Modelling and Simulation of the Melting Process in Electric Arc Furnaces—Influence of Numerical Solution Methods

Increasing demands on the steel market are leading to introduction of many technological innovations regarding the electric arc furnaces (EAFs). The area with significant potential is also advanced computer support, based on mathematical models estimating the process values which are not continuously measured, such as chemical compositions and temperatures of the steel, slag and gas. To achieve optimal process control using EAF models, two crucial characteristics of the later are required, i.e. sufficient accuracy and calculation speed, both affected by selection of the modelling approach and ordinary differential equation (ODE) solving method. The aim of this paper is to investigate the estimation accuracy and calculation speed of an EAF model, evaluated by three solving methods, i.e. fixed step Euler, variable step Runge‐Kutta and Backward Differentiation Formula (BDF). The results are showing that the selection of the ODE solver has an enormous effect on simulation outcome. All three methods proved to be appropriate to obtain the estimated process values; however, achieving a desired level of precision leads to significant deviations in computational speeds. Thus, when aiming for optimal model based EAF control, proper selection of the ODE solver is as important as the modelling approach, but too often neglected.