Three-Phase Cassie Arc Equations for Electric Arc Furnace

This article presents three-phase arc equations based on the general arc equation with the assumption of the Cassie model. A new set of arc equations is developed, which considers the three arcs with coupled equations instead of three independent arc equations. In the general arc equation, the arc conductivity is a function of the difference between input and output powers. In the proposed three-phase arc equations, corresponding to every arc, the input power is the sum of delivered electric power and the received heat power from the two other arcs. The output power is the sum of heat powers transferred to the surrounding environment and the other two arcs. A large set of actual three-phase instantaneous voltage and current recorded at Mobarakeh Steel Company (MSC) in Isfahan, Iran, is utilized. The optimized model parameters are attained by minimizing the sum of square errors every half-cycle. The model accuracy is investigated by comparing the results derived from actual records and their corresponding model outputs. As model parameters change every half-cycle, they are considered time series using ARMA models. ARMA coefficients are attained corresponding to every record to form a database. MATLAB codes that generate model parameters time series using the ARMA coefficients database are enclosed.