Simulation of an electric arc furnace electrode position system.

Balan, Radu ; Maties, Vistrian ; Hancu, Olimpiu 等

Abstract: Electric arc furnaces (EAFs) are commonly used in steelmaking and in smelting of nonferrous metals. Usual EAFs work at power levels from 10MW to 100MW. The power level is directly correlated to production throughput, so it is important to control the EAF at the highest possible average power with a low variance to avoid breaker trips under current surge conditions. To obtain the electric arc, usually there are used three graphite electrodes. The power level depends by the positions of the electrodes. As a result, the realization of a competitive control system is very important because it led to reduction of the energy consumption, pollution, and increases the safety of the process. This paper presents some aspects concerning modeling of the electric arc, modeling of the EAF electrical system, modeling and adaptive control of EAF process--hydraulic control system of electrode position. Finally, a simulation application is presented.

Key words: electric arc furnace, modeling, simulation, nonlinear control

1. INTRODUCTION

In the metallurgic industry for the melting of the scrap or other metals it is used the electric arc furnace (EAF). The electric arc allows to obtain high temperatures necessary to melt or/and to realize some chemical reactions. To obtain the electric arc, usually there are used three graphite electrodes which are supplied by a three-phase power transformer that has in the primer 20-30 KV respective 100-800V in the secondary. The electric power (10.. 100 MW) depends by the length of the arc which can be controlled using an efficient hydraulic control system of electrode position. The circuit closes through the metal mass that will be molten. The principle needs a very high-energy consumption, which implies a very efficient control system to reduce as much as possible energy consumption. Many times the weight of the electrodes is very high; it could reach tenth of tons. The hydraulic control system becomes complex. The acceleration and deceleration imposed for the electrodes must ensure variable velocities from the hydraulic control system with the aim of avoiding damage of the resistance structure. The electric arc appears when the electrodes are near the metal mass. To close the circuit, the electric arc must to appear at least between two electrodes and the metal mass. Usually the distance between the electrode and the metal mass is 5-15 cm. The resulted current is initially very high and is the duty of the control system to move the electrode such that the current is brought in normal limits. If the length of an electric arc gets over a certain value, the electric arc extinguishes. In this case, the positioning system must reposition in the correct form the electrode so that the electric arc reappears. Another example is the boiling phenomenon of the metal mass, which leads to a variable length of the electric arc. The realization of a competitive control system is very important because it led to reduction of the energy consumption, pollution, and increases the safety of the process. For example, Siemens realized an application that uses neuronal networks for the optimization of the control system of the electrodes movement. Also, there are researches regarding the use of the fuzzy-neural network (Hong et al. 2006) or adaptive control. Modeling the phenomenon that takes place in an EAF is very difficult to realize (Boulet et al. 2003). Close to the hydraulic and electrical subsystem, modeling can take into account the dynamic models of the chemical and thermal processes as well as optimization problems.

2. THE ELECTRODE POSITIONING SYSTEM

To obtain an efficient control system, it is very important to understand the mechanics of the hydraulic system that positions the electrodes. A usual model is presented in (Billings, 1981); in this model, the electrode dynamics is modeled as a combination of a mass, a spring and a damper. Thus, the dynamics of the electrodes are represented by a damped second order system:

m[??] = F + d[??] + kx - mg (1)

In this equation, x represents the electrode position, F is the hydraulics force, d and k stand for the damper and spring constants, m is the electrode mass and g is the acceleration of gravity. Notice that the electrode mass changes, as electrode materials are consumed during the steel-melting process. Due to the considerable weight of the electrodes, moving them upwards requires a much bigger force than in the opposite direction. As a consequence, when designing an electrode positioning controller, different gains should be used.

In (Hauksdottir et al. 1995) a simple second-order model of the electrode positioning system is given by the following transfer function:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where K is the gain factor, t is a time constant and the exponential captures a delay of [T.sub.d] seconds. The parameters of the electrode positioning transfer function were estimated using measurements in closed loop.

3. A MODEL BASED PREDICTIVE ALGORITHM

The previous sections indicates the fact that the modeling of the process in an electrical arc furnace it is difficult to be realized and exists more aspects that cannot be sufficient known. During furnace operation, the characteristics of the bath change as the solid scrap melts into liquid steel, until metal pool. This leads to large changes in the charge conductance; it is possible to consider this variation as a disturbance to the process. But the main disturbances to the process are due to scrap movements, mainly in the beginning of the melt-down, when it not exists a liquid bath. As a result, some times the scrap touches the electrodes, which cause short circuits. Another problem is the strong coupling effect between the electrodes. This means that when the position of one electrode is changed, the currents in the others also changes. As a consequence of the parameter variations of the process as well as the fact that the process's model can present many unknowns, it is justified the usage of the adaptive control (Balan, 2001). In what it follows, it will be made the assumption that each associated subsystem to the three electrodes may be approximate by a linear parametric model with unknown parameters that follows to be on-line identified. In fig. 1 it is presented the bloc scheme of the proposed control system. Used notations: [MBPC.sub.k], k=1..3--model based predictive control algorithm; Modelk, k=1..3--sub-process model of electrode positioning k; HPk, k=1..3- k hydraulic subsystems; [x.sub.1]..[x.sub.3]--positions of the three electrodes; [I.sub.1p]..[I.sub.3p]--setpoint values of the currents on the three branches; [I.sub.1]..[I.sub.3]--electrical currents on the three branches; [u.sub.1]..[u.sub.3]--command signals of the hydraulic actuators;

[FIGURE 1 OMITTED]

It is used a linear model of the form:

Y(t) + [a.sub.1]y(t - 1) + ... [a.sub.n]y(t - n) = [b.sub.1]u(t - 1 - d) + ... + [b.sub.m]u(t - m - d) (3)

where y[.] is the output signal (electrical current), u[.] is the control signal (command signal of the hydraulic actuators), n, m define the model dimension, d is dead time, [a.sub.i], [b.sub.i] are process's model parameters. Identification may be realized by example by using the recursive least square algorithm.

4. SIMULATION EXAMPLE

Based on what was previously shown, it was realized an application that permits simulation and testing the identification algorithms and control. Application permits:

--choosing the type of the algorithm (On-Off, PID, adaptive-predictive) used for controlling the position of each electrode and choosing some parameters of the control algorithms;

--choosing the process parameters: order ([n.sub.p], [m.sub.p], [d.sub.p]) of the hydraulic system, the characteristics of the electric system ([r.sub.0], [r.sub.4], [k.sub.1], [k.sub.2], [k.sub.3] from fig. 8), volumetric efficiency of EAF;

--choosing the order of the model and some parameters of the identification algorithm (forgetting factor etc.);

--include perturbations: interrupt arc, scrap break down, random length of the arc, noise on current measure etc. The user can modify during the simulation most of the control algorithm parameters and of identification, the process characteristics; it can be chosen different algorithms of control for the three electrodes.

In fig. 2...4 is presented an example of evolution of the outputs (electrical current) of the control signal as well as the window for animation of the EAF process. It was used adaptive model based predictive control. It was noted 1, 2, 3 the corresponding electrodes signals 1, 2, 3.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

5. CONCLUSIONS

In this paper were presented some aspects concerning the modeling and adaptive control of the position of the electrodes in an electrical arc furnace. The realized application (last reference) permits testing the control algorithms, study of the error effects on modeling, simulation of perturbations etc. For facilitating the practical implementation, application can be developed by extend of the possibility of choosing the component subsystems, using the multiple models, optimization strategies.

6. REFERENCES

Boulet, G. Lalli, M. Ajersch (2003). "Modeling and Control of an Electric Arc Furnace", Proceedings of the American Control Conference, Denver, Colorado, pp 3060..3064

Billings, S.A. (1981). "Modeling and identification of a three-phase electric arc furnace", chapter 3, pp. 63-80. IEE, Institution of Electrical Engineers, London and New York

Hauksdottir, A.S., T. Soderstrom, Y.P. Thorfinnson, and A. Gestsson, (1995). "System identification of a three-phase submerged arc furnace". IEEE Transaction on Control System Technology, 3:4, pp. 377-387

Hong, Z., Sheng, Y., Li, J., Kasuga,M., Zhao, L., (2006) "Development of AC Electric Arc-Furnace Control System Based on Fuzzy Neural Network", International Conference on Mechatronics and Automation, ICMA06, Luoyang, China, 25-28 june.

Balan R., "Adaptive control systems applied to technological processes", Ph.D. Thesis 2001, Technical University of Cluj-Napoca, Romania. Available from: http://zeus.east.utcluj.ro/mec/mmfm/download.htm, Accessed : 29.05.2007