Multiscale Nonlinear Dynamic Characteristics of

2012 International Conference on High Voltage Engineering and Application, Shanghai, China, September 17-20, 2012

Multiscale Nonlinear Dynamic Characteristics of Leakage Current for Monitoring Polymer Insulators in Salt-Fog Conditions 1

Yong Liu1, B. X. Du1, Nan Chen2 and Zhen Yin2

School of Electrical Engineering and Automation, Tianjin University 92 Weijin Road, Tianjin 300072 China 2 Tianjin High Voltage Power Supply Company, Tianjin 300250, China Abstract—Based on the present investigation of leakage current for evaluating and monitoring outdoor insulators, the multiscale nonlinear technique is proposed to analyze the dynamic characteristics of leakage current through the artificial contamination experiments. Contamination tests were conducted in a laboratory by employing heavy salt fog without the deposition of non-soluble contamination. Based on the corresponding relationship between the leakage current and the behavior in heavy-fog conditions, the temporal series of leakage current are extended to two phase space by using a phase-space reconstructed method. In accordance with the dynamic behaviors on the insulator surface, the multiscale entropy of leakage current is obtained to investigate the underlying nonlinear characteristics in relation with the variation of contamination degree, ambient temperature and relative humidity. Associated with the quantitative analysis of mutiscale technique, the results can be helpful to improve the accuracy of insulator monitoring for reducing the accidents.

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INTRODUCTION

It is known that leakage current driven by the source voltage will pass through the insulator surface during the running period of polymer insulators, which is associated with the influence of wet and contaminated conditions. Thus, it becomes one of the most widely used methods for monitoring the insulator performance. The surge counting, the peak recording and the charge measurements in the leakage current have already been employed for monitoring the contaminated conditions. However, it is pointed that the time-domain magnitude of leakage current cannot well reflect the surface performance as the increasing value of the current may be caused by either the higher conductive current or the surface discharges [1]. And the discharges can have more negative effects on the insulator, especially propagate to induce the flashover accidents. According to the investigation on both the time-domain and the frequency-domain characteristics of leakage current, the current has been proven to be a complicated non-linear dynamic system. The non-linear analysis method has been employed to extract the related indicators of 1-dimentional current waveforms in relation with the variation of environmental factors, which is helpful to realize the dynamic performance of outdoor insulator, even the propagation of flashover events. Gubanski et al have classified the patterns of 978-1-4673-4746-4/12/$31.00 ©2012 IEEE

leakage current including the non-linear characteristics to check the availability of permanent work for silicone rubber insulators in polluted and clean tropical environments [2]. Du et al have investigated the non-linear properties of discharge activities to reflect the switches of discharge states and the underlying mechanism of flashover process. Therefore, the application of non-linear analysis method on the current can reflect the dynamic performance and its transforming properties, which is helpful to enhance the working reliability of outdoor insulator [3]. Entropy is considered as one estimator for the complexity and regularity of a non-linear system. Richman et al proposed the sample entropy for the analysis of physiologic signals, which is proved to be suitable for the complicated signals. And then, the multi-scale entropy was proposed by Costa, which can reveal different states and the related parameters of a system. In this paper, an artificial fog chamber is established to simulate various of salt-fog condition in consideration that salt fog is one of the prominent factors to affect the running performance of outdoor insulators. The multiscale nonlinear analysis method is proposed to obtain the multiscale entropy of leakage current at different developing stages of the flashover process. The results reveal the dynamic propagation of surface discharges by the current entropy under different scales and give the quantitative indicator by the related varying ratio for the performance estimator. II.

EXPERIMENTAL ARRANGEMENT

An actual suspension silicone rubber insulator (diameter 24 mm) with alternate sheds (FXBW4-35/70) was applied as the specimen, with the specific configuration shown in Figure 1. The specimen was made of high temperature vulcanized silicone rubber (HTV SiR) with alumina trihydrate (ATH: Al2O3·3H2O) filler contents of 38 parts per 100 by weight (pph). The specimen surface was wiped by ethyl alcohol for 24 hours before and after each test at room temperature. The experimental arrangement is shown in Figure 1. The specimen was hung vertically in an artificial salt-fog chamber with the volume of 1000 × 480 × 1015 mm3. The ac voltage of 30 kV was applied as the test voltage, making an electric field of ac 68.2 kV/m. The salt fog, with the conductance from 1.0

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to 5.0 mS/cm and the injection rate of 2.1cm3/min, was generated by an ultrasonic vibration salt-fog generator filled with saline water. The relative humidity was controlled from 70% to 100% and the ambient temperature was in the range of 25 oC to 40 oC. The experiment was conducted by injecting the salt fog into the chamber for 2 hours and then the test voltage was continuously applied. The leakage current was recorded on the specimen by using a 50-Ω shunt resistor in connection with an analog to digital (A/D) converter. The sampling frequency of the A/D converter was 22.05 kHz. III.

DATA PROCESSING METHODS

A. Sample Entropy For a time series {u(j): j=1, 2,···N, N is the length of the time series}, it can be obtained N-m+1 vectors Xm(i) in the phase space, where 1 ≤ i ≤ N-m+1, Xm(i)={ u(i+k): 0 ≤ k ≤m-1}. Then, the maximum distance between any two vectors is defined: d[X(i),X(j)] = max {|u(i+k)-u(j+k)|: 0 ≤ k ≤m-1} (1) To ensure the definition validity of the vectors Xm(i) and Xm+1(i), the calculation number should be limited within N-m. is defined as the (N-m-1)-1 numbers of the distance The between Xm(i) and Xm(j) below the threshold value r. Then, the parameter Bm(r) can be obtained: (2)

Figure 1. Schematic of experimental arrangement.

As the same, the is defined as the (N-m-1)-1 numbers of the distance between Xm+1(i) and Xm+1(j) below the threshold value r. Then, the parameter Am(r) can be obtained: (3)

the original signal; at the scale of τ, the constructed series are . (6) (3) the threshold value r is generally selected as 0.25·σ, where σ is the standard deviation of original time series. And then, the sample entropy of the constructed time series at different scales can be obtained, which is called the multiscale entropy, which can reflect the complexity of the system at different scales. C. MsEn Analysis of Typical Signals Figure 2 shows the MsEn of typical signals at different scales, including Sine signal, white noise and Henon map. The signals are generated as follows. (1) Sine signal: y=3*sin(x) (7) (2) Henon map: (8) ߙ=1.4, ߚ=0.3, x0=0, y0=0. From Figure 2, it can be found that under the investigated scales, the entropy of white noise shows the highest value and has the decreasing tendency with increasing the scale. It indicates that through comparing the invested typical signals, the white noise has the most complex characteristics and the complexity degree has the lowest value at the highest scale. Then entropy of Henon map shows the increasing tendency with the scale increasing to 3, but shows the decreasing tendency with the increase of the scale, which will be lower than the entropy of Sine signal when the scale is higher than 13. Such tendency indicates the Henon map has the highest complexity. That is to say, the multiscale entropy method can reveal the nonlinear characteristics of complex time series at different scales, which is better than the sample entropy at only one scale. Meanwhile, the MsEn of Sine signal shows the lower value at the lower scale, and becomes the almost invariable value at the higher scale, which is in accordance with the periodicity and regularity of Sine signals. Figure 3 shows the MsEn of white noise with variation of calculation number points. It can be found that there is only little difference among the MsEn of white noise with the 2

Therefore, the sample entropy (SampEn) is defined. Then, based on the statistics, the SampEn can be obtained. (5) B. Multiscale Entropy (MsEn) Before the calculation of MsEn, the original time series should be coarse graining processed to calculate the corresponding sample entropy at different scales as the following procedures. (1) Considering the given time series are u(i), i-1,2,···N. (2) Constructing the continuous coarse graining processed time series. At the scale of 1, the constructed time series are 978-1-4673-4746-4/12/$31.00 ©2012 IEEE

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Sin White Noise Henon

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calculation number points from 5000 to 15000. Therefore, the obtained results of MsEn are not sensitive to the calculation numbers, which is advantageous to enhance the calculation speed and cannot record a mass of data in the field. 2 N=5000 N=8000 N=10000 N=15000

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Figure 4. Temporal waveforms of leakage current under different humidity conditions: (a) 70%, (b) 80%, (c) 90%, (d) 100%.

Figure 3. Multiscale entropy (MsEn) of white noise with variation of calculation number points.

IV.

RESULTS AND DISCUSSION

A. Leakage Current Waveforms under different test conditions Under 1.0 mS/cm and 30 oC, the leakage current against the relative humidity are shown in Figure 4, which increases with increasing the humidity. This is due to the easier formation of conductive layer with the increasing humidity. Under the low humidity, there is insufficient moisture available to lower the surface resistivity. As a result, the current conducting across the surface is lower. Because of the moisture absorption being mostly dependent on the humidity level, when the humidity increases, the surface starts absorbing more moisture from the surrounding salt-fog environment, consequently causing a drop in the surface resistivity that makes the increasing current. Under 1.0 mS/cm and 80%, the leakage current against the temperature are shown in Figure 5. The increasing temperature leads to a significant increase in the current. It is considered that the temperature effect is not only on the condensation and evaporation process but also on the salt-fog formation. With increasing the temperature, both the condensation and the evaporation are accelerated. Therefore, the total salt fog on the insulator surface is sufficiently available to lower the surface resistance, resulting the significant change of the current. Under 80% and 30 oC, the leakage current against the saltfog conductance are shown in Figure 6. With the conductance from 1.0 to 3.0 mS/cm, the current increases; while from 3.0 to 5.0 mS/cm, the current decreases. It is generally known that the leakage current can be divided into two components: one is current by the dry-band discharge, and the other is by the electrolytic conductivity. The wet degree of insulator surface becomes more with increasing the conductance, even forming the electrolytic layer. With the conductance from 1.0 to 3.0 mS/cm, the conductive layer is not uniform, the dry-band discharge occurs frequently and dominates the current; while from 3.0 to 5.0 mS/cm, the conductive layer is more uniform to 978-1-4673-4746-4/12/$31.00 ©2012 IEEE

Figure 5. Temporal waveforms of leakage current under different temperature: (a) 25 oC, (b) 30 oC, (d) 40 oC.

Figure 6. Temporal waveforms of leakage current under different contaminated conditions: (a) 1.0 mS/cm, (b) 2.0 mS/cm, (c) 3.0 mS/cm, (d) 4.0 mS/cm, (e) 5.0 mS/cm.

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minimize the dry-band activity, the dry-band discharge occurs infrequently and the electrolytic current dominates the current. B. Multi-scale Entropy Analysis of Leakage Current As described in Figures 4 to 6, the temporal waveforms of leakage current reflect that both the amplitude and distortion of the waveforms are dependent upon the environmental conditions. It is generally realized that the temporal distortion of leakage current contain more valuable information on the degradation process due to the droplet deformation and the discharge activities with different frequencies on the insulator surface. Therefore, it is necessary to clarify the nonlinear characteristics in the leakage current in order to estimate the surface performance of the insulator. Figure 7 shows the relationship among the multiscale entropy of leakage current, the humidity, the temperature and the contamination level, which can reflect the complex 0.8

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ACKNOWLEDGMENT The research work is sponsored by Innovation Foundation of Tianjin University (2704).

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REFERENCES

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CONCLUSIONS

Leakage currents and their multiscale entropy (MsEn) value were investigated for evaluating the dynamic behaviors on the insulator surface under contaminated environments with multieffects of relative humidity, ambient temperature and contamination level. Associated with the temporal variation of leakage current, the related MsEn value was obtained to reveal the nonlinear characteristics during the contaminated process. The multiscale entropy technique was effective for the reflection of surface dynamic behaviors at different scales. The nonlinear complexity of the contaminated insulator performance can be revealed by the slope of MsEn variation.

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dynamic behaviors of insulator surface at different scale. For all the investigated conditions, the MsEn value shows the increasing tendency with the increase of the scale. When the scale achieves the higher value, it becomes the relatively steady value. Such tendency is in accordance with the variation of insulator surface and can be used to determine the surface performance. With the increase of the relative humidity, the slope of the increasing MsEn shows the decreasing tendency, as shown in Figure 7a. This reveals that the less complex behaviors on the insulator surface under the higher humidity, which is due to the more concentration of fog droplets resulting the increase of conductive currents with low frequency characteristics. With the increase of ambient temperature, the slope of the increasing MsEn shows the decreasing tendency, but becomes almost the same above the room temperature, as shown in Figure 7b, which can reflect that the temperature has less effect on the complexity of surface behaviors. In Figure 7c, the variation of MsEn value is complicated, in which the MsEn value and the related slope under 3.0 mS/cm are the lowest value, which is in accordance with the same tendency of temporal variation of leakage current. These results correspond with the dependence of the leakage current upon the salt-fog conductance: the leakage current increases with increasing the conductance from 1.0 to 3.0 mS/cm, but decreases from 3.0 to 5.0 mS/cm as shown in Figure 6.

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(c) under different contamination Figure 7. Multi-scale entropy of leakage current under different conditions.

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B. X. Du and Yong Liu. “Pattern Analysis of Discharge Characteristics for Hydrophobicity Evaluation of Polymer Insulator”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 18, No. 1, pp. 114-121, 2011. B. X. Du, Yong Liu, H. J. Liu and Y. J. Yang. “Recurrent Plot Analysis of Leakage Current for Monitoring Outdoor Insulator Performance”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 16, No. 1, pp. 139-146, 2009. Yong Liu and B. X. Du. “Recurrent Plot Analysis of Leakage Current on Flashover Performance of Rime-iced Composite Insulator”, IEEE Transaction on Dielectrics and Electrical Insulation, Vo. 17, No. 2, pp. 465-472, 2010.