by Ute Ebert and Jannis Teunissen (CWI)
Electric power grids will play a key role to transport energy in a sustainable way. However the switches in present high voltage grids operate on SF6 gas, which is the worst greenhouse gas known. To investigate alternative gases, CWI (the national research institute for mathematics and computer science in the Netherlands) and Eindhoven University of Technology (TU/e) now start their third project with Hitachi Energy as the main industrial partner. While TU/e performs experiments, CWI simulates the pre-spark phenomena in these gases. These discharges are surprisingly different from discharges in air and pose new numerical challenges.
Energy transmission by electric power grids plays a dominant role in the transition to a sustainable energy supply. It is foreseen that by 2050, electricity production will double and two-thirds of this electricity will be delivered by renewable energy sources, leading to massive changes and investments in electric grids. To interrupt an electric current in these grids (in particular, in high-voltage transmission lines across countries) one cannot simply separate two electrodes like in a light switch, because an energetic and destructive electric discharge would then form in the gas between the electrodes. Specialised switchgear is therefore required, in which these discharges extinguish in a controlled manner.
Today’s switchgear uses gaseous SF6, which has favourable properties for current interruption. However, SF6 is also the most potent greenhouse gas. Its global warming potential is 23,500 times that of CO2 on a 100 years’ horizon, but its residence time in the atmosphere is estimated as 800 to 3,200 years by different authors, which further increases its climate impact [L1]. In 2006, the European Union therefore has banned the use of SF6 in all application fields – except in high-voltage switchgear, because no alternative was available. However, legislation in the US and in the EU [L2] now requires industry to replace SF6 with alternative gases with significantly lower global warming potential as soon as technically possible.
Alternatives for SF6 gas have been identified in recent years, but now the behaviour of electric discharges in these gases needs to be better understood, as one cannot simply replace one gas by the other in existing equipment. Researchers at CWI and at TU/e now start their third project on studying discharges in relevant gases, funded substantially by the Dutch national research funding agency, NWO, and with matching by Hitachi Energy (previously part of ABB Corporate Research, Baden Switzerland). While the Eindhoven team performs experiments, the CWI team develops computational methods and analytical approximations for electric gas discharges in general, and for air and for the new gases specifically.
Simulating the growth of electric discharges is computationally challenging. Electron processes take place on micrometre and picosecond scales, while a full discharge develops on scales three to six orders of magnitude larger. We therefore have developed computational techniques such as adaptive mesh refinement and parallelisation for dynamic 3D simulations. To describe the evolution of the species in a discharge, so-called drift-diffusion-reaction models are commonly used. They are coupled to the Poisson equation for the electric field. The reaction and drift terms strongly depend on the changing electric field, which leads to highly non-linear growth and the formation of elongated “streamer” channels in air (see Figure 1).
We have recently made important progress towards the validation of discharge models by comparing the propagation  and branching  of simulated streamer discharges in air with dedicated experiments by the partners in Eindhoven. However, the new gases pose new physical and computational challenges.
First, positive discharges in air develop rather smoothly (see Figure 1) due to a process called photoionisation, but photoionisation will likely be much weaker or negligible in the new gases. This will lead to highly stochastic discharge growth that cannot be described with drift-diffusion-reaction models, but instead requires computationally more expensive particle models .
Figure 1: Positive streamer in air. The discharge growth results from the electric field enhancement at the head of the growing channel (source: ) .
Second, the lifetime of free electrons in the new gases is extremely short, typically much less than a nanosecond, because they rapidly attach to gas molecules. This means that a much higher voltage has to be applied before a discharge can start, and that the resulting electric fields can be much higher. Another effect is that the conducting channel behind a discharge rapidly disappears, as visible for negative discharges in one of the new gases in Figure 2.
Figure 2: Negative streamers in a new insulating gas. Source: https://arxiv.org/pdf/2308.08901.pdf.
Third, electric discharges cause gas heating, which in turn affects both gas and discharge properties. This process has to be understood in the new gases, but it takes place on significantly longer timescales than are usually considered in streamer discharge simulations.
From a modelling point of view, there are thus several challenges that need to be addressed. The range of models and methods that have been developed for discharges in air  – particle and fluid models, adaptive mesh refinement, adaptive particle management, model reduction, etc. – needs to be extended so that streamer phenomena, evolution on longer timescales and gas-heating effects can be understood in the new gases.
Within the new project, we will continue to develop and use both gas-specific models and general methods of gas discharge physics (that are also applicable to lightning physics and other application fields). Together with our experimental colleagues, Sander Nijdam and Tom Huiskamp in Eindhoven, we aim to contribute to making our electric energy supply even more sustainable, and in parallel to develop more fundamental knowledge on electric gas discharges.
 X. Li, et al., “Comparing simulations and experiments of positive streamers in air: steps toward model validation”, Plasma Sources Sci. Technol., vol. 30, no. 095002, 2021.
 Z. Wang, et al., “Quantitative prediction of streamer discharge branching in air”, Plasma Sources Sci. Technol., vol. 32, no. 085007, 2023.
 S. Nijdam, J. Teunissen, and U. Ebert, “The physics of streamer discharge phenomena – a topical review”, Plasma Sources Sci. Technol., vol. 29, no. 103001, 2020. [Online]. Available: https://iopscience.iop.org/article/10.1088/1361-6595/abaa05.
Ute Ebert and Jannis Teunissen, CWI, The Netherlands