*3.1. Input*

Different scenarios for which automatic operating strategies are to be generated and compared can be defined by the user in an additional worksheet of the Excel file used for the furnace parameters. First, the masses and compositions of scrap, two coal types, and two slag formers (usually lime and dolomite) charged with three scrap baskets are defined. Although the input file is currently limited to this, the model allows the addition of both more baskets and additional types of coal or slag formers. The scrap composition can be defined separately for each basket. Furthermore, the initial conditions before charging of the first basket, namely, the mass, temperature, and composition of the hot heel present in the furnace have to be set. In addition to the values defining the initial conditions and charged material, the minimum and maximum values have to be set for the electric power and voltage, oxygen input for lances, post-combustion and burners, carbon injection, off-gas mass flow, slag former injection, natural gas for burners, and the voltage. The variation of these parameters between the selected minimum and maximum values over the course of each simulation is determined according to a set of rules that in turn can be adjusted through the parameters shown and described in Table 1.

One minimum and several maximum values can be given for each parameter. The model automatically selects all possible combinations and runs a simulation for each case. This can be combined with the variation of parameters, such as the composition of coal and slag formers, allowing a large number of scenarios to be simulated and compared automatically.


#### *3.2. Control of Operation Chart Parameters*

Using predefined rules, the model determines the desired value for each parameter from the selected minimum and maximum values during the simulation, replacing the fixed operation chart determined from measured data. The rules are derived from the current operating strategies and operation charts from the regular operation of different EAF. The simulation starts with the charging of the first basket and is terminated after the scrap charged with the final basket has melted and a predefined carbon content and temperature of the melt have been reached. After and before the charging of each basket all values of the operation chart are set to their minimum (power off) values for the delays defined by tstart-delay and tstop-delay to account for the power-off time associated with the raising and lowering of the electrodes, as well the opening and closing of the roof as necessary, when scrap is charged into the furnace. The condition for charging the next basket is that the sum of the currently remaining solid scrap volume and the volume of the scrap charged with the next basket are below the maximum allowed scrap volume Vscrap-max. If no additional basket is defined and the conditions for tapping are met, all operation chart parameters are reduced to their minimum values and the simulation is terminated. The charging of the second and additional baskets is triggered by an event function that constantly checks if the necessary conditions have been met. Initially, once the conditions are met for charging of the next basket, all operation chart parameters are reduced to their respective minimum values and the simulation continues until tstop-delay has passed. The simulation is then stopped and reinitiated with new starting values and continues with a power-off period determined by tstart-delay and the following power-on period just as with the first basket.

A hyperbolic tangent function is used to allow rapid but continuous changes between states where necessary. It can assume values between one and zero and is based on a controlling variable and a threshold. ϕ(a,b) indicates a hyperbolic tangent function that has the value zero as long as the variable a is smaller than the threshold b, and rapidly changes to one if a increases to values higher than b. For example, the factor indicating the charging of the next basket would be based on the maximum allowed scrap volume Vscap-max, the scrap volume in the next basket Vscrap-next, and the actual scrap volume Vscrap, as shown in Equation (1):

$$
\Phi\_{\text{basket}} = \varphi \left( V\_{\text{scrap}}, V\_{\text{scrap-max}} - V\_{\text{scrap-max}} \right). \tag{1}
$$

It would become zero once the free volume is large enough to charge the next basket. Such factors are used for all conditions and delays defining the operation chart.

The electric power is reduced for the initial period after charging until bore down has progressed far enough to allow the arc to burn inside the scrap, at which point significantly less radiation is received by the wall and roof, and maximum power can be used. Later during the process, power is reduced once the full bath surface is uncovered and the flat bath phase begins. During any stage of the process, the power will be reduced if the wall temperature reaches the critical temperature Twall-crit. The voltage is assumed to be a linear function of the power and the current is determined accordingly.

The oxygen lance mass flow is initially set to the percentage defined by Olance-min and increases once the burner power conditions set by Clance-burner is fulfilled with another increase to its maximum value once the complete bath surface is free of solid scrap. The ratio of the first and second increase is determined by the parameter Clance-bath. Post-combustion oxygen flow is started with the maximum value once the additional delay tpost-delay has passed and a minimum of 5% of the scrap has melted. It is stopped once the mass of solid scrap remaining divided by the initial amount of scrap has reached Cpost-scrap. The burners are started with full power and both oxygen and natural gas input are stopped once the remaining scrap has reached Cburner-scrap. Carbon injection is started after meltdown of the last scrap charge has progressed far enough to create a free bath surface as defined by Ccarbon-bath. Once the melt temperature approaches the desired tapping temperature or the amount of remaining scrap reaches Ccarbon-scrap, carbon injection is phased out. Oxygen lancing is reduced proportionally with the reduction in carbon injection.

Off-gas extraction is started at the minimum mass flow and increased with the injection of gases and carbon. Because the injection of slag formers using lances is not practiced at the furnaces this automatic control was initially designed for, no rules have been defined for this purpose and the mass flow is permanently set to zero. The practice could, however, be included by simply defining the necessary factors and rules, as the process model does include the necessary equations and simulations based on measured data have been run successfully for furnaces where the injection of lime is practiced. Cooling water flows and inlet temperatures are assumed to be constant for these simulations.
