As a major energy consumer, steel plants can help stabilize the power grid by shifting production from periods with high demand. Electric arc furnaces can be operated at different power levels, affecting the energy efficiency, the duration of melting tasks, and the rate of electrode degradation, which has previously been neglected. We thus propose a new mixed-integer linear programming (MILP) formulation for optimal scheduling under time-of-use electricity pricing that captures the tradeoffs involved. It relies on the resource-task network (RTN) for modeling processing tasks with variable electrode mass depletion and replacement tasks that regenerate the mass. Results for an industrial case study show that the high-power mode, which allows for faster execution and to fit more tasks in low-price periods but is the least energy-efficient and consumes the largest mass of electrode, is mostly avoided. It indicates that electrode replacement plays an important role in total cost minimization.