Patent Publication Number: US-2009219968-A1

Title: Control system for an arc furnace

Description:
The present invention relates to a control system for an arc furnace, an arc furnace which incorporates the same, and a method of controlling an arc furnace. 
     An arc furnace is an electric furnace in which the heat is produced by an electric arc between adjacent electrodes or between the electrodes and the furnace charge. The heat produced in this manner is used to heat and smelt the charge. Typically, the arm assembly, which carries the electrodes, weighs in the range of 2 to 50 tons, and is moved vertically for control purposes by a hydraulic cylinder or other actuator. Since the length of the electric arc depends, amongst other things, on the ever-changing level of charge, be it solid or liquid, under each electrode, it is necessary to control the positioning of the electrodes within the furnace. 
     The regulation system for controlling the positioning of the electrodes influences many important aspects of furnace performance, such as energy input, arc stability, solid charge melting pattern, and electrode consumption. All these parameters are interrelated in a complex manner and there are many differences of opinion on control strategies. 
     At present, one of the accepted regulation systems is one that aims to control the impedance of the electric arc produced by the electrodes. In particular, this system attempts to hold the ratio of voltage to electrical current constant. In use, a voltage signal taken from a phase from the power supply to ground, and a current signal are each separately measured and compared. If the voltage and current are each at a desired pre-selected setpoint, the output from this comparison of signals is arranged to be zero. If, however, the current exceeds its setpoint, which would simultaneously cause the voltage to decrease, a non-zero output signal is generated. This output signal causes the arm assembly to lift, thereby causing the electrodes to lift, which in turn reduces the current in order to maintain the impedance at a constant value. 
     In general, existing arc impedance regulators of the type described above are based on analogue electronics, with built-in drift and tolerance factors, leading to frequent recalibration requirements. Although some systems have turned to digital electronics to address these problems, these systems generally require large and expensive computing systems. 
     It would therefore be desirable to provide an arc furnace impedance regulator that addresses the above-mentioned problems in a cost-effective, and yet efficient, manner. 
     In one aspect the present invention provides a control system for controlling a vertical position of at least one electrode of an arc furnace, where the arc furnace comprises a furnace transformer having a primary, input side and a secondary, output side which is electrically connected to the at least one electrode, the control system comprising: at least one current-measuring device for measuring a current as drawn by the arc furnace; a voltage-measuring device for measuring a voltage as applied across the arc furnace; and a control unit for dynamically determining a setpoint for the vertical position of the at least one electrode based on the measured values of current and voltage, and providing an actuating output for driving a lifting arrangement to adjust the vertical position of the at least one electrode so as to follow the dynamically-determined setpoint. 
     Preferably, the at least one current-measuring device is operative to measure the current on one or both of the input and output sides of the furnace transformer. 
     In one embodiment the at least one current-measuring device comprises a first current-measuring device for measuring the current on the input side of the furnace transformer and a second current-measuring device for measuring the current on the output side of the furnace transformer. 
     Preferably, the voltage-measuring device is operative to measure the voltage between a bus of the furnace transformer and a furnace hearth. 
     Preferably, the control unit comprises a processor which is operative to run a control algorithm for dynamically determining a rate factor r, where r=x 2 /k, with x being a deviation in a setpoint value and k being a system-dependent constant, and provide the actuating output based on the dynamically-determined rate factor r. 
     In one embodiment x=n−p and p=(a/b)*(c/2), with n being a set point value, a being the current value as measured by the at least one current-measuring device, b being a rated secondary current value of the furnace transformer, and c being a count range of the processor. 
     In one embodiment k=Int((T m *E t /1000)/100)*100, with T m  being the melting point (liquidus) of the slag in degrees Kelvin and E t  being the total electrical energy required to drive the arc furnace in terms of kWh per metric ton of a charged material. 
     In one embodiment the processor is operative to provide a drive voltage v as the actuating output for driving the lifting arrangement. 
     In one embodiment v=(r/k)*(ABS(x)/x)*l, with l being a scale voltage for a drive unit of the lifting arrangement. 
     Preferably, the processor is a programmable logic controller (PLC). 
     The present invention also extends to an arc furnace comprising the above-described control system. 
     In its preferred embodiments the arc furnace is used in the smelting of materials, such as ore fines, or the melting of materials, such as metallic fines. 
     In another aspect the present invention provides a method of controlling a vertical position of at least one electrode of an arc furnace, where the arc furnace comprises a furnace transformer having a primary, input side and a secondary, output side which is electrically connected to the at least one electrode, the method comprising the steps of: measuring at least one current as drawn by the arc furnace; measuring a voltage as applied across the arc furnace; dynamically determining a setpoint for the vertical position of the at least one electrode based on the measured values of current and voltage; and providing an actuating output for driving a lifting arrangement to adjust the vertical position of the at least one electrode so as to follow the dynamically-determined setpoint. 
     Preferably, the current measuring step comprises the step of: measuring a current on one or both of the input and output sides of the furnace transformer. 
     In one embodiment the current measuring step comprises the steps of: measuring the current on the input side of the furnace transformer; and measuring the current on the output side of the furnace transformer. 
     Preferably, the voltage measuring step comprises the step of: measuring a voltage between a bus of the furnace transformer and a furnace hearth. 
     Preferably, the setpoint determining step comprises the step of: dynamically determining a rate factor r, where r=x 2 /k, with x being a deviation in a setpoint value and k being a system-dependent constant; and the actuating output providing step comprises the step of: providing an actuating output based on the dynamically-determined rate factor r for driving a lifting arrangement to adjust the vertical position of the at least one electrode so as to follow the dynamically-determined setpoint. 
     In one embodiment x=n−p and p=(a/b)*(c/2), with n being a set point value, a being the current value as measured by the at least one current-measuring device, b being a rated secondary current value of the furnace transformer, and c being a count range of the processor. 
     In one embodiment k=Int((T m *E t /1000)/100)*100, with T m  being the melting point (liquidus) of the slag in degrees Kelvin and E t  being the total electrical energy required to drive the arc furnace in terms of kWh per metric ton of a charged material. 
     In one embodiment the actuating output providing step comprises the step of: providing a drive voltage v as an actuating output for driving a lifting arrangement to adjust the vertical position of the at least one electrode so as to follow the dynamically-determined setpoint. 
     In one embodiment v=(r/k)*(ABS(x)/x)*l, with l being a scale voltage for a drive unit of the lifting arrangement. 
     In one embodiment the method is used in the smelting of materials, such as ore fines, or the melting of materials, such as metallic fines. 
     Advantages of the preferred embodiments of the present invention include: 
     (1) Repeatability of Digital Processes 
     The impedance regulator is calibrated during commissioning and all control parameters are stored in non-volatile memory. Thus, the system only needs to be re-calibrated when system parameters change, such as when a different furnace transformer is installed. 
     (2) Adaptive Power Control Feature 
     The input power is monitored and compared to the theoretical input power on the specific transformer tap. The result gives a good indication as to what the conditions in the furnace are like. The impedance regulator then adjusts the impedance setpoint to compensate for these conditions, thus ensuring that the power input is always as close to the theoretical optimum as possible. Because the arc furnace operates under this condition, it achieves better meltdown times, which also leads to better kWh/ton and electrode consumption figures. 
     (3) Reduction in Electric Flicker 
     Electric flicker occurs when alternating current temporarily does not flow through the electrodes, and then suddenly begins to flow. This distortion of the current sine wave causes less power transfer into the metal, and more electrode wear. It also induces resonant oscillations back into the power grid. Typically, electricity suppliers require flicker to be controlled to within certain guidelines. If flicker is not kept to within these guidelines, the user is often severely fined. The impedance regulator of the present invention is in relative terms a far more stable system, which greatly assists in reducing flicker. 
     (4) Reduced Wear 
     By achieving very precise control of the electric arc, it has been found that the present invention greatly reduces wear on the furnace as a whole, and in particular on the delta closures and walls of the furnace. 
     (5) Production of Reports 
     The PLC of the present invention interfaces with a computer-based supervisory system that logs all the furnace operating parameters and graphically displays those parameters so that trends can be studied. The supervisory system also generates a manager&#39;s report consisting of all the alarms and events that were logged in a 24-hour period, as well as the maximum, minimum and average values in this period for furnace parameters, such as power and current. 
     (6) User-Friendliness 
     The present invention is extremely user-friendly in requiring very little input from the operator to operate the furnace. Advantageously, the layout and presentation of the operating panels of the invention are similar to those used in more traditional arc furnaces, such as Amplidyne and Barnes. Thus, an operator who is familiar with any of these systems will require virtually no training at all to successfully operate the present invention. 
     (7) Versatility 
     The high speed of the PLC, coupled with the versatility of the digital control algorithm, lends itself to a wider range of melting applications than the melting of scrap alone. With some adjustments to the gain and response parameters, the present invention can also be utilized for submerged arc processes as well as a combination of open arc and submerged arc processes, such as slag smelting and the smelting of ore fines to recover their contained metals. The present invention, for example, has been found to be extremely successful in recovering ferrovanadium from vanadium pentoxide, ferrochromium from chromite fines, cobalt from raw ores and slags, zinc from steel plant dusts, lead from blast furnace slags, and also in the re-melting of metallic fines, such as those containing, besides iron, vanadium, chromium and manganese. 
     In summary, a primary advantage of the present invention is in yielding the accuracy of digital systems, but at a lower cost due to the invention being implemented using standard, off the shelf PLC equipment. The present invention therefore represents a smaller and cheaper alternative to the existing systems. 
    
    
     
       A preferred embodiment of the present invention will now be described hereinbelow by way of example only with reference to the accompanying drawings, in which: 
         FIG. 1  schematically illustrates an arc furnace system incorporating an impedance regulator in accordance with a preferred embodiment of the present invention; 
         FIG. 2  is a graph illustrating comparative power profiles, on start-up, of an arc furnace utilizing the impedance regulator of the present invention and a conventional, prior art arc furnace; and 
         FIG. 3  illustrates a plot of the correction factor r, where r=x 2 /k, as employed in operation of the impedance regulator of the present invention. 
     
    
    
     The arc furnace system comprises an arc furnace  12  and an electrical supply system  14  for supplying electrical energy to the arc furnace  12 . 
     The arc furnace  12  comprises a furnace shell  16  which contains material, typically in fine or granulated form, to be smelted or melted to provide a molten metallic phase, an electrode assembly  18  which, in operation, extends into the material as contained in the furnace shell  16 , and a supporting unit  26  for movably supporting the electrode assembly  18  in relation to the furnace shell  16 . 
     The electrode assembly  18  comprises a bus bar  20  and a plurality of, in this embodiment first to third electrode units  22   a - c , which each comprise an electrode  30  and an electrode head  32  to which one, upper end of the electrode  30  is electrically and mechanically connected, in this embodiment through an electrode pad, where the mechanical connection is exposed to extreme mechanical conditions, including vibration and torsion. 
     The supporting unit  26  comprises a supporting arm  36  which extends over the furnace shell  16  and supports the electrode assembly  18 , a supporting mast  38  to which the supporting arm  36  is vertically movably disposed, and a drive unit  40 , in this embodiment a hydraulic unit, which is operable to raise and lower the supporting arm  36 , and hence the electrode assembly  18  as supported thereby. Positioning of the electrodes  30  within the furnace shell  16  is essential, as this position determines inter alia the length of the electric arc. Typically, the combined weight of the electrode assembly  18  and the supporting arm  36  would be in the range of from about 2 to about 50 tons. 
     The electrical supply system  14  comprises a first, main transformer  46  which is electrically connected at an input side to a high-voltage supply as received from an electrical utility and at an output side provides a lower, intermediate voltage, typically between 30 and 33 kV, and a second, furnace transformer  48  which is electrically connected at an input side to the output side of the main transformer  46  and at an output side provides a still lower, furnace voltage at a high current, which is supplied to the electrode assembly  18 , as will be described in more detail hereinbelow. In a typical arc furnace facility, the main transformer  46  would be electrically connected to a plurality of furnace transformers  48  of a plurality of arc furnaces  12 . 
     In this embodiment the furnace transformer  48  includes a tap changer  52 , which provides for the tapping of the furnace transformer  48  to provide for control of the furnace voltage to one of a plurality of predetermined voltages. This control of the furnace voltage, and the associated current, enables the arc furnace  12  to be operated with a range of arcs, each requiring a defined arc voltage and current. 
     In this embodiment the tap changer  52  comprises a tap  54  which is movable between one of a plurality of tap contacts along the primary winding at the input side of the furnace transformer  48 , and a control unit  56 , in this embodiment a motorized unit, for moving the tap  54  such as to be switched between the tap contacts as required. 
     The electrical supply system further comprises a delta closure  62  which comprises a plurality of connectors  64 , in this embodiment copper terminal plates, which are electrically connected to the output side of the furnace transformer  48  and provide for electrical connection to furnace power cables  66  which are electrically connected to the bus bar  20  of the electrode assembly  18 . 
     In this embodiment the transformers  46 ,  48  are located within a vault to ensure a clean, secure environment, and the delta closure  62  is located on a wall of the vault adjacent to the arc furnace  12 . 
     The electrical supply system further comprises a control unit  74  for controlling the drive unit  40  of the support assembly  26  in vertically positioning the electrodes  30  of the electrode units  22   a - c  in the furnace shell  16 . 
     The control unit  74  includes at least one current-measuring device  76  for measuring the current as drawn by the arc furnace  12 , and a voltage-measuring device  78  for measuring the voltage as applied across the arc furnace  12 . 
     In this embodiment the control unit  74  includes first and second current-measuring devices  76   a, b , where the first current-measuring device  76   a  measures the current on the input side of the furnace transformer  48  and the second current-measuring device  76   b  measures the current on the output side of the furnace transformer  48 . 
     In this embodiment the voltage-measuring device  78  measures the phase voltage between the bus of the furnace transformer  48  and the furnace shell  16 . 
     The control unit  74  includes a programmable logic controller (PLC)  80  which is operatively connected to the at least one current-measuring device  76  and the voltage-measuring device  78  through respective analogue-to-digital (A-to-D) converters, which provide digital values which are representative of the measured analogue values of current and voltage, and the drive unit  40  of the support assembly  26  through a D-to-A converter, which provides an analogue signal to the drive unit  40  representative of the digital value corresponding to the determined rate of movement, such as thereby to enable control the position of the electrodes  30  of the electrode units  22 - c  within the furnace shell  16 , and thus the arc as generated between the electrodes  30 . 
     In this embodiment the PLC  80  is controlled via a closed-loop control algorithm. By ensuring that the response time of the PLC  80  at least matches the mechanical response time of the support assembly  26 , high-speed and accurate control of the electrode assembly  18  is achieved, avoiding problems associated with unwanted resonance. 
     In this embodiment the PLC  80  utilizes a control algorithm based on a rate factor r, which represents the required rate of movement of the electrodes  30 , as manifested by movement of the supporting arm  36  of the supporting assembly  26 . 
         r=x   2   /k   (1) 
         x=n−p   (2) 
         p =( a/b )*( c/ 2)  (3) 
     where:
         k is a system-dependent constant;   n is a set point value;   a is the current value as measured by the at least one current-measuring device  76 ;   b is the rated secondary current value of the furnace transformer  48 ; and   c is the count range of the PLC  80 .       

     The rate factor r is a mathematical correlation of actual data which was collected when operating arc furnaces of different sizes, namely, 450 kVA, 800 kVA, 1 MVA, 2 MVA and 3 MVA, when smelting ore fines and melting metallic fines. 
     In this embodiment an initial set point value n l  is determined as follows. 
         n   l =( d/b )*( c/ 2)  (4) 
     where: d is the full load rated current of the arc furnace  12 . 
     By way of example, for a step down transformer ratio d/b of 10/250 and where the PLC  80  has a count range of 4000, then employing Equation (4). 
         n   l =(10/250)*(4000/2)         n l =80       
     Using this initial set point value n lr  provides initially for stable operation of the arc furnace  12 , and, during operation, the set point value n is altered in order to compensate for furnace conditions and thereby provides for optimization of the arc as generated between the electrodes  30  so as to input an optimum energy into the material in the furnace shell  16 . In this embodiment the PLC  80  is operative to compare the actual power as input into the arc furnace  12 , as determined from the values of voltage and current as measured by the at least one current-measuring device  76  and the at least one voltage-measuring device  78 , with the power as should theoretically be achieved for the set tap  54  of the furnace transformer  48 , and alter the set point value n as a function of this comparison. 
     In this embodiment the system-dependent constant k is initially accorded a calculated value, in order to provide initially for stable operation of the arc furnace  12 . 
     The system-dependent constant k is determined as follows: 
         k =Int(( T   m   *E   t /1000)/100)*100  (5) 
     where:
         T m  is the melting point (liquidus) of the introduced material in degrees Kelvin.   E t  is the total electrical energy required to drive the process in terms of kWh per metric ton of introduced material.       

     By way of example, for oxide materials, the melting point T m  and the total electrical energy E t  are determined as follows. 
     
       
         
           
             
               T 
               m 
             
             = 
             
               1189.157 
               + 
               
                 
                   C 
                   0 
                 
                 × 
                 
                   ( 
                   
                     12.22238 
                     + 
                     
                       ( 
                       
                         
                           - 
                           0.14321 
                         
                         × 
                         
                           C 
                           0 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         0.030606 
                         × 
                         
                           C 
                           4 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         0.022817 
                         × 
                         
                           C 
                           6 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           - 
                           0.54851 
                         
                         × 
                         
                           C 
                           5 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           - 
                           0.3636 
                         
                         × 
                         
                           C 
                           7 
                         
                       
                       ) 
                     
                   
                   ) 
                 
               
               + 
               
                 
                   C 
                   5 
                 
                 × 
                 
                   ( 
                   
                     
                       ( 
                       
                         
                           - 
                           0.26564 
                         
                         × 
                         
                           C 
                           5 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         0.209113 
                         × 
                         
                           C 
                           6 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           - 
                           1.13507 
                         
                         × 
                         
                           C 
                           7 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           - 
                           0.3511 
                         
                         × 
                         
                           C 
                           4 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       33.49343 
                       ) 
                     
                   
                   ) 
                 
               
               + 
               
                 
                   C 
                   4 
                 
                 × 
                 
                   ( 
                   
                     
                       - 
                       6.53514 
                     
                     + 
                     
                       ( 
                       
                         0.107294 
                         × 
                         
                           C 
                           4 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           - 
                           0.35228 
                         
                         × 
                         
                           C 
                           7 
                         
                       
                       ) 
                     
                   
                   ) 
                 
               
               + 
               
                 
                   C 
                   6 
                 
                 × 
                 
                   ( 
                   
                     
                       ( 
                       
                         
                           - 
                           18.8445 
                         
                         + 
                         
                           ( 
                           
                             0.800383 
                             × 
                             
                               C 
                               6 
                             
                           
                           ) 
                         
                       
                       ) 
                     
                     + 
                     
                       
                         C 
                         7 
                       
                       × 
                       
                           
                       
                        
                       38.97819 
                     
                   
                 
               
             
           
         
       
     
     where:
         C 0 =% FeO×100×1.625/C S      C 4 =% SiO 2 ×200/C S      C 5 =% CaO×100/C S      C 6 =% MgO×100/C S      C 7 =(% Al 2 O 3 +% Cr 2 O 3 )×100/C S      C S =% FeO*1.625+% SiO 2 +% CaO+% MgO+% Al 2 O 3 +% Cr 2 O 3          

         E   t =( E   O   +H   React )/3.6/0.85 
     where:
         E O  is the energy output in MJ.   H React  is heats of reaction in MJ, which represents the sum of the thermodynamic enthalpy change (ΔH 295K ) associated with every reaction taking place in the process, with examples being:       

       ZnO+C═Zn+CO ΔH 295K =+237.551 kJ/mol C 
       FeO+C═Fe+CO ΔH 295K =+161.514 kJ/mol C.         The term 3.6 is the conversion factor for 3600 kJ, which corresponds to 1000 kWh.   The term 0.85 represents the efficiency factor for converting electrical energy into heat energy.
 
The energy output E O  is determined as follows:
       
     
       
      
       E 
       O 
       =En 
       Ga/Fu 
       +En 
       sl 
       +En 
       Met  
      
     
     Where: 
     
         
         
           
             En Ga/Fu  is the energy value associated with the furnace off gas and fume. 
             En Sl  is the energy value associated with the furnace slag. 
             En Met  is the energy value associated with the molten metallic phase. 
           
         
       
    
     For example, for smelting a material producing a slag having a liquidus of 1345° C. and a power requirement of 957 kWh/t, following Equation (5), the system-dependent constant k is determined as follows. 
         k =Int(((1345+273)×(957/1000))/100)×100         k=1500       
     In one embodiment the PLC  80  is operative to adjust the system-dependent constant k, within a range of +/−5%, in order to optimize power usage, with the system-dependent constant k being influenced by inter alia the furnace size, the type of material being melted, the optimum operating temperature and the slag fluidity. Experimentation has, however, established that the system-dependent constant k usually has a value of between about 500 and about 3000, such that the optimal value of the system-dependent constant k is fairly rapidly determined. 
     In this embodiment the drive unit  40  of the supporting assembly  26  is actuated by an analogue drive voltage v which is output by the D-to-A converter of the PLC  80 , with the scale of the drive voltage v determining the rate of movement of the drive unit  40 , and the PLC  80  is operative to derive the control voltage v in accordance with the following output algorithm. 
         v =( r/k )*( ABS ( x )/ x )* l   (6)     where: l is the scale voltage for the drive unit  40  of the supporting assembly  26 .   
     The drive voltage v is one of a positive or negative voltage, in this embodiment with a positive voltage defining a vertically-downwards movement and a negative voltage defining a vertically-upwards movement. 
     By way of exemplification,  FIG. 2  illustrates representative plots of the input power profile of a conventional arc furnace as compared to the input power profile of an arc furnace  12  as achieved by use of the control unit  74  of the present invention. These plots clearly illustrate the function of the control unit  74  in providing a greater energy input to the arc furnace  12 . 
     Operation of the arc furnace system will now be described hereinbelow in the smelting of a batch of molten steel, which is known as a “heat”. 
     The furnace shell  16 , where empty, is first charged with a small quantity, typically about 20 kg, of the material to be smelted. 
     The arc furnace  12  is then operated to smelt this material, which causes a small puddle of the molten product to form in the bottom of the bowl of the furnace shell  16 . 
     Thereafter, more material is fed into the puddle of the molten product in the bowl of the furnace shell  16 , where smelting is accomplished by supplying energy to the feed material as fed into the furnace shell  16 . In this embodiment the feed material is fed continuously into the furnace shell  16  using a feeder, where the feed rate of the feeder matches the electrical energy as supplied by the electrodes  30 . In preferred embodiments the feeder is one of a vibratory or belt feeder. 
     In this way, the small puddle of the molten product develops into a large pool of the molten product which fills the bowl of the furnace shell  16 . 
     Although the energy required to drive the various reactions and produce various gaseous and liquid products can be electrical energy or chemical energy, where the chemical energy is supplied by at least one component, such as metallic silicon, which comprises part of the feed material, the electrical energy as supplied via the electrodes  30  is usually the largest contributor of energy in the smelting operations. 
     In this process, the electrode assembly  18  is lowered such that the electrodes  30  of the electrode units  22   a - c  strike an arc on the feed material, which starts the melting cycle, where the vertical position of the electrode assembly  18 , and thus the electrodes  30  within the furnace shell  16 , is controlled by the control unit  74  in the manner as defined hereinabove, in order to optimize operation of the arc furnace  12 . Under such intelligent control, the secondary current, the arc length and the energy input are regulated. By controlling the vertical position of the electrodes  30  in this manner, electrode consumption, refractory wear, flicker, and total energy costs are all reduced, whilst furnace productivity and delta closure life are simultaneously increased. 
     Initially, the tap changer  52  of the electrical supply system is set such that the tap  56  is located at an intermediate voltage tap contact, but, after a short period, typically a few minutes, the electrodes  30  penetrate the feed material sufficiently so as to allow the tap changer  52  of the electrical supply system to be set such that the tap  56  is set to a high-voltage tap contact, also referred to as a long-arc tap. The long arc maximizes the transfer of power to the feed material and a pool of molten product develops in the furnace shell  16 . Setting the tap changer  52  of the electrical supply system such that the tap  56  is set initially to a high-voltage tap contact can lead to radiation damage to the furnace shell  16 . 
     At the start of melting, the arc is erratic and unstable, with wide swings in current being observed and accompanied by rapid movement of the electrodes  30 . As the temperature of the furnace atmosphere increases, the arc stabilizes and once a molten pool is formed, the arc becomes quite stable and the average power input increases. 
     As the falling feed material makes contact with the surface of the molten product, the heat generated by the electrical arcs causes the feed material to be converted into at least three products, these being a gas which can contain carbon monoxide and low boiling point elements, such as zinc and phosphorous, a metallic phase, and a molten slag phase which contains silica and calcia as its major components and overlies the metallic phase. Where the feed material comprises sulphides, the feed material is converted into a further molten product, known as matte, which is sandwiched between the metallic and slag phases. 
     When the bowl of the furnace shell  16  is full, the feeding of feed material into the furnace shell  16  is stopped and the electrode assembly  18  is raised such that the electrodes  30  of the electrode units  22   a - c  are removed from the furnace shell  16 . 
     The slag phase is then removed from the furnace shell  16  by tipping the bowl of the furnace shell  16 , such that the slag phase is poured into a ladle. Where the bowl of the furnace shell  16  also includes a matte phase, as generated from the use of sulphides, the matte phase is poured into a separate ladle. 
     Following the removal of the slag phase and any matte phase, the furnace shell  16  is then returned to the upright position, and the procedure repeated by the introduction of additional feed material. 
     After repeatedly charging the bowl of the furnace shell  16  and removing the generated slag phase and any matte phase, typically in up to eight cycles, the bowl of the furnace shell  16  becomes full of the desired metallic phase. 
     The furnace shell  16  is then tapped to pour off the molten metallic phase into a ladle. This tapping of the molten metallic phase is achieved by tilting the furnace bowl through an angle of just over 90 degrees from the upright position. 
     Following tapping of the molten metallic phase, the furnace shell  16  is tilted back to its upright position for use with a new charge of material. During this period, the electrodes  30  and the furnace shell  16  are inspected for refractory damage, and, if necessary, repairs are made. 
     In one embodiment, when metallic fines, such as ferrochromium, ferromanganese and ferrovanadium constitute the feed material, the resulting molten metallic phase is refined, such that certain elements, for example, zinc, phosphorus, sulphur, aluminium, silicon and carbon, as well as dissolved gases, such as oxygen, are substantially removed from the resulting molten metallic phase. 
     EXAMPLE 
     The present invention will now be described by way of example with reference to the following non-limiting Example. 
     In this Example, the arc furnace  12  is a 2.5 MVA furnace which has a full load rated voltage of 207 V and a full load rated current of 7200 A, and was used to smelt a mixture of chromite sand, containing 38 wt % Cr 2 O 3 , and silicon carbide fines. 
     In this Example, the furnace transformer  24  has a rated secondary current value of 7500 A, and the PLC  80  has a count range of 4000. Following Equation (4), the initial set point value is determined as follows. 
         n   l =(7200/7500)*(4000/2)         n l =1920       
     Where the total electrical energy E t  required to drive the smelting operation is 1225 kWh/t of Cr 2 O 3 , and the liquidus T m  of the slag is 1415° C., then following Equation (5), the system-dependent factor k is determined as follows. 
         k =Int(((1415+273)*(1225/1000))/100)*100         k=2000       
     For a system-dependent factor k of 2000, the rate factor r is determined in accordance with Equation (1).  FIG. 3  illustrates a plot of the rate factor r as a function of the measured values of current. 
     Following Equation (6) and for a voltage scaling factor l of 10, the PLC  80  is operative to provide for a drive voltage v in the range of from 0 to +10 volts or 0 to −10 volts, which, in this Example, is the quantitative signal required to drive the drive unit  40  of the supporting unit  26  to move the electrode assembly  18  one of vertically upwards or downwards. 
     Table I illustrates a set of parameters for a range of measured values of current, which include the representative value of current p as determined by the PLC  80 , the deviation x between the set point value n and the representative value of current p, the rate factor r, the drive voltage v corresponding to the rate factor r, and the speed of movement s corresponding to the drive voltage v. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 Electrode Speed: 
               
               
                 Voltage 
                 Current 
                 PLC Value 
                   
                   
                   
                 down (+) or up (−) 
               
               
                 (V) 
                 (A) 
                 p 
                 Deviation x 
                 Rate Factor r 
                 Drive Voltage v 
                 (mm/s) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 207 
                 0 
                 0 
                 1920 
                 1843 
                 9.22 
                 114 
               
               
                 207 
                 720 
                 192 
                 1728 
                 1493 
                 7.46 
                 92 
               
               
                 207 
                 1440 
                 384 
                 1536 
                 1180 
                 5.90 
                 73 
               
               
                 207 
                 2160 
                 576 
                 1344 
                 903 
                 4.52 
                 56 
               
               
                 207 
                 2880 
                 768 
                 1152 
                 664 
                 3.32 
                 41 
               
               
                 207 
                 3600 
                 960 
                 960 
                 461 
                 2.30 
                 29 
               
               
                 207 
                 4320 
                 1152 
                 768 
                 295 
                 1.47 
                 18 
               
               
                 207 
                 5040 
                 1344 
                 576 
                 166 
                 0.83 
                 10 
               
               
                 207 
                 5760 
                 1536 
                 384 
                 74 
                 0.37 
                 5 
               
               
                 207 
                 6480 
                 1728 
                 192 
                 18 
                 0.09 
                 1 
               
               
                 207 
                 7200 
                 1920 
                 0 
                 0 
                 0.00 
                 0 
               
               
                 207 
                 8330 
                 2221 
                 −301 
                 45 
                 −0.23 
                 −3 
               
               
                 207 
                 8490 
                 2264 
                 −344 
                 59 
                 −0.30 
                 −4 
               
               
                 207 
                 9360 
                 2496 
                 −576 
                 166 
                 −0.83 
                 −10 
               
               
                 207 
                 9990 
                 2664 
                 −744 
                 277 
                 −1.38 
                 −17 
               
               
                 207 
                 11000 
                 2933 
                 −1013 
                 513 
                 −2.57 
                 −32 
               
               
                 207 
                 11420 
                 3045 
                 −1125 
                 633 
                 −3.17 
                 −39 
               
               
                 207 
                 12220 
                 3259 
                 −1339 
                 896 
                 −4.48 
                 −55 
               
               
                 207 
                 13100 
                 3493 
                 −1573 
                 1238 
                 −6.19 
                 −77 
               
               
                 207 
                 13500 
                 3600 
                 −1680 
                 1411 
                 −7.06 
                 −87 
               
               
                 207 
                 13990 
                 3731 
                 −1811 
                 1639 
                 −8.20 
                 −101 
               
               
                   
               
            
           
         
       
     
     Finally, it will be understood that the present invention has been described in its preferred embodiment and can be modified in many different ways without departing from the scope of the invention as defined by the appended claims.