10. Arc dynamics --- power system analyzing with dynamic arc characteristics
10.3 Breaking of zero skipping current
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Current interruption by an AC circuit-breaker is done at the instant of current zero. In an AC circuit which has been supplying charging current (leading current) beforehand, the DC components' amplitudes of the short circuit current can be higher than AC components' ones. This is due to the fact that, if a short circuit is initiated at the time of the peak point of the charging current wave form, the short circuit current wave-form starts to the same direction from the peak point of the charging current. The current in reactance(s) is always continuous. (See Fig. 10.2) In case of higher charging current, relatively lower short circuit current and long time constant of DC component decrement, the first current zero would be much delayed. So also the possible short circuit current interruption timing would be delayed.

It is known that synchronous generators' short circuit impedances are time-varying ones. If a generator's impedance is predominant in a circuit, e.g. power systems near power stations, the decrement of AC component of the short circuit current is significant. So much more delay of the first current zero would be introduced.
In a certain case, during more than 0.1s, the first current zero does not appear. Thus the fault clearing is delayed and as the most serious matter, the breaking ability of the relevant circuit-breaker does not last for such long time interval. The situation is severer for today's systems with longer time constants of DC component decrements.
Fortunately today's SF6 gas and air-blast circuit breakers have certain values of arc resistances during the current breakings. The effect of arc resistance of a circuit-breaker is, generally, significant for the damping of the DC component. But year by year, losses in power systems are lowing due to high capacity and low loss facilities. Furthermore, the arc resistance of a circuit-breaker is also lowering due to smaller number of breaking points per pole of the circuit-breaker, e.g., one breaking point per pole of a 550kV circuit-breaker. Therefore careful examination is required hereafter.
In the example attached (Appendix 10.2), 500MVA generator connected to the low voltage side is supplying line charging current of the transmission line connected to the high voltage side of the transformer, when grounding short circuit occurs at the line and short circuit current flows. The current is broken by a circuit-breaker at the high voltage side. Here, for representing the circuit-breaker, Cassie arc model is applied, the parameters applied to which are:
Furthermore, for convenience to introducing to EMTP/TACS, Cassie's equation shown in Table 10.1 is converted to the following form:
The original equation
These forms can be directly introduced to TACS data (see attached data).
In the calculation, for simplification, arc resistance is inserted only to one phase of mostly asymmetrical current flowing. Without the arc resistance, zero skipping current last more than 100ms, so the current may not be interrupted by an ideal (without arc resistance) circuit-breaker. But by inserting the arc resistance after the contact separation of the circuit-breaker, the current immediately falls to zero and is interrupted.
Therefore, within the conditions here applied, short-circuit currents are safely interrupted. For evaluations in actual power systems, appropriate parameters of both circuit-breaker arcs and circuits shall be introduced.

This page is based on Prof. E.Haginomori's lectures in Tokyo Institute of Technology, and edited by Japanese ATP User Group. Copyright (C) Eiichi Haginomori and Japanese ATP User Group.