Mathematical modeling of electrical parameters of AC–EAF
Authors: Dmitrievskii B. S. , Bashkatova A. V. 
Published: August 2019

The article presents one of the possible options of mathematical model formation of an electric arc steel-making furnace (EAF). A lot of reports on this subject were studied in order to make a model that most accurately reflects the control object behavior (for EAF). The basic building principles demonstrate the fact that the primary element is substitution pattern of electric circuit of the installation. Cassie nonlinear differential equation was used to get a mathematical model of an electric arc. This nonlinear differential equation is very popular among the researchers. Model update is provided by calculating the electrical circuit parameters on the secondary side of transformer low voltage and by studying statistics from home and foreign scientists’ contributions. Different values of the “time-constant” of arc conductivity were used to analyze the control object behavior at different instants of time. It made it possible to take into account the nonstationarity of the state of electrode sheaths that were influenced by external disturbances, temperature variations, pressure and gas composition in the course of production processes. Such an approach made possible to form an aggregate picture of the control object behavior under the conditions of a nonstationary state of the arc combustion area at different stages of melting; to evaluate possible regulation characteristics and to determine control system requirements. The structural scheme of the model of a three-phase AC–EAF was formed. All necessary calculations of circuit elements and modeling were performed using the MATLAB Simulink package. The block diagram includes AC voltage source, direct-current resistance, and inductance of the transformer on secondary side and a low-voltage circuit, a model of an AC electric arc. The model was used to analyze the dynamic characteristics of electric arc as being an electrical object to show the voltage–dependence of current – current-voltage characteristics. The configuration of current-voltage characteristics determines burning behavior of the arc, existence domain, stability and control quality. Current-voltage characteristics were studied under the conditions of different values of the voltage on the secondary side of transformer and arc length and for different values of the “time-constant arc conductivity”. The model was also used to analyze the static characteristics. The dependence of the arc length on the current for different voltage of the transformer steps is nonlinear. Recommendations on the choice of control actions and the construction of control systems for different stages of melting are given. For example at the initial stage of melting, the control system should perform minimization problems of number of breaks under the condition of an insignificant domain of the arc existence and limit the value of lead-in power. The simulation results show that the nonstationarity of the process leads to the need to use self-organizing control systems capable of adjusting to the continually varying state of the object.