Arc Interruption Theory

Contents

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Key learnings:

Arc Interruption Theory Definition: Arc interruption theory is defined as the process of stopping electrical arcs that occur when circuit contacts open.
Methods of Arc Interruption: There are two main methods: the high resistance method, which increases resistance to zero current, and the low resistance method, which uses the natural zero point of AC current.
Restriking Voltage: Restriking voltage is the voltage across breaker contacts at the moment an arc is extinguished.
Energy Balance Theory: This theory explains that an arc can be extinguished if heat is dissipated faster than it is generated between the contacts.
Voltage Race Theory: This theory states that interrupting the arc is possible by reducing ionization between contacts faster than it occurs.

Arc interruption theory is how a breaker kills the plasma after the contacts part. The insulating material (gas, oil, vacuum or air) in a circuit breaker has to do two jobs:

Hold off voltage between the open contacts.
Put the arc out as the contacts open.

On a fault the relay trips the breaker. As the poles part, an arc is drawn in the ionized gap. The insulator and the interrupt scheme then have to quench that column before the voltage can reignite it.

Methods of Arc Interruption

Two interrupt methods are used.

High resistance method,
Low resistance method or current zero interruption method.

In the high-resistance method, arc electrical resistance is raised until current falls to zero and the column cannot restart. The rise must not be so abrupt that L di/dt puts a damaging voltages spike on the circuit. Lengthening or cooling the column are the usual ways to raise that resistance.

Limitations of High Resistance Method

The high-resistance column looks resistive, so most of the arc energy lands in the circuit breaker. The tank and mechanism must take that heat. The method is used on DC breakers and on many low- and medium-voltage AC air-break poles.
The low-resistance method is an AC current-zero scheme. The arc dies at a natural zero. The gap then has to gain dielectric strength faster than the transient voltage can reignite it.

Two textbook models describe how that extinction happens:

Energy balance theory,
Voltage race theory.

Terms used in those models:

Restriking Voltage

The transient voltages that appears across the breaking poles at the instant the arc goes out.
Recovery Voltage

The power-frequency voltage left on the poles after the transients have died and the arc is out on every pole.
Active Recovery Voltage

The instantaneous recovery voltage at the instant the arc goes out.
Arc Voltage

The voltages across the poles while current still flows as an arc. It stays low through most of the loop, then rises sharply as current approaches zero.

Energy Balance Theory

Cassie energy balance: just as the contacts part, restriking voltage is still zero so arc heat is nil. When the gap is fully open the resistance is huge, so heat is again nil. Peak heat sits between those limits. If the gap dumps heat faster than the column generates it, the arc collapses. Cooling, stretching or splitting the column are the usual tools.
Voltage Race Theory

Slepian race: the arc is ionized gas between the circuit breaker poles. Gap resistance is tiny while the contacts still touch and rises as they part. If ions recombine, or insulation is driven in, faster than new ions form, the arc goes out. Ionization at zero current is set by the voltages called restriking voltage.

An ideal lossless expression for restriking voltage is

Here, v = restriking voltage.
V = voltage at the instant of interruption.
L and C are series inductor and shunt capacitance up to the fault.
That formula is a 1-cos wave. Lower L C raises the oscillation frequency and the rate of rise (RRRV). Peak of this simple model is about 2V, not an unbounded voltage.
The variation of v versus time is plotted below:

With loss, resistance damps that swing, as in the next figure. The sketch assumes current lags voltage by 90 electrical degrees, the inductive worst case (current zero at voltage peak). The actual angle depends on when in the cycle the fault hits.

Arc voltage itself adds to restriking voltage, but it also opposes current and pulls current toward the applied voltages. Hence the current is then not at peak when voltage passes through zero.