WO2006089315A1

WO2006089315A1 - Arc furnace control

Info

Publication number: WO2006089315A1
Application number: PCT/ZA2006/000024
Authority: WO
Inventors: Ian James Barker
Original assignee: Mintek
Priority date: 2005-02-20
Filing date: 2006-02-14
Publication date: 2006-08-24
Also published as: ZA200705345B

Abstract

An arc furnace control method wherein a recursive estimator is used to estimate, in real time, parameters of an equivalent electrical circuit of the furnace and the estimated parameters are used to control operation of the circuit.

Description

ARC FURNACE CONTROL

BACKGROUND QF THE INVENTION

[0001] This invention relates to the operation and control of an arc furnace.

[0002] As used herein the expression "arc furnace" covers: (a) open-arc furnaces where the arc is partly or totally exposed, e.g in steel scrap melting;

(b) submerged-arc furnaces where a tip of an electrode is submerged in a burden of feed materials, e.g. in ferro-alloy smelting.

[0003] In the following description, reference is made to a 3-electrode furnace wherein each electrode is connected to a respective phase of a 3-phase alternating current (a.c.) supply. This, however, is only by way of a non-limiting example for the principles of the invention can be applied to a furnace with a different number of electrodes eg. a furnace with 6 in-line electrodes, or a furnace with 3 main electrodes and a fourth, smaller, stinger electrode unit to open a taphole in a furnace.

[0004] In order to control an arc furnace effectively it must be possible to control the electrical circuit, and the metallurgy of the furnace.

Electrical Control

[0005] An arc furnace requires instrumentation for monitoring its electrical circuit and for controlling its electrodes. Problems are however associated with the measurement of circuit parameters of an arc furnace. Direct measurement, which requires a connection to the hearth of the furnace, is troublesome and is prone to errors of up to about 3θ'%. Without a hearth connection there is however a problem with a lack of observability. U.S. patent No. 4296269 describes concepts, some of which have been embodied in a controller which is known commercially as a Minstral controller, which does not require a hearth connection and which overcomes this problem by using an assumption about the reactances, generically termed the

"equal-reactance assumption".

[0006] When the reactances are inter-related in the manner described in the aforementioned patent, they constitute 1 unknown instead of 3 (in a 3-electrode furnace). The reactances do not necessarily have to be exactly equal to achieve this for they could be offset from one another, or be in fixed ratios to one another, by predetermined amounts. The controller is then able to produce a value for each of the 3 resistances and one value characterising the reactances. The values of the resistances determined in this way are significantly more accurate and reliable than those measured directly, and are therefore very useful in the operation of the furnace. In practice the reactances do however vary slightly, and do not exactly follow whatever assumption is made, but it appears that the resulting errors in the values of the calculated resistances are small in comparison with directly measured values. Similar considerations would apply in a furnace with more than 3 electrodes.

[0007] One disadvantage with the Minstral controller is that it cannot distinguish between the three reactances in a furnace, because of the basic assumption that these reactances are inter-related. These reactances are caused primarily by the inductance from the magnetic field around the conductors in association with the a.c. circuit, but there is also a small pseudo-reactance that is caused by the non-linear behaviour of any arcs in the circuit. There could potentially be advantages if the pure magnetic inductance (i.e. excluding any contributions from arcs) could be measured individually for each electrode, as this would provide useful information for the operation of the furnace, such as an estimation of electrode lengths. Any deviations in these magnetic inductances would not be large (e.g. a variation of up to about 0.1 milli-ohm in about 1.2 milli-ohm), which is why the effect of this on the Minstral controller's estimation of the resistances is not major.

[0008] It is desirable to distinguish between the power dissipated by arcing and the power dissipated by resistive heating, to provide information on the metallurgy of the furnace, and to quantify the amount of pseudo-reactance caused by the arcing, thereby enabling a more accurate controller calculation to be done. Because the distinction between these two modes of power dissipation depends on distortion of the sinusoidal waveform, it requires some form of high-speed data acquisition to detect it.

[0009] The magnetic inductance associated with any one electrode will increase if the electrode grows longer. It has been observed that the reactance will change by, very roughly, about 0.10 to 0.13 milli-ohm for every metre that the electrode length changes. If the equal-reactance assumption is used on a furnace where the electrode lengths are significantly unbalanced, then any differences between the reactances will reflect as similar errors in the calculated resistances. Hence if the typical resistances are, say, 1.0 milli-ohm, and if one of the electrodes is, say, 1.0

metre shorter than the others, then errors of the order of 10% in the calculated resistances are likely to arise. While such differences in the electrode lengths are possible, they are not common, and so under normal operation the errors in the calculated resistances are typically ± 3% to 5%. [0010] The pseudo-reactance caused by the non-linear behaviour of the arc may also create an imbalance in the reactances and so affect the accuracy of the resistance calculation. In a fairly large submerged-arc furnace, with a power factor of about 0.8, the pseudo-reactance is typically about 5% of the total reactance. At this level, variations in the pseudo-reactance do not affect the resistance calculations in the Minstral controller significantly. This fraction of the total reactance rises however with an increasing power factor and with the extent of arcing, and hence a problem may arise under certain unfavourable circumstances.

[0011] To the applicant's knowledge it is currently not possible to distinguish between the inductances associated with each electrode, and to quantify the amount of pseudo-reactance due to arcing.

Metallurgy Control

[0012] The control of the electrical circuit is only part of the control problem of a submerged-arc ferro-alloy furnace. The other major part is the control of the metallurgy, and in particular the control of the carbon balance.

[0013] When ferro-alloys are made in a submerged-arc furnace, the reaction is usually the reduction of a metal oxide ore by carbon. The electricity flowing through the reaction zone provides the chemical heat required for the reaction. The raw materials are normally a mixture of ores and a carbonaceous reducing agent, optionally with a small quantity of fluxes to get the slag melting temperatures correct.

When this mixture enters the reaction zone, the ores and fluxes melt, while the carbonaceous reducing agent remains as solid particles. [0014] The carbon particles react relatively slowly with the metal oxide ore, in a fixed stoichiometric ratio. If there is an excess of carbon in the feed materials, then carbon will tend to accumulate in the reaction zone of the furnace. Electrically, this carbon is significantly more conductive than the other material in the reaction zone, and the accumulated carbon lowers the electrical conductivity of the reaction zone. If the electrodes are being controlled on resistance, then the controllers need to raise the electrodes in order to keep the overall resistance constant. This affects the mode of power dissipation in the reaction zone and the metallurgy. Thus, for the metallurgical reactions, there is an optimum in terms of the amount of carbon in the reaction zone, and any amount greater or less than this will degrade the performance of the process. Changes in the inventory of carbon in the conduction path also affect the relative amount of arcing in the furnace, and so a measure of the amount of arcing can fairly quickly provide useful information about the state of the metallurgy.

[0015] The electrode length affects the magnetic field around the electrode, and hence the inductance associated with that electrode. Therefore, the measurement of the individual inductances should provide some indication of the lengths of the individual electrodes.

[0016] All arc furnaces need to slip fresh segments of electrodes regularly through the electrode clamps to make up for wear off the tip, and to control this properly requires some indication of the length of each electrode. With a submerged-arc furnace the tip is buried in the burden in the furnace and hence the electrode length is difficult to measure. Furthermore, most submerged-arc furnaces use self-baking electrodes, also called Søderberg electrodes, which must be slipped in a controlled way regularly, in small amounts, and not irregularly in large and erratic jumps. Sometimes an operator of a furnace will burn down the burden, pull the electrodes up to top stops, and physically measure their lengths. Thereafter, the operator tries to calculate or estimate the rate of wear off the tip, and then balance this against the rate of slipping, but the accuracy of this deteriorates with time. Otherwise there is no option but to monitor conditions around the furnace and try to adjust the slipping accordingly. If the furnace electrodes are not properly controlled on resistance, one electrode can end up considerably shorter or longer than anticipated. This will upset the metallurgy of the furnace, and can lead to the production of significant amounts of off-grade product material that has a lower market value.

[0017] Hence the availability of a measure of the inductance associated with each electrode could be a very useful indication of the length of the electrode, and could possibly be used in the control of the slipping of the electrodes.

Prior Art

[0018] US patent No. 6058134 to Toivonen describes a technique for finding circuit parameters in an arc furnace by solving various sets of equations that are derived for real power, reactive power and total power at various frequencies including the fundamental frequency. Toivonen's technique is based on a frequency-domain approach wherein Fourier transforms are calculated and circuit parameters are then estimated in the frequency domain. Toivonen's technique inter alia depends on the assumption that the inductance is the same at the mains frequency and at the harmonic frequencies. In fact the inductance can be substantially different because of the pseudo-reactive behaviour of a non-linear arc. Toivonen's approach has two further drawbacks. Firstly, it does not address the issues of residual conductivity and the time constant of the arc, parameters which could prove to be useful in monitoring the metallurgy in a furnace. Secondly, it provides a distinction between the power dissipated by arcing and that dissipated by resistive heating on the assumption that the arc voltage is a square wave, which is not necessarily the case.

[0019] The invention is concerned with a method of operating and controlling an arc furnace which at least partly addresses the aforementioned requirements, and the 5 drawbacks associated with existing controlling processes.

SUMMARY OF INVENTION

[0020] The invention provides a method of operating and controlling an arc furnace which has a plurality of electrodes connected to a polyphase power supply by means of at least one power transformer, the method including the steps of recursively ) estimating in real time values of parameters of circuit elements of an equivalent electrical circuit for the arc furnace in operation, and using the estimated parameter values to control at least part of the operation of the arc furnace.

[0021] The recursive estimation can be used to predict parameter values using information selected from the following: voltages applied to electrodes of the 5 furnaces; currents supplied to electrodes of the furnace; differentiated values, with respect to time, of currents supplied to electrodes of the furnaces; and the position of at least one tap changer on the at least one power transformer.

[0022] Preferably the differentiated values are produced by an analogue differentiation process or an equivalent process.

] [0023] Measurements of the currents can be made on the primary or secondary side of the power transformer or at some intermediate point. Similarly measurements of the voltages can be made on the primary or secondary side of the power transformer or at some intermediate point.

[0024] The power transformer may have its primary winding in a star configuration or in a delta configuration.

[0025] The parameters for which the values are predicted may be selected from: resistance of an electrode; inductance of an electrode; arc voltage of an electrode; the time constant of an arc; its residual conductivity; power per electrode; and fraction of the power per electrode that is dissipated in an arc.

[0026] Techniques which are described in the specification of US patent No. 4296269 and adopted for the Minstral controller, may be adopted in whole or in part in the method of the present invention. Calculations which are relied on in this citation require information about the phasors of the secondary currents and voltages. Through the use of the method of the invention these phasors are readily determined by doing a convolution digitally between the waveform of the corresponding variable and a cosine and a sine wave at the fundamental frequency.

This produces the real and imaginary components respectively of the phasor. Although this convolution at the fundamental frequency is similar to taking a Fourier transform it excludes all higher frequencies.

[0027] As the phasor information can be determined from waveforms obtained through the method of the invention, phasor diagrams for the various currents and voltages can be plotted on a suitable display. These diagrams are potentially particularly useful inter alia for setting up and checking a controller which implements the method of the invention. [0028] The estimated parameters can be used in various ways to control the operation of the furnace, for example to control electrode hoists transformer taps and the rate of slipping of each electrode and to adjust the composition or relative proportions of raw materials fed to the furnace particularly the ratio of carbon to reducible ores.

[0029] On a three-electrode furnace with the secondary windings connected in delta, skewed secondary voltages are achieved by using different tap positions on the three phases, a practice which is known as differential tapping. It may be desirable to have skewed secondary voltages if a furnace is not well balanced. Differential tapping may be needed, for example, to lessen the relative amount of the negative-phase-sequence component in the power drawn from the mains, or to boost the current in one of the electrodes where otherwise the current would be particularly low.

[0030] Differential tapping does however create a mismatch in the secondary voltages, and this causes a circulating current to flow in the delta part of the circuit.

This circulating current is undesirable in that it loads the transformers without delivering any currents to the electrodes, and hence the extent of differential tapping is usually relatively small. It is possible though to analyze a differential tapping situation by normal circuit analysis methods and determine what the currents and voltages are in the electrodes. The recursive estimating can then be done on these currents and voltages. Thus it falls within the scope of the invention to use the information produced by the recursive estimation to control the skewed voltages in an appropriate manner eg. to maintain a specific relationship between the voltages, or to take action to correct the skewed voltages. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The invention is further described by way of example with reference to the accompanying drawings in which:

Figure 1 is a schematic representation of apparatus used for implementing the method of the invention;

Figure 2 illustrates an equivalent circuit of an arc furnace used in a time-domain model of the circuit, which forms the basis of the method of the invention;

Figure 3 illustrates a structure of a digital filter for a three-electrode furnace; and

Figure 4 is a block diagram representation of a furnace control arrangement based on the apparatus of the invention cascaded with a Minstral-type controller which is at least partly based on the description in the specification of US patent No. 4296269.

DESCRIPTION OF PREFERRED EMBODIMENT

[0032] In the method of the present invention parameters of circuit elements in an equivalent electrical circuit of an arc furnace are estimated from waveforms of the voltages and currents in the furnace. The parameters typically include the resistance, inductance (or its reactance) and arc-related parameters such as arc voltage, in each limb of the circuit.

[0033] Apparatus 10, which implements the method of the invention, is shown schematically in Figure 1. Analogue signals 12, 14 and 16 which respectively represent a set of currents in the high-power circuit of the furnace, transformer tap positions, and a set of voltages in the high-power circuit of the furnace, are fed through isolating and scaling amplifiers 18 to a unit 20 which contains a multiplexer and an analogue-to-digital converter (ADC). Luu J4j i ne current signals rz are a.c. ana are typically trom U to 5 amps. I hey are normally obtained from the outputs of current transformers (not shown) that are located on the high-power lines. After isolating and scaling, these signals are differentiated with respect to time using analogue devices and the resulting derivatives are also applied to the ADC. This is done to boost the high-frequency end of the spectrum and thereby accentuate the information about the arcing. This aspect is further described hereinafter.

[0035] The tap position signals 14 are direct current (d.c.) and are typically from 4 to 20 milli-amp d.c. The tap position signals may be obtained in a digital form, using any appropriate device, e.g. a computer which may be the computer 26 referred to hereinafter.

[0036] The voltage signals 16 may be 110 volts a.c. They are normally obtained from the outputs of voltage transformers (not shown) that are located on the high- power lines.

[0037] The values given for the signals 12 to 16 are illustrative only and are non- limiting.

[0038] A computer 22 runs a control program which causes the unit 20 to sample the waveforms and to present the sampled values to software in the computer 22. The waveforms thus arrive as a succession of data sets, with each set being in the nature of a snap-shot set of the instantaneous values of each of the analogue signals, at the corresponding observation time. At each such observation time, the software in the computer 22 then converts these current and voltage waveforms into a set of data consisting of the currents flowing through the electrodes, designated /o, /i, and /₂, and the voltages on the electrodes, designated VQ, V-_\ , and vfc. In cases where this conversion requires information about the transformer tap ratios, use may be made of the transformer tap position signals to select the corresponding ratios from a table of such values.

[0039] The estimation of circuit parameters is updated from each successive set of data, shortly after it arrives in the computer 22. As indicated in Figure 1 , these estimates of circuit parameters might, for example, be displayed for operator information 24, be sent through a data link to another computer 26, be logged to a disk file 28 for later use or analysis, or be used directly in the control 30 of the furnace.

[0040] The apparatus 10 is linked through some form of data communications line to a scada type of computer system for logging of real-time data from the plant, as well as for interacting with operators and other users.

[0041] Control signals which come either directly from the apparatus or from the scada system are routed through a programmable logic controller (PLC) or similar device, connected to the controller or scada. These signals are typically timed on/off signals for driving electrode hoists or electrode slippage controls, or analogue signals such as mass set points for a weighing-batching system to control the composition of raw materials fed to the furnace.

[0042] The method of the invention uses a time-domain model of the furnace circuit which is based on the arrangement shown in Figure 2. In this Figure an arc 32, a resistor 34 and an inductance 36 are included in each branch of the star configuration and the phases are respectively numbered 0, 1 and 2. [0043] A model of the arc which is based on multiple parameters as opposed to the single parameter/square wave model relied on by Toivonen, is preferably used in the method of the invention and, in the following example, a version of what is known as Cassie's model of the arc is used in the simulation which is carried out. This model was originally published by Cassie¹ and is well described in Brown². Although it is preferred to make use of Cassie's arc model it is to be understood that this is by way of example only, and that any other satisfactory technique for modelling the arc could be used in the method of the invention.

Circuit equations

[0044] A voltage balance between the top of electrode i and the hearth gives the following equation:

L. — ⁱ' + v,_τr] +R,.i_i = v_i -v_n , i = 0, 1 , 2 .- .. _Λ

¹ dt ^Ara ' ' ' ^B ' ' ' Equation 1

[0045] Equation 1 can be rearranged as follows:

^r = -£(^vι - ^v*ά - ^R\ -'i)- J- ' ' = 0. 1. 2 Equation 2

where v_Ar_ci is the voltage across the arc under electrode i (see Cassie's model), and the other symbols are as defined in Figure 2.

Cassie 's model of the arc: basic equations

[0046] An arc is a non-linear circuit element, whose characteristics vaguely resemble those of a constant-voltage device. The waveform of the voltage on an arc is thus more like a square wave than a sinusoid. An arc model based on a square wave has only one parameter, and that is the magnitude of the wave. A simple square wave was tried for the arc voltage waveform in each phase, but this exhibited a number of undesirable properties, mainly from the numerical integration side. A version of Cassie's model was adopted which requires up to 3 parameters. It has been found that model works well, and that the additional parameters have some meaning in their own right in terms of the metallurgy of the furnace.

[0047] The gases in the column of an arc are ionised, and the conductivity depends on the extent of ionisation. A dynamic energy balance around the ionisation of the arc in electrode i yields the following equation:

-^- = v_Arcι . /, - Zf₁ , . (H, - H₀,) Equation 3

[0048] In equation 3, H_\ is the energy contained in the ionisation. The first term on the right side, vλr_ci-'i, '^s the electrical power being dissipated in the arc. The second term on the right side is a linearisation of the relationship governing the rate of discharge of the arc. The residual energy parameter H_0\ is normally small compared to Hi, and so, to a first approximation, the rate of discharge of the energy is proportional to the energy. k_\\ is a constant of proportionality.

[0049] It is assumed that the electrical conductivity, σ_u of the arc is proportional to the energy in the ionization:

^σi ^{= k}2>-^H\ Equation 4

[0050] Ohm's law is used to inter-relate the voltage, the current and the conductivity

of the arc:

^Arci = 'i/^σi Equation 5

[0051] Equations 3, 4 and 5 are the basic equations of the version of Cassie's model and with equation 2 are solved numerically using standard numerical integration techniques to simulate the evolution of the circuit with time. The implementation of these equations in a computer program forms a software model of the electrical circuit of the arc furnace (referred to hereinafter as the software model 44).

[0052] Using equations 3, 4 and 5 it can be shown at steady state with dHJdt = 0, and if H_0J is small enough, that:

Equation 6

[0053] Equation 6 shows that Cassie's model at steady state and without a residual energy term becomes a constant-voltage device. Thus, in dynamic form, Cassie's model produces a waveform for the arc voltage that looks like a distorted square wave. If an arc voltage parameter, v_Arci, is defined as V(/ci//c2j), then the nominal magnitude of the distorted square wave will be approximately VA_ΓCI-

[0054] Following on from equation 4, a residual conductivity parameter, σ_Oj, is defined as k_%.Ho_\. From tests it appears that the residual conductivity parameter is strongly correlated with the temperature of the material in the reaction zone and in the furnace and that it may have a physical significance related to the metallurgy of the process.

[0055] The parameter Zc_{1 \} can be replaced by 1/TJ, where τ_\ is the time constant for the

discharge of the ionisation in the arc. In concept, this discharge time constant is much like the RC time constant for the discharge of a resistor-capacitor circuit. From results obtained from the recursive estimator this discharge time constant for an arc

is typically about 1 millisecond. Prediction of Parameters of Elements of Arc Furnace Equivalent Circuit

[0056] The recursive estimation is done using a digital filter which is shown in block diagram form in Figure 3. The digital filter includes software which takes the voltage and current waveforms (Vj and i_u where i = 0,1 ,2) and produces estimates of the circuit parameters (resistances, inductances and arc parameters: R₁, L₁, v_Arci_, Ooi and

Tj, where i = 0,1 ,2) that best match the observed behaviour of the waveforms.

Derived parameters such as the power consumed by each electrode, and the fraction of this power for each electrode that is dissipated in its arc, may also be generated simultaneously.

[0057] The digital filter operates in a cyclic fashion in real time, performing one iteration each time a snap-shot set of observations of the waveforms is brought in from the analogue-to-digital converter in the unit 20, as opposed to an estimator that is run in a batch mode. The term "Kalman filter" is also used. An explanation of digital filters can be found in Jazwinksi³ and Bozic⁴.

[0058] The actual power circuit of the furnace is designated by the reference 40 in

Figure 3. The equivalent circuit of this power circuit is the circuit depicted in Figure 2. The actual voltages 45 are supplied to the furnace electrodes. Signals corresponding to these voltages, which are designated V₀, y-i, and V₂, derived through the measurement system shown in Figure 1 , are also fed into the digital filter as the vector of inputs 42 to the software model 44 of the electrical circuit (see Figure 3).

[0059] The power circuit 40 of the furnace responds to the applied voltages by allowing a current to flow through each electrode. Signals 49 corresponding to the electrode currents, /O, h and Z₂, plus analogue-generated derivatives of these currents, d/₀/df, d/Vdf and d/₂/df, all obtained through the measurement system shown in Figure 1 , are also available to the filter. These currents and their derivatives form a set (denoted by a vector Y₂) of actual signals.

[0060] The software model 44, in response to the sampled furnace electrode voltages 45, and in conjunction with the current values of the predicted means of the circuit parameters 54, generates a vector Y_p of predicted mean values of the electrode currents and the derivatives thereof (block 48). The actual outputs Y_a of the electrode currents and the derivatives thereof (block 49) are then compared to the corresponding predicted mean values Y_p by a comparator 50 which determines the vector of differences, ΔY, between the actual and predicted outputs i.e., ΔY = Y_a - Y_p, (block 51).

[0061] An adjustment algorithm 52 operates on these differences ΔY to modify the predicted means of the circuit parameters 54. This continually-updated vector of parameters is then outputted as the estimates from the filter.

[0062] It has been found that without the d//df signals, the estimator does not work nearly as well. The differentiation process enhances the distortion around the fundamental sinusoids of the mains supply, and it is this distortion that contains important information about the arcing in the furnace. Although the software uses a time-domain approach and not a frequency-domain approach the differentiation nonetheless boosts the magnitudes of the higher frequencies. This analogue differentiation is effective in producing good results and can play an important part of the invention.

[0063] The a.c. current signals from the arc furnace supply can be obtained from standard current transformers on the high-tension primary lines or on intermediate transformer windings, however, a related signal could be obtained from a Rogowski coil, which could be located around any of the current conductors, including the secondary busbars or even the electrodes themselves. A Rogowski coil is a core- less helical coil arranged in a loop around a conductor that carries the a.c. current, and the signal is derived from the voltage induced in this helical coil (unlike a normal current transformer where a current is induced to flow in the secondary winding to oppose the magnetic field induced by the current in the main conductor). By the very nature of magnetic induction, the voltage picked up by the Rogowski coil is proportional to di/dt in the main conductor. A reference herein to a di/dt signal is intended to include a signal of this type which is produced without directly implementing an analogue differentiating process on the current signal.

[0064] The parameters which are predicted (block 54) through the use of the adjustment algorithm are used to provide visible information and loggable data on the functioning of the arc furnace, and to control the arc furnace either to achieve a more effective operation or to achieve a desired end product. The aspects of data display and storage (24, 28) and the step 30 of furnace control, shown in Figure 1 , are collectively designated in a block labelled 24, 28 and 30 in Figure 3. As is explained hereinafter the predicted parameters can be used to control at least the following: the electrode hoists, the slipping of each electrode, carbon balance and metal grade, and electrical aspects including transformer tap positions.

Control of the electrode hoists

[0065] The recursive process provides estimates of the resistance and reactance per electrode, and of derived variables, such as the power per electrode. The electrode hoists can be controlled automatically in response to these estimated values, using a suitable algorithm.

Control of electrode slipping

[0066] The erosion of an electrode is typically of the order of 0.5 to 1.0 metre per day. At the same time, the electrode is normally slipped through the contact shoes at a similar rate. Hence it typically takes of the order of a few days for an electrode's length to get badly out of balance, unless there is some sudden unexpected change like an electrode break. This slow rate of change therefore allows plenty of time for human monitoring and input, to evaluate and then make a considered adjustment of the system.

[0067] There is however a difficulty associated with electrode slipping for a relatively accurate assessment of the length of the electrode is not easy to make. The tip of each electrode is always buried beneath the burden of a submerged-arc furnace, and cannot be seen. In the implementation of this system the principles of the invention are used to provide an estimate of the inductance associated with each electrode in the furnace and to distinguish between the inductances of 3 electrodes. These estimates of the inductances provide information about the lengths of the electrodes. Alternatively, the reactance equivalent of the inductance of each electrode may be used in place of the inductance.

[0068] The inductance in each phase of the circuit is an indication of the length of the corresponding electrode, but the apparatus can take a relatively long time (of the order of hours to days) to estimate these inductances adequately. It is possible to apply a simple control loop between the estimated inductance and the rate of slipping, but this may be too coarse an approach. Instead use is made of an "electrode management system", in which graphical trends get displayed to a human operator, who alters the rate of slipping accordingly.

[0069] The inductance information and electrode length information are matched using software or by eye. For each electrode an electrode length equivalent of its inductance is plotted and an electrode length signal is then calculated as a function of time, by subtracting the accumulated erosion from the accumulated slip. This is then plotted on the same graph. The operator then moves the plots (on a computer system by "dragging" the plots with a mouse) to get a reasonable fit between them. The software accommodates this by adjusting the rate of erosion per MWh, or by changing the zero point of the conversion between reactance and length. If a spot reading of an actual electrode length becomes available (e.g. by burning down and measuring the length), then this can be added as a reference point on the corresponding graph.

[0070] Ongoing estimates of the electrode length can be obtained from the graph. The accuracy of such an estimate is typically of the order of 200 to 300 mm.

Control of carbon balance and of metal grade

[0071] The carbon/reductant balance can be directly controlled by automatically selecting recipe set points on a weighing-batching system, or indirectly, through an intermittent, off-line scheme in which, in response to information from the apparatus, a decision is made on the usage of raw materials which are then manually entered into an automatic batching system for feeding the furnace.

[0072] The rate of change in the carbon inventory in the furnace is the difference between the addition of fresh carbon and its consumption by the reactions in the process. There may also be a small loss of carbon, firstly through material that gets washed out of the taphole unreacted and, secondly, through burnoff from the surface of the burden. In the absence of some abnormal upset, like a batching system malfunction, the carbon inventory normally takes of the order of several hours to get badly out of balance.

[0073] Part or all of the information for the carbon balance can be based on the estimates of the parameters from the control apparatus, particularly those parameters which are related directly to the arc behaviour, viz. arc voltage, residual conductivity, and discharge time constant. Other information could also be used, such as intermittent analyses of the product material coming from the furnace.

[0074] The carbon balance in the furnace is dependent on the general mass and heat balance for the furnace. A prior offline study of the process must be undertaken to generate one or more functions, using a technique such as multi-linear regression or neural-net analysis, relating the relative amount of carbon in the furnace to the estimated parameters from the control apparatus and, possibly, to information from other sources.

[0075] As the general parameters distinguish between electrodes, it is possible to control different recipes for the zones around each electrode individually. This could have distinct advantages for the process, as often there is an asymmetry in a furnace caused by factors such as the locations of the tapholes.

[0076] Of benefit is the fact that the quantity of certain elements, e.g. silicon, in the alloy that is tapped from a furnace, has been found to correlate with the amount of arcing. When the temperature of the hot reaction zone in the furnace rises, it favours the reduction of the mόre-difficult-to-reduce metals such as silicon from their oxides in the slag. Arcing is associated with an increase in the temperature of the reaction zone in a furnace.

[0077] Control can thus be exerted over the relative amount of arcing. This affects the temperature in the reaction zone and so enables the %Si in the end product to be controlled. It is believed that similar results can be achieved with this technique in respect of other constituents.

[0078] The extent to which the dissipated power is split between the arc and the basic burden resistance beneath each electrode provides useful information about how a submerged-arc ferro-alloy furnace is operating. The interpretation of this information depends however on the type of material that the furnace is processing.

[0079] Ferro-alloy processes are conventionally categorised as "wet" or "dry", depending on whether slag is normally present inside the furnace or not. Silicon and ferro-silicon furnaces are categorised as dry, while ferro-chrome and ferro- manganese furnaces are categorised as wet.

[0080] In a "dry" process (i.e. one which does not normally have slag), lifting the electrode a small amount (of the order of a few millimetres to centimetres) tends to draw out the arc resulting in a higher arc voltage. It has been noted that if the arc voltage under an electrode is unduly high a floor of a crater beneath the electrode is "burnt" away, and recedes. This burning down is apparently associated with the production of Si (or FeSi as the case may be), which is highly desirable. Conversely, lowering the electrode tends to extinguish the arc. If the arc gets completely or partly extinguished, then material starts to build up under the electrode, and the electrode has to be raised. After ^'about 5 to 10 minutes the burden resistance (Rj) changes in response to electrode movement. If for example the arc voltage of an electrode i rises, then in time its Rj will start to fall, and vice versa. Unfortunately, these effects are not always repeatable. Nevertheless, movement of an electrode like this to affect the amount of arcing forms the basis of furnace control using the principles of the invention.

[0081] In the case of a dry process, the maintenance of a high-temperature reaction zone in a cavity around the tip of each electrode is important. Proper management of this reaction zone includes carbon control as well as control of the hoist and of the slippage of the electrode. Estimates from the control apparatus give information about conditions in this reaction zone, particularly of its temperature. This information can be used to make decisions about the operation of the furnace. Secondly, it is possible to implement a more automated form of control over the hoists, possibly in a nonlinear fashion, so as to sustain the best conditions in the cavities.

Electrical aspects

[0082] Parameters produced by the apparatus of the invention are noisy and relatively slow to respond (~3 to 10 seconds) to changes in furnace conditions. It is better to use a Minstral-type control system for direct control of the furnace and, then in a cascade arrangement, to use the parameters to manipulate the set points of the

Minstral-type control loops. This allows for control of the electrode resistances and power levels, through manipulation of the electrode hoists and transformer tap changers, and has the advantage that the response is fast and direct, and therefore

the control loops can be made tight. [0083] Figure 4 shows^'a typical layout of a cascade control scheme wherein a slave loop is represented by a secondary controller such as a Minstral controller 70, actuators 72 for electrode hoists and transformer tap changers, the power circuit of the furnace 40 and the electrical signals 76 for the Minstral controller, which is known per se in the art. A master control loop is represented by a.c. measured signals 78, the parameters 54 produced in accordance with the techniques described hereinbefore, a mapping algorithm 84, and resistance set points 86 to the controller 70.

[0084] In manipulating the Minstral resistance set points, constraints of the various operating limits can arise. For example, lowering the resistance leads to higher electrode currents. If these electrode currents are constraints, then the Minstral controller's response is to tap down the transformer voltages. This may lead to lower power levels which adversely affect production and hence, in creating this cascade structure, such limits need to be carefully accommodated. This may be achieved by adjusting the outputs of the mapping algorithm 84.

[0085] The mapping algorithm 84 allows for various options. For example, one can use as input either the arc voltage vxrci, or the burden resistance R₁, or a combination thereof. The form of the mapping can be selected at least from the following techniques:

Technique 1 :

[0086] In this approach, the mapping algorithm is as follows: take R₁, smooth it using a digital smoothing filter, add an offset, limit this within a band, and pass the result as a set point to the Minstral resistance controller.

[0087]This has the effect of striving to keep a constant difference (i.e. the offset) between the smoothed R,- and the Minstral resistance. This difference is in effect a resistance equivalent of the arc voltage, which means that with this approach an attempt is made to keep a constant arc voltage.

[0088] The delay inherent in the digital smoothing filter is an important factor, and it is necessary to incorporate a formulation of filter that gives a phase lead rather than a lag, for frequencies lower than about 2 to 3 cycles per minute.

Technique 2:

[0089] In this approach, either vΑrci, or R₁ can be used (though the gain will be different for the two cases) as an input to the mapping. The input is then passed through a conventional PID (Proportional, Integral, Derivative) controller to generate the Minstral set point. The output of the mapping is then subjected to the same constraints as in Technique 1.

[0090] This approach has the effect of attempting to maintain a predetermined value of vΑr_ci, or Rj, and must be set up carefully, or it may lead to excessive movements of the electrodes. The effectiveness thereof is dependent on the settings of the PID controller (i.e. the set point, the gain, the integral time and the derivative time). References:

1. Cassie, A M, "Arc rupture and circuit severity a new theory". International Conference on large electric high tension systems, Paris, 1939, pp. 1-14.

2. Brown, T E, "The electric arc as a circuit element". Journal of the Electrochemical Society, vol. 102, 1955, pp. 27-37.

3. Jazwinski, A H, "Stochastic processes and filtering theory". Academic Press,

New York, 1970.

4. Bozic, S M, "Digital and Kalman filtering". Edward Arnold, London, 1979.

Claims

1. A method of operating and controlling an arc furnace which has a plurality of electrodes connected to a polyphase power supply by means of at least one power transformer, the method including the steps of recursively estimating in real time values of parameters of circuit elements of an equivalent electrical circuit of the arc furnace in operation, and using the estimated parameter values to control at least part of the operation of the arc furnace.

2. A method according to claim 1 wherein the parameter values are estimated using information selected from the following: voltages applied to electrodes of the furnaces; currents supplied to electrodes of the furnace; differentiated values, with respect to time, of currents supplied to electrodes of the furnaces; and the position of at least one tap changer on the at least one power transformer.

3. A method according to claim 2 wherein the differentiated values are produced by an analogue differentiation process or an equivalent process.

4. A method according to any one of claims 1 to 3 wherein the parameters for which the values are estimated are selected from the following: resistance of an electrode; inductance of an electrode; arc voltage at an electrode; power per electrode; fraction of the power per electrode that is dissipated in an arc; the time constant of an arc; and the residual conductivity of an arc.

5. A method according to any one of claims 1 to 4 wherein the estimated parameter values are used to control at least one of the following: electrode hoists; transformer taps; the rate of slipping of each electrode; the composition or relative proportions of raw materials fed to the furnace; the composition of a product produced in the furnace.

6. A method according to any one of claims 1 to 5 wherein the estimated parameter values are used to maintain a specific relationship between the voltages which are applied to the furnace.

7. A method according to any one of claims 1 to 6 wherein the estimated parameter values are used to control the reductant balance in the furnace.

8. A method according to any one of claims 1 to 7 which includes the steps of using the estimated parameter values to estimate the reactance associated with each electrode in the furnace, and deducing the length of the electrode from the estimated reactance.

9. A method according to claim 8 wherein the deduced length of the electrode is used to control the slipping thereof.

10. A method according to any one of claims 1 to 9 which includes the steps of using the estimated parameter values to manipulate set points of a secondary controller, and using the secondary controller to control the furnace directly.

11. A method according to claim 10 wherein the secondary controller is responsive to at least one of the following: the voltage of an arc; the resistance of the burden in the furnace.

12. A method ^'according to any one of claims 1 to 11 wherein the parameter values are estimated using Cassie's model for arcs in the furnace.

13. A method according to any one of claims 1 to 12 wherein the recursive estimation is done using a digital filter which includes a software model of the equivalent electrical circuit which, using sampled values of voltages supplied to electrodes of the furnace, predicts values of electrode current and derivatives, with respect to time, thereof.

14. A method according to claim 13 which includes the step of using an adjustment algorithm which operates on differences between actual and predicted values of electrode currents and derivatives thereof to modify the estimated parameters.