Simulating the Electrical Parameters of an AC Arc Furnace in Electrosmelting

A mathematical model is proposed for an arc furnace in electrosmelting. So that the model will describe furnace behavior as accurately as possible, research on this topic is analyzed, and basic design principles are formulated. Specifically, the starting point is to derive the equivalent circuit of the furnace. Cassie’s nonlinear differential equation for the conductivity, which has been widely adopted by researchers, is employed in formulating the mathematical model of the arc. In the model, we use calculations of the circuit parameters on the low-voltage secondary side of the transformer and also draw on literature data. To investigate furnace behavior at different times, different values are adopted for the time constant of arc conductivity. By that means, the nonsteady state of the regions close to the electrodes under the influence of external perturbations may be taken into account. The variation in temperature, variation, and pressure of the gas in the furnace during the electrosmelting process is also taken into account. This approach permits realistic description of the furnace behavior with nonsteady arc combustion at different stages of the process; assessment of the possible control parameters; and determination of the requirements on the control system. The basic structure of the model of a three-phase ac arc furnace is derived. MATLAB Simulink software is used in all the calculations of the circuit components and in modeling. The structure includes an ac voltage source; the resistances and inductances on the secondary side of the transformer; the corresponding short-circuit resistances and inductances; and a model of the ac arc. The model is used for dynamic analysis of the arc as an electrical object. Specifically, the dependence of the voltage on the current (the volt–ampere characteristic) is determined. The shape of the volt–ampere characteristic determines the arc combustion, the regions where the arc exists and is stable, and correspondingly the quality of control. The volt–ampere characteristic is investigated with different voltages on the secondary side of the transformer and different arc lengths and also for different values of the time constant of arc conductivity. The model also permits analysis of the static characteristics. The current dependence of the arc length is nonlinear at various voltage stages of the transformer. Recommendations are made regarding the selection of the control signals. Control systems are devised for different stages of smelting. For example, in the initial stage (melting), the control system must minimize the number of disruptions when the region of arc existence is small and must limit the power introduced. Simulation shows that, when the process is nonsteady, adaptive control signals must be used, because they are able to adjust to the continuously changing state of the arc furnace.