COMPUTER METHODS FOR THE DETERMINATION OF THE CRITICAL PARAMETERS OF POLLUTED INSULATORS I. F. GONOS S. A. SUFLIS F. V. TOPALIS I.A. STATHOPULOS NATIONAL TECHNICAL UNIVERSITY OF ATHENS DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING Eletri Power Division Tel. +3-1-7723627, 7723582, Fax. +3-1-7723628, 772354 E-mail: igonos@softlab.ntua.gr, topalis@softlab.ntua.gr, stathop@power.ee.ntua.gr 42 Patission Str., GR 16 82 Athens GREECE ABSTRACT The aim of this paper is the investigation of the dieletri behaviour of polluted insulators using experimental data and omputer methods. A omputer programme was developed based on a mathematial model, introdued by the authors, whih was presented in previous papers. The model allows the determination of the ritial parameters (voltage, urrent and voltage gradient) for the flashover of the insulator, using only the geometrial harateristis of the insulator and the equivalent salt deposit density of the pollution layer over the surfae of the insulator. Different types of insulators were investigated (ap and pin, pin type and stab type) and the variation of the ritial parameters upon the density of the pollution layer was determined. The influene of the geometrial dimensions and the shape of insulator to the ritial parameters were also investigated. Analytial relations between the ritial parameters of the insulators and the salt deposit density were defined using the omputed results by means of urve fitting methods. A similar proedure allowed the definition of analytial relations between the ritial parameters and the dimensions, the shape and the type of the insulator. 1. INTRODUCTION A major problem of the insulation systems is the aumulation of airborne pollutants due to natural, industrial, or even mixed pollution, during the dry weather period and their subsequent wetting, mainly by high humidity. This problem was the motivation for the installation of a test station in order to perform laboratory tests on artifiially polluted insulators. The results of those experiments [1, 2] permitted the evaluation of the ar onstants of the insulator with a quite high auray, by means of a mathematial proedure, presented in [3]. It has been proved that, the omputed values of the ar onstants are independent of the insulator type and the kind of pollution. The definition of the ar onstants allowed the formulation of a generalised model for the dieletri behaviour of polluted insulators, independently of the type of the insulator and the kind of pollution [3-5]. A omputer programme was developed, based on that model, for the alulation of the ritial parameters of polluted insulators. Comparisons show a very good agreement between the omputed parameters and the measured ones, presented in [1, 2]. The omputations of this paper aim to the determination of analytial relations between the ritial parameters of the flashover and the geometrial harateristis of the insulator as well as the salt deposit density of the pollution layer on the surfae of the insulator.
The determination of analytial relations whih define the dependene of the ritial values of the flashover upon the known parameters of the insulator, provides a useful tool for the design of insulators and for the insulation o-ordination of overhead lines. 2. GENERALISED MODEL OF THE POLLUTED INSULATOR The most simple model for explanation and evaluation of the flashover proess [6, 7] of a polluted insulator onsists of a partial ar spanning over a dry zone and the resistane of the pollution layer in series (Fig. 1). Fig. 1: Equivalent iruit of polluted insulator. The applied voltage U should satisfy [6] the following equation: ( ) U = I r x + I r L x α (1) where x is the length of the ar, L is the repage distane of the insulator and I is the leakage urrent. r is the resistane per unit length of the pollution layer defined by the formula: r 1 = π D X d s (2) D d is the equivalent diameter of the polluted insulator and X s is the surfae ondutivity. The value of X s is given as a funtion of the equivalent salt deposit density C. X s is obtained in Ω -1 and r in Ω/m, for C expressed in mg/m 2 and D d in m [2, 3]. r a is the resistane per unit length of the ar [7]: r a = A I ( n+1 ) (3) where A and n, are the ar onstants. The values of A and n were determined through a mathematial proedure and experimental tests, arried out by the authors of this paper in [3]. Those values were
found to be A=131.5 and n=.374 for ap and pin, stab type and pin type insulators independently of the kind of pollution and the geometrial dimensions of the investigated insulators. di The ritial ondition for developing a partial ar into a omplete flashover is >. An equivalent dx expression is that the resistane per unit length of the ar must be less than or equal to the resistane per unit length of the pollution layer ( ra r ). At the ritial ondition, when the partial ar has already developed into a omplete flashover, the urrent I obtains its ritial value I whih is given [8] by the formula: I D A r = D r d 1 n + 1 (4) where D r is the diameter of the insulator disk. The ritial voltage U is given [2, 3] by the following formula: U A = + n + 1 ( L π n D K K) ( π A D X ) r s r s n n+ 1 (5) This equation provides the value of U as a funtion of the geometrial harateristis L and D r of the insulator, the onstants A and n and the surfae ondutivity X s (pollution). K s is the oeffiient of the shape of the insulator whih is a funtion of the geometrial parameters of the insulator. K is the modified oeffiient of the pollution layer resistane with onsideration of the urrent onentration at the ar foot point [8] whih is also funtion of the above known parameters. The ritial voltage gradient E is alulated dividing the ritial voltage by the reepage length of the insulator. It is given by the following formula: E U = L (6) 3. RESULTS The first part of this investigation was the appliation of the developed mathematial model to 17 different types of insulators and the alulation of the ritial voltage, ritial urrent and ritial voltage gradient of the insulators. Thereafter, urve fitting methods were applied in order to determine simplified analytial expressions of the ritial parameters versus the equivalent salt deposit density C. The first 9 insulators of this investigation are of ap and pin type, the next one is of pin type and the last 4 insulators are of stab type. The harateristis of these insulators are presented in Table 1. The insulators were onsidered to be uniformly ontaminated. The ritial voltage, ritial urrent and ritial voltage gradient were determined by means of the proedure whih is desribed above and using the values of the ar onstants A=131.5 and n=.374 [3].
Ins. 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 Dr 26.77 26.77 25.4 25.4 25.4 25.4 29.21 27.94 32.7 25.4 28. 25.4 2. 18. 2. 15. 15. H 15.87 15.87 16.51 14.6 14.6 14.6 15.87 15.56 17.78 14.6 17. 14.5 16.5 29. 32. 24.8 29.4 L 33.2 4.64 43.18 27.94 43.18 31.75 46.99 36.83 54.61 3.5 37. 3.5 4. 6.5 96. 37. 4. D d 13.3 15.4 15.27 13. 15. 14.12 16.22 15.48 18.16 13.95 14.72 13.12 9.87 13.46 14.97 11.16 11.2 K s.79.86.9.684.916.716.922.757.957.696.8.74 1.29 1.43 2.4 1.6 1.14 Table 1: Charateristis of the investigated insulators. The omputations show that the variation of ritial parameters U, I and E upon the equivalent salt deposit density C follow the analytial expression of the power funtion: f( C)= k C k 2 1. A typial omputation of U, I and E is presented in Figures 2, 3 and 4 respetively. 25 U [kv] 2 1.8 I [A] 1.6 1.4 15 1.2 1 1.8.6 5.4.2.5.1.15.2.25.3.35.4.45.5 C [mg/m2] Fig. 2: Critial voltage U of the insulator No. 1 vs. the equivalent salt deposit density C..5.1.15.2.25.3.35.4.45.5 C [mg/m2] Fig. 3: Critial urrent I of the insulator No. 1 vs. the equivalent salt deposit density C..8 E [kv/m].7.6.5.4.3.2.1.5.1.15.2.25.3.35.4.45.5 C [mg/m2] Fig. 4: Critial voltage gradient E of the insulator No. 1 vs. the equivalent salt deposit density C.
The appliation of urve fitting methods resulted in the following forms of the ritial parameter U, I and E : b (7) U = ac I E f = e C (8) a = L C b (9) where: C is the equivalent salt deposit density and L the repage distane of the insulator. The values of the oeffiients a, b, e and f are always positive. Further investigation shows that the values of the oeffiients a and e of U and I respetively are funtions of the geometrial harateristis L, D r and K s of the insulator (Figures 5, 6 and 7) and therefore of the type of the insulator. On the ontrary, the exponent b of U seems to be independent of the dimensions, hanging its value only with the type of the insulator. Its value lies between.32-33 for ap and pin insulators,.35-36 for stab type insulators and.31-.32 for pin type insulators. The exponent f of I seems to be onstant and independent of all the dimensions and even the type of the insulator. Its value was found equal to.719. 15 14 13 stab type 12 11 a 1 9 ap and pin 8 7 6 5 25 3 35 4 45 5 55 6 65 L [m] Fig. 5: Critial voltage oeffiient a (U b = ac ) vs. the repage distane L of the insulator.
24 22 2 18 16 a 14 12 1 8 6 4.6.8 1 1.2 1.4 1.6 1.8 2 2.2 Ks Fig. 6: Critial voltage oeffiient a (U b = ac ) vs. the oeffiient K s of the insulator shape. 3.2 3 2.8 2.6 e 2.4 2.2 2 1.8 1.6 1 15 2 25 3 35 Dr [m] f Fig. 7: Critial urrent oeffiient e ( I = e C ) vs. the diameter D r of the insulator disk.
Moreover, the use of urve fitting methods allow the determination of the following relationships between the oeffiient a of U and the reepage distane L: a = 117. L + 2. 437 (ap and pin) (1.a) a = 212. L + 1975. (stab type) (1.b) A similar relations between the exponent a of U and the oeffiient K s of insulator shape for any type of insulator was found to be: a= 11352. 2. 481 (11) K s The respetive relation between the exponent e of I and the diameter D r of insulator for any type of insulator is: e = 79. + 643. (12) D r The above equations lead to the onlusion that the ritial value of the voltage inreases linearly with the inrease of the reepage distane or/and the oeffiient of the insulator shape where as the ritial value of the urrent inreases linearly with the inrease of the diameter of the insulator. Only the ritial voltage behaviour of the pin type insulator deviates from the linearity. 4. CONCLUSIONS The developed simulation model and the omputations presented in this paper lead to the onlusion that the ritial parameters U, I and E of the investigated types of insulators follow the analytial form of the power funtion. This power funtion is defined using only the geometrial harateristis of the insulator. Experimental tests on some types of the investigated insulators show a very good agreement between the measured values and the omputed ones. The validity of these equations, independently of the insulator type, renders the determination of the ritial parameters using only the geometrial harateristis of the insulator and the distribution of the pollution layer. The distribution of ontaminants and onsequently, the evaluation of loal layer ondutivities an be obtained by means of simple measurements. Another onlusion of the paper is that some geometrial harateristis of the insulator (reepage distane and insulator shape) affet linearly the ritial voltage where as other harateristis (diameter) affet linearly the ritial urrent. On the other hand, the type of the insulator seems to affet exponentially only the ritial voltage keeping the value of the urrent onstant when the other dimensions are not hanged.
Referenes [1] G. Atsonios, G. Katsibokis, G. Panos, I. Stathopulos: Salt Fog Tests on Pin Type Insulators in the PPC Researh Center. Pro of Int. Symp. High Tehnology in the Power Industry, pp. 72-76, Lugano, 1987. [2] K. Ikonomou, G. Katsibokis, A. Kravaritis, I. Stathopulos: Cool Fog Tests on Artifiially Polluted Insulators. Pro. of 5th Int. Symp. on High Voltage Engineering, Vol. II, Paper No. 52.13, Braunshweig, 1987. [3] G. Theodorakis, F. Topalis, I. Stathopulos: Parameter Identifiation of the Polluted Insulator Model. Pro. of Int. Symp. on Simulation and Modelling, pp. 13-16, Lugano, 1989. [4] S. A. Suflis, I. A. Stathopulos, F. V. Topalis: On the Dieletri Behavior of Non-Uniformly Polluted Insulators. in Greek., CIGRE, Greek Committee, Athens, November 1995. [5] S. A. Suflis, I. F. Gonos, F. V. Topalis: Computation Methods in Simulation of the Dieletri Behavior of Non-Uniformly Polluted Insulators. Proeedings of the IMACS International Symposium on Soft Computing in Engineering Appliations (EURISCON 98), Athens, June 22-25, 1998. [6] F. Obenhaus: Fremdshihtuebershlag und Kriehweglaenge. Deuthe Elektrotehnik, H. 4, S. 135-137, 1958. [7] L. L. Alston, S. Zoledziowski: Growth of Disharges on Polluted Insulation. Pro. IEE, Vol. 11, No. 7, pp. 126-1266, 1963. [8] Zhang Renyu, Zhu Deheng, Guan Zhiheng: A Study on the Relation between the Flashover Voltage and the Leakage Current of Naturally or Artifiially Polluted Insulators. Pro. of 4th Int. Symp. on High Voltage Engineering, Vol. II, Paper No. 46.1, Athens, 1983.