Recovery rate analysis of plasma switch and comparison with experimental results Zhang, J.; van Heesch, E.J.M.

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1 Recovery rate analysis of plasma switch and comparison with experimental results Zhang, J.; van Heesch, E.J.M. Published in: Proceedings of the 20th Symposium on Physics of Switching Arc, 2-6 September 2013, Nové Msto na Morav, Czech Republic Published: 01/01/2013 Document Version Accepted manuscript including changes made at the peer-review stage Please check the document version of this publication: A submitted manuscript is the author's version of the article upon submission and before peer-review. here can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. he final author version and the galley proof are versions of the publication after peer review. he final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA: Zhang, J., & Heesch, van, E. J. M. (2013. Recovery rate analysis of plasma switch and comparison with experimental results. In Proceedings of the 20th Symposium on Physics of Switching Arc, 2-6 September 2013, Nové Msto na Morav, Czech Republic General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal? ake down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 25. Dec. 2018

2 RECOVERY RAE ANALYSIS OF PLASMA SWICH AND COMPARISON WIH EXPERIMENAL RESULS J. Zhang 1, E.J.M. van Heesch 1 1 Electrical Engineering Departement, echnology University Eindhoven, Den Dolech 2, 5612 AZ, Eindhoven, the Netherlands, jin.zhang@tue.nl; E.J.M.v.Heesch@tue.nl Abstract: As a most important component in power system networks, electric circuit breakers and switches protect the electric components from being damaged by fault currents. Breakdown strength and recovery rate are the two essential characteristics of an electric switch. By applying a supercritical fluid (SCF - a potential insulating medium for high voltage switches, the recovery rate of switches can be significantly improved, owing to the combined advantages of gas and liquid. In this work a simple model for recovery rate investigation of an electric switch is proposed, aiming to roughly indicating the recovery rate of a SCF switch. he accuracy of the model is discussed through comparison with the experimental recovery rate of an air-flushed plasma switch. Both advantage and disadvantage of this model are discussed. Keywords: supercritical switch, recovery rate Introduction As one of the most important elements in power system networks, electrical circuit breakers and switches exist in all voltage levels, for protection of electrical components from damage by overload or short circuit. In high voltage networks, Sulfur-Hexafluoride (SF 6 as the insulating medium dominates due to its excellent interrupting capability and fast dielectric strength recovery after current interruption [1]. However, SF 6 is the most potent greenhouse gas and the degeneration products from SF 6 are toxic [2]. he negative effects of SF 6 on environment encourage the search for a new interrupting medium in high voltage applications. Supercritical fluid (SCF switches attract our keen attention, owing to its combined advantages of gas and liquid: high breakdown strength (large heat capacity and fast dielectric recovery (large heat conductivity and small viscosity. In this work, one simple thermodynamic model is proposed to evaluate the recovery rate of a plasma switch. Recovery rate analysis of an air-flushed plasma switch is proceeded regarding to both theoretical model and experimental results. he object of this work is to have a simple model which can roughly indicate the recovery rate of a SCF switch. hermodynamic model In order to analyze the recovery performance of a plasma switch, physical model of a simplified plasma switch with plane electrodes is shown in figure 1. he switch is composed of one anode, one hollow-cylindrical trigger electrode mounted inside the anode, and one plane cathode. he anode is 40.0 mm cup with a hole of 21.0 mm in diameter, one cylindrical trigger electrode with inner diameter 9.0 mm and outer diameter 18.0 mm is mounted in the hole of anode, formed a gap distance of 1.5 mm between the trigger electrode and anode. he axial thickness of the plane cathode is 50 mm, and distance between anode and cathode is in range of 6-10 mm. he air is blown into the spark gap from both the trigger gap and the centre of the Fig. 1. Physical model of plasma switch and example spark channel generated between the electrodes. l

3 trigger electrode, then flows out via six symmetrical exists. In this work the recovery rate analysis of the gas insulated plasma switch is based on this switch geometry. he gas temperature decay model of the spark channel inside a plasma switch is generated by an adapted version of the model with spherical electrodes in [3]. It is axisymmetric in radial direction. he parameter distribution in axial direction is assumed to be homogenous. he initial parameters are: background air pressure at steady state P air = 2.6 bar; background air temperature air = 296 K; spark gap width l gap = 7.35 mm; air flushing volume velocity V air = 10 m 3 /h (at SP 24 m 3 /h. We apply a peak voltage of 25 kv to a switch with plane electrodes. Once the switch breaks down, energy of value ΔE 0.7 J is instantaneously deposited into a cylindrical spark channel of initial diameter 50 µm and length lgap. he gas density inside the channel is kept constant initially, being equivalent to the background density ρ 0, based on the assumption in [4]. From the Caloric equation of state (1, it is clear that due to the energy deposition, the gas temperature inside the channel increases to a value arc0. Here C V is the heat capacity of the hot gas, which is read from the profile versus gas temperature in [5]. It was reported that energy deposition does not result in higher gas temperature than a limited value (e.g. in air limit =43000 K [6]. he spark diameter increases to such a value that the activated gas volume can contain the deposited energy at the desired maximum temperature of 43k Kelvin [7]. he gas pressure can be calculated as the derivative of the Residual Helmholtz energy [8], seen in equation (2. Equation (2 clearly shows that with suddenly rising temperature and constant density, the gas pressure jumps to a value P arc0 much larger than the background pressure P 0. Due to the significant pressure difference between in- and outside of the spark channel, it tends to expand. In this process conservation of mass is applicable. he volume expansion process can be seen as adiabatic expansion, during which no heat transfer to environmental gas is considered. Once the pressure within and outside the spark channel balances, adiabatic expansion stops, and heat transfer contributes to further temperature decay. he time constant of adiabatic expansion is much smaller than that of the heat transfer, so it is reasonable to assume that these two processes can be considered separately: at first adiabatic expansion is responsible for the temperature decay of spark channel; once volume expansion is completed, heat transfer is seen as the only further contribution to energy dissipation by the environment. During the adiabatic expansion, the variation of pressure and temperature with respect to gas volume are shown in equation (3, (4, where 0 and 1 stands for before and after the adiabatic expansion, respectively. During the subsequent process, the internal energy dissipation due to heat transfer is described by equation (5. he term is the sum of the products of heat transfer coefficient and corresponding surface area. he detailed expression is ƩhA=h conv A conv +h cond A cond, where A cond is contact surface between spark channel and electrodes; h cond =k aver /x represents the heat conduction coefficient, in which kaver is the averaged thermal conductivity coefficient of the hot gas during the temperature decay process and x=5 cm is the axial thickness of the electrodes; the heat convection from spark channel to the surrounding gas is characterized as flow across a single circular cylinder, where the contact surface area is A conv =2π r arc l gap and heat transfer coefficient hconv is shown in equation (6. In equation (6, k f is the coefficient of thermal conduction at film temperature f (arithmetic mean of the spark channel wall temperature and the far-end gas temperature; L is the characteristic dimension for heat transfer calculation, in present model equaling the diameter of the cylinder. For the case of flow across a circular cylinder, the Hilbert correlation gives the functional forms between the three dimensionless numbers [9], Nu (Nusselt number, Pr=ν/D (Prandtl number, and Re=uL/ν (Reynolds number as described in equation (7, where u is the velocity of air flowing through the gap; ν is the kinetic viscosity of the gas; D is the thermal diffusivity of the gas. All the parameters are evaluated at the film temperature f. he constants for equation (7 can be found in table 1[10]. he temperature decay as function of time is derived in equation (8. It is reported that when the temperature inside the spark channel drops to a value of 550 K, the breakdown voltage of the gas recovers to 80% of the static breakdown strength [11], so in our model the recovery time of the switch is defined as the time when the temperature of the gas inside the spark channel drops to value of 550 K. Figure 2 gives modeling results of radius, pressure as well as temperature of the spark channel in relationship with time.

4 E C v V ( arc0 arc0 arc0 g r p R 1 P P q h arc1 arc0 conv arc arc ( Cp / CV ( Cp / CV 1 Varc0 arc1 Varc0, Varc1l arc0 Varc1 d ha( arc g C parcvarc dt m 1/3 Nuk / L, Nu C Re Pr [Pr 0.7 ] f g t exp( 0 g C pv /( ha (3, (6, (1 (2 (4 (5 (7 (8 ab. 1. Constants for the Hilpert correlation, Equation (10, for circular cylinders in cross flow, Pr>=0.7. Re C m Comparison with experimental results In order to investigate the recovery rate of a switch experimentally, a 2-8 bar air-blown plasma switch with the same geometry as in the described model is connected to a pulse voltage source with 30 kv peak value and up to 1 khz various repetition rate. he ratio of the number of shots undergoing normal firing (fully charged waveform to the number of total shots (in this work 200 shot, δ=n nomral /N total, is recorded as a function of repetition rate under various air flushing velocities. he reciprocal of the repetition rate at which δ 80% is taken as the recovery time of the switch. he experimental recovery time of the switch is compared with the modeled value, with recovering criterion inside the spark channel defined in previous section, to test the feasibility of the model. Plots of recovery time drawn from experiment as well as from modeling as function of gas flow rates are given in figure 2. Fig. 2. Modeling results for air flushed gap, of temperature (a, density (b, and pressure (c of gas in spark channel in time domain. Discussion and conclusion It can be seen that the recovery time of the switch decreases with higher gas flow rate both in experiment and modeling case. For all flushing rates the predicted recovery times are of the same order of magnitude as the experimental data, though almost twice of the value in experiment. his simple thermodynamic model is assumed to be suitable for the prediction of recovery rate in SCF. he reason is as follows: I. although SCF has high density similar as liquids, its compressibility is high as gases. his makes adiabatic expansion law applicable for SCF; II. Heat transfer model afterwards is applicable for both gases and liquids. he recovery time of a SC switch after breakdown accompanied by 0.1 J energy deposition is calculated by this model. he predicted

5 Recovery time (ms XX th Symposium on Physics of Switching Arc recovery time of the switch insulated with 296 K, 150 bar SC nitrogen, under fixed gap width 0.4 mm is as small as 270 µs, with nitrogen flow rate 1000 Liter/h (at SP 138 m 3 /h. here are several factors that might cause the discrepancy. First of all, the heat transfer coefficient is taken from the value corresponding to the average temperature of the hot gas over the temperature decay trajectory, and is kept constant in the process. Secondly, during the heat transfer process, heat convection is taken as the main contribution, while in practice, heat conduction inside the spark channel also plays an important role, especially for high pressure gas above critical pressure, whose heat conductivity has a high peak value ( mw m -1 K -1 [12]. his will cause a smaller recovery time of the switch than predicted by the model in this Experiment Model Flow rate (m 3 /h Fig. 3. Comparison of experimental and model results of recovery time of the airplasma switch. Gap width 7.35 mm, flow rate 0-40 m3/h (at SP 0-96 m3/h. Fig. 2. Comparison of experimental and model results of recovery time of the airplasma switch. Gap width 7.35 mm, flow rate 0-40 m3/h (at SP 0-96 m3/h. work, especially with a high pressure gas, e.g. SCF insulated switch. Moreover, radiation, which is not accounted for as well, also reduces the recovery time. hirdly, the breakdown energy is taken as a constant input parameter while from the experimental measurements it is observed that the breakdown voltage varies slightly with experimental settings such as repetition rate and gap width. Last but not least, in this thermodynamic model, the breakdown energy is assumed to convert in to gas heat content instantaneously after breakdown, while it has been reported that in practice after the gas breakdown, the energy stored in vibrational levels takes time to transfer to rotational and eventually to kinetic levels (gas heating level [13]. Under situations like high gas pressure and gas species such as nitrogen this relaxation time has an un-ignorable magnitude and should be considered in a more detailed model. References [1] A. Iturregi, E. orres, I. Zamora, O. Abarrategui, International Conference on Renewable Energies and Power Quality, Valencia (Spain, [2] Zenz, C., O.B. Dickerson, E.P. Horvath, Occupational Medicine. 3rd ed. St. Louis, MO., p. 498, [3] suruta, K.; Ebara, H, Proceedings of the 3rd International Conference on Properties and Applications of Dielectric Materials, vol., no., pp.377,380 vol.1, 8-12 Jul [4] M. N. Plooster, Shock waves from line sources, [5] Kian Eisazadeh-Far, Hameed Metghalchi and James C. Keck, J. Energy Resour. echnol. 133(2, , [6] Yusupaliev, U., Bulletin- Lebedev Physics Institute C/C Of Kratkie Soobshcheniia Po Fizike, Vol 34; Number 9, pp , [7] S. Refael, E. Sher, Combustion and Flame, Volume 59, Issue 1, Pages 17-30, [8] Eric W. Lemmon, Richard Jacobsen, Steven G. Penoncello, and Daniel G. Friend, J. Phys. Chem. Ref. Data 29, 331, [9] Jakob, M., and Hawkins, Elements of Heat ransfer, 3rd. ed., pp 270, [10] David P, Introduction to hermal Systems Engineering hermodynamics Fluid Mechanics and Heat ransfer Solutions Manual, 1st Edition. [11] Gautam, Mangal Sen, hesis (Ph.D., he University Of British Columbia (Canada, [12] NIS Chemistry WebBook. NIS Standard Reference Database Number 69. [13] H.. Nagamatsu And R. E. Sheer, Jr., AIAA Journal, Vol. 3, No. 8, pp , 1965.