CALCULATION of CORONA INCEPTION VOLTAGES in N 2 +SF 6 MIXTURES via GENETIC ALGORITHM

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1 CALCULATION of COONA INCPTION VOLTAGS in N +SF 6 MIXTUS via GNTIC ALGOITHM. Onal G. Kourgoz e-ail: onal@elk.itu.edu.tr e-ail: guven@itu.edu..edu.tr Istanbul Technical University, Faculty of lectric and lectronics, Maslak,(34469), Istanbul, Turkey Key words: Corona Incetion Voltage, Genetic Algorith, real-value coding ABSTACT In this aer, AC corona incetion voltages of ixtures of N +SF 6 in non-unifor field were studied. The electrode ga sacing and the relative gas ressure were varied within the range of - and of - kpa resectively. The results were first easured exerientally and then estiated by eans of Genetic Algorith. The coarison of easured and couted values show that there is a good agreeent between two values. The corona incetion voltages of the ixtures can be found correctly by the Genetic Algorith. Therefore, Genetic Algorith can be considered an alternative tool to estiate the incetion voltages. I. INTODUCTION It is well known that SF 6 has excellent dielectric characteristics and is the ost coonly used insulating gas at resent. However, its disadvantages such as green house effect, high sensitivity to conductor surface roughness and high cost liit its alications. Using a ixture of SF 6 with an inexensive sile gas like CO, N and air can iniise the above robles. These gases are used as electrical insulation uroses for high voltage equient. Several investigations have been reorted in the literature on the breakdown and corona incetion behaviour of SF 6, N and N +SF 6 ixtures [-]. However, there is still insufficient inforation regarding the alternating breakdown and corona incetion voltages of such ixtures with sall aount of SF 6 in nonunifor field gas. Pure N insulation though would result in unrealistic designs for the required levels. But even by adding of soe SF 6, an insulating caability is achieved which is realistic in relation to ractical use. The resent aer describes a study of corona incetion voltages of various N +SF 6 ixtures in rod-lane ga under alternating voltages. These results were first easured exerientally and then estiated by eans of Genetic Algorith. arlier researchers have shown that for the calculation of corona incetion voltage based on the streaer criterion. It is well known that the sile streaer breakdown criterion [3-4 ] x c (α-η) dx = K () can be used to deterine the lowest ossible voltage which can cause breakdown or corona incetion in SF 6. α and η are ionization and attachent coefficients resectively. These coefficients are functions of the electric field and the gas ressure. Here x c is the critical avalanche length which is the distance between the highly stressed electrode and the oint in the electrode ga where α=η. quation () has also been used in several reorts [-6] to redict the discharge voltages of unifor and quasi-unifor field gas insulated with SF 6 -N ixtures. However, based on equation (), Nitta et al. [7] have described a rather sile ethod to deterine the discharge voltages of long gas insulated with coressed SF 6. In this ethod, a detailed knowledge of field distribution in the ga is not essential, and only the ratio between the average and the axiu field strengths is required. In the breakdown criterion, we are interested only in the value of α =α-η in a narrow interval around the liiting value of the araeter /, i.e. (/) li which is defined by α(/)=. In this range we ay consider the variation of α / with / to be linear [7]. The effective ionization coefficient α can therefore be exressed as, α /=β[(/)-(/) li ] () The value of β is 7 kv - and of (/) li is 877. V(c.kPa) - for SF 6. The streaer breakdown criterion of equation () then becoes

2 x β ( x) dx -β..x c. (/) li =K (3) In a unifor field ga, (x) is constant and x c is equal to the ga length a. The breakdown voltage V d in such cases as obtained fro equation (3) is given by V d =.d=k/β+(/) li..a (4) For unifor or nearly unifor field gas, the streaer foration directly grows to a breakdown. However, in non-unifor field gas it is not always so. For extreely non-unifor field gas, at low ressures, the streaers develo into a steady corona discharge. Because of the stabilization effect of this corona, the breakdown voltage is substantially higher than the corona incetion level. In such cases, the criterion for streaer foration corresonds to the corona incetion. Since in non-unifor field gas x c is generally a sall fraction of the total ga length ad, the field in the vicinity of the highly stressed electrode along its axis of syetry can be aroxiated by [8] (x)= ax ( + x ) where ax is the field at the ti of the electrode and () = ( + ) (6) Here and are the radii of curvature in the two directions orthogonal to each other. Fro (x c )/=(/) li, x c can be deterined as x c = ax (7) / ). ( li Following Nitta and Malik et al.[7-8], the discharge incetion voltage in non-unifor field gas can be calculated fro equations (3), () and (7) exressed as: V d =(/) li.u..a (+ C ) (8) u, utilization factor = av / ax C= 4. K β.( / ) li Fro unifor field breakdown data, a value of K=. has been suggested for SF 6 [8]. The value of the constant C is therefore.33 (kpa.c). for ure SF 6. quations (4) and (8) give the iniu discharge voltage in unifor and non-unifor field gas for electrodes with sooth (9) surfaces. quation () can be used to forulate a breakdown criterion for SF 6 -N ixtures if the effective ionization coefficient is known for the ixtures. However, since to our knowledge such easureents have not been reorted in the literature,. Therefore, the assutions ade in deriving equations (4) and (8) are valid for SF 6 -N ixtures and the discharge voltage in SF 6 -N ixtures can be exressed as K d = + β V ( / ) li.. a () in unifor field gas and Vd = li.u..a ( + C / ) () in non-unifor field gas, C = f ( z) = 3 4. K β.( / ) li () Since K(SF 6 )=. and <K(N )<8, it is lausible to assued K <=K(SF 6 ). In our calculations we have assued K <K(SF 6 ) in equation () and the resulting values of ( ) ' li and C are given in Table. In this study, constants of ( ) ' li and C are deterinated by using genetic algoriths and then corona incetion voltages are found by using this constant. These results are coared with exeriental results. II. GNTIC ALGOITHMS Genetic algoriths (GAs) are adative search rocedure, based on the Darwinian nature of evaluation. The genetically rocess in living organis life can be odelled by couter. Generic algoriths are increasingly coonly used in a variety of searches, otiizations of colex engineering robles, and achine learning alications [9]. For the otiization robles, the ajor advantages of GAs ay be outlined as follows []. They search fro a oulation and not fro a single araeter set. They are caable of searching for solutions fro disjointed feasible doains. They can oerate on irregular functions and those that are no differentiable. They don t require the coutations of gradients. The basic GAs ay be outlined as follows []. Genetic algoriths begin with a oulation of randoly generated candidate solutions. Solutions are reresented by chroosoes. This rando solution is called oulation. Mutation, crossover and reroduction rocess are alied to a oulation to roduce new ebers. It s evaluated

3 the fitness of each chroosoe in the initial oulation. Two arent chroosoes fro a oulation according to their fitness are chosen under selection to create new child (offsring) for the next generation. The arents are crossovered deending on crossover robability to for a new child (offsring). After the utation of the new offsring, deending on a utation robability, it is laced in a new oulation. The new generated oulation is used with the sae set of trials, selected and reroduced. This rocess is reeated until the end condition is satisfied. In this study, the genetic algorith with real-value coding is alied to a high voltage easureent syste to coute (/) li and C constants. In the work here, the fitness is defined as follows Fitness = (3) (V V ) Here, V and V reresent the easured and redicted values. As the difference values in the easured and redicted decreases, fitness value increases. For the highfitness values, difference between easured values and redicted values can be iniized. It is necessary to coute the growth of a single critical electron avalanche. The resent aer at first describes a study of corona incetion voltages of ixtures of N +SF 6 exerientally and then estiates the corona incetion voltages. These results ay be coared with revious investigations. The araeter GAs is chosen as follows; the size of the oulation is ket as, robability of crossover as.7, robability of utation as., tournaent robability as.7, scale for utation as.. III. XPIMNTAL ST-UP xerients were carried out using a rod-lane electrode syste with a rod ti radius of and lane disc diaeter of 7 (Fig. ). HV Test Transforer Hz, / kv kva C Voltage Divider C Test Chaber kv Volteter Fig. Test Circuit U ~ a N + SF 6 In all exerients, the electrode ga sacing and the relative gas ressure were varied within the range of - and of - kpa resectively. lectrodes were ounted in a ressure vessel of diaeter and 6 length. In rod lane arrangeent, the rod was connected to the high voltage suly while the lane was earthed. The incetion voltage was deterined by observation with a sensitive oscillograh. The voltage dro, across a Ω resistor inserted in the earth lead, caused by corona current, was easured with an oscillograh. The ean value of corona incetion voltages and standard deviation were calculated by eans of ten voltage alications. In the exerients, the SF 6 +N gas ixtures with 4,,, % SF 6 content were used. u, the utilization factor of the electrode syste was couted fro Stenbigler theory []. Table. u, field utilization factor for various electrode systes a(c) u,.4,.66,.8,.,. IV. APPLICATION and TST SULTS xeriental and theoretical investigations of the corona incetion voltages are reorted for rod-lane gas using AC voltages in the ressure range of - kpa. The different ratio of SF 6 -N ixture is used in this calculation. It is shown that corona incetion voltages of SF 6 +N gas ixtures can be affected electrode ga configuration, gas ressure, gas ixture ratio. Also the easured corona incetion voltages are in reasonable agreeent with the streaer corona incetion voltages given by equation (). The constants of ( ) ' li and C in q. are deterinated by using genetic algoriths. The corona incetion levels for non-unifor field gas filled SF 6 -N ixtures can be estiated with a reasonable degree of accuracy using the streaer breakdown criterion. Variation of corona incetion voltages versus to electrode ga sacing for different ressure range is shown in Fig.-. Table. Variations of (/) li and C with different SF 6 content SF 6 -N Mixture ( SF ) 6 z = % ' li V(c.kPa) - C (kpa.c) Where ( ) ' li and C vary with the gas ixture ratio and the values of these constant are calculated by Genetic Algorith for SF 6 -N ixtures. u= av / ax is the field utilization factor while,a and are gas ressure (kpa), electrode ga sacing and radius of rod electrod (c).

4 kpa 4 kpa 3 kpa kpa kpa Predicted Values... Fig. Variation of corona incetion voltages versus to electrode ga sacing for % SF kpa 4 kpa 3 kpa kpa kpa Predicted Values... Fig.4 Variation of corona incetion voltages versus to electrode ga sacing for % SF 6 +9% N kpa 3 kpa kpa 3 kpa kpa kpa 3 4 kpa 3 kpa kpa kpa Predicted Values... Fig.3 Variation of corona incetion voltages versus to electrode ga sacing for % SF 6 +8% N V. CONCLUSION In this aer the calculation of the corona incetion voltages SF 6 +N ixtures was reorted. The described ethod is based on GAs. xeriental easureents and estiated values of corona incetion voltages using rodlane ga indicate that there is a reasonably good degree of agreeent between the easured and the estiated values for different electrode ga sacing and ressures. Hence, GAs roosed to estiate the corona incetion voltages in the different exeriental cases has shown a very good erforance with an accuracy of. % aroxiately. The behaviour of The GAs gives an idea of how well the GAs is converging. Therefore this aroach can be acceted as a sile alternative tool to solve the difficulties in ost exeriental studies. Predictid Values... Fig. Variation of corona incetion voltages versus to electrode ga sacing for 4% SF % N FNCS. N.H. Malik and A.H. Qureshi, A eview of lectrical Breakdown in Mixtures of Sulhur- Hexafluoride and other Gases. I Trans. On lectrical Insulation. Vol I-4, No., Kuffel, A.Yializis., "Iulse Breakdown of Positive and Negative od-plane Gas in SF 6 -N Mixtures", I Trans. on Power Aaratus and Systes, PAS-97, No. 6. Nov/Dec. 978, H. aether, lectron Avalanches and Breakdown in Gases, Butterworth and Co J. M. Meek and J. D. Craggs, lectrical Breakdown of Gases, Clarendon Press, Oxford, 93.

5 [] M. rel, "Das N -SF 6 Gasgeisch als Isolierittel der Hochsannungstechnik", TZ-A, BD. 96, H., 97, [6]. G. Baugartner, Dielectric Characteristics of Mixtures of Sulhur-Hexafluoride and Nitrogen Proc. III Intern. Conf. On Gas Discharges, I Conf. Pub. 8, 974, [7] T.Nitta and Y. Shibuya, "lectrical Breakdown of long gas in Sulhur-Hexafluoride", I Trans. on PAS, PAS-9, No.3, 97,.6-7. [8] N. H. Malik, A. H. Qureshi, Calculation of Discharge Incetion Voltages in SF 6 + N, I Trans. on lectrical Insulation, Vol. I-4, No.,.7-76, 979. [9] K.Kayoada, Y. Yaada, T. Nishio, H. Kotera, Coact Modeling Aroach Genetic Algoriths for Accurate Theral Siulation, Heat Transfer- Asian esearch 3(),. []. Haut, S. Haut, Practical Genetic Algoriths, John Willey & Sons, 998. [] S. N. Yurt,. Özkol, M. O. Kaya, C. Hacıyev, Otiization of the PD coefficient in a Flight Siulator Control Via Genetic Algoriths, Aircraft ngineering and Aerosace Tecnology, Vol. 74,. 47-4,. [] H.Steinbigler, Anfangsfeldstarken und Ausnutzungsfaktoren rotationssyetrischer elektrodenanordnungen in Luft, Technische Hochshule, Dissertation, München, 969.