Mathematical Modeling and Experimental Validation of an Electric Arc Furnace

Abstract

The following paper presents an approach to the mathematical modeling of 3-phase AC, electric arc furnace (EAF) processes for control-design and process-optimization purposes. The EAF can be, from the modeling point of view, considered as a combination of electrical, hydraulic, chemical, thermal and several energy-balance sub-processes or sub-models. In this paper the modeling of the electrical and hydraulic submodels is presented in detail, since the two represent a very complex and important sub-system of the complete EAF model. The presented sub-models are obtained in accordance with different mathematical, electrical and mechanical laws. Several parameters, which are necessary to successfully identify the scrapmelting process, were fitted experimentally, using the measured operational data of an 80 MVA AC furnace during different periods of the melting process. Similar data has also been used for the validation of the developed model in typical EAF operating situations. The aim of the presented EAF modeling is to obtain an accurate, robust and realistic mathematical model of the scrap-melting process, which will later be used for control-design purposes, the optimization of the energy consumption and the development of an operatortraining simulator. The main advantage of our modeling approach over the existent EAF-related models is a more macroscopic level of modeling, which accurately simulates the electrical and hydraulic processes under different conditions in the EAF.KEY WORDS: EAF; electric model; hydraulic model; experimental validation; harmonic analysis. reactances; etc.) and non-electrical (transformer and reactor taps; number of short circuits and arc breakages; electrode controller outputs; electrode position; temperatures of the cooling panels; composition and weight of the additives; consumption of oxygen, carbon, gas; etc.) values sampled over a 1-s time window. At this stage of the model's development, nearly all of the electrical and some of the mechanical values were used to obtain the correct parameters of the sub-models describing the electrical properties of the EAF. Additionally, since the properties of the electric arcs are dependent on the position of the hydraulically actuated electrodes, the presented hydraulic sub-model for the electrode control completes the particular modeling assembly. Measurements and Modeling EAF Operation DataFor the purposes of this study, the measurements were made during different operational situations in the EAF melting process. The obtained data included measurements of the effective values, i.e., the root mean squares (RMS), sampled over a 1-s window of the following: phase voltages; phase-to-phase voltages; arc voltages; phase currents; power factors; arc resistances and reactances; total circuit resistances and reactances; apparent, active, reactive and arc power; total energy consumption; etc. The measurements were made with the electrode-control and data-acquisition system (E.M.P.E.R.E.). 8) ModelingThe following section presents the approach to mod...

Modeling and Validation of an Electric Arc Furnace: Part 2, Thermo-chemistry

“…The proposed models complement the previous work on the modeling of the electrical and hydraulic processes in an EAF 1) and the work presented in part 1, and represent the final stage of the complete EAF model. The EAF sub-models derived in this paper address the most common chemical reactions, which appear during the steel melting process and include the oxidation and reduction of both chemical elements, such as iron, carbon, silicon, manganese, chromium and phosphorus; and chemical compounds, such as iron oxide, carbon monoxide and dioxide, silica, manganese oxide, chromium oxide and phosphorus oxide.…”

Mechanism of Metal Decarburization and Formation of Carbon Oxide in an Arc Furnace

“…Предложена математическая модель, позволяющая рассчитывать кривые содержания углерода в метал-ле, окисленность шлака и скорость нагрева металла с учетом обезуглероживания при непрерывной загрузке ЖМО в ДСП и подаче кислорода через ТКГ. Модель и ее программа [18,19,20] применимы для расчета управляемого окислительного рафинирования при не-прерывной загрузке, нагреве и плавлении окатышей в ванне дуговой печи. Abstract.…”

Theoretical Estimation of Peak Arc Power to Increase Energy Efficiency in Electric Arc Furnaces

“…A complete mathematical modeling of the electric arc furnace is proposed by Logar et al,12) that integrates relevant concepts like the Cassie-Mayr modeling with the arc reactance model proposed by Köhle and also incorporating a function adding chaotic behavior to the voltage-current relation of the arc, their research work reproduces in a very accurate way the real furnace data. Electric arcs have been modeled by means of numerical modeling by Bakken, Gu & Larsen.…”

“…(10), where E is the voltage field of 11.5 Volts/cm and the constant 40 V is due to the voltage drops at the fall The voltage drop at the electrodes fall region has already been considered as a cathode resistance to get accurate results in modeling of AC-EAFs. 12) As for the DC arcs the voltage drop at the electrodes fall regions is due to the work needed to extract and accelerate electrons from the electrode to the scrap or steel bath but in the AC arcs this function is in two directions, from cathodes to anodes when the electrode acts as cathode in half of the 50 or 60 Hz cycle, and from the steel/scrap to the graphite when the electrode acts as anode in the other semi-cycle of the alternating current. Figure 4 shows a characteristic curve of the cathode and anode voltages versus the arc length (this figure shows a case where an axial distance goes from the tip of the graphite electrode for the negative half-cycle of the AC arc).…”