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Automation Control and Modelling of Electric Arc Furnace

Automation Control and Modelling of Electric Arc Furnace

The electric arc furnace (EAF) constitutes the main process in scrap / DRI (direct reduced iron) based steelmaking and the second most important steelmaking process route in terms of global steel production. It is the main process for recycling of ferrous scrap. It was invented in 1889 by Paul Heroult. It was initially used mainly for the production of special steels, but established itself as one of the main steelmaking processes in the later part of the 20th century.

In comparison to the blast furnace- basic oxygen furnace route of steelmaking, the EAF steelmaking route reduces the energy consumption by upto 61 % and the carbon emissions by around 77 %. The process efficiency and productivity have improved dramatically through the introduction of technical improvements such as (i) the increased use of oxygen, carbon, and other sources of chemical energy, (ii) foaming slag, and (iii) post-combustion of carbon mono-oxide. However, a considerable potential for further optimization remains. This becomes apparent in the difference between the theoretical energy demand of around 400 kWh per ton for the melting and heating of the scrap and the actual average consumption of the present day EAF that is around 375 kWh per ton of electrical energy and a similar amount of chemical energy, resulting in a total efficiency of around 50 %.

Nowadays, the EAFs are operated with increased arc voltages and secondary currents in order to enhance productivity. Power inputs of upto 300 MVA are achieved for EAFs. Operating such a high arc power needs an accurate control of the melt-down process. An arc, which radiates its high power towards the furnace walls, causes huge damage. By preventing such an undesired behaviour, downtimes are kept at a low rate and high furnace productivity is maintained. In order to achieve this objective, a closed-loop power control has to be set up. Such a power control needs to react to occurring events in the melt-down progress, in especially to furnace walls which are not covered by scrap or suitable foaming slag practice. The crucial point is to achieve this kind of information about the process.

The parameters necessary for analysis and optimization of the process, however, in many cases cannot be measured directly due to the harsh conditions inside the furnace. For example, the temperature and composition of the melt and slag can be determined only through spot measurements and potentially with some delay caused by the necessary analysis of the sample. While methods for the direct and continuous measurement of these parameters are being developed, they are not yet available for most of the furnaces. Also, plant trials which are necessary to evaluate the impact of different optimization strategies can be impossible due to prohibitive cost or safety concerns. Hence, mathematical models are a valuable source of information regarding otherwise unknown process parameters. Simulations can also be used as a less expensive, faster, and safer alternative for the plant trials. For the EAF, a wide range of models has been developed with different purposes and modelling approaches.

The EAF can be described as a chemical reactor which utilizes electricity to transform scrap to liquid steel. The trend in electric arc furnace development is to get a higher productivity by increasing the arc voltage and achieving higher currents for melting scrap faster and more efficiently. However the higher voltage and current can cause tremendous damage to the furnace refractory if the arcs are not covered with slag. Common way to control the melt-down presently is to control the transformer tap based on the energy input. This means that no on-line information is used to control the process and the operators manually adjust the set point with the information from the operational diagrams.

The growing complexity of the EAF process in combination with increasing demands in productivity and reduced environmental impact needs control strategies taking into consideration the dynamics of the system requiring adaptation of the static preset operating points in real-time. Also, when the productivity increases, the operator is required to make faster decisions. In the ‘state of the art’ EAF process, automation is needed to assist the operator.

The conventional automation of EAF mainly targets (i) the automation of the electric regime, (ii) the automation of the thermic regime, and (iii) the positioning of the EAF electrodes. A modern and powerful process control system assures a safe and user-friendly plant operation even under difficult conditions. It provides high reliability and availability to pave the path for a smooth process.

The automation solutions in EAF steelmaking are ideal for new as well as existing EAFs of any size. They optimize production of a wide range of steel grades, including carbon steels, stainless steels, and special steels while accommodating variable charging ratios of scrap, DRI, and hot metal. This leads to fewer steel treatment correction steps, a minimum number of down-graded heats and exact adherence to tight production schedules as the basis for just-in-time delivery to the down-stream processing units.

The automated process control is based on several real time measurements for example temperature on the cooling system, sound of the furnace, harmonic distortion on the current, vibration of the furnace vessel, and off gas analysis. The use of automated process control can lead to reduction of power on time, optimization of injected carbon, arc stabilization, and reduction of power off time.

Considering the great complexity of the specific procedures for steelmaking in the EAF, the complex operation of this technological aggregate implies the systematically covering of the steps namely (i) quantifying and maintaining a certain prescript technological state (state of inertia) for the aggregate which is achievable through conventional normal automation, and (ii) complex automation of EAF, which relies on the controlling of the processes for obtaining the maximum criteria function objective according to the mathematical model.

The automation solution of EAF combines the advantages of PLC (programmable logic controller) based automation systems (such as proven quality and stability, low hardware costs, fine-grained scalability, reliable process control, user friendly operation, clear visualization, and powerful engineering tools) with specific technology solutions which are tailored to the specific needs of the plant.

The basic automation uses high-speed microprocessor based systems for technological controls and sequential controls. The automation system is divided into several automation units, which are coordinated to execute the required tasks. Each automation unit is connected to the associated electrical periphery, normally using remote I/O (input-output) connection, for sensoring and actuating. The task of the operating and monitoring carried out through HMI (human machine interface) is the preparation of the increasing quantity of information about the process in a way that the operator receives a clear and easy-to-understand representation of the plant. The HMI system supports a simple and systematic operation of the EAF.

The process control system of EAF at Level 1 includes basic automation and technological control functions to enable EAF steel production in an effective and safe way. A user friendly and redundant HMI configuration combined with the application of fail-safe state-of-the-art control devices ensure high availability of the automation system. Typical features of EAF process control include the following.

Adjustable profiles – The overall automation concept allows defining individual production schemes for transformer tap changer, reactor tap changer, electrode control curves, burners, RCBs (refining combined burners) and injectors which minimize the operator actions.

Modular structure – Highly developed standard solutions make it easy to implement logic and communication to external systems such as scrap yard, dedusting system, material handling, carbon / lime injection, foaming slag control, off-gas analyzer system, and power plant.

System and process diagnostics – Diagnostic functions like condition monitoring, heat / day / month reporting and trend recording support trouble-free and reliable EAF operation.

Software simulation – All implemented functions are simulated according to specific operational rules. This covers e.g. hydraulic station, movements, and process operations. The simulation of the complete heat cycle verifies the correct functionality of the automation software.

Further, advanced modern automation solutions also use state-of-the-art measurement equipment. The typical measurement equipment, such as temperature/Celox hand lance is used as a standard tool for electric steelmaking. In order to further improve the performance of EAF, some of the measurement systems which can be used are (i) contactless temperature measurement, (ii) continuous EAF off-gas analyzing system, and (iii) use of robot system for temperature and Celox measurement and sampling.

The new contactless temperature measuring system, fully integrated into the RCB technology, provides a perfect method to predict the exact tapping time during power on. The measured temperature is evaluated with control models for repeatable results and a consistent process. The contactless temperature measuring system includes three main functions namely (i) burner mode in which during the power-on times contactless temperature measuring system can be used as a burner to preheat the scrap using various power settings, (ii) lance mode to which the system switches over to provide a supersonic oxygen stream as soon as the scrap is heated to the point where a reaction occurs between carbon, iron, and oxygen, (iii) temperature mode to which the system switches over from lance mode when a defined homogenization level of the liquid phase is reached, and the temperature measurement cycle can start. Fig 1 shows scheme of RCB temperature system.

Fig 1 Scheme of RCB temperature system 

Based on the above method there is no need of lances for temperature measuring. This results in a high level of safety for the operators and in reduced consumable costs. The energy consumption input decreases. This system allows an exact prediction of tapping with the several benefits including, (i) increase in the productivity through power-off reduction, (ii) repeatable results for consistent process, (iii) decrease of operating and consumable cost, and (iv) decrease in the energy consumption input with accurate tapping.

Continuous EAF off-gas analyzing system is a solution for the EAF off-gas measurement, which carries out fully automatic continuous gas analysis. The gas sampling device is placed in the water cooled primary EAF off-gas duct. The off-gas is continuously analyzed during power on time and during the power off time with fully automatic sample probe purging and cleaning is performed. Hence, the system enables nearly maintenance-free operation, even under the very hot, corrosive and extremely dust-laded environment conditions at the sampling position directly after the EAF elbow.

The automation system has normally modular structure. It covers every level from basic plant control (Level 1) to integration with production tracking functions and management of manufacturing orders in-progress (Level 3 and Level 4). Specific control process modules optimize operations and provide shop floor workers and process technologists with essential support. The plant business line automation systems can be combined with cutting-edge technology solutions for the optimization of energy savings and productivity. Moreover, the automation solutions employ innovative sensors, which work together with sophisticated control models for dynamic, real-time control.

The process control of EAF provides a fully automatic, end-to-end solution for electrode control in three-phase EAF. It regulates and dynamically adjusts the electric arc and makes the most efficient use of electrodes. The solution relies on artificial intelligence to optimize the melting process. It also includes a melt-down control module with melting programmes to ensure accurate reproduction of the melting process to ensure maximum furnace productivity. The electrode control and its add-on units can be integrated into any system environment and architecture. There are three basic control systems for the process control in the EAF. These are (i) the electrode control system, (ii) the foaming slag control system, and (iii) the condition based scrap melting system.

Electrode control system – It is the key control system for EAF. Approaches towards an automated power control normally rely on evaluations of the arc current and voltage. Other measurement techniques are frequently not applicable due to the extreme conditions in the furnace environment.

Electrode control system is a closed-loop electrode control system. The basic task is to control the position of the electrodes, more specific to maintain the electrical operating point. The performance of this very basic task is first of all affecting several key performance indicators (KPIs) of the steel melting shop, such as specific electrical energy consumption, electrode consumption, and productivity etc. Its performance is also crucial for reducing stress of the mechanical and hydraulic systems as well as for the limitation of the power grid disturbances. It is common sense that best performance of this basic task is achieved by impedance based electrode control. Basic additional functions for reducing over current, short-circuits, and electrode breakages are state-of-the-art and keep downtimes to a minimum. Adaptation to the characteristics of the actuation system is needed for best performance, i.e. the characteristics of the hydraulic valves.

The above mentioned basic functions of the electrode control definitely influence the performance of the EAF. However, performance of the furnace depends largely on selection of the electrical operating points. By taking the overall design of the furnace into consideration, operational diagrams are set up, also called melting profiles, or power programmes. These are used for providing the electrical set-point of the furnace, i.e. the transformer tap, reactor tap, and impedance set-points. These diagrams normally depend on total energy input. This functionality is covered by Level 2 systems or similar solutions. The selection and sequence of set-points in this operational diagram has direct impact on the KPIs of the EAF.

Nowadays, add-on modules for the electrode control are in use to adapt the set-points provided by the operational diagrams in order to meet the actual melting conditions inside the furnace, i.e. by evaluating the thermal load of the water-cooled panels. Optimization modules can be used to increase the power input into the furnace by dynamically adjusting the impedance set-points to the melting progress. Normally, the furnace operator is still responsible for taking further control actions based on his subjective perception of sound emissions and his visual impression of the furnace.

Foaming slag control system – For automated foaming slag operation, several approaches exist which use sound measurements. Foaming slag control system is a sensor system. It is based on structure-born noise and is an approach to evaluate the amount of foaming slag in the EAF. In regards to trends and reproducibility, this method has proved to successfully follow the real foaming slag situation in the arc furnace. Fig 2 shows the foaming slag control system in the EAF.

Fig 2 Foaming slag control system in EAF

The foaming slag control system evaluates the sound propagation from the electric arcs, where the sound is created, to the furnace shell, where the resulting vibration is detected by the acceleration sensors, also called structure-borne sound sensors. The electric arcs serve as acoustic sources. By calculating the damping of the sound propagation, the height of the foaming slag is determined.

The great advantage of this method is to determine not just an average slag height around the electrodes, but particularly a specific height in the complete area between each electrode and the furnace shell. The one-dimensional view is actually extended by the foaming slag control system to a two-dimensional measurement of the slag height distribution. Due to the mounting of three sensors opposite to the corresponding electrodes, the slag height can be determined independently in three zones of the furnace (Fig 2). Hence the spatial distribution of the slag height can be evaluated and displayed in the visualization. On the time scale the slag foaming is divided into different periods. The periods are determined by the specific energy input. They are characterized by different reference slag height settings.

Three structure-borne sound sensors, each assigned to one electrode segment, are used to record signals. They are mounted to the furnace shell by welding three adapter plates onto the panels opposite to the respective phase / electrode. The adapter plate is positioned around 800 mm above the steel bath level. The sensors are connected using temperature shielded signal cables, which have to be protected from excessive heat and mechanical destruction. In order to enable an easy change of the furnace vessel, the cables are connected using Harting sockets or connector boxes which are mounted at or close to the furnace vessel. In addition to the structure-borne sound signals, the current signals are recorded by using Rogowski coils. The high-speed sampled signals are forwarded to the data acquisition and computation module.

The foaming slag level is calculated based on the combination of structure-born noise and current signals. With the detection method, operating personnel are in a better position to check the quality and reproducibility of process control in the foaming slag phase with a high degree of accuracy. The process can be optimized with regard to stability, process time, and power consumption on this basis.

The outstanding chance of the correct spatial measurement of the slag height is to regulate the carbon injection by an individual control of the carbon valves in order to achieve a uniform slag distribution. For the regulation of the carbon injection, a control system based on Fuzzy algorithms has been developed. It allows for implementing easily appropriate rules for the carbon injection which can be adapted to the specific situations of the particular furnace configuration. As the carbon valves are normally not designed for a continuous analog control, the output signal is transformed into a pulsed width modulation, which yields in an appropriate carbon supply.

The carbon is injected in a pulsed modulation mode, where pulse width and frequency are controlled by the foaming slag control system in order to inject the right quantity of carbon from each of the three valves. This enables the foaming slag control system to apply exactly the needed amount of carbon for each valve in order to achieve a most uniform, sufficient and stable slag height. During the end period, where the foamy slag is partly poured out, the slag height is lowered and fluctuates

The foaming slag control system ensures that slag foaming levels are uniformly high throughout the foaming process. As a result, the energy efficiency of the arcs is increased while at the same time the amount of injected carbon is reduced. The system also offers a reliable basis for closed-loop foaming slag control based on exactly determining the slag level and supplies signals for triggering the carbon / oxygen lances or coherent burners installed in the furnace.

Condition based scrap melting system – The condition based scrap melting system dynamically controls the electrical energy input during the scrap melt-down period and partly also during the flat bath period by immediately reacting upon the state of the scrap and the melt. This yields in a condition-based optimization of the melting process.

The condition based scrap melting system uses the same hardware as described before for the foaming slag control system. Similar to the foaming slag control system, the condition based scrap melting system measures the sound propagation from the electric arcs, where the sound is created, to the furnace shell, where the resulting vibration is detected by acceleration sensors. By measuring the current of the three arcs and the wall vibration opposite to the electrodes, two different condition-based status signals are calculated dynamically (i) the shielding of the panels by scrap or slag, (ii) scrap state at the arc base, especially the appearance of ’cold’ heavy scrap.

These two signals support characterizing the melting process. Combined with additional information about the furnace, a new condition-based control of the electrical energy input is realized. The additional information include the thermal load of the furnace panels, the specific energy input, electrical data, and further boundary conditions of the process. A controller regulates the secondary voltage by switching the transformer tap, calculates new individual impedance set points for the three phases, and switches the series reactance. The controller maximizes the power input by taking into account the actual wall shielding and the thermal load.

The main feature and advantage of the condition based scrap melting system is its ability to detect a loss of wall shielding much earlier compared to the resulting temperature rise of the panels, which results from the increased radiation impact. This time lead of around 60 seconds enables the condition based scrap melting system to react by redistributing the power respectively the radiation of the three arcs. This immediate redistribution moderates or avoids the thermal impact of the corresponding panels.

The condition based scrap melting system controller reacts in two different ways on the loss of wall shielding and the thermal load of the panels. First of all, on a long time scale when the loss of shielding and the expected or measured temperature increase last for a longer time or is very distinct, the transformer is tapped down. Hence the secondary voltage is adapted. On the other hand, transformer tap is increased when the melt conditions allow for, e.g. at high arc shielding and low panel temperatures.

The transformer tap switching is activated by a hysteresis loop to avoid unnecessary switching operations. Second, on a short time scale, the same input signals are evaluated to control the impedance set-points of the three phases individually, which yields in an asymmetric electrical furnace operation. Based on the calculated shielding and panel temperature prediction or measurement, a fuzzy controller calculates an optimal radiation power distribution. Using a new developed radiation model and an analytical electric model, the corresponding impedance set-points are calculated in an iterative loop in order to fulfill best the optimum radiation distribution. So an almost immediate redistribution of the radiation power can be achieved to moderate or avoid the thermal impact instantaneously.

The main advantage of the condition based scrap melting system is the yielding in a smoother and more stable operation with less transformer tap switching operations and an increased energy input whenever it is permitted by the melt situation.

EAF expert system

EAF expert system has been conceived as an integrated process control supervisor. It automatically recognizes deviations from the expected behaviour and re-tunes the melting program, acting on the electric power planning, on the chemical package, on the slag and steel metallurgy. Equipment constraints are integrated into the control. The EAF expert system acts as a process supervisor which integrates basic automation and technological functions to enable EAF steel production in an effective and safe way, supporting each operation from the charging phase upto the tapping procedure. Because of its extensive sensor- based and camera-based process monitoring, the new generation of machine pulpits can be installed in an arbitrary position and does not need dedicated windows to have a direct visual feedback from the process, increasing operator safety and process awareness.

EAF expert system can also integrate a number of stand-alone technologies to further maximize the productive time, utilization factor, and safety, through remotely controlled mechatronic units. EAF expert system is the latest evolution of EAF concept to automatically control each stage of the melting process, from the electric power planning to the combustion optimization as well as the slag and steel metallurgy management for every operation needed in the EAF cycle.

EAF expert system performs a pre-calculation of the complete heat, tracing the defined melting practice. It gives a preview of the melting process and steel condition at tapping and automatically adjusts power profile and material additions to optimize the process. It decides the charge set point for proper scrap bucket loading. The cost optimizing calculation selects the scrap types and determines the needed quantities as well as the total amount of DRI to be added. It also determines the slag forming agents with respect to a given minimum slag mass and aim basicity. Further, it calculates the cost optimized quantities of alloying additives for the furnace or the tapping ladle.

EAF expert system determines the amount of electrical energy necessary for melting the prepared and charged materials and for heating the steel bath upto tapping temperature, considering the energy input from blown oxygen. EAF expert system provides on-line monitoring of power consumption and transmission of predicted power consumption targeting the prevention of peak loads and high tariff rates. For furnaces with continuous DRI feeding facilities, DRI feed rate is dynamically controlled for targeting a constant steel temperature, taking into account the DRI temperature.

EAF expert system has a powerful data mining engine which is normally developed and specifically tailored for the control application. Relevant data variables are collected and automatically classified into structured relations. Extensive statistical process analyses are applied to a huge quantity of information, discriminating from expected consistent behaviour and anomalies. Persistent deviations from expected process conditions lead to continuous optimization of carbon mono-oxide combustion and efficient use of fuel, by adapting the melting profile to the variable operational conditions. The integrated control of the melting process as a whole, together with the real-time tracking of the furnace variables out-lining relevant deviations from expected process conditions, affords a significant opportunity to improve energy efficiency and productivity.

The real-time on-line off-gas analysis, through the in-situ laser system, promotes the process tracking and permits further optimization by a viable closed-loop control acting on fuel and oxygen post combustion. Quick response off-gas analysis provides the fast feedback information for the regulation of the oxygen injection during the refining stage, controlling the steel decarburization and limiting the bath oxidation at the same time.

The core of the EAF expert system is the ‘melt-model’ which automatically identifies deviations of the process control variables and corrects them to avoid losses or wasting of available energy sources. It coordinates the data, collected in real-time by multiple on-board sensors, and the calculated process variables based on the pre-set static melting profiles. The ‘melt-model’ coordinates a closed-loop control integrated by the model for the electrical power and the model for the chemical package. It manages the interaction of the electrical and chemical melting profiles to achieve energy use optimization, as well as slag and steel metallurgy control, involving, among other features, arc coverage by foaming slag management, post-combustion optimization, electrical energy consumption reduction, and oxygen and carbon consumption optimization. Fig 3 shows closed loop control of melt-model expert system.

Fig 3 Closed loop control of melt-model expert system

The EAF expert system adapts to continuously changing operating conditions while keeping the performance of the EAF at top. It integrates the electrode control system, the foaming slag control system, and the condition based scrap melting system.

The main benefits of the expert system are (i) reduction of tap-to-tap time by upto 10 %, (ii) reduction of energy consumption by upto 5 %, (iii) reduction of alloying material costs by upto 5 %, and (iv) reduced energy costs by avoiding peak tariff rates.

Modelling of EAF steelmaking process

A process model is an ‘algorithm to predict the behaviour of an open or closed system’. It allows predictive control and operator assistance, off-line process optimization, improved understanding of the underlying physical phenomena, and the on-line estimation of parameters which cannot be determined directly through measurements. The term process model refers to the deterministic models based on physical and thermodynamic relationships, and thus excludes purely statistical approaches.

Presently a majority of the EAF steelmaking makes use of Level 1 and Level 2 automation systems. Within these automation systems, there is a requirement of process models. During the production cycle, a number of important quantities are unknown or cannot be measured for fundamental reasons, such as (i) the current (average) temperature of the solid material (scrap, DRI etc.) is not observable (ii) the current melt and slag temperature are difficult of measure, (iii) the current mass of the melt in the furnace cannot be measured.

The process model (for on-line and off-line use) is an important part of the EAF process and operation optimization cycle (Fig 4). The instrumentation of the furnace (weighting of scrap, and DRI etc.) continuously delivers measurement data during the operation which is fed into the model. To enhance the models’ abilities to predict important parameters like melt mass and temperature, new or more precise measurements can be implemented. The more precise data gives than better opportunities to test and furthermore enhance the model. Such more detailed or accurate models allow better control during the operation (on-line model) or the development of optimized process operation modes.

Fig 4 Process modelling for EAF operation optimization

The instrumentation of the EAF allows for a quantitative time dependent measurement of the energy and mass inputs. This data can be used for on-line or off-line modelling of the melt-down process. EAF process models have proven to be useful for improving process understanding and control as well as resource and energy efficiency by providing information which cannot be measured directly during the process due to the extreme conditions inside the furnace.

The use of on-line process models can hence enhance the knowledge on the current process state and thus support optimized process operation by providing additional input data for process control. Additionally, these models can use extrapolated input data to predict the future trends of the process variables. The same models can be used off-line with real or artificial process operation data to optimize the plant operation or to analyze the impact of process innovations. During the installation and optimization of such a process model the requirements of the model justify and support the implementation of advanced measurement systems, e.g. in order to get precise data on the energy and mass inputs into the furnace.

In the case of complex processes such as the EAF process, analytical models are normally more difficult to develop than the statistical models and may not reach the same degree of accuracy. They do, however, allow for extrapolation and are transferable since the physical and thermodynamic description is more universal.

The development of EAF models started in 1974 and in simpler forms and they became state-of-the-art within the following decades. The model developments have been undertaken into several directions, e.g. (i) determination of overall process characteristic and process control, (ii) CFD (computational fluid dynamics) modelling of the off-gas system or the heat transfer inside the furnace, and (iii) modelling of meltdown and slag chemistry and slag foaming.

Modelling and optimization of the EAF process constitutes a complex task due to the large number of variables such as the different charge materials, the share of different energy carriers, and the target composition and temperature. The different process phases, discontinuous changes during charging of material and many variations of the process with different furnace types, feed-stocks, desired steel qualities, and operation strategies have led to the development of various modelling approaches. A number of models have been developed using different approaches both for the complete process as well as local phenomena or single process phases.

Due to the wide range of different applications of modelling the EAF and the complexity of the process, numerous approaches have been applied to derive models for the process. There are purely statistical or data-driven models, including neural networks, used, for example, to evaluate the power consumption or the electrical system of an EAF. Another class of models for the evaluation of EAF energy consumption uses a statistical approach based on parameters which are determined using physical relationships such as the expected power delivery from the use of oxygen or natural gas.

Process models have been developed not only for the complete process but also to describe specific phenomena within the EAF, for example, the heat transfer at the electric arc, the reaction of injected carbon with the slag, or the influence and potential of energy recovery within the off-gas system. In some cases these have then been incorporated into more comprehensive EAF process models.

The process models are normally based on lumped zones with no spatial discretization except for the scrap charge which is discretized into multiple zones in some models. Heat and mass flows are exchanged between these zones and the surroundings and chemical reactions are normally considered within certain zones. Energy and mass balances are then used to track the temperature and composition of each zone. While most of these process models are dynamic, pseudo-dynamic approaches based on predefined process steps have also been proposed.

The models use different approaches, but have some important common properties namely (i) the physical conservation laws of mass, energy, and species are derived and solved, (ii) the general numerical method is to set-up and solve a set of non-linear ordinary differential equations (in most cases the small explicit integration scheme is used), (iii) the models need initial values and (in general time dependent) data for the time dependent inputs like electrical inputs, chemical inputs and mass loads (scrap, DRI etc.) etc.

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