Enhance Neher-McGrath formulation to model current uncertainty

Electric current fluctuates constantly in the circuit due to uncertainty of demand and load on the grid, as well as other factors. The current variation imposes significant effects on ampacity along the circuit, but is largely ignored. Users are advised to select “next size up” wire to address such an issue empirically. Whether this empirical rule ensures safe installation of wire and equipment is questionable. This study starts with the Neher and McGrath (NM) formulation and derives uncertainty of the operating temperature. Using the reliability constraint on the rated temperature, the uncertainty expression is substituted back to the NM equation to solve for the maximum current. The result is a stochastic version of the NM equation, which can be used to derive the derated ampacity for overcurrent protection. A comparison of the existing NEC tabulated ampacity values indicates that, depending on the degree of current variation, the “next size up” rule may not be sufficient.