A dynamic, first-principles process model for a steelmaking electric arc furnace has been developed. The model is an integrated part of an application designed for optimization during operation of the furnace. Special care has been taken to ensure that the non-linear model is robust and accurate enough for real-time optimization. The model is formulated in terms of state variables and ordinary differential equations and is adapted to process data using recursive parameter estimation. Compared to other models available in the literature, a focus of this model is to integrate auxiliary process data in order to best predict energy efficiency and heat transfer limitations in the furnace. Model predictions are in reasonable agreement with steel temperature and weight measurements. Simulations indicate that industrial deployment of Model Predictive Control applications derived from this process model can result in electrical energy consumption savings of 1–2%.