Emission of electromagnetic radiation and ionisation phenomena in inhomogeneous fields in air under lightning impulse voltages

Transcription

1 17 July 2000 Ž. Physics Letters A Eission of electroagnetic radiation and ionisation phenoena in inhoogeneous fields in air under lightning ipulse voltages A.A. Kanellias ), I.F. Gonos, F.V. Topalis, P.D. Bouras, I.A. Stathopulos National Technical UniÕersity of Athens, Electrical Engineering Departent, 9 Iroon Polytechniou, Zografou, Athens, Greece Received 14 March 2000; received in revised for 2 June 2000; accepted 14 June 2000 Counicated by B. Frice Abstract This Letter deals with the ionisation phenoena in non-unifor ediu air gaps stressed by lightning ipulse voltages. The application of the Townsend theory for hoogeneous fields, still yields quite reasonable results for the tested inhoogeneous experiental electric field setup. Measureents taen on rod plane air gaps, with clearance of 20 to 50 c, show that the inception of the ionisation phenoena is related with an increase of the voltage across the gap that is characterised by a potential step of the voltage wavefor. This phenoenon is related with the eission of infrared radiation. q 2000 Published by Elsevier Science B.V. Keywords: Inhoogeneous field; Townsend theory; Ionisation; Potential step; Standard lightning ipulse; Electroagnetic radiation 1. Introduction Air has been the insulating abient ost coonly used in electrical installations. Aong its greatest assets, in addition to its abundance, is its self-restoring capability after breadown. The ore significant echaniss for ionisation in a gas discharge are: cosic rays, X-rays, and nuclear radiation. The processes considered include ion generation by electron ipact, photoionisation and interaction with etastable atos, theral ionisation and electron detachent. In a given two-electrode configuration in air, the space charges are gathered near the electrode with the opposite polarity and in this way they for a ) Corresponding author. Tel.: q ; fax: q cloud of space charges. If the space charges are stationary, the field is electrostatic and ore precisely a space-charge field. It can be assued that equilibriu exists between the applied Coulob forces up to a specific value of the applied voltage, so that the field is still electrostatic. For higher voltage values, which do not lead to a breadown, the equilibriu disappears and partial discharges are developed. The value of the applied voltage for the inception of partial discharges is called partial discharges inception voltage or inception voltage. The relevant value of the field strength, for the inception of partial discharges, is called partial discharges inception field strength or inception field strength w1 4 x. Consider a unifor field between two electrodes in the air. A cloud of free electrons is fored around the anode. The rise of the applied voltage causes r00r$ - see front atter q 2000 Published by Elsevier Science B.V. Ž. PII: S

2 94 ( ) A.A. Kanellias et al.rphysics Letters A oveent of the free electrons, partial discharges and finally leads to the breadown. In other words, the inception voltage in the hoogeneous field is the identical with the breadown voltage w2 4 x. Two typical gas breadown echaniss have been nown: the Townsend echanis and the streaer Ž or channel. echanis. For several decades there has been controversy as to which of these echaniss govern spar breadown. The echanis of the appearance of the ionisation phenoena in air is approxiated satisfactorily for field factors Žthe ratio of the hoogeneous field strength to the axiu inhoogeneous field strength for the sae gap length. greater than 0.2 with the ionisation theory according to Townsend, to Paschen law and to channel theory w2,3 x. If the cloud of free electrons is fored in inhoogeneous electrostatic field, with field factor less than 0.2 i.e. in a space-charge field, the inception field strength and the relevant inception voltage can not be calculated but only be easured w1 4 x. The experients presented in this Letter have been carried out under noral conditions Ž ps1.013 bar, us208c.. It is well nown fro experiental tests that these values depend on the shape of field electrodes, the atospheric conditions Žteperature, huidity, pressure, pollution, etc.., the duration of voltage application and the shape of the applied voltage. These paraeters also influence the value of the breadown voltage and the value of the respective electric field strength, which decrease with the increase of the space-charge density w2 4 x. More inforation concerning the echanis of the inception of the ionisation phenoena and generally the breadown in gases in strongly inhoogeneous fields can be attributed to the released energy of free electrons after their forced retardation at the anode. The respective echanis in solid insulating aterials has already been investigated in w5 7 x. The ai of this Letter is to investigate the ionisation phenoena in strongly inhoogeneous fields in ediu air gaps under noral conditions and in particular to exaine whether the application of the hoogeneous Townsend theory still yields reasonable results for a particular inhoogeneous electric field setup. The spectru of the electroagnetic radiation that is eitted at the beginning of the ionisation is also estiated. The test voltage is the standard lightning ipulse of the wavefor 1.2r50 s ŽFront tie 1.2"30% s, half tie 50"20% s.. The ipulses are positive. The equation of voltage is U Že yt r68.5 e ytr where t is introduced in s. Fro this equation one can obtain the pea value of the applied voltage; it is 0.96U 0. This type of voltage facilitates the detection of the ionisation phenoena, isolating the fro other factors as the long duration of the voltage stress or the change of the polarity. The influence of the pea value Ž fro 40 up to 90 V. of the applied voltage to the inception of the ionisation and to the spectru of the radiation is also investigated. 2. Test arrangeent and easuring procedure The investigated electric field is a vertical rod-toplane air gap with a gap length d varying between 20 c and 50 c which is placed in a huidity and teperature controlled chaber. The diaeter of the rod electrode is 16. The tip of the rod electrode is terinated with a cone that ends to a spherical surface. The radius R of the tip is 0.5. The diensions of the grounded plane electrode are 1.25 = The rod and the plane are ade of brass. The test arrangeent is shown in Fig. 1. It includes an 8-stage high ipulse voltage generator with a charging capacity of up to 200 V and with energy of up to 2 Ws per stage. The ipulse voltage is easured by eans of a 1.2 MV daped capacitive voltage divider. The control apparatus and the easuring instruents Žfast transient digitizer, oscilloscope, pea-volteter, volteters, aeters, etc.. are placed in a Faraday cage with a 50 db signal attenuation up to 1 GHz. A high frequency reject filter and an isolating transforer shield the power supply of the instruents fro noise and disturbances. The ains supply is regulated to a constant value of 230"0,1 VAC, 50 Hz by eans of a voltage stabiliser. The atospheric conditions are ept constant and repeatable throughout the experient, using the entioned chaber. The repetition tie of successive ipulses was at least 1 in Žiniu perissible tie interval between discharges of the used ipulse generator. up to 15 in. No influence of the repetition tie of successive ipulses on the results could be stated.

3 ( ) A.A. Kanellias et al.rphysics Letters A aplitude DU of the distortion is the easure of the electric charge of the discharge. 3. Experiental results and discussion Fig. 1. Siplified circuit for the easureent of the charge ipacts V.St: Voltage stabiliser F: Line voltage filter S.C: Shielded cabin Sb: Switchboard and control panel I.Tr: Isolating Transforer R.Tr: Regulating transforer S.D: Synchronising device T.D: Triggering device HV.Tr: High voltage transforer I.G: Ipulse voltage generator C 1, C 2: Capacitive voltage divider C : Measuring capacitance Z: Series atching resistance Osc: Ipulse voltage oscilloscope R.T.P: Rod-to-plane air gap The applied voltage U Ž its polarity is controlled by the orientation of the rectifiers inside the ipulse generator. is easured by eans of the capacitive voltage divider C 1, C 2, whereas the potential steps DU are easured by eans of the capacitive quadripole C s 0.1 F. Therefore, the partial dis- charges in the field ay be recorded by the potential increase on the easuring capacitor C Ž Fig. 1.. This procedure was also followed for the observation of ionisation phenoena in surface discharges wx 6. Each tested air gap is stressed by successive ipulses. The pea value of the ipulses is gradually increased step-by-step until the observation of the first distortion of the voltage across the capacitor C. The distortion appears as a potential step on the recorded wavefor. This distortion indicates a partial discharge i.e. the inception of ionisation. The Figs. 2a, 3a and 4a deonstrate the ipulse voltage applied on the tested electrode configuration with a gap length of 40c and different voltage pea values. Typical recordings of the voltage across the capacitive quadripole C are presented in Figs. 2b, 3b and 4b. The easureents show that only one potential step appears on all the recorded wavefors. The aplitude DU of this step increases with the increase of the pea value U of the applied ipulse voltage. It can be assued that there is a certain nuber of free electrons that are collected by the anode Ž rod electrode.; the nuber of free electrons depends on the value of the applied field. The axiu value of the applied field before the appearance of the potential step that has been calculated using the analysis of hyperbolic tip wx 8, is given by the following equation: 2Uˆ Ê s Ž 1. RlnŽ 4d R. where R is the radius of the rod tip and d is the gap length. Defining the ean field strength: Û Es Ž 2. d the field factor of the electrode arrangeent is w2 4 x: E RlnŽ 4d R. ns s Ž 3. ˆ 2 d E The field factor of the electrode arrangeent for Rs0.5 and ds c is given in Table 1. As it can be seen in this table the field is strongly inhoogeneous Žn- 0.2 wx. 2 in all the investigated gaps. Therefore the relations concerning the ipact ionisation phenoena fro Townsend theory do not apply w1 3 x. In this case the study of the inception of ionisation phenoena can be perfored exclusively by eans of easureents.

4 96 ( ) A.A. Kanellias et al.rphysics Letters A Fig. 2. a: Applied ipulse voltage U with a pea value of 84.4 V b: Voltage across the capacitive quadripole C voltage, Potential step DUs1.1 V. under the above ipulse Fig. 3. a: Applied ipulse voltage U with a pea value of 74.1 V b: Voltage across the capacitive quadripole C voltage, Potential step DUs0.8 V. under the above ipulse

5 ( ) A.A. Kanellias et al.rphysics Letters A Fig. 4. a: Applied ipulse voltage U with a pea value of 65.6 V b: Voltage across the capacitive quadripole C voltage, Potential step DUs0.6 V. under the above ipulse The pressure value in inhoogeneous fields is an iportant paraeter. Up to a critical pressure p, depending on the nature of the gas, the field is strongly inhoogeneous, i.e. the field strength E a for the inception of the ionisation is less than the breadown field strength E. For pressure values d higher than the critical one it is E a(e d. The critical pressure for the air is 12 bars wx 2. Due to the fact that a d This eans that the ionisation phenoena appear before the breadown Ž Figs. 2, 3 and 4.. The electric charge Q of the partial discharges can be calculated fro the following forula: QsC DU Ž 5. The variation of charge Q upon the pea value U and the electrode distance d is shown in Fig. 5. Fro this figure it is obvious that ore charge is transported Ž associated with ionisation. at a constant voltage level with decreasing distance. the easureents are perfored under noral conditions Ž ps1.013 bar, us208c. it is: E -E Ž 4. The approxiation of the relation QsfŽ U. us- ing curve fitting ethods results to the following forula: BUˆ Qsf Uˆ sae Ž 6. Ž. where A and B are constants. The values of the for different electrode distances d are given in Table 2. The constant A is given in electric charge units Ž nc. and the constant B in 1rV for U is expressed in V. The exponential increase of the charge is attributed to the proliferation of free electrons by eans of their ipact on the air olecules. It sees Table1 Field factor of the air gaps d Ž c. n

6 98 ( ) A.A. Kanellias et al.rphysics Letters A Fig. 5. Electric charge Q of partial discharges versus the pea value U of the applied voltage. Energy of the air gap versus the pea value U of the applied ipulse voltage. that the Townsend echanis applies to the investigated fields, as in any inhoogeneous field with field factor n According to Townsend the charge is given by this forula: H 0 l ads Qsn qe Ž 7. 0 where n0 is the nuber of the free electrons existed initially, q the electron charge, a the ionisation coefficient and l the ean length of the field lines in the area where the ionisation appears. Assuing that lsd, it is obtained: Q(n0 qe ad Ž 8. The electric charge Q of the partial discharges is greater under voltages with higher pea values U Ž Fig. 5. because of the faster rise Ž du rdt. of the applied voltage. As it is shown in Fig. 5 the phenoena of the ionisation inception becoe stronger with the increase of the insulation distance d. This is justified because the field factor n is inversely proportional to the distance d Ž Table 1.. The observed potential steps on the easuring capacitor ay be attributed to the excess charging brought about during the intervals of high conductance. Treating the change of charge on the reference capacitor as equivalent to the sae aount of charge traversing the specien directly fro its point electrode to the plane, one can get the net charge transferred by individual currents pulses, or even, the nuber of transferred electrons. Assuing that the change of energy of the easuring capacitor is copletely transferred into inetic energy of the injected electrons, it follows that the average electronic energy within a pulse ay be given by the potential Table2 Coefficients A and B of Qs fu Ž. versus the gap length d. Ž. Ž. Ž y1. d c A nc B V

7 ( ) A.A. Kanellias et al.rphysics Letters A wx increase on the easuring capacitor 9. The analytic expression for the evaluation of the net energy increase in the electric field of the easuring capacitor ay be written as: Ž. 1 DW s 2 QDU 9 where DW is the energy increase in the electric field of the capacitor for a given potential step DU. The 1 factor 2 results fro the average velocity of the electrons which are stopped after collision and reach axiu inetic energy prior to collision. The nuber of the electrons N required to for the potential step DU on the easuring capacitor is given by the ratio DQre where e is the charge of an electron. The average inetic energy of the above electrons Žin ev. for each of the potential steps, ay be given by the equation wx 9 : DW s 1 2 fdu Ž 10. N where f is a correction factor, depending on the value of the easuring capacitance and is associated with the tie constant of the easuring circuit. The value for the factor f is 1.16 for the investigated set-up wx 9. It can be concluded fro the expression DW s fu Ž. of Fig. 5 that the inception of the ionisation phenoena is related to the eission of infrared radiation Žas the spectru of infrared radiation is in the range of ev.. It ay be assued that the breadown channel appears Ž streaer or leader. when this radiation becoes ionising by a further voltage increase wx 2. The relation DWsfŽ U. is fitted by the follow- ing analytical expression: Ž. BUˆ DWsf Uˆ sa e 1 Ž where A and B are constants that are given in 1 1 Table 3, in dependence upon the electrode distance Table3 Coefficients A and B of DW s fž U. versus the gap length d. 1 1 Ž. Ž. Ž y d c A ev B V d. The constant A1 is given in J and B1 in V for DW expressed in J and U in V. It is concluded fro Eqs. Ž.Ž. 6, 8 that: ad(buˆ Ž 12. Substituting the value of U ˆ : DW lnž A 1 Û s / Ž 13. B 1 fro this equation in Eq. Ž 12., the following for is derived for the ionisation coefficient a versus the gap length d: B DW DW ads ln (ln Ž 14. B A A ž / ž / This equation sees to govern the echanis of the foration of free electrons, due to collisions during the self-aintained or even the non-aintained ionisation, depending on the value of DW. Therefore the breadown is related to the appearance of radiation. According to easureents, this radiation is in the range of infrared ev. Therefore the following relation is valid for the breadown: ln -ad-ln Ž 15. A A ž / ž / 1 1 where the constant A is expressed in ev Conclusions The theory of Townsend for hoogeneous fields has been applied to the inhoogeneous electric fields that were investigated in this Letter. The results of the application are reasonable for this particular inhoogeneous electric field setup. Fro the easureents perfored, it is concluded that the inception of the ionisation phenoena is related with a potential step. The initially existing free electrons for the inception of ipact ionisation can be attributed to field eission as well as to terrestrial radioactivity and to cosic radiation. The increase of free electrons is exponential. It is related with the eission of infrared radiation that can be attributed to the forced retardation of electrons at the anode. It can be as-

8 100 ( ) A.A. Kanellias et al.rphysics Letters A sued that the breadown channel appears Žstreaer or leader. when this radiation becoes ionising due to a further voltage increase. References wx 1 G. Oberdorfer, Lehrbuch der Eletrotechni, Band I, R. Oldenbourg Verlag, Muenchen, wx 2 G. Hilgarth, Hochspannungstechni, B.G. Teubner, Stuttgart, wx 3 E. Kuffel, W.S. Zaengl, High Voltage Engineering, Pergaon Press, Oxford, wx 4 W. Philippow, Taschenbuch Eletrotechni, Band 2, Starstrotechni, VEB Verlag Techni, Berlin, wx 5 P.D. Bouras, I.A. Stathopulos, E.A. Kayafas, Entwiclung der Teilentladungen an der Isolation Hartpapier in Transforatorenoel unter Stosspanungsbean-spruchung, in: e&i, jahrgang 106, H 2 Ž 1989., S wx 6 P.D. Bouras, C. Dervos, M. Eleftheriou, C. Kagarais, Phys. Scr. 42 Ž wx 7 C. Dervos, P.D. Bouras, E.A. Kayafas, I.A. Stathopulos, IEEE Trans. Elec. Insul. 25 Ž wx 8 T. Hiba, H.R. Zeller, J. Appl. Phys. 59 Ž wx 9 C. Dervos, P.D. Bouras, E.A. Kayafas, Phys. Status Solidi Ž. a 112 Ž