배전케이블의 XLPE 절연체에서 교류 고전계하에 발생하는 트링에 의한 절연열화 현상의 시간과 공간영역에서의 프랙탈 특성

조영신□이홍기．□심미자．．□김상욱

서울시립대학교 화학공학과, 우석대학교 화학공학과．

서울시립대학교 생명과학과．．

Fractal Characteristics of Electrical Treeing Deterioration Phenomena in XLPE Insulation of Power Distribution Cable in Time and Space Domain

Y. S. Cho, H. K. Lee．, Shim．．, S. W. Kim

Dept. of Chem. Eng., Seoul City Univ., ．Dept. of Chem. Eng., Woosuk Univ.

．．Dept. of Life Sci., Seoul City Univ.

Introduction

The electrical trees grown in the polymeric insulator from the electric field concentrated region such as conductive inclusions, rough electrode surfaces(micro edges), voids, cracks, etc. are the main causes of dielectric failure[1]. The topology and dynamics of electrical treeing phenomena depend on electrical characteristics of dielectrics, electrode geometry and the shape and magnitude of applied stress[2]. It was reported the phenomena have the fractal properties of self similarity in space and time domain[3]. The fractal dimension(DF) and coefficients in space and time domain of the growing electrical tree in XLPE were calculated by the following equations[3],

[eqn: D_F ``= `ln`N(s) / ln({1 over s })]                      (1)

[eqn: b `=` ln`N(s) / ln `t]                           (2)

[eqn: q `= `ln`l` / ln `t]                              (3)

where N(s): sum of grids covering the tree, s: grid scale, t: voltage applying time, l: leading tree length. It was investigated the dynamics of treeing growth occurring in the XLPE insulating part of power distribution 22.9 kV CN/CV cable. The dynamic change of fractal characteristics was investigated in time scale and space domain. Treeing phenomena were numerically studied by the terms of fractal properties to quantify the complexity or degree of treeing deterioration under the AC electrical stress.

Experiment

Specimen used in this study was a block of needle-plane electrode geometry of XLPE insulation in power distribution 22.9 kV CN/CV cable(Hanil Power Line Co.). Needle electrode which had well controlled curvature of radius of 3 □ was inserted into the sample at 100℃ with zig. It was annealed for 12 hrs and cooled down slowly to minimize the mechanical defects by thermal stress. The test specimen was set in silicon oil at 25℃ for 20 mins and the AC 7.5 kV of 60 Hz was applied to the needle electrode until dielectric breakdown. The electrical tree was observed by microscope and analyzed by using image analyzer(Image Pro Plus). The tree was covered by grids and the sum of grids covering the tree and leading tree length vs. voltage applying time were plotted on the double logarithmic paper. From the slope of the linear relations, the complexity of electrical treeing deterioration phenomena was numericallized[4,5].

Results and Discussion

Fig. 1. Electrical tree covered with grids of 60 □.

Fig. 1 shows the electrical tree observed in XLPE under the supplied electrical stress of 7.5 kV for 1350 secs at 25℃. The initial tree was started from the needle electrode and propagated toward the counter plane electrode step by step. At the initial stage, low density tree was observed but as the voltage applying time increased the branching density of tree increased. To measure the complexity of treeing phenomena or the degree of treeing deterioration, tree was covered with grids as shown in Fig. 1 and all the grids which were covering a portion of the tree were accounted.

Fig. 2. Estimation of the fractal dimension by using a scale covering method.

To measure the complexity of electrical tree, scale covering method was introduced. The sum of grids covering the tree and grid scale was plotted at various voltage applying time. A good linear relation was observed. So that all the electrical trees in this system had the fractal characteristics and the fractal dimension or the complexity of the tree was 1.46(50 secs), 1.54(80 secs) and 1.42(1350 secs) respectively.

Fig. 3. Dependence of the fractal dimension(DF) and leading tree length(l) vs. voltage supplying time(t)

Fig. 3 shows the leading tree extent or the development of spatial tree length at X and Y axes and the fractal dimension at various voltage applying time. As the voltage applying time increased, the leading tree length on X-axis increased until the voltage applying time was 270 and then decreased slightly and then remained almost same. This type of tree growth behavior has been reported to be observed in polyethylene by S. Maruyama et al.[6]. At the initial stage, the low density dendrite tree was observed but as the voltage applying time increased the tree extent rate decreased and the fractal dimension increased to some extent. The reason of this behavior was explained by the change of internal gas pressure[7]. As the tree propagated toward plane electrode, the electric field at the tree tip decreased and the probability of partial discharge decreased. The gas was condensed on the treeing channel and the gas pressure decreased. So the tree in the fine branch was not observed through microscope that the tree extent decreased and the change of the fractal dimension was observed. But the damaged polymer was not healed automatically like the gas and liquid insulator. The fractal dimension is proportional to the degree of treeing deterioration and depends on voltage applying time[4,5,6]. As the voltage applying time or tree length increased, the fractal dimension increased. It is clear that the fractal dimension of the tree depends on treeing propagation characteristics. All the tree in XLPE had fractal characteristics and the fractal dimension showed almost same value of 1.4 under 7.5 kV after 300 secs.

Fig. 4. Fractal parameters in time and space domain

To check whether the tree has fractal properties in time and space domain, the level of coefficient b which is the slope in ln N(s) vs. ln t plot by the equation(2). At the test condition of 7.5 kV, the magnitude of b was 2.05. The fractal parameters were measured from the slope of the linear relation in Fig. 4. To estimate the dynamics of changing in time scale, the ln tree-length vs. ln voltage-applying-time was plotted as shown in Fig. 4. At the initial stage, the linear relationship was observed and the parameter of X and Y-observation axes were 1.31 and 1.68 respectively. But as the voltage applying time increased longer than 80 secs, the linear relation was not observed and the value was saturated and showed the same value regardless of the voltage applying time.

References

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3. O.L. Rezinkin, M.M. Rezinkina, and A.V. Dolbin, 1995-ISEI M, 161(1995).

4. Y.S. Cho, M.J. Shim, and S.W. Kim, IUMRS-ICA-95 Seoul, 453(1995).

5. Y.S. Cho, S.H. Lee, H.K. Lee, M.J. Shim, J.S. Lee, and S.W. Kim, Proc. of 1st Intern. Conf. on HNTTI'96, Dandong, China, 755(1996).

6. S. Maruyama, S. Kobayashi, and K. Kudo, T. IEE Japan, 113-A, 480(1993).

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