Model Of Electric Arc Research Articles

An Iterative-adaptive Mathematical Model of Electric Arc in Contact-arc Quenching Systems of Electromagnetic Contactors

An Iterative-adaptive Mathematical Model of Electric Arc in Contact-arc Quenching Systems of Electromagnetic Contactors

Arc Quality Index Based on Three-Phase Cassie–Mayr Electric Arc Model of Electric Arc Furnace

In steel recycling, the optimization of Electric Arc Furnaces (EAFs) is of central importance in order to increase efficiency and reduce costs. This study focuses on the optimization of electric arcs, which make a significant contribution to the energy consumption of EAFs. A three-phase equivalent circuit integrated with the Cassie–Mayr arc model is used to capture the nonlinear and dynamic characteristics of arcs, including arc breakage and ignition process. A particle swarm optimization technique is applied to real EAF data containing current and voltage measurements to estimate the parameters of the Cassie–Mayr model. Based on the Cassie–Mayr arc parameters, a novel Arc Quality Index (AQI) is introduced in the study, which can be used to evaluate arc quality based on deviations from optimal conditions. The AQI provides a qualitative assessment of arc quality, analogous to indices such as arc coverage and arc stability. The study concludes that the AQI serves as an effective operational tool for EAF operators to optimize production and increase the efficiency and sustainability of steel production. The results underline the importance of understanding electric arc dynamics for the development of EAF technology.

Electric arc models with non-zero residual conductance and with increased energy dissipation

Electric arc models with non-zero residual conductance and with increased energy dissipation

Modified Voronin models of electric arc with disturbed geometric dimensions and increased energy dissipation

Modified Voronin models of electric arc with disturbed geometric dimensions and increased energy dissipation

Experimental Study of Arc Discharge Induced Electrode Erosion and Its Influence on Arc Behaviors

Substantial energy dissipation in arc discharge results in strong wall and electrode erosion in a circuit breaker chamber, which largely alters arc plasma properties and thus affects the arc behaviors. Due to the strong vaporization rate, the generated vapor will give rise to a gas flow. Vapor flow and gas-dynamics will change the local partial vapor pressure, which in return adjusts the vaporization rate. The understanding of arc induced vaporization is of great importance to study dynamic arc behavior and the power interruption performance in circuit breakers, which however has not been fully studied. Significant progress has been made in the experiments and modelling of electric arc. Due to the surface ablation and metal erosion, a theoretical model needs to be established to estimate the influence of metal vaporization on the arc behaviors. In this work, we show the experiment of a low-voltage arc discharge and point out the most important factors that determines the metal vaporization rate, namely the discharge current. Beyond an explanation of the physical process of plasma induced erosion, we outline the general approach to study and model the arc induced metal vaporization.

Simulation of Scrap Melting Process in an AC Electric Arc Furnace: CFD Model Development and Experimental Validation

The electric arc furnace (EAF) is a critical steelmaking facility that melts the scrap by the heat produced from electric arc and burners. Simulation and optimization of EAF scrap melting are of great interest to the steel industry, which helps to improve product quality and production efficiency. However, the relevant computational fluid dynamics (CFD) modeling of this process has not been reported so far. The present study established a three-dimensional (3D) integrated CFD model to simulate the scrap melting process in the alternating current (AC) EAF. The scrap melting model was developed to simulate the dynamic scrap melting and collapse based on the dual-cell approach and the stack approach. The electric arc model and the coherent jet model were introduced and integrated with the scrap melting model to estimate the electrical and chemical energy inputs need for melting. The CFD-compatible Monte Carlo method and electrode regulation strategy were developed respectively to predict the arc radiative heat dissipation and track the instant electrode movement. The experiments for the scrap melting by both electric arc and coherent jet burner were designed and implemented in the industry-scale NLMK 150-ton EAF for the model validation. The proposed model was applied to simulate the scrap melting process under the NLMK EAF typical run, and the scrap melting behavior, the electric arc performance, and the burner performance were evaluated and discussed based on the simulation results.

Arc Voltage Distortion as a Source of Higher Harmonics Generated by Electric Arc Furnaces

Due to high unit capacities, electric arc furnaces are among the receivers that significantly affect the power system from which they are supplied. Arc furnaces generate a number of disturbances to the power grid, including fast-changing voltage fluctuations causing the phenomenon of flickering light, asymmetry, and deformation of the voltage curve. The main issues discussed in the article are problems related to the distortion of current and voltage waveforms, resulting from the operation of electric arc furnaces. An analysis of the indices characterizing the voltage distortion recorded in the supply network of the arc furnaces is presented. The changes in the range of current and voltage waveform deformation in individual smelting phases in the arc furnace are also presented. Furthermore, the changes in the degree of deformation of the current and voltage waveforms in the individual smelting phases in an arc furnace are presented. A multi-voltage electric arc model used in computer simulations is proposed.

The Use of the Integral Method in the Determination of the Mayr-Voronin and Cassie-Voronin Simplified Mathematical Models of Electric Arc with the Changeable Length of the Plasma Column

The article discusses the possibility of extending the usability of wellknown integral method formulas used to determine the parameters of the Mayr and Cassie mathematical models of fixed-length arc. Simulation tests discussed in the article involved the simplified variants of the Mayr-Voronin and Cassie-Voronin models of electric arc with dissipated power proportional to the volume of the elongated column. Results obtained in the tests proved the usability of the above-named formulas when calculating the parameters of modified arc models within a wide range of elongation rate changes.

Energy optimization of the electric arc furnace for operations at a fixed electrical power level

This paper presents an optimal control problem (OCP) that finds the optimal voltage and impedance setpoints that improve the electrical efficiency of an EAF for operations at a fixed power level. In the optimization framework, an electric arc model and an EAF process model are embedded into a dynamic optimization framework that aims at minimizing the radiation losses of the process. A numerical case study shows a reduction of 5% of the electrical power consumption of the process and an increment of 2% in the energy efficiency. It is demonstrated that the electrical power consumption of the process can be reduced under a mono profile setting of the EAF.

Diagnostics of Electric Arc versus the Development of Universal Mathematical Models

The article presents universal mathematical static current-voltage characteristics- based models of electric arc and indicates primary issues concerned with arc diagnostics related to the determination of the above-named models. Particular attention was paid to the experimental determination of AC-powered arc voltage. Diagnostics-related purposes involved the use of bridge systems with one or two sources of current. Computer-aided simulations involving sinusoidal and trapezoidal current-based excitations made it possible to demonstrate the possibility of obtaining minimum values of bridge unbalance voltage. Such a condition indicated the proper determination of AC-powered arc ignition voltage.

A statistical-based criterion for incipient fault detection in underground power cables established on voltage waveform characteristics

The incipient faults which mainly occur due to the electric arc occurrence in the power cables with insulation defects are hardly detectable by the conventional protective relays, and over time can develop into a permanent fault in the system. Employing Kalman filter, this paper puts forward a method to detect the incipient faults and to discriminate them from other similar incidents in the power system. The proposed method is established on the comparison between the waveform of the measured voltage and fundamental component of the measured voltage, estimated by Kalman filter algorithm in the sending end of the cable during the fault. Employing the difference between the measured and estimated waveforms, the incipient fault detection and discrimination are carried out within two stages. In the first stage, event detection is relegalized by comparing the standard deviation of the obtained error with a certain threshold. The second stage is conducted to find the incipient fault based on the non-attenuating characteristic and quasi-periodic nature of the incipient fault. The feasibility of the proposed method is verified through computer simulation using four different electric arc models and also the acquired experimental data from real incipient faults.

The Mayr-Pentegov Model of Electric Arc Involving the Use of the Exponential Function and Enabling the Approximation of Static Characteristics

The article presents the justified use of functions containing the exponential component for the approximation of the static current-voltage characteristics of electric arc. The Author proposed a new function approximating the above-named characteristics which were next used in the mathematical Mayr-Pentegov model, expressed in two, i.e. differential and integral, forms. The two forms constituted the basis enabling the development of macromodels using controlled voltage and current sources. The article also presents families of dynamic current-voltage characteristics obtained through the simulation of processes in a circuit containing macromodels of arc powered by the source of current characterised by sinusoidal and trapezoidal waveforms and various frequency. The article demonstrates the usability of the proposed variants of the Mayr-Pentegov model.

Vacuum contactor operation with parallel connection of independent consumers

This work presents a model of a transformer substation with parallel connection of independent consumers via vacuum switches. Several options of an electric arc model are considered upon switching off a vacuum switch such as: KEMA model and “black box” model. Modern computer models of vacuum switches were analyzed. Since the model data were not suitable for the conditions of the experiment, a simulation computer model was developed that reflects the specifics of the operation of the substation and of the transition process upon disconnection of one or several vacuum switches. The results of the developed methodology of analyzing transition processes were verified. To check the results of computer simulation, an experimental model was constructed, it consisted of: an electric load (inductive nature), a power supply, two vacuum switches, and a measuring circuit. The circuit is switched on and off using a pneumatic system controlled by a microcontroller. The primary purpose of the work is to check mutual influence of vacuum switches upon parallel disconnection, since there may be a restrike caused by effects of switching overvoltage between neighboring switches upon irregular disconnection. The effects of a transition process in one switch on the total current of the entire system were identified. A stand for a projected trial was demonstrated as well.

The Effect of the Selection of a Function Approximating Static Characteristics on the Modelling of Electric Arc

The article presents selected tapering functions useful when creating hybrid models and functions approximating static current-voltage characteristics of arc. The research work involved the formation and verification of families of static current-voltage characteristics with defined values of voltage ignition and the extension of approximating possibilities of the formulas through the use of tapering functions. The effective use of various functions approximating static characteristics in the modelling of dynamic states in the circuit with electric arc was verified through simulation.

The Mayr-Pentegov Model of Electric Arc with Selected Static Current-Voltage Characteristics

The basic properties of the Mayr-Pentegov mathematical model of the electric arc were described. A set of generalized functions has been selected to approximate static voltage-current characteristics. On their basis, derivatives of the conductance function relative to the squared current, which are used to calculate the non-linear damping function, were determined. Families of static characteristics dependent on parameters of approximating functions are presented. As a result of the simulations of processes in the circuit with the electric arc model, the family obtained dynamic voltage-current characteristics. By using wide ranges of parameter changes, the usability of the developed model using various approximations of static characteristics was demonstrated.

Detection of the natural frequency of transmission power lines applying S-transform on Transient Recovery Voltage

This paper presents a new approach for detecting the natural frequency of transmission power lines applying S-transform on Transient Recovery Voltage (TRV). TRV usually appears between terminals of a circuit breaker during an isolation of a fault. The TRV phenomenon contains wideband frequency information such as the natural frequency of the system that depends not only on the electrical transmission line characteristics but also on the location of the fault. S-transform was applied to the TRV signal and the energy content in the time-frequency contours was evaluated using Parseval's theorem. This analysis ensures the accurate identification of the natural frequency of the resulting system by locating the maximum relative of the energy content. The case studies studied involved taking actual systems and using frequency-dependent phase models. The experiments were performed to show that the proposed approach can robustly determine the frequency associated with the parameters of the line. Different cases were considered: distances, inception angles, fault resistances, circuit breakers and models of electric arc. The simulation results demonstrate that using S-transform to analyse TRV provides a simple and reliable method for determining the natural frequency and opens a new way for studying the behaviour of protections and faults in power systems.

Зависимость процессов в дугогасительной решетке от радиуса движущейся электрической дуги

In electrical apparatuses containing an arc chute, arc occurs initially on the contacts arranged between the insulating walls spaced at a relatively wide distance from each other, after which the electromagnetic forces drive the arc into the area occupied by the chute plates. Electric arc is a complex phenomenon, in which a large number of physical interactions occur within a very short period of time. An analysis and calculation of arc processes in the arc quenching devices of electrical apparatuses imply simultaneous consideration of thermal gas dynamic, kinetic, electrical (network), arc, and mechanical processes. This adds much difficulty to a search of acceptable models that would satisfy all these requirements. The difficulties of solving the equations that are based on the general principles of thermodynamics and the laws of continuum mechanics are connected, in particular, with the validity of boundary and initial conditions, which are usually selected with due regard for experimental data (it should be noted that the experimental techniques in studying an arc are quite sophisticated and costly). In the course of many years, many electric arc modeling methods have been developed. The following three basic types of electric arc models should be pointed out: a physical model, a black box model, and a parametric model. These models cannot show all physical processes in an electric arc, but they can describe the variations of the main parameters. The physical processes accompanying the arc motion can slow down or even stop its displacement, which may lead to an emergency. Therefore, it is very important to select the arch chute parameters in such a way that it would offer the lowest resistance to the arc motion. In this regard, it is of primary importance to estimate the electric arc channel radius. The article is devoted to calculating the electric arc channel radius. The calculations presented in the article can be useful in selecting the parameters of arc chute plates.

Computing of 3D Bifurcation Diagrams With Nvidia CUDA Technology

This paper presents three-dimensional bifurcation diagrams in the form of a point cloud. The diagrams were created by means of parallel calculations using the electric arc model. A simple dynamic DC electric model that can show complex bifurcations with periodic and chaotic responses is presented. The Nvidia CUDA massively parallel architecture was used to perform the calculations. The paper shows cross-sections of the bifurcation cloud obtained as a result of calculations. It also presents an interactive tool specially developed to visualize the cloud. The reader can access the tool by using the Web address provided in this paper. This tool enables to freely specify the plane and axis of the cut in order to obtain the desired cross-section of the cloud - it is possible to obtain exactly such diagrams as those presented in the paper, as well as many others.

Mathematical modeling of electrical parameters of AC–EAF

The article presents one of the possible options of mathematical model formation of an electric arc steel-making furnace (EAF). A lot of reports on this subject were studied in order to make a model that most accurately reflects the control object behavior (for EAF). The basic building principles demonstrate the fact that the primary element is substitution pattern of electric circuit of the installation. Cassie nonlinear differential equation was used to get a mathematical model of an electric arc. This nonlinear differential equation is very popular among the researchers. Model update is provided by calculating the electrical circuit parameters on the secondary side of transformer low voltage and by studying statistics from home and foreign scientists’ contributions. Different values of the “time-constant” of arc conductivity were used to analyze the control object behavior at different instants of time. It made it possible to take into account the nonstationarity of the state of electrode sheaths that were influenced by external disturbances, temperature variations, pressure and gas composition in the course of production processes. Such an approach made possible to form an aggregate picture of the control object behavior under the conditions of a nonstationary state of the arc combustion area at different stages of melting; to evaluate possible regulation characteristics and to determine control system requirements. The structural scheme of the model of a three-phase AC–EAF was formed. All necessary calculations of circuit elements and modeling were performed using the MATLAB Simulink package. The block diagram includes AC voltage source, direct-current resistance, and inductance of the transformer on secondary side and a low-voltage circuit, a model of an AC electric arc. The model was used to analyze the dynamic characteristics of electric arc as being an electrical object to show the voltage–dependence of current – current-voltage characteristics. The configuration of current-voltage characteristics determines burning behavior of the arc, existence domain, stability and control quality. Current-voltage characteristics were studied under the conditions of different values of the voltage on the secondary side of transformer and arc length and for different values of the “time-constant arc conductivity”. The model was also used to analyze the static characteristics. The dependence of the arc length on the current for different voltage of the transformer steps is nonlinear. Recommendations on the choice of control actions and the construction of control systems for different stages of melting are given. For example at the initial stage of melting, the control system should perform minimization problems of number of breaks under the condition of an insignificant domain of the arc existence and limit the value of lead-in power. The simulation results show that the nonstationarity of the process leads to the need to use self-organizing control systems capable of adjusting to the continually varying state of the object.

Estimation of the Intensively Blasted Electric Arc Model Sensitivity to Selected Variables

Results of measurements carried out on the fabricated experimental modular-type arc heater serve as input data for the designed simplified model of the intensively blasted electric arc burning in argon inside the cylindrical arc heater's anode channel. The axial dependence of the arc temperature and radius is expressed using the exponent, the current density on the cathode tip and the arc temperature at the end of the near-cathode boundary layer. These quantities form the vector of state variables that is sought to minimize the value of the objective function expressing the deviations between measured and computed values. On a typical example, the paper demonstrates the sensitivity of the modelling to individual state variables.