000Hz. Based on the specific tree growth mechanism and the fractal nature of tree structures, a dynamic model has been developed to qualitatively predict the electrical tree growth characteristics in XLPE cable insulation when subjected to an electrical stress under high frequency voltage, and then the tree growth rate equation and life formula of tree growth to breakdown are derived.We performed electrical tree growth tests in XLPE cable insulation samples at high frequency and compared the results, which showed that the proposed model was in good agreement with the expreriment.So,it seems that the proposeed model can be applied to the qualitative analysis of aging law of electrical tree in XLPE cable insulation.

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The approach of coupling CFD (Computational Fluid Dynamics) to model control system is a novel "grey-box" method. The principal theories of CFD and system identification are presented in this paper respectively. The principle and steps of CFD-based system identification are given in detail. Some applications are analyzed; and the key problems and developing trends of the method proposed in this paper are indicated. S 3268 978-1-4244-8738-7/11/$26.00 c 2011 IEEE