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In steel recycling, the optimization of Electric Arc Furnaces (EAFs) is of central importance in order to increase efficiency and reduce costs. This study focuses on the optimization of electric arcs, which make a significant contribution to the energy consumption of EAFs. A three-phase equivalent circuit integrated with the Cassie–Mayr arc model is used to capture the nonlinear and dynamic characteristics of arcs, including arc breakage and ignition process. A particle swarm optimization technique is applied to real EAF data containing current and voltage measurements to estimate the parameters of the Cassie–Mayr model. Based on the Cassie–Mayr arc parameters, a novel Arc Quality Index (AQI) is introduced in the study, which can be used to evaluate arc quality based on deviations from optimal conditions. The AQI provides a qualitative assessment of arc quality, analogous to indices such as arc coverage and arc stability. The study concludes that the AQI serves as an effective operational tool for EAF operators to optimize production and increase the efficiency and sustainability of steel production. The results underline the importance of understanding electric arc dynamics for the development of EAF technology.