Computer Modelling of Electric Arc Furnace Electrode Position Control System Orest Lozynskyi , Yaroslav Paranchuk, Oleksii Kobylianskyi Lviv Polytechnic National University Institute of Power Engineering and Control Systems Electromechanotronics and Computerized Electromechanical Systems Department Lviv, Ukraine Orest.y.Lozynsky@lpnu.ua yparanchuk@yahoo.com kobyalex@gmail.com September 5-8, 2017 Lviv, Ukraine

INTRODUCTION An efficacious approach towards modernizing the automatic regulation system (ARS) is the use of mathematical and computer simulation of EAF electric modes. This will allow one to study the effectiveness of different structures and laws of electrodes re- positioning, as well as to substantiate the optimal structural solutions and strategies for EM control and implementation of the quality stabilization of EM coordinates which is performed by electrode position ARS in different load modes and at different technological stages of steel melting with different parameters of stochastic characteristics of arc length perturbations and different requirements to the EAF operation indicators. The existing computer models for the change of ARS structure, control laws and perturbations characteristics lack a user-friendly interface, which complicates computer-aided studies aimed at searching for best solutions for ARS structure and optimal control strategy models.

Fig.1. Functional diagram of the electrode position ARS model OBJECTIVES The research aims at developing a three-phase computer model of the electrode position ARS in the instantaneous coordinates with a user-friendly interface, which would enable high-adequacy simulation of the electric modes that are characteristic of different technological stages of steels and alloys melting. It will also make it possible to carry out high-accuracy studies of the indicators of regulation dynamics and effectiveness of modes control for different structural and systems solutions and laws of the electrode position regulation signal generation, as well as to study the models of optimal control of EAF melting modes. Fig.1. Functional diagram of the electrode position ARS model

The quality of implementation of the optimal strategies of steel melting modes control is to a great extent determined by the properties of the electrode position ARS being used. The existing regulators of the EAF electric mode mainly operate under the differential law of the electrode position signal generation, i.e. they apply the law Ur = aUa - bIa , where Ua and Ia are root-mean-square values of the arc voltage and current, respectively. On the intervals of a set (steady-state) mode establishing, Ur = aUa.z - bIa.z = 0. . Fig.1. Electrode position control system

Fig.3. Structural diagram of the Simulink model of the electrode position ARS for the electric arc furnace ДСП-200 in the instantaneous coordinates

The model consists of the following main modules: the module of the three-phase symmetrical electrical power network (EPN), furnace transformer unit (FTU) and secondary current lead (short circuit FTU+LVC), which present the model of the EAF electric circuit (yellow), to which the model of the three-phase arcs with the corresponding DCVC is connected. These models were made using the elements of the SimPowerSystems library (red); each phase channel includes the modules of the sensors of the average values of voltage and current, comparator units and units for generating the electrode position control signal according to the corresponding law (differential, impedance or deviation of arc voltage or arc current) (blue), as well as the modules of the drive and mechanism of electrode position (in the model presented in Fig. 3, this is the electromechanical drive with the rack-and-pinion gear) (green); the model also includes elements which add more realistic behaviour to the system (dark blue) the module of the generator of the determined perturbations (in particular, extreme ones which cause operational short circuit (s.c.) or arc extinction (a.e.) and can be symmetrical or asymmetrical) and steady-state random arc length perturbations, which, according to the stochastic characteristics, correspond to the technological stages under consideration (violet); the module of computing the integral characteristics of the coordinates and indicators that comprehensively characterize the electrical and technological efficiency of control of the ARS structure for a specific technological stage and control strategy and the dynamics of EAF EM coordinates regulation.

Fig.4,a shows the change of the root-mean-square arc current id (t) and voltage ud (t) and the current ia (t) and speed ωa (t) of the electric drive of the electrode position mechanism in phase A at correcting the three-phase symmetrical operational short circuit, recorded on the electric arc furnace ДСП-200. Fig. 4,b shows the change of these same coordinates of phase A in the mode of correcting the three-phase symmetrical operational short circuit obtained on the developed Simulink model. ωa Ia Id Ud t , s Id ×250, A Ud , V ω, rad/s Ia , A a) b) Fig.4. Time dependencies of the coordinates at correcting the operational s.c. with the АРДМТ-12 regulator on the ДСП-200 furnace (a) and on the developed Simulink model of the electrode position ARS of this furnace (b).

U2ph , V Id ×250, A Ud , V U2ph Id Ud t , s Fig.5 shows time dependencies of the change of the instantaneous values of voltage u2ph (t) and current id (t) of the FT secondary winding, and arc voltage ud (t) in phase A in the quasi-stationary mode of correcting the random perturbations for the non-linear DCVC of the arc based on the arctangent function, which were obtained on the developed computer model. Fig.5. Model time dependencies of the change of the arc voltage ud (t) and arc current id (t) and FTU secondary voltage u2ph (t) for the furnace ДСП-200

t , s Id Ud ωa Ia The model was also tested in the modes of one-phase and two-phase s.c. and a.e. in different combinations by phases. The results confirm the adequacy of correcting the said perturbations of the electrode position (arc length) ARS in all the test modes. Fig.6 shows the change of the root-mean-square values of the arc voltage ud (t) and arc current id (t), and the current ia (t) and speed ωa (t) of the electric drive motor of the electrode position mechanism in all the three phases at correcting the one-phase s.c. in phase A for the differential law of arc length regulation, which were obtained on the Simulink model. Fig.6. Time dependencies of the EM coordinates of the furnace ДСП-200 and electrode position motor in each of the phases in the mode of correcting the s.c. in phase A

Fig.8 presents the model time dependencies of the implementation of correcting the steady-state random perturbations of the arc length at the feed melting stage. The comparison of the integral indicators of the dynamics (in particular, dispersion) of the EM coordinates regulation in conditions of steady-state random arc length perturbations at different technological stages which were obtained experimentally on the electric arc furnace ДСП-200 and on its Simulink model in the instantaneous coordinates showed that the values of Bartlett’s M-criterion are lower than the corresponding reference values taken for a 5% significance. This suggests that the sufficient precision of simulating the change of EM coordinates of steel melting in the electric arc furnace ДСП-200 has been attained in the developed Simulink model both at the level of the root-mean-square values and at the level of the instantaneous values in the symmetrical and asymmetrical load modes (perturbations). Therefore, the conclusions and generalizations made on the basis of the model experiments will be reliable for assessing the efficacy of different control laws, design and systems solutions on specific electric arc furnaces, including super powerful ones. а) b) Id ×250, A Ud , V P×20000, Wh f , mm Id P Ud f t,s Fig.8. Time dependencies of the arc current id (t) and arc length random perturbations fd (t) at the feed melting stage in the electric arc furnace ДСП-200 (a) and those obtained on its Simulink model (b)

CONCLUSIONS The developed Simulink model offers a user-friendly interface for changing the structure of electrode position (arc length) ARS, for implementing different laws of regulation and strategies of optimal control and for generating determined and random arc length perturbations similar to the real ones, as well as broad functionality for setting up various mathematical experiments and on-line computation of the integral indicators of coordinates regulation quality and electrical and technological efficiency of melting modes control. The developed computer model adequately simulates the processes of steel melting EM coordinates change in symmetrical and asymmetrical load modes at different technological stages of melting and makes it possible to obtain on-line integral indicators of electrical and technological efficiency of using different ARS structures, electrode position laws and optimal control strategies. The developed Simulink model is an effective tool for comprehensive study of the efficiency of the strategies of multi-criteria optimal control of electrical melting modes and of the indicators of electromagnetic compatibility of the EAF and power supply network modes.

THANK YOU FOR ATTENTION September 5-8, 2017 Lviv, Ukraine Orest Lozynskyi Yaroslav Paranchuk Oleksii Kobylianskyi Lviv Polytechnic National University Electromechanotronics and Computerized Electromechanical Systems Department Orest.y.Lozynsky@lpnu.ua yparanchuk@yahoo.com kobyalex@gmail.com