**1. Introduction**

Studies show that about 20% of industries have to change 5% to 10% of their circuit breakers (CBs) by 2020, due to the increase of the short circuit level [1]. Techno-commercial studies prove the feasibility of fault current limiters (FCL) and many investigations have been initiated and reported by EPRI and CIGRE [2] to design a practical FCL. Hybrid FCLs are among the most powerful current limiters developed so far and the most a ffordable idea in terms of cost [3]. In one of the hybrid FCL designs, a simple multi-contact fast switch (FS), along with the inherent features of the series arcs, has been used to commutate the current to current-limiting parallel branches [3]. Mechanical FSs can also be used in HVDC interrupters [4–6] where a rapid operation is required and semi-conductor switches are not preferred due to their high cost-loss, harmonic e ffects, sophisticated control, and continuous maintenance. Electromagnetic driven switches make 100-μs close/open times possible, which, in comparison with semiconductor power devices, are low-loss in ON-state and more reliable.

The actuating mechanism of many fast switch designs is based on electromagnetic repulsion. The theory of such a mechanism is thoroughly presented in [7] and the first patent filed in the late 60 s. Some more recent works on the design of such operating mechanisms have been reported elsewhere [8–10]. In a recent study, a design has been introduced to cut o ff 2 kA at 12 kV single-phase voltage [3,11,12], where only the mechanical model and the mechanism of FS were considered. The electrical simulations for modeling the drive and study of the e ffects of di fferent parameters on the contact speed, *uc*, shows these FSs can reach *uc* = 70 m/s through the optimum design [13], and then the arc characteristics will be severely a ffected by this fast elongation.

Because of the di fficulties in the simulation of a fast elongating arc (FEA) in subsonic regimes, there is only a limited number of relevant papers in the literature. Some other researches were conducted on electrical simulations for modeling the drive, studying the e ffect of di fferent parameters on *uc* [14–16], and application of this drive for AC circuit breakers [17], in combination with vacuum CBs [18,19] or HVDC interrupters [4,10,20]. The latter has resulted in a patent registered by ABB [21]. None of these studies investigated the characteristics of FEA in FS.

Just in [22], the first 2 ms of FEA has been modeled using a black-box approach for a very limited range of arc currents and elongation speeds, without paying attention to the arc physics. Therefore, this model is only applicable to the specific geometry within a limited range of speeds and currents. It is, also, vulnerable to the problems arising in attempts to represent electric arc dynamic processes accurately utilizing ordinary mathematical models [23]. Another reason for the study of FEA is that of replacing the greenhouse SF6 gas, where almost all environmentally friendly alternatives shall be used at pressures higher than what SF6 was utilized at. At higher pressures, the thermal conductivity is reduced at the arc quenching temperature range, i.e., below 4–5k K, which is vital for the current interruption, and so the input energy to the arc could be reduced through the fast opening method.

The model consists of the magnetohydrodynamics (MHD), the moving mesh, and the net emission coe fficient (NEC), which is the di fference between the radiated and absorbed power, considering the contact e ffect with a circumstantial treatment of heat transfer in solid parts, including the contacts. The *uc* as the output of another electromechanical finite element model (FEM) is simulated and imported into this model. Details of the electromechanical FEM model of the Thomson coil circuit, as well as technical methods for electro-mechanical measurement of fast elongated arc parameters, including the measurement noise, shift noise, and the practical way to consider their e ffects in simulations and experimental setup including FS geometry, are available in [24]. The first motivation of this study is to understand the physical mechanisms of arcs elongated inside the fast switches before the current zero (CZ).

A mathematical model is presented for variable-length AC arcs in contactors with elongating speeds of about 1 m/s, where the arc voltage is described by a series arc concept [25]. It is only applicable to cylindrical arcs when the temperature distribution is radial homogenous. Another already presented mathematical model for variable-length arcs tries to relate the arc voltage with the arc volume, but it is only applicable to the welding arcs when the length is changing vertically with rather low speeds [26]. All of these purely mathematical models are either modified versions of the Cassie-Mayr model and rely on energy balance inside the arc, or a modified Ayrton model for DC static arcs [27], or even a static model of welding arcs without diagonal cooling [28]. The relation between the arc length and its voltage and current has been essential, however, in other fields like arc welding, where a robust method is proposed to measure the arc length in [29]. Also, a technique to find the arc current and voltage from arc length in welding has been patented [30]. This fact can express the importance of presenting a reliable model for fast elongating arcs to solve the most critical issue related to the current commutation in hybrid FCLs/HVDC circuit breakers.

Although there are plenty of studies on the current interruption in high-voltage (HV) gas circuit breakers [31–33], vacuum interrupters [34], and medium voltage load breakers [35–37], only a few reviews on the low-speed load break switches, mostly relying on experimental findings without MHD simulations [38,39], are available. Just a few studies deal with simulations for VCB [40] and air breakers at a contact speed of about 2.5 m/s [33], which will result in a short gap before the CZ. This is the second reason for this study. In [41], the gap memory e ffect concerning the interrupted current is illustrated, which is more pronounced at longer contact gaps, similar to what we have here in FS.
