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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 1, JANUARY 2004
Power Engineering Letters____________________________________________________ Modeling Leakage Current and Electric Field Behavior of Wet Contaminated Insulators M. A. M. Piah, Student Member, IEEE, and A. Darus, Member, IEEE
Abstract—The behavior of leakage current and electric field of insulators primarily depends on the environmental stresses. A mathematical analysis based on dimensional analysis technique is applied to develop the correlation of leakage current (LC) and electric field with the physical variables of the environmental stresses. The final model is established by relating the analytical results with the experimental results. Index Terms—Dimensional analysis, electric field, insulators, leakage current.
I. INTRODUCTION
In practice, the LC ( ) that flows on the insulator surface depends on the dominant parameters such as applied electric field ( ), electrolyte flow-rate ( ), electrolyte conductivity ( ), environmental pressure ( ), and humidity ( ). These parameters relationship can be expressed as follows: (1) where is an unknown function. The dimensional matrix of the parameters is written according to their corresponding fundamental dimensions with MLTQ combination, where , , , and are the mass, length, time, and charge, respectively
M
OST high-voltage insulators are being used in outdoor applications. Environmental pollution can cause the outdoor insulators to become progressively coated with dirt and chemicals in the long term. In the presence of wet atmospheric conditions, the contamination particles on the insulator surface will dissolve into the water and provide a continuous conducting path between the high-voltage electrode and ground. In service, the surface resistance of the insulator decreases considerably in the presence of wet contaminated conditions. Under high electric field stress, a resistive surface leakage current (LC) flows and results in nonuniform heating of the contamination layer that eventually causes dry-bands to be formed at the narrow sections where the LC density is highest. The continuous formation of dry-bands causes the fluctuation of LC level due to the nonuniform surface resistance [1]. The magnitude of LC varies with the contamination level and the volume of electrolyte that flows on the insulator surface [2]. In addition, the surrounding atmosphere of energizing insulator has influenced the insulator performance based on the characteristics of the LC [3]. The variation of LC and the formation of dry-bands lead to dynamic changing on electric field intensity across the insulator. This letter describes the analytical technique on the development of mathematical relationship of LC and electric field behavior with the environmental stresses using the dimensional analysis (DA) technique.
The rank ( ) of the dimensional matrix is 4, and the number . Therefore, according to Buckinghamof parameters theorem [4], the solution can be expressed in the form of independent dimensionless products ( ), which have dimension . By taking , , , and as repeated variables, the two dimensionless products can be written as follows: (2) (3) where , , , and are the power indexes of the repeated variables. The dimensional expression for both and are as follows:
(4)
(5)
II. MATHEMATICAL ANALYSIS The DA technique has been used successfully on a very wide range of applications in all experimentally-based areas of physical sciences and engineering [4]. Manuscript received March 31, 2003. The authors are with the Institute of High Voltage and High Current, Universiti Teknologi Malaysia, Johor 81310, Malaysia (e-mail:
[email protected]). Digital Object Identifier 10.1109/TPWRD.2003.820409
By equating the powers of fundamental units on both sides of (4) and (5), the power indexes can be calculated from the homogeneous linear algebraic equations. Therefore, the equations of LC and electric field as a function of environmental physical variables can be written as follows:
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(6) (7)
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 1, JANUARY 2004
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Fig. 1. Comparison between experiment and model of LC.
Fig. 3.
LC contour at different electrolyte flow-rate and conductivity.
Fig. 2. Comparison between experiment and model of electric field.
where and are the dimensional constants and must be determined from the experiment. Fig. 4. Electric field contour at different electrolyte flow-rate and conductivity.
III. RESULTS AND DISCUSSION The experiment is conducted at a stable atmospheric condition with constant environmental pressure and humidity. Equations (6) and (7) are simplified as follows: (8) (9) Equation (9) is modified by adding to adapt with the experimental results. The values of the factors A and B are determined from the experimental results and are dependent on the insulator materials and the environmental condition as well. The analytical results obtained from the model are compared with the experimental results and shown in Figs. 1 and 2. It is observed that the results calculated from the model are in good agreement with the experimental results. The model of LC and electric field are used to plot their behavior at any different levels of electrolyte conductivity and flow rate as shown in contour plots of Figs. 3 and 4. From the plots, it is observed that for the model to be accepted as a reference, the electrolyte flow-rate has to be between 0.1 to 0.7 ml/min while the range of the electrolyte conductivity is generally between 1.0 to 3.5 mS/cm. Beyond this range, the validity of the model could not be accepted. This is due to the existing
of anomalous circumstances such as discharge phenomena and electrolyte evaporation, which is not considered in the analysis when developing the model. IV. CONCLUSION An analytical method based on dimensional analysis technique has been described on modeling the leakage current and electric field behavior of the insulator under multiple stresses condition. The proposed method is very practical and useful on a very wide range of applications in all experimentally based areas. REFERENCES [1] T. Sorqvist and S. M. Gubanski, “Leakage current and flashover of field-aged polymeric insulators,” IEEE Trans. Dielect. Elect. Insul., vol. 6, pp. 744–753, Oct. 1999. [2] S. H. Kim and R. Hackham, “Effects of saline-water flow rate and air speed on leakage current in RTV coatings,” IEEE Trans. Power Delivery, vol. 10, pp. 1956–1964, Oct. 1995. [3] V. M. Moreno and R. S. Gorur, “AC and DC performance of polymeric housing materials for HV outdoor insulators,” IEEE Trans. Dielect. Elect. Insul., vol. 6, pp. 342–350, June 1999. [4] H. L. Langhaar, Dimensional Analysis and Theory of Models. New York: Wiley, 1951.
