Historically, modeling of arc behavior advanced the development of large capacity circuit breakers. A great step forward in understanding arc-circuit interaction was made in 1939 when A. M. Cassie (Cassie 1939; Cassie and Mason 1956) published the paper with his well-known equation for the dynamics of the arc (arc model) and then, in 1943, O. Mayr (1943) followed with the supplement that takes care of the time interval around current zero. Much work was done afterward to refine the mathematics of these arc models and to confirm their physical validity through practical measurements (CIGRE Working Group 13.01 1988, 1993).
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Kriegel, M., & Uzelac, N. (2019). Simulations as Verification Tool for Design and Performance Evaluation of Switchgears (pp. 379–397). https://doi.org/10.1007/978-3-319-72538-3_12
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