- Volume 60 Issue 2
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Evaluation of Discharge Current Employing Generalized Energy Method and Integral Ohm's Law Using Finite Element Method
유한요소법을 이용한 일반화된 에너지법과 옴의 적분법에 의한 방전 전류 계산
- Received : 2010.01.11
- Accepted : 2010.01.18
- Published : 2011.02.01
The terminal current in voltage driven systems is an essential role for characterizing the pattern of electric discharge such as corona, breakdown, etc. Until now, to evaluate this terminal current, Sato's equation has been widely used in areas of high voltage and plasma discharge. Basically Sato's equation was derived by using the energy balance equation and its final form described physical meaning explicitly. To give more general abilities in Sato's equation, we present a generalized approach by directly using the Poynting's theorem incorporating the finite element method. When the magnetic field effect or the time-dependent voltage source is considered, this generalized energy method can be easily applicable to those problems with any dielectric media such as gas, fluid, and solid. As an alternative approach, the integral Ohm's law resulting in small numerical errors has an ability to be applied to multi-port systems. To test the generalized energy method and integral Ohm's law, first, the results from two prosed methods were compared to those from Sato's approach and an analytic solution in parallel plane electrodes. After verification, the generalized method was applied to the tip-sphere electrodes for evaluating the terminal current with three carriers and the Fowler-Nordheim field emission condition. From these results, we concluded that the generalized energy method can be a consistent technique for evaluating the discharge current with various dielectric materials or large magnetic field.
Supported by : 한국과학재단
- 정재승, 문재덕, "관형 코로나 방전전극을 이용한 이온 풍속의 최대화", 전기학회논문지, vol. 59, no. 12, pp. 2256-2261, December 2010.
- 서길수, 조국희, 김영배, 이형호, "고전압.대전류 pulse 방전의 전압.전류특성에 관한 연구", 대한전기학회 하계학술대회 논문집, pp. 1981-1983, July 2000.
- N. Sato, "Discharge current induced by the motion of charged particles," J. Phys. D: Appl. Phys., No. 13, pp. L3-6, 1980.
- R. Morrow and N. Sato, "The discharge current induced by the motion of charged particles in time-dependent electric fields; Sato's equation extended," J. Phys. D: Appl. Phys., No. 32, pp. L20-L22, 1999.
- J. L. Coulomb, G. Meunier, and J. C. Sabonnadiere, "Energy methods for the evaluation of global quantities and integral parameters in a finite elements analysis of electromagnetic devices," IEEE Trans. Magn., Vol. MAG-21, No. 5, pp. 1817-1822, September 1985.
- P. Hammond, Energy Methods in Electromagnetism, Oxford University Press, New York, 1981.
- Markus Zahn, Cheung Fung Tsang, Shing-Chong Pao, "Transient electric field and space-charge behavior for unipolar ion conduction," Journal of Applied Physics, Vol. 45, No. 6, pp. 2432-2440, June 1974. https://doi.org/10.1063/1.1663610
- F. M. O'Sullivan, "A model for the initiation and propagation of electrical streamers in transformer oil and transformer oil based nanofluids," Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, USA, 2007.
- 이호영, 이세희, "유한요소법과 전계-열전자 방출 모델에 의한 절연유체 내 공간전하 전파해석", 전기학회논문지, vol. 58, no. 10, pp. 2011-2015, October 2009.