# Single-Phase Circuit Breaker (with arc)

Single-pole single-throw circuit breaker with Mayr arc representation

## Library

Switches & Breakers / Fundamental Components

## Description

The Single-Phase Circuit Breaker (with arc) block represents a single-phase circuit breaker with Mayr arc representation controlled by an external control signal vT. If vT is less than the threshold, then the breaker is closed. If vT is greater than or equal to the threshold, then the breaker opens with an arc during the current interruption. The external signal can open and close the breaker repeatedly.

The table shows how the external signal `vT` controls the block behavior.

ConditionBlock Behavior
`vT` < ThresholdThe circuit breaker is closed. Port 1 is connected to port 2.
`vT` ThresholdThe circuit breaker is either opening or open. Port 1 is connected to port 2 via a nonlinear conductance.

The Single-Phase Circuit Breaker (with arc) block has a higher computational overhead than the Single-Phase Circuit Breaker block. If the fidelity of the representation of arc current or voltage is your overriding requirement, use the Single-Phase Circuit Breaker (with arc) block and use a global Simulink® variable-step solver. Otherwise, use the Single-Phase Circuit Breaker block.

### Mayr Arc Model Equations

The defining equations for the breaker are

`$x=\mathrm{ln}\left(g\right)$`
and
`$i=gv,$`
where:

• g is the arc conductance.

• x is an internal state variable.

• v is the voltage across the breaker.

• i is the current through the breaker.

When the breaker is open,

`$\frac{dx}{dt}=0.$`

When the breaker is closed,

`$\frac{dx}{dt}=\frac{1}{\tau }\left(\frac{g{v}^{2}}{P}-1\right),$`

where:

• τ is the arc time constant.

• P is the cooling power.

## Parameters

Arc time constant, tau

The default value is `0.3e-6` `s`.

Cooling power, P

The default value is `30900` `W`.

Initial arc conductance, g0

Conductance between ports `1` and `2` when the breaker is closed. The default value is `1e4` `S`.

Threshold

Threshold voltage for the control port `vT`. The block uses the threshold voltage and the value of `vT` at the start of the simulation to determine whether the breaker is initially open or closed. When the voltage rises above the threshold, the breaker opens. When the control port voltage falls below the threshold, the breaker closes. The default value is `0` `V`.

## Ports

The block has the following ports:

`1`

Electrical conserving port

`2`

Electrical conserving port

`vT`

Scalar control port, which is either a physical signal or an electrical port

## References

[1] Schavemaker, P. H., and L. Van der Sluis. “The Arc Model Blockset.” Proceedings of the Second IASTED International Conference POWER AND ENERGY SYSTEMS (EuroPES). Crete, Greece, June 25-28, 2002, pp. 644-648.