21, rue d Artois, F-75008 PARIS B2-308 CIGRE 2010 http : //www.cigre.org Investigation of electrical tree characteristics developed in composite insulation using colour coding techniques M. ABDERRAZZAQ Yarmouk University Jordan abder@yu.edu.jo
SUMMARY This paper investigates the variation of color characteristics of a pictured electrical tree, which is initiated and grown in a composite insulation slab before being examined by advanced microscope. The scope of the present work is not restricted to the tree structure itself but extends to cover a complete treed region. Therefore, the current paper characterizes the relationship between the tree structure and the change of color parameters represented by hue, saturation and value of examined points. The image colors are created by relative retardation orthogonal components of the polarized white light used to illuminate the specimens in the microscope. A software package is employed to analyze the depicted colors by assigning a set of values to each pixel of image components. A Matlab program is written to determine the color mapping of examined image. Three large matrices of examined points for the hue, saturation and value of the employed color model were constructed. The variation of each color parameter is linked with the tree frame and may be introduced as a stress indicator according to the proximity of the examined point from that frame. This approach offers a quantitative method, which converts a treed image into numerical array of data without a need for a complex mathematical procedure. The paper provides a correlation between the direction of tree growth and the rate at which each color parameter changes in that direction. Each point in the image is identified by a set of three numbers ranging from 0 to 255. The Microsoft Excel is employed to process the results and to provide a simple comparison among various cases of the analyzed data. The change in the color map between each case and the other is used as an indicator of strain pattern variation. Despite the dependence of the obtained results on the materials used and conditions applied, there is a clear relationship between tree growth and color variation. KEYWORDS Composites, water, tree, image, red, green, blue and strain. 2
1. INTRODUCTION In the last three decades, there was a significant increase in the number of applications of composite materials. They are widely used in transmission systems, especially in power transformers, cables, and capacitors [1]. The interest in composites over traditional dielectrics is a result of improved knowledge in the properties of such materials such as the tolerability, corrosion advantages and high strength-to-weight ratio. However, composite characteristics depend very strongly on the electrical stress, which can be developed under abnormal conditions such as the presence of moisture, impurities, voids and protrusions. Treeing is one of the aging effects that are usually caused by enhancement of voltage stresses at such conditions. The damage propagates over time until enough insulation is breached and breakdown takes place. Therefore, the interest in previous works was in characterizing electrical trees and determining the weight of each condition affecting this phenomenon. Some researchers have focused on the damage of the resin, surrounding the tree structure, as a function of local electrostatic energy dissipation by partial discharges [2-5]. Others considered the growth behaviour of trees as a function of applied voltage and they matched that growth with the fractal dimension of tree [6]. A third group of researchers assumed that protrusions, contaminants and micro-voids cause enhancement of local electrical fields and, consequently, an initiation of trees [7]. Nevertheless, a complete understanding of treeing, using experimental and theoretical tools is always essential [8,9]. Although electrical trees were extensively studied in the last three decades, the main concern was on the tree development rather than on the change of the stressed material. This change occurs as a response to the tree growth. The previous experiments were conducted to create conditions similar to that governing the growth mode of electrical trees. Therefore, it is more useful to concentrate on the differences between defected and sound insulation rather than restricting the interest on the damage itself. On the other hand, the change observed in the insulating material during the tree growth should not be looked at as a external variation, but it can also be specified via the color change of internal strain of tree images. In the present paper, an image of electrical tree, surrounded by polyester resin matrix, is analyzed using color coding techniques. The change in the color parameters for a specific area in the treed region is used to differentiate between one state of the material and another. 2 UNDERSTANDING COLOR MODELS Color is an important part of peoples' daily life. Although it has a major role in taking decisions, many people have insufficient knowledge about color techniques and characteristics. Therefore, it is necessary to specify the changes in these colors resulted from the variety of conditions affecting the color perception and interpretation. Among these conditions are the differences in light source, object size, background and direction [10]. A color model is a method of describing each part of the image as a combination of multiple components. Color pixels usually contain Red, Green and Blue (RGB) values. This model is most widely used since it has a convenient mapping to hardware. Display hardware allows for independent control of the contribution of each of the RGB colors. However, the RGB model lacks intuitive appeal. Given a color, it proves hard to estimate its correct RGB values, which indicates that such system does not match well with perceptual properties. When colors are classified, they can be expressed in terms of their hue (color), lightness (brightness) and saturation (vividness). Hue is the term used in the world of color for the classification of red, yellow, blue and other colors. Mixing primary colors produces other colors and the continuum of these hues results in the color wheel [12-14]. Hue is also employed to describe a dimension of color as experienced by the users of such color. On the 3
other hands, colors can be separated into bright and dark when their lightness capabilities are compared with hue. Finally, the saturation characterizes the vividness of colors or the dominance of hue for different objects. The color model containing these properties is known as Hue, Saturation and Value (HSV) color model. Closely allied to the concept of a color model is the concept of a color space, which is a set of component values allowable in a color model [12,15]. In other words, a color space is an implementation of a color model that generates real colors. 3 EXPERIMENTAL Specimens of composite insulation were fabricated at room temperature using a polyester resin matrix (resin C) with a layer of reinforcing material, cast midway between the electrodes. All specimens were exposed to an a.c. voltage of 4kV rms for a period of 240 hours (10 days). A settling down period is necessary to enable the strain patterns, arising from casting process, to gain more stability. The fresh specimens need at least 10 days for relaxation under dry conditions. The tree image is observed within the specimen via a circular polariscope, consisting of a microscope fitted with the quarter wave and polarizing plates. The optical system was adjusted to a standard magnification level during all stages of strain development to minimize errors due to the influence of magnification. 4 DIGITALIZATION OF TREE IMAGE The digital representation of an electrical tree image requires a precise determination of all color components contained in the treed region. This can be achieved by conducting an overall measure of color components of the optically examined insulation area. These components are combined to form pixels in accordance to a color model. The pixels, with the constituent color component measurements, are the digital representation of the considered image. The current understanding of a treed image is not limited to the tree itself but includes the area surrounded by the tree branches. Therefore, the color parameters vary according to the location of measured points of tree images. The current model can be constructed using simple program with few lines of ready-to-apply instructions. Alternatively, it is possible to employ a specialized software to analyze the color model embedded in tree image. ColourMania 2.7 is one of free-to-download software packages, which has intuitive interface, eyedropper and screen magnifier [16, 17]. The color modes include RGB and HSV values, brightness adjustment and color display in different formats. This version of software has the capability of faster refresh on screen magnifier and better handling of color wheel drawing than previous releases. To determine the color characteristics of the tree image, the picture of such an image is overlaid by a net of identical squares with equal areas. The dimensions of squares should be correctly selected. A wrong selection of relatively large squares can significantly affect the accuracy of the colour values prevailing in each square. Therefore, in the current study the smallest grid settings of horizontal and vertical spacing available in Microsoft office are used. The width and length of the sample picture (8.84cm x 6.96cm) were divided into 1428 squares (42 x 34 divisions). Each square has a dimension of 2.1mm x 2.1 mm and an area of 4.41 mm 2. For each square, a set of three values (HSV) of color characteristics was recorded. The color parameters are captured at the same positions. Figure 1a shows a complete area of tree image, whereas, Figure 1b illustrates the same image but overlaid by a net of squares. 4
(a) (b) Figure 1: (a) Investigated electrical tree image. (b)overlaying of tree with a net of square 5 RESULTS To study the relationship between the color values in the squares of Figure 1b and the tree distribution in the studied image, three matrices were formed. Each matrix has 34 rows and 42 columns to specify one of the color parameters; hue, saturation or value. Therefore, each element of the matrix determines one of the color characteristics in a certain position on the treed area. The horizontal and vertical measurements have started from the top left corner of Figure 1b(x=0,y=0). In all subsequent figures the x and y axes are given in units, which refer here to the squares. Figure 2 below shows the surface plotting of hue map over the examined insulation area, whereas, an interesting form of this mapping is given by plotting this relationship in the contour form as shown in Figure 3. Figure 2: Hue map using surface plotting Figure 3: Hue map using contour plotting In all cases studied it is worth matching between the tree location in the image and its shape. To correctly understand such figures, it is worth remembering that hue is related to the color wheel, which can vary from 0 to 360 degrees. However, the color hue in the last few rows of image, where no branches exist, is relatively stable value (60 degrees). 5
The mapping of color saturation is given in Figure 4, whereas, Figure 5 illustrates the same relationship but in the contour form. Unlike the hue, the degree of color saturation, which characterizes the dominance of hue in a selected point, is given as a percentage value. The highest saturation is depicted in the middle of the image. This indicates the level of vividness of dominating colors in that part of the image. As in the case of hue mapping, the saturation shows a high degree of stability in the last few rows of treed image. With the exception of pin-tip area, the saturation is clearly low (6 to 16%). The third element in the HSV model is the color value, defining brightness (lightness) of examined image. Figure 6 illustrates the surface plotting form of the color value variation, which is depicted in each image point defined by x-y coordinates. Figure 7 shows the contour plotting of Figure 6 described above. Figure 4: Saturation map using surface plotting Figure 5: Saturation map using contour plotting Figure 6: Value map using surface plotting Figure 7: Value map using contour plotting The color value is theoretically varied from 0 to 255 pixels. However, the maximum value, measured in this image, is 254 pixels. The highest color values are shown in the last five rows of the depicted image, which are clearly brighter than all areas of the image. This fact is simply illustrated by the contour plot, in which the darkest areas occupy the upper rows of the image and the lightest are distributed on the lower ones. By inspecting individual squares in each row of examined image, it is easy to find that the color value (lightness) is significantly changed when a piece of tree is contained in that square. If the adjacent squares are empty of tree branches the lightness is increased and, consequently, the color values are improved. Nevertheless, the complete understanding of this mapping can only be achieved when all color parameters are considered together. As the tree growth starts from the tip of the H.V. electrode and ends at the opposite earth electrode, it would be useful to match the tree growth direction with the average change in 6
Mean Color Value, pixels Mean Hue Value, degree Mean Saturation, % hue, saturation and value of the image colors. To achieve this goal, mean values of color parameters in each row is determined along the vertical direction of examined image. Figure 8 illustrates the variation of hue mean value along the examined image, whereas, Figures 9 and 10 show the same relationships but for color saturation and value, respectively. 350 300 250 200 150 100 50 0 1 4 7 10 13 16 19 22 25 28 31 34 Row number 80 70 60 50 40 30 20 10 0 1 4 7 10 13 16 19 22 25 28 31 34 Row Number Figure 8: Mean hue value along the image Figure 9: Mean saturation value along the image 300 250 200 150 100 50 0 1 4 7 10 13 16 19 22 25 28 31 34 Row Number Figure 10: Mean color value along the image 6 DISCUSSION Treeing is one of electric field effects, which the insulation material may experience when it is exposed to excessive voltage for enough time. The treeing process is not completed at the same time, but in consecutive stages. Therefore, the same image may contain several areas stressed at different degrees. If the space occupied by the tree itself is considered the most stressed area, the proximity of a point to that tree can be used as an indicator of a relative strain in that point. In other words, for each insulation point, defined by an x-y coordinate, there is a specific stress value. When an insulation point is stressed, the effect is not restricted to the internal structure and physical integrity of the material itself but extends to include the changes in the outer appearance and colors of that point. To study the transformation occurs to the internal structure of the material from one state to another, various types of experiments and analytical tests are needed. This task is not only complicated but it is also expensive and time consuming. Alternatively, it is more useful to express the material state by its color characteristics in that state. It was found in a previous work that the internal strain is strongly related to the colors of stressed treed region [18]. This means that all variations in the color characteristics can be linked to the development of stress in the examined treed region. On the 7
other hand, if it is assumed that the tree stem and branches are the most stressed points in the examined image, then the stress in the interfacial area can be correlated to the difference in the color characteristics of both branched and non-branched areas. Therefore, the horizontal and vertical growths of tree are precisely described by the abrupt variations in the color model characteristics when the grabbing tool, provided by the ColourMania 2.7 software, is moved from one point to another. For example, in a square occupied by a piece of tree branch, the HSV values were 349, 70 and 225 respectively. However, when the grapping tool is moved to the adjacent non-branched square, the above HSV values became 338, 24 and 254 respectively. This means that the changes in HSV values are 3.15%, 65.7% and 12.8% respectively. It is clear that the significant change occurred in the color saturation or vividness of the dominant color. The change in the color value indicates that the brightness of nonbranched square is relatively higher than treed square. However, the hue is only changed by 3.15% which means that there is no significant variation in the color dimensions or movement in the color wheel. From the stress point of view, it is expected that the two above adjacent squares must have small difference in stress level. Consequently, the hue is not significantly affected by this level of stress discrepancy, but other color characteristics can be more sensitive to these changes in stress. Hue mapping, shown in Figures 2 and 3, is useful to illustrate the spectrum of color variations in the examine image. The following findings are worth mentioning in this field. Firstly, the hue change is relatively small in general. However, the last rows, which are free of tree branches, have shown unchanged hue but with a reasonable difference from that of treed squares. Secondly, the hue change band was not wide, which means that the number of colors existing in the examined image is limited. The angle of hue wheel movement is restricted due to the dominance of purple-like color in the image. Thirdly, the color contours shown in Figure 3 define the areas which have the same hue. Although it is difficult to have exact matching between the tree boundaries and the contours, it is easy to notice the impact of tree dimensions on depicted hue map. Therefore, it is useful to observe the common change in hue along the vertical direction of tree growth as shown in Figure 8. The hue oscillation around a fixed band of values is noticed in the intensively-treed region. The band of this oscillation starts to increase as we approach the pin tip, where the tree was initiated. Figures 4 and 5 illustrate the color saturation mapping on the examined image. In the first few top rows of Figure 1b, the differences in saturation level are small and the saturation itself is low. By moving down, the saturation starts to grow with a noticeable difference in values in the same row of squares. In this zone, the branches are separated by tree-free areas, which cause a difference in vividness of adjacent squares. In the lower rows, the color saturation starts to decrease significantly. The contour plotting indicates that the largest area is the middle one, where the tree occupies this zone. These findings agree with the results shown in Figure 9, where the common trend of saturation changes from pin to plane electrodes. Therefore, the color saturation sensitivity to stress variation can be efficiently applied in the branched area. The lower value of difference in color saturation means that the stress level is almost similar. The farthest the points from the tree frame, the lowest the saturation they have. The color value mapping shown, in Figures 6 and 7, can be used to characterize the stress from brightness point of view. This is the easiest color parameter to analyze. The top rows shown in Figure 1b are the darkest ones, and, therefore, it is expected to have the lowest color value. The brightness is improved in the next lower set of rows. The area below the tree frame is the brightest one and, consequently, the highest in color value. If the latter area is the less stressed one, it is possible to use the color value as a measure of stress. This can be proved by inspecting the color values in a row of squares, which contains treed and non-treed areas. In one of these rows, there was a series of color values 250, 254, 254, 254, 253, 254, 254, 253, 254, 228, 254, 231, 253, 254, 254 pixels. The abrupt change in color value from 254 to 228 or 8
to 231 pixels agrees with the transformation from a non-treed square to the treed squares. The contour plot illustrates the gradual change of color values in the examined image. The highest brightness is noticed in the last zone of the sample, below the tree image. This zone is free of color contours compared with the upper dark zone. Figure 10 determines the general trend of color brightness change along the vertical line of tree growth. The results obtained from this relationship are in well agreement with that obtained from the surface and contour plots. One of the interesting features of this relationship is the small standard deviation among the color values in the same row. The maximum percentage of this standard deviation is 4.66%, compared with 47.3% and 12% for color hue and saturation, respectively. The standard deviation values refer to the color characteristics uniformity of the various color modes. Nevertheless, in most strain patterns, observed in previous work, the tip of the H.V. electrode is usually surrounded by a purple, an orange or another red-related color [18]. For different specimens and conditions, the colour parameters of an image, characterising a strain pattern, can exhibit a specific mode of changes. This could be attributed to a number of factors including the type of material, curing process and the material construction [11, 19, 20]. Nevertheless, the analysis of strain patterns development from a sequence of images, captured periodically, can be a universal approach and more effective measure than tree growth criterion. Therefore, the valuable application of such approach implies that the relationship between colour characteristics and strain patterns is not limited to searching for the colour changes from one condition to another but extends to cover the variations of such patterns in different composites. In cast specimen, the adhesion of the reinforcement to the resin affects the whole area adjacent to that barrier. The stronger the adhesion of the composite components, the higher the complexity of the strain colour map developed near the barrier. Nevertheless, this approach can be used to set a new measure for a mechanical impact of various degradation mechanisms on insulators including water absorption and treeing. 7 CONCLUSIONS Electrical treeing phenomenon in dielectrics can be characterized in terms of color modes depicted in the treed image. The differential stress in a treed image was related to the variations in the hue, saturation and value color parameters. The mapping of these parameters on the examined image was obtained by setting three matrices for HSV model. The variation of matrix elements were linked to the stress changes in each position of the image. Among all color parameters, the most sensitive one to the stress changes was the color saturation or vividness, whereas, the least one was the color hue. The scope of change for color parameters was varied. Hue has shown a limited range of change, due to the limited colors dominating in the examined image. The higher magnitudes of color saturation were evident in the tree zone, whereas, the color brightness has shown a decrease with the tree growth. The contour plots of color parameters mapping were of significant assistance to identify the boundaries of the stressed areas. Finally, the standard deviations of color parameters were calculated for each row of matrices to specify the uniformity of color changes and stress variations. BIBLIOGRAPHY [1] H. Uehara and K. Kudo Barrier Effect of Treeing in Composite Insulating Materials with Heat-adhesive Interfaces of Different Polymers ( IEEE TDEI, Vol. 12, 2005, pages 1266-1271). [2] S. J. Dodd, A Deterministic Model for the Growth of Non-conducting Electrical Tree Structures, (J. Phys. D: Appl. Phys. Vol. 36, 2003, pages 129-141). 9
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