*5.2. Speed and Stability*

For the simulator mode, the model speed and stability are most important. After charging a basket, the simulation is initiated and the solver takes 3–5 s to run the initial steps. After this initial delay, the simulator can be run at higher speed, allowing up to 20 seconds of the process to be simulated per second of real-time. Therefore, periods during meltdown or refining where no user input is necessary can be simulated at high speeds, whereas lower speeds can be selected during phases where frequent user inputs are necessary.

Figure 10 shows the progression of the selected simulation speed and the actual speed attained by the simulator during an example heat where two baskets were charged and a total process time of 2646 s was simulated in 272 s of real-time. The speed actually attained was calculated for each second of simulated process time. For most of the time, the simulation matched the selected speed; however, there were numerous instances where the speed dropped below the selected speed which was then compensated by an increased speed until the simulation and the target speed synchronized again. This never took more than a few seconds and the actual delay between the target time and the simulation stayed within less than 20 s. The short periods of re-synchronization were barely noticeable for the user, and inputs could be made precisely at the desired time and state of the simulated process.

**Figure 10.** Selected and attained simulation speed.

Figure 11 shows the simulated and the target time during the first 55 s of the same simulation. The delay during initialization is visible at 0–6 s, after which the simulation synchronized with the desired speed and closely matched the target time. After the initiation of the basket, deviations from the target time remained small and lasted for no more than 5 seconds.

**Figure 11.** Simulated and target time.

Although results obtained with the automatic control and simulator cannot be validated using measured data, the internal consistency of the model can be evaluated using energy and mass balances. An energy balance using all heat flows calculated during the simulation yielded and error in the order of magnitude of 10−<sup>10</sup> kWh, which was assumed to be a numerical error and was irrelevant for the simulation results. The mass balance prepared for each element gave a maximum error of 0.1% of the respective total mass, which was of no relevance for the simulation results.

The above examples illustrate the potential of the simulator developed. The simulator can be run in different modes depending on the aim of the simulation and, consequently, the simulator is applicable for different purposes such as process development, online predictions, and training of electric arc furnace operators. Simulators of this type are also applicable for dynamic optimization problems [40] and as soft sensors for evaluating parameters that are crucial for the EAF operators [3]. Another notion highlighting the importance of developing fundamental process models further is the fact that the computational load of comprehensive computational-fluid-dynamics-based approaches [41] remains—at least for the time being—too high for online applications.
