Vacuum circuit breaker postarc current modelling based on the theory of Langmuir probes

High-resolution measurements on the postarc current in vacuum circuit breakers (VCBs) reveal a period, immediately following current-zero, in which the voltage remains practically zero. The most widely used model for simulating the interaction between the postarc current with the electrical circuit lacks a proper explanation for this event, and hence, it needs to be complemented. We demonstrate that the breaker's electrical behavior during this zero-voltage period can be explained by using the theory of a Langmuir probe. Such probes are used to investigate plasma properties such as the ion density and the electron temperature, and we extrapolate its theory to the VCB. After the voltage-zero period, when the transient recovery voltage starts to rise, the breaker's electrical behavior is mainly determined by the expansion of an ionic space-charge sheath in front of the cathode. In addition to the current from the Langmuir probe model, the time change of the electric field inside the sheath gives a displacement current. Instead of solving the complicated plasma equations to find the displacement current, we use an approximation by simulating it with the aid of a voltage-dependent sheath capacitance. We programmed the model as a function block in Matlab's SimPowerSystems to facilitate its application in different electrical circuits.