1 THE DYNAMIC RESPONSE OF A SUBMERGED ...

THE DYNAMIC RESPONSE OF A SUBMERGED-ARC FURNACE TO ELECTRODE MOVEMENT M. A. Reuter, M. Oosthuizen, I. J. Barker , M. S. Rennie and A. de Waal Mintek, Private Bag X3015, Randburg 2125, South Africa

Abstract: The three electrodes in a furnace are inter-dependent electrically and they thus form an interactive multivariable system. The a.c. conduction is also nonlinear due to arcing. However, the evidence shows that an assumption of resistive conduction is adequate insofar as it allows the system to be decoupled. The dynamic response to electrode movement can then be described in terms of resistance changes, and can be divided into short-term and long-term effects. This paper presents some results of electrode perturbation tests on various furnaces. The mechanisms causing the two effects appear to be different, and both are subject to considerable variations. Indeed, it is difficult to study such systems scientifically because of variability, and this suggests that alternative methods such as neural nets, as applied in Mintek’s intelligent furnace controller, are more appropriate. The presented results also have some interesting implications in connection with Westly’s formula. Keywords: System identification, Dynamic behaviour, Neural nets, Noise, Arc resistance, Multivariable systems, Ferro-alloys. 1. INTRODUCTION Most submerged-arc furnaces are provided with one or more forms of electrode control, and yet our understanding of how the furnace responds to electrode movement is still very rudimentary. The system is difficult to analyse because it is non-linear, the form, magnitude, and timing of its dynamics vary with time, it is subject to considerable noise and disturbances, it is a multivariable problem, it depends on the metallurgy of the furnace, and there are limitations on the extent to which the electrical system can be driven, or be allowed to drift. Due to the above points the system has proved to be a very difficult one on which to do any conclusive experimental tests to prove or disprove a conjecture. It is the purpose of this paper to try to document what is known about this system, even if this knowledge is not particularly complete. This paper will also try to quantify the effects. It is not the purpose of this paper to discuss the control per se of this system. There are two possible approaches that can be considered for analysis of the problem, viz. a mechanistic modelling approach, and an empirical “black box” approach (e.g. Reuter, 1994). This paper will take mainly an empirical approach by reporting general principles and trends that can be observed. Some of the mechanisms involved will also be discussed, but will not be analysed in much detail. There are many concepts and theories in the industry about what occurs within the burden of the furnace, but because of the difficulty in studying the insides of a furnace while it is running, it is hard to distinguish scientific fact from popular myth.

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It seems reasonable to compare a submerged-arc furnace with an open-arc furnace in terms of electrode behaviour. For example, Billings (1979) reported on the dynamic behaviour of open-arc furnaces. Although the electrical circuits are similar, the processes that occur inside the furnaces are different. In an open-arc furnace the arc itself is very fast in responding, the hoist movement is relatively fast and continuous, and the dynamics to be considered are primarily the mechanical dynamics of the hoist. In the submerged-arc furnace the electrodes are moved slowly and intermittently, and the molten crater that forms within the burden is the source of the dynamics. Several studies have been reported on the chemical processes that take place in the furnace. The Pyrosim software package from Mintek (see Jones, 1994) and a variety of other software (Bale and Erickson, 1992) are particularly appropriate in this regard. Most of the studies reported have been done assuming equilibrium conditions, which is often not the case in furnaces, and have almost never been integrated with an electrical study, so their use at present for understanding the movement of electrodes is rather limited. Recently, researchers associated with the Elkem company (see for example Halvorsen et al, 1992, and Valderhaug, 1992) have published very enlightening studies of the silicon/ferrosilicon process which include the dynamics of the process. Schäfer (1984) has reported on the electrical conduction in the silicon/ferrosilicon process. Rennie (1979 and 1984) reported on the use of perturbation tests on the electrodes of submerged-arc furnaces to identify the furnace. He also attempted to tie the results of plant tests to a model of the reaction zone in the furnace. The approach was essentially a steady-state one, but was the first attempt to quantify the effects, and to make use of such tests in the metallurgical operation of the furnace. 2. SUBMERGED-ARC FURNACES Submerged-arc smelting furnaces are commonly used for the production of ferro-alloys, calcium carbide, silicon, and similar products. In the typical configuration (Fig. 1), there is a refractory-lined hearth in which three electrodes are suspended. The hearth is kept filled with raw materials, and the conduction of current in the region of the electrode tips heats up the materials and creates molten craters beneath the surface of this burden. Reactions then take place in and around these craters. The molten products are removed intermittently by tapping the furnace, while the off-gas permeates up through the burden. The three electrodes are commonly arranged in a triangle, and are fed from a three-phase alternating current (a.c.) supply. Electrode voltages are low and currents are high, typically around 100 to 300 volts and 50 to 150 kiloamperes, so that resistances are of the order of 0.5 to 5 m . Each electrode is mounted on a hoist, which enables the electrode to be moved up and down over a distance of a metre or so within a minute or two.

Fig. 1 A submerged-arc furnace In most cases the raw materials are metal-oxide ores and carbon, with minor amounts of fluxing agents. There are two broad categories of process: the “dry” process in which there is very little slag formed, and the “wet”

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process in which there is a pool of molten slag in the crater region. Silicon and ferro-silicon are dry processes, while most of the other processes are wet.

Fig. 2 Three-phase circuit of an arc furnace 3. THE ELECTRICAL CIRCUIT The electrical conduction takes place from around the tip of the electrode, through the crater region where the power dissipation is intense, to a pool of product around the base of the hearth that links the three craters electrically. The circuit is thus a star, with the pool in the hearth as the star point, and each electrode as an arm (also called a phase) on the star. It is convenient to start by regarding the power-dissipating element in each electrode as a resistor (although in reality it is more complicated than this - see below). In addition, the magnetic fields around the high-current conductors create an inductive reactance in each electrode circuit. The equivalent circuit is thus as shown in Fig. 2. In this circuit the reactances tend to remain relatively constant, but the resistances vary significantly. 3.1 The interaction effect. When an electrode is raised, the resistance in that phase will be seen to increase, and when it is lowered the resistance will decrease. The star point in the circuit is not connected to the power supply, so its voltage is free to float according to requirements of the circuit. The result is that when the resistance in one of the phases is varied by moving that electrode, the star-point voltage changes and the currents in all three phases get affected. This is known as the interaction effect (see Barker et al., 1991). Furthermore, the three electrode currents are all affected differently. A specific example of this effect is shown in Table 1. If the electrode currents are then used to control the electrode hoists, one then has a typical interactive multivariable control problem. The skewness of this effect is worse with a lower power factor, and this is the source of major problems on many furnaces, particularly large ones. Table 1 Example of the interaction effects. Note how all three currents are affected when only one electrode is moved. (Calculated from the ciruit with a delta voltage of 300V, and reactances of 1.3 m ) R1 (m )

R2 (m )

R3 (m )

I1 (kA)

I2 (kA)

I3 (kA)

Balanced furnace

1.2

1.2

1.2

98

98

98

Raise electrode 3

1.2

1.2

2.0

100

87

80

Difference (%)

0 0

0 0

0.8 (+67)

2 (+2)

11 (-11)

18 (-18)

One way to avoid the interaction effect would be to use resistance-based control, or something equivalent such as impedance-based control, because this decouples the phases so that they can be controlled individually. The problem is that the voltage of the star point cannot be measured accurately because of voltages induced in the measurement lines by the magnetic fields associated with the high currents in the nearby conductors. The errors in the resulting resistances are at best about 10 to 30 percent. This makes such direct measurements useless for control. The patented Minstral controller developed by Mintek (see Anon, 1991) makes use of a different

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measurement system which avoids a connection to the hearth and thereby provides values of the resistances which are much more accurate. With this equipment it is possible to study the electrical behaviour in a furnace, and this was used extensively in this study. 3.2 Nature of the power-dissipating element. If the power-dissipating element were a pure resistor then the normal linear ac circuit analysis could be done. In particular, the movement of an electrode would result simply in the resistance in that phase changing, and the changes in the currents and powers would then follow directly from the ac circuit equations. Furthermore, the power dissipation in phase i would then be given by:

Pi

Ii

2

Ri .

Note specifically that the power depends on the square of the current, for the case of the pure resistor. An arc can have a variety of characteristics, but for analysis purposes it is convenient to start with the assumption that the arc is simply a constant-voltage device (see Barker, 1980), characterised by the arc voltage, Va . In this case, the movement of an electrode would result in a change to the arc voltage in that phase. The interactions produced in the currents and powers can still be calculated (although not as easily), but they are not the same as those produced in the pure-resistive case, although the general skewed effect is similar. Also, the power dissipation in phase i would then be given by:

Pi

I i Vai

Note specifically that the power is now proportional to the current, and not to its square. Westly (1974 and 1975) studied a large number of furnace installations around the world, and concluded that the equation that relates power to current most generally is given by:

C3

I el / PT

2/ 3

where: PT is the total furnace power in MW,

I el is the electrode current in kA, and, C3 is a constant called the Westly “C3” factor. This Westly equation can be rewritten as:

PT

I el1.5

This index of 1.5 seems to suggest that the power-dissipating element may be a combination of arc and resistive heating. However, the actual situation is again more complicated than this, as explained below. Because arcs are non-linear, they also generate harmonics in an ac circuit. Significant harmonic analysis can be performed on any submerged-arc furnace. Sometimes it is even possible to see the distortions on an oscilloscope trace of the waveforms. Other effects, such as an apparent increase in the reactance of the circuit (see Barker 1980), can also be observed. All of this indicates that arcing does indeed occur in submerged-arc furnaces. 4. MOVEMENT OF AN ELECTRODE In the dry processes, there is a cavity directly beneath the electrode in which there is an arc, and this is where most of the power is dissipated. This cavity is very hot and is a necessary part of the metallurgical process. Over short time periods, small movements of the electrode do little more than shorten or lengthen this arc. Electrode movements may also dislodge some raw materials so that they fall down into the hot crater and cool it and subsequently alter the resistance. In the wet processes, there is a region of molten slag and carbon beneath the electrode. Carbon has a lower density than most slags so it tends to float towards the top of this region, generally termed the “carbon bed” in the furnace. Electrically, carbon is very conductive, while slag has a relatively high resistivity. There may also be 4

some arcing that takes place between the particles of carbon or between the carbon bed and the electrode. Movement of the electrode over short time periods must thus displace or replace the arc, or the carbon bed, or the slag layer, or some combination of these. The magnitudes of the consequent changes in resistance would depend upon what the mechanism of displacement is. In both the wet and the dry processes, the long-term effect of electrode movement must be to move the location of the hot crater in the furnace upwards or downwards. This would be part of the expansion, contraction, and general movement of the crater. As the boundaries of the crater move, so some of the material that was molten freezes up, while either new material or previously-frozen material melts in. This crater movement is also affected by the tapping of the furnace, when part of the molten material gets drained out of the crater. In some cases, there are small individual craters around each electrode that barely communicate with each other, while in other cases there is one large crater that virtually fills the entire hearth (see Kelly, 1958). This slow movement of a crater would affect its electrical conduction over periods of the order of several minutes to several hours, but again these mechanisms are not well studied or quantified. Fig. 3 shows the result of a step test on a ferrosilicon furnace. Note that, in this case, the movement of electrode 2 results in a change in the resistance of that same electrode, but has no effect on the resistances of the other two electrodes. In other words, this supports the pure-resistor theory of power dissipation. There are also no obvious dynamic transients. Note also that all three currents are affected, which demonstrates the interaction effect, and shows graphically why current is a poor variable by which to control the hoist. 1.2

0.8

0.6

0.4

Resistance elec. 1

0.2

electrode 2 moves up

Resistance elec. 2 Resistance elec. 3

time

5

11:50:48

11:50:12

11:49:36

11:49:00

11:48:24

11:47:48

11:47:12

11:46:36

11:46:00

11:45:24

11:44:48

11:44:12

11:43:36

11:43:00

11:42:24

11:41:48

11:41:12

11:40:36

11:40:00

11:39:24

11:38:48

11:38:12

11:37:36

11:37:00

11:36:24

11:35:48

11:35:12

11:34:36

0 11:34:00

resistance (milli ohm)

1

120 115 110

current (kA)

105 100 95 90 85 80

Current elec. 1 Current elec. 2

electrode 2 moves up

75

Current elec. 3 11:50:48

11:50:12

11:49:36

11:49:00

11:48:24

11:47:48

11:47:12

11:46:36

11:46:00

11:45:24

11:44:48

11:44:12

11:43:36

11:43:00

11:42:24

11:41:48

11:41:12

11:40:36

11:40:00

11:39:24

11:38:48

11:38:12

11:37:36

11:37:00

11:36:24

11:35:48

11:35:12

11:34:36

11:34:00

70

time

Fig. 3 Step test on an electrode in a FeSi furnace. The movement of electrode 3 affects the resistance for this electrode only, but all three currents are affected. The step-like appearance of the graphs are due to the logging system. The noise on the signals is typical and unavoidable. Fig. 4 shows another similar test on the same furnace. Note in this case that the movement of electrode 3 has an effect on both electrode 3 and electrode 2. The effect on resistance in the same phase is much the same as before, but the effect on resistance 2 is only transient. Fig. 5 shows yet another test; this time the transient interaction is on the leading phase, unlike that in Fig. 3. One can only presume that this transient type of interaction is not an electrical phenomenon but a physical or metallurgical one, perhaps caused by material being physically pushed from one reaction crater into another.

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1.6 1.5 1.4

resistance (milli ohm)

1.3 1.2 1.1 1 0.9 0.8

Resistance elec. 1 Resistance elec. 2

0.7

Resistance elec. 3

electrode 3 moves up

12:19:36

12:19:00

12:18:24

12:17:48

12:17:12

12:16:36

12:16:00

12:15:24

12:14:48

12:14:12

12:13:36

12:13:00

12:12:24

12:11:48

12:11:12

12:10:36

12:10:00

12:09:24

12:08:48

12:08:12

12:07:36

12:07:00

12:06:24

12:05:48

12:05:12

12:04:36

0.6

time

Fig. 4 Movement of electrode 3 affects the resistances of both electrodes 2 and 3 1.6

1.4

resistance (milli ohm)

1.2

1

0.8

0.6

0.4 Resistance elec. 1 Resistance elec. 2

0.2

Resistance elec. 3

electrode 1 moves up

12:04:18

12:03:42

12:03:06

12:02:30

12:01:54

12:01:18

12:00:42

12:00:06

11:59:30

11:58:54

11:58:18

11:57:42

11:57:06

11:56:30

11:55:54

11:55:18

11:54:42

11:54:06

11:53:30

11:52:54

11:52:18

11:51:42

11:51:06

0

time

Fig. 5 Movement of electrode 1 affects the resistance of both electrodes 1 and 2 Fig. 6 shows the results of a step test on a ferromanganese furnace. Here it should be noted that there is a detectable transient in the form of a settling back after the initial step response. This type of response seems to be fairly typical of the wet type of process. The magnitudes and the time duration of such transients vary widely, even on the same electrode in the same furnace. Typically, they seem to have time constants of about 10 to 40 7

minutes, and the relative amount of settling back varies from nothing (as in the ferrosilicon examples above) to about 80 % of the initial jump. The initial jump is probably caused by displacement/replacement effects around the tip of the electrode, while the longer term changes are probably associated with overall movement of the crater. A suitable transfer function for this type of response is a lead-lag element as given in the next column. This transfer function can also be trivially applied to the dynamic-less response in the ferrosilicon furnace.

G ( s)

K

1

s 1

2

s 1

where: 2 1

K

is approximately 10 to 40 minutes is approximately 1.0 to 5.0 times 2 can vary considerably, but is of the order of 2 to 10 m /m.

Fig. 6 Change of resistance in an ferromanganese furnace In Figs. 3 to 6 the resistances were determined by the Minstral system, which bases its calculations on the assumption of pure-resistive heating. Apart from the occasional transient interaction, good decoupling was obtained between movements of the individual electrodes as inputs, and the resulting changes in the resistances as outputs. This same decoupling can also be seen on an operating furnace whenever one deliberately moves an electrode under manual control. This shows that the assumption of pure resistance and no arc is reasonable for doing circuit calculations, even though the ferrosilicon process is known to dissipate power primarily through an arc. Furthermore, the authors (and others) have observed this extent of decoupling of the resistances on every plant that they have studied, irrespective of the type of process. This fact, that the behaviour of the conduction closely follows the pure-resistive law when the electrode is moved, is apparently contrary to Westly’s equation, and to the observed evidence of arcing. Possibly, the difference is that the immediate response to electrode movement is close to being of the nature of a simple change in resistance (even when there is a bit of arcing), while in the longer term this change causes the craters to change in size, shape, or location, thereby affecting the cell constant of the conductive path through the crater (Westly’s equation after all applies to average furnace behaviour, which is probably close to the steady-state behaviour). If so, then the apparent similarity of Westly’s formula to a combination of the formulas for arc and resistive heating is misleading, and the actual reason for Westly’s index of 1.5 is the combination of resistive conduction with a changing crater size. If so, there are significant and useful metallurgical implications. However, the evidence is still too tenuous to draw any firm conclusions. 4.1 Noise and disturbances on the resistance signal The disturbances that have been observed can be divided into the following four categories: There is a cyclical variation that follows the tapping cycle of the furnace. Some plants tap continuously; most, however, start and stop with a repetition period of about 1 to 4 hours. There are random fluctuations that could loosely be described as “white” or “pink” noise. Sudden unexpected step discontinuities that are over within a few seconds. There is usually a slow drift, over a range of time periods.

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The magnitueds of these fluctuations are a function of the metallurgy. 5. DISCUSSION All furnaces exhibit fluctuations to a greater or lesser extent. The “trade off” in doing control is in setting the furnace electrically and in particular balancing it as much as possible, against not moving the electrodes excessively and so disturbing the metallurgy. The problem of controlling on electrode current, with its consequence of the interaction effect, against the problem of controlling on resistance, with its measurement inaccuracies, still haunts most furnaces. This dilemma can be overcome with a Minstral type of controller, but as yet not many furnaces make use thereof. This dilemma is fundamental and has to be resolved before any more sophisticated forms of control can be contemplated. On top of the electrode regulation problem, there is still a problem with the choice of electrical operating point, and the interaction of this with the metallurgy of the furnace. Some progress in the modelling of this scenario has been made by relating the electrical to metallurgical aspects using neural nets (Reuter et al., 1995). Because the operator cannot see inside the furnace, he cannot easily determine tell where the tips of the electrodes are riding within the burden. He has difficulty in particular in distinguishing between a short electrode that is riding high in the furnace, and an under-carboned situation in the mix, because both tend to cause high resistances with the result that the electrode moves down and its hoist then sits on bottom stops. There are other indications of where the electrode tips are riding, and of the carbon balance, but these indications are fuzzy in nature and are not particularly reliable in the short term. This suggests that an artificial-intelligence approach, such as fuzzy control or an expert system, would be more suited to this part of the control system, and indeed such approaches are being developed (see Reuter et al., 1995). 6. CONCLUSIONS There is no single “perfect” model to describe the effects of electrode movement in submerged-arc furnaces. Some of the factors that play a part producing these effects have been discussed, as well as some of the implications. The approach is still very empirical. This suggests that the use of neural nets might be a way to proceed (Reuter et al., 1995). The apparent dichotomy between Westly’s formula for the conduction and the behaviour observed during step tests. Some of the implications have been discussed. More broadly, there is a long-standing need to get a better understanding of the processes that take place within the reaction zone of the furnace. These mechanisms need to be dynamic, and they need to interrelate the electrical and metallurgical sides of the furnace operation. REFERENCES Anon. (1991). Minstral series 4 electrical control system for submerged-arc furnaces. Brochure published by Mintek, Randburg, South Africa. Barker, I.J. (1980). Arcing in the electrical circuit of a submerged-arc furnace. Elektrowärme International 38 No B1/80, pp B28-B32. Barker, I.J., A. de Waal, M.S. Rennie and J. Klopper. (1991). The interaction effect in submerged-arc furnaces. In: 49th Electric Furnace Conference Proceedings pp305-310. Iron and Steel Society, Warrendale, USA. Billings, S.A., F.M. Boland, H. Nicholson (1979). Electric arc furnace modelling and control. Automatica 15, pp137-148. Bale, C.W. and G. Erickson (1990). Metallurgical thermochemical databases - a review. Can. met. Q. 29(2), pp. 105-132. Halvorsen, S.A., A. Schei, J.H. Downing (1992). A unidimensional dynamic model for the ferrosilicon process. In: 50th Electric Furnace Conference Proceedings pp 45-59. Iron and Steel Society, Warrendale, USA.

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Jones, R.T. (1987). Computer simulation of pyrometallurgical processes. In: Apcom 87, Vol.2, Metallurgy, pp. . S. Afr. Inst. Mining and Metall. and Mintek, Johannesburg. Kelly, W.M. (1958). Design and construction of the submerged arc furnace. Carbon and Graphite News, 5 (April/May). Union Carbide Corporation, New York, USA. Rennie, M.S. (1984). The operation, control, and design of submerged-arc ferroalloy furnaces. In: Proc. Mintek 50, pp. 777-785. The Council for Mineral Technology, Randburg, South Africa. Rennie, M.S. (1979). The application of on-line data and the development of models relating to the production of charge chrome. In: Proc. of the 37th Electric Furnace Conference pp. 202-209. Iron and Steel Society, Warrendale, USA. Reuter, M.A. (1994). Hybrid neural net modelling in metallurgy. Proceedings of the 2nd International Symposium on Metallurgical Processes for the Year 2000 and Beyond, Ed. H.Y. Sohn, Volume 1, pp. 907-927, TMS, Warrendale, USA. Reuter, M.A., C. Pretorius, J. Klopper, M.S. Rennie, and I.J. Barker (1995). An intelligent control system for submerged-arc furnaces. To be presented at the 7th Infacon, Trondheim, Norway, June 1995. Schäfer, J. (1984). Über die Leistungsumsetzung im Reduktionsofen bei der Herstellung von Silizium. Dr. Ing. Dissertation, Engineering Faculty, University of Hannover. Hannover, Germany. Valderhaug, A.M. (1992). Modelling and control of submerged-arc ferrosilicon furnaces. Dr. ing. thesis, Dept. of Engng Cybernetics, The Norwegian Inst. of Technology. Published as report 92-81-W. Trondheim, Norway. Westly, J. (1975). Critical parameters in design and operation of submerged arc furnaces. In: Proc. 33rd Electric Furnace Conference pp 47-53. Iron and Steel Society, Warrendale, USA. Westly, J. (1974). Resistance and heat distribution in a submerged arc furnace. Proc. of the First International Ferro-Alloys Congress pp 121-127. S. Afr. Inst. Mining and Metallurgy, Johannesburg, South Africa.

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