More Exact Analytical Solution of the Equations Describing the Electrical Circuit of the Resonant Inverter – Barrier Discharge System
Keywords:
arrier discharge, ozone, analytical solution, ozone generator, simulation, discharge gap, resonance
Abstract
The article presents the results of an analytical study of the characteristics of the resonant power supply circuit of an ozone generator based on a volumetric barrier discharge, including an inverter and a high-voltage high-frequency transformer. The ozone generator resonant power supply system, which is most often used in such installations, is considered. To build such power supply system, a lumped choke is installed in the transformer primary or secondary circuit. It is shown that there is an exact solution for such a circuit, the analytical expressions for the parameters in which contain the circuit component values and the moments at which the discharge in the ozone generator gas gap extinguishes and ignites. These moments are the roots of a nonlinear system of two equations, the parameters of which are the ratios of the transformer secondary winding voltage to the ozone generator discharge burning voltage, the ozone generator dielectric layer capacitance to the ozone generator gas gap capacitance, and the inverter operation frequency to the circuit natural frequency, which is determined by the ozone generator dielectric layer capacitance. The resonance conditions in this circuit are formulated. The obtained analytical results are compared with the data from numerical simulation of the circuit by a commercial computer program for electrical engineering calculations. The comparison results show excellent agreement throughout the entire range of the parameters studied, which are typical for the operation of real ozone generating systems.
References
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7. Wubs J.R. et al. Impact of the Electrode Proximity on the Streamer Breakdown and Development of Pulsed Dielectric Barrier Discharges. – Plasma Sources Science and Technology, 2022, vol.31, DOI: 10.1088/1361-6595/ac511f.
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11. Wang Y. et al. A Novel Repetitive High-Voltage Resonant Pulse Generator for Plasma-Assisted Milling. – IEEE Transactions on Plasma Science, 2021, vol. 49, pp. 2350–2358, DOI: 10.1109/TPS.2021.3092417.
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13. Paschen F. Ueber die zum Funkenübergang in Luft, Wasserstoff und Kohlensäure bei verschiedenen Drucken erforderliche Potentialdifferenz. – Annalen der Physik und Chemie Magazine, 1889, 273(5), pp. 69–96.
14. Tang X., Li Z., Zhang M. A Wide-Range Frequency Model for Dielectric Barrier Discharge Type Ozone Generators Powered by Series Resonant Inverters. – IEEE Access, 2019, vol. 7, pp. 124309–124314, DOI: 10.1109/ACCESS.2019.2901718.
15. Лысов Н.Ю. и др. Исследование влияния неоднородности разрядного промежутка на параметры генератора озона. – Электричество, 2024, № 11, с. 36–42.
16. Емельянов Ю.М., Филиппов Ю.В. Об эквивалентной электрической схеме озонаторов (ответ на статью В.В. Ястребова "К вопросу об эквивалентной электрической схеме озонаторов"). – Журнал физической химии, 1960, т. 34, № 12, с. 2841–2843.
#
1. Epelle E.I. et al. Ozone Application in Different Industries: A Review of Recent Developments. – Chemical Engineering Journal, 2023, vol. 454, DOI: 10.1016/j.cej.2022.140188.
2. Ozone Generator Market Report 2025 [Электрон. ресурс], URL: https://www.researchandmarkets.com/reports/5752104/ozone-generator-market-report#tag-pos-3 (дата обращения 30.03.2025).
3. Rao J., Liu K., Qiu J. A Novel All Solid-State Sub-Microsecond Pulse Generator for Dielectric Barrier Discharges. – IEEE Transactions on Plasma Science, 2013, vol. 41. No. 3, pp. 564–569, DOI: 10.1109/TPS.2012.2228885.
4. Dong L. et al. Collective Vibration of Discharge Current Filaments in a Self-Organized Pattern Within a Dielectric Barrier Discharge. – Physical Review E, 2012, vol. 85, No. 6, DOI: 10.1103/PhysRevE.85.066403.
5. Dong L. et al. Concentric-Roll Pattern in a Dielectric Barrier Dischar-ge in Air. – Physics of Plasmas, 2010, vol. 17, DOI: 10.1063/1.3466854.
6. Kettlitz M. et al. Comparison of Sinusoidal and Pulsed-Operated Dielectric Barrier Discharges in an O2/N2 Mixture at Atmospheric Pressure. – Plasma Sources Science and Technology, 2013, vol. 22, DOI: 10.1088/0963-0252/22/2/025003.
7. Wubs J.R. et al. Impact of the Electrode Proximity on the Streamer Breakdown and Development of Pulsed Dielectric Barrier Discharges. – Plasma Sources Science and Technology, 2022, vol.31, DOI: 10.1088/1361-6595/ac511f.
8. Heuser C. Zur Ozonerzeugung in Elektrischen Gasentladungen: Ph.D. Thesis. Aachen: RWTH Aachen University, 1985, 111 p.
9. Lunin V.V. et al. Teoriya i praktika polucheniya i primeneniya ozona (Theory and Practice of Ozone Production and Application). M.: Izd-vo Moskovskogo universiteta, 2016, 416 p.
10. Samoylovich V.G., Gibalov V.I., Kozlov K.V. Fizicheskaya himiya bar'ernogo razryada (Physical Chemistry of Barrier Discharge). М.: Izd-vo МGU, 1989, 176 p.
11. Wang Y. et al. A Novel Repetitive High-Voltage Resonant Pulse Generator for Plasma-Assisted Milling. – IEEE Transactions on Plasma Science, 2021, vol. 49, pp. 2350–2358, DOI: 10.1109/TPS.2021.3092417.
12. Aqui-Tapia J.A. et al. Analysis and Assessment of Use of Voltage and Current Inverters Applied to the Ozone Generation in High Frequency. – IEEE Transactions on Plasma Science, 2021, vol. 49, pp. 1396–1405, DOI: 10.1109/TPS.2021.3065917.
13. Paschen F. Über die zum Funkenübergang in Luft, Wasserstoff und Kohlensäure bei verschiedenen Drucken erforderliche Potentialdifferenz. – Annalen der Physik und Chemie Magazine, 1889, 273(5), pp. 69–96.
14. Tang X., Li Z., Zhang M. A Wide-Range Frequency Model for Dielectric Barrier Discharge Type Ozone Generators Powered by Series Resonant Inverters. – IEEE Access, 2019, vol. 7, pp. 124309–124314, DOI: 10.1109/ACCESS.2019.2901718.
15. Lysov N.Yu. et al. Elektrichestvo – in Russ. (Electricity), 2024, No. 11, pp 36–42.
16. Emel’yanov Yu.M., Filippov Yu.V. Zhurnal fizicheskoy hi-mii – in Russ. (Journal of Physical Chemistry), 1960, vol. 34, No. 12, pp. 2841–2843
2. Ozone Generator Market Report 2025 [Электрон. ресурс], URL: https://www.researchandmarkets.com/reports/5752104/ozone-generator-market-report#tag-pos-3 (дата обращения 30.03.2025).
3. Rao J., Liu K., Qiu J. A Novel All Solid-State Sub-Microsecond Pulse Generator for Dielectric Barrier Discharges. – IEEE Transactions on Plasma Science, 2013, vol. 41. No. 3, pp. 564–569, DOI: 10.1109/TPS.2012.2228885.
4. Dong L. et al. Collective Vibration of Discharge Current Filaments in a Self-Organized Pattern Within a Dielectric Barrier Discharge. – Physical Review E, 2012, vol. 85, No. 6, DOI: 10.1103/PhysRevE.85.066403.
5. Dong L. et al. Concentric-Roll Pattern in a Dielectric Barrier Discharge in Air. – Physics of Plasmas, 2010, vol. 17, DOI: 10.1063/1.3466854.
6 Kettlitz M. et al. Comparison of Sinusoidal and Pulsed-Operated Dielectric Barrier Discharges in an O2/N2 Mixture at Atmospheric Pressure. – Plasma Sources Science and Technology, 2013, vol. 22, DOI: 10.1088/0963-0252/22/2/025003.
7. Wubs J.R. et al. Impact of the Electrode Proximity on the Streamer Breakdown and Development of Pulsed Dielectric Barrier Discharges. – Plasma Sources Science and Technology, 2022, vol.31, DOI: 10.1088/1361-6595/ac511f.
8. Heuser C. Zur Ozonerzeugung in Elektrischen Gasentladungen: Ph.D. Thesis. Aachen: RWTH Aachen University, 1985, 111 p.
9. Лунин В.В. и др. Теория и практика получения и применения озона. М.: Изд-во Московского университета, 2016. 416 с.
10. Самойлович В.Г., Гибалов В.И., Козлов К.В. Физическая химия барьерного разряда. М.: Изд-во МГУ, 1989, 176 с.
11. Wang Y. et al. A Novel Repetitive High-Voltage Resonant Pulse Generator for Plasma-Assisted Milling. – IEEE Transactions on Plasma Science, 2021, vol. 49, pp. 2350–2358, DOI: 10.1109/TPS.2021.3092417.
12. Aqui-Tapia J.A. et al. Analysis and Assessment of Use of Voltage and Current Inverters Applied to the Ozone Generation in High Frequency. – IEEE Transactions on Plasma Science, 2021, vol. 49, pp. 1396–1405, DOI: 10.1109/TPS.2021.3065917.
13. Paschen F. Ueber die zum Funkenübergang in Luft, Wasserstoff und Kohlensäure bei verschiedenen Drucken erforderliche Potentialdifferenz. – Annalen der Physik und Chemie Magazine, 1889, 273(5), pp. 69–96.
14. Tang X., Li Z., Zhang M. A Wide-Range Frequency Model for Dielectric Barrier Discharge Type Ozone Generators Powered by Series Resonant Inverters. – IEEE Access, 2019, vol. 7, pp. 124309–124314, DOI: 10.1109/ACCESS.2019.2901718.
15. Лысов Н.Ю. и др. Исследование влияния неоднородности разрядного промежутка на параметры генератора озона. – Электричество, 2024, № 11, с. 36–42.
16. Емельянов Ю.М., Филиппов Ю.В. Об эквивалентной электрической схеме озонаторов (ответ на статью В.В. Ястребова "К вопросу об эквивалентной электрической схеме озонаторов"). – Журнал физической химии, 1960, т. 34, № 12, с. 2841–2843.
#
1. Epelle E.I. et al. Ozone Application in Different Industries: A Review of Recent Developments. – Chemical Engineering Journal, 2023, vol. 454, DOI: 10.1016/j.cej.2022.140188.
2. Ozone Generator Market Report 2025 [Электрон. ресурс], URL: https://www.researchandmarkets.com/reports/5752104/ozone-generator-market-report#tag-pos-3 (дата обращения 30.03.2025).
3. Rao J., Liu K., Qiu J. A Novel All Solid-State Sub-Microsecond Pulse Generator for Dielectric Barrier Discharges. – IEEE Transactions on Plasma Science, 2013, vol. 41. No. 3, pp. 564–569, DOI: 10.1109/TPS.2012.2228885.
4. Dong L. et al. Collective Vibration of Discharge Current Filaments in a Self-Organized Pattern Within a Dielectric Barrier Discharge. – Physical Review E, 2012, vol. 85, No. 6, DOI: 10.1103/PhysRevE.85.066403.
5. Dong L. et al. Concentric-Roll Pattern in a Dielectric Barrier Dischar-ge in Air. – Physics of Plasmas, 2010, vol. 17, DOI: 10.1063/1.3466854.
6. Kettlitz M. et al. Comparison of Sinusoidal and Pulsed-Operated Dielectric Barrier Discharges in an O2/N2 Mixture at Atmospheric Pressure. – Plasma Sources Science and Technology, 2013, vol. 22, DOI: 10.1088/0963-0252/22/2/025003.
7. Wubs J.R. et al. Impact of the Electrode Proximity on the Streamer Breakdown and Development of Pulsed Dielectric Barrier Discharges. – Plasma Sources Science and Technology, 2022, vol.31, DOI: 10.1088/1361-6595/ac511f.
8. Heuser C. Zur Ozonerzeugung in Elektrischen Gasentladungen: Ph.D. Thesis. Aachen: RWTH Aachen University, 1985, 111 p.
9. Lunin V.V. et al. Teoriya i praktika polucheniya i primeneniya ozona (Theory and Practice of Ozone Production and Application). M.: Izd-vo Moskovskogo universiteta, 2016, 416 p.
10. Samoylovich V.G., Gibalov V.I., Kozlov K.V. Fizicheskaya himiya bar'ernogo razryada (Physical Chemistry of Barrier Discharge). М.: Izd-vo МGU, 1989, 176 p.
11. Wang Y. et al. A Novel Repetitive High-Voltage Resonant Pulse Generator for Plasma-Assisted Milling. – IEEE Transactions on Plasma Science, 2021, vol. 49, pp. 2350–2358, DOI: 10.1109/TPS.2021.3092417.
12. Aqui-Tapia J.A. et al. Analysis and Assessment of Use of Voltage and Current Inverters Applied to the Ozone Generation in High Frequency. – IEEE Transactions on Plasma Science, 2021, vol. 49, pp. 1396–1405, DOI: 10.1109/TPS.2021.3065917.
13. Paschen F. Über die zum Funkenübergang in Luft, Wasserstoff und Kohlensäure bei verschiedenen Drucken erforderliche Potentialdifferenz. – Annalen der Physik und Chemie Magazine, 1889, 273(5), pp. 69–96.
14. Tang X., Li Z., Zhang M. A Wide-Range Frequency Model for Dielectric Barrier Discharge Type Ozone Generators Powered by Series Resonant Inverters. – IEEE Access, 2019, vol. 7, pp. 124309–124314, DOI: 10.1109/ACCESS.2019.2901718.
15. Lysov N.Yu. et al. Elektrichestvo – in Russ. (Electricity), 2024, No. 11, pp 36–42.
16. Emel’yanov Yu.M., Filippov Yu.V. Zhurnal fizicheskoy hi-mii – in Russ. (Journal of Physical Chemistry), 1960, vol. 34, No. 12, pp. 2841–2843
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2025-04-24
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