ARC flash calculations using a physics based circuit model

Arc Flash calculations in the IEEE 1584™, "IEEE Guide for Performing Arc Flash Calculations" calculate the arcing current and the incident energy using logarithmic curve fit equations. These equations are the result of a regression analysis of multiple arc flash tests and describe the arcing current and incident energy over the full range of bolted fault currents. These equations are a multiple variable fit to the test data rather than a physics based model. Several papers have been presented with many circuit models to represent the arc in the electrical circuit. This paper will present a circuit model of the arc and subsequently derive the arcing current and incident energy as a function of the circuit arc voltage and arc resistance. The model presented also fits the non-linear behavior of the arcing current over the entire range of bolted fault currents. The arc voltage model is then related to the single parameter: the length of the arc gap. Having an accurate arcing model has a second advantage. It allows the electrical energy during an event to be calculated specifically for the energy of the arc. This solution then allows calculation of the energy based on the event let-through characteristics. The implication of this result is very powerful. This model implies that the IEEE arcing currents are in fact based on a physical circuit model similar to the model present here. The arcing voltage and arcing resistance are then shown to be are independent of current.