Abstract
The article shows that the high speed and current-limiting properties of a self-recovering current-limiting device with a liquid metal cause interest in their use in power supply systems. However, the level of research, both in our country and abroad, does not allow to proceed to the creation of industrial designs of such kind of current-limiting devices. More research is needed. To study the process of a short circuit in the AC (an alternating-current network) proposed a mathematical model that allows precise, detailed and deployed to investigate their current-limiting properties. The model takes into account the resistance of the electric arc during the switching process. Period of the burning time of the arc can be divided into infinitely small areas, arc resistance each of which is assumed to be linear.
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