Mayr Model Research Articles

Modeling and Comparison Study of Industrial AC-Arcs

Electric arcs are a necessary heat source in many industrial processes that take place in Submerged Arc Furnaces (SAFs). Arcs exhibit non-linear electrical characteristics and behave in a complex manner. Therefore, an improved understanding of their behavior enables better control of furnace operation. Modeling of industrial arcs is a multiphysics process that involves simultaneously solving several coupled physical phenomena, such as electromagnetics, fluid dynamics, and heat transfer, including a radiative heat transfer from the plasma arc. Coupling fluid dynamics and electromagnetics is known as Magnetohydrodynamics (MHD). For practical applications, however, there are also simpler approaches to arc modeling, either based on simplified physical principles or empirical behavior. In this paper, a combined Cassie–Mayr model (CMM) and a channel arc model (CAM) are implemented and coupled with a submerged arc furnace electrical circuit model. The complete circuit model parameters such as resistances and inductances are estimated using modeling of a full size furnace, and then, actual measurements from a SAF are used to validate the models by comparing current and voltage waveform. Both models are then used to estimate harmonic distortion in a SAF for different arc current ratios, which should help operators to estimate the arc current in real time thus be able to lower and raise the electrode to keep operating conditions constant.

Inferring the evolution of reproductive isolation in a lineage of fossil threespine stickleback, Gasterosteus doryssus.

Darwin attributed the absence of species transitions in the fossil record to his hypothesis that speciation occurs within isolated habitat patches too geographically restricted to be captured by fossil sequences. Mayr's peripatric speciation model added that such speciation would be rapid, further explaining missing evidence of diversification. Indeed, Eldredge and Gould's original punctuated equilibrium model combined Darwin's conjecture, Mayr's model and 124 years of unsuccessfully sampling the fossil record for transitions. Observing such divergence, however, could illustrate the tempo and mode of evolution during early speciation. Here, we investigate peripatric divergence in a Miocene stickleback fish, Gasterosteus doryssus. This lineage appeared and, over approximately 8000 generations, evolved significant reduction of 12 of 16 traits related to armour, swimming and diet, relative to its ancestral population. This was greater morphological divergence than we observed between reproductively isolated, benthic-limnetic ecotypes of extant Gasterosteus aculeatus. Therefore, we infer that reproductive isolation was evolving. However, local extinction of G. doryssus lineages shows how young, isolated, speciating populations often disappear, supporting Darwin's explanation for missing evidence and revealing a mechanism behind morphological stasis. Extinction may also account for limited sustained divergence within the stickleback species complex and help reconcile speciation rate variation observed across time scales.

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.

Modeling and Simulation of a Transient Process and an Analysis of Transient Characteristics in the Switching Operation of Disconnectors

High-voltage switchgears can generate high-frequency and high-amplitude electromagnetic interference during their operation, which may lead to abnormal outputs of the measurement devices, thus giving rise to measurement errors or protective relay malfunctions and impacts on the stable running of the power grid. Considering the air breakdown delay, a dynamic reignition model consisting of the hyperbolic model, the static model and the improved Mayr model is proposed to analyze the transient process during the on/off operation of open-type disconnectors. Meanwhile, the influence of arc resistance, line length and breakdown delay on the model were analyzed, and an experimental circuit was built to verify the simulation results through a comparison. It was found that the proposed model could reflect the high-frequency voltage and current during the on/off operation more accurately and thus provide an effective method for the precise modeling of the switching operation of the disconnector.

Ground Fault Identification in Distribution Network Based on MMC Injection Detection Signal Strategy

In order to improve the identification efficiency and accuracy of distribution network ground fault identification methods, this paper proposes a distribution network ground fault identification method based on MMC injection detection signal strategy. Extract the fault information of distribution network grounding line, calculate the current component of three-phase current, and obtain the grounding fault data of distribution network.The detection current of distribution network is obtained by injection signal detection strategy. The fault information matrix is formed by using the detection current information, and the time-frequency characteristics of MMC injection detection signal strategy are obtained according to the actual situation.The wavelet transform is used to remove the clutter in the fault feature vector, and the normalized processing is used to obtain and process the ground fault vector.According to the wavelet function, the characteristics of the distribution network ground fault signal are determined. Cassie model and Mayr model are used to obtain the final distribution network ground fault identification model to realize the distribution network ground fault identification.The experimental results show that the accuracy of the method can reach 96.1%, and the time of fault identification is only 25s. The above results show that the method can effectively improve the effectiveness of distribution network ground fault identification.

Parameter Determination Method of Cassie-Mayr Hybrid Arc Model Based on Magnetohydrodynamics Plasma Theory

This paper proposes an improved alternating current (AC) arc model based on the Cassie-Mayr hybrid model and magnetohydrodynamics (MHD) theory. The undetermined parameters of the traditional Cassie-Mayr arc model are mainly obtained by subjective methods such as empirical value, approximate expression, and indirect estimation which are complex, inaccurate, and dependent on experimental data. To overcome these disadvantages, an axisymmetric two-dimensional arc model is established based on the MHD theory, and the undetermined parameter values of the Cassie-Mayr hybrid arc model are obtained based on the results of MHD numerical simulation. The accuracy of the proposed modified Cassie-Mayr model is verified by comparing with experimental data, and the results of the modified Cassie-Mayr model, traditional Mayr model, and Cassie model are discussed. The arc characteristics of serval loads are studied and analyzed based on the modified model.

Generalized Mayr Model for Arcs in MV Switches With Splitter Plates

The effect of splitter plates (SP) on current interruption at medium voltage (MV) level is theoretically investigated in the framework of Mayr&#x0027;s arc model, which is generalized to take into account the electrode fall voltage, <i>V</i>₀, of the SP. The model is analytically solved in the current zero (CZ) region where the current (before CZ) and the voltage (after CZ) can be linearized with respect to time. The current turns out to be successfully interrupted if the total electrode fall voltage, <i>NV</i>₀, for <i>N</i>&#x00A0;&#x2212;&#x00A0;1 SP plus contact electrodes, is larger than twice the transient recovery voltage, <inline-formula><tex-math notation="LaTeX">${\boldsymbol{U}} \approx {\dot{\boldsymbol{U}t}}$</tex-math></inline-formula>, at the characteristic arc decay time, <i>t &#x003D; &#x03C4;</i>, after CZ: <inline-formula><tex-math notation="LaTeX">${\boldsymbol{N}}{{\boldsymbol{V}}_0} &gt; 2{\dot{\boldsymbol{U}\tau }}$</tex-math></inline-formula>. For <inline-formula><tex-math notation="LaTeX">${\boldsymbol{N}}{{\boldsymbol{V}}_0} &lt; 2{\dot{\boldsymbol{U}\tau }}$</tex-math></inline-formula>, an additional thermal condition must be satisfied, where also the current rate, <inline-formula><tex-math notation="LaTeX">${\dot{\boldsymbol{I}}} = {\boldsymbol{\ dI}}/{\boldsymbol{dt}}$</tex-math></inline-formula> before CZ, and the arc cooling power, <i>K</i>, are involved. The intuitive results lead to a simple understanding of the electrical effect of SP on current interruption at MV and serve as an initial design rule for the number of SP in different gases.

Modeling and simulation of arc grounding fault of middle and low voltage distribution network based on ATP-EMTP

In middle and low voltage distribution networks, single-phase grounding fault is most like to occur, so the mathematical model to accurately reflect the characteristics of grounding arc is the basis of network fault analysis. Based on arc-gap balance theory, this paper analyzes the characteristics of the classic Mayr model and Cassie model, establishes an arc model with reasonable combination of Mayr and Cassie, and further studies the influence of arc length parameters on arc characteristics, and reflects the physical characteristics of the grounding arc. Finally, the arc model is simulated in a 10 kV distribution network in the fault form of intermittent arc grounding. By comparing the results with the actual situation, the correctness of the arc model is verified, which lays a good foundation for the following fault analysis of distribution network.

Parameter estimation of extended free-burning electric arc within 1 kA

A long electric arc, as a common phenomenon in the power system, not only damages the electrical equipment but also threatens the safety of the system. In this work, a series of tests on a long electric arc in free air have been conducted. The arc voltage and current data were obtained, and the arc trajectories were captured using a high speed camera. The arc images were digitally processed by means of edge detection, and the length is formulated and achieved. Based on the experimental data, the characteristics of the long arc are discussed. It shows that the arc voltage waveform is close to the square wave with high-frequency components, whereas the current is almost sinusoidal. As the arc length elongates, the arc voltage and the resistance increase sharply. The arc takes a spiral shape with the effect of magnetic forces. The arc length will shorten briefly with the occurrence of the short-circuit phenomenon. Based on the classical Mayr model, the parameters of the long electric arc, including voltage gradient and time constant, with different lengths and current amplitudes are estimated using the linear least-square method. To reduce the computational error, segmentation interpolation is also employed. The results show that the voltage gradient of the long arc is mainly determined by the current amplitude but almost independent of the arc length. However, the time constant is jointly governed by these two variables. The voltage gradient of the arc with the current amplitude at 200–800 A is in the range of 3.9 V/cm–20 V/cm, and the voltage gradient decreases with the increase in current.

Reignition After Interruption of Intermediate-Frequency Vacuum Arc in Aircraft Power System

Intermediate frequency (IF) electric power supply system has been widely applied in airplanes. Reignition after interruption of 360-850 Hz vacuum arc in axial magnetic field (AMF) is studied in this paper. According to the experimental results, the current interruption ability decreases from 22.4 kA at 360 Hz to 14.0 kA at 850 Hz. With the increase of frequency, the rate of change of current, di/dt, at current zero (CZ) reaches the breaking threshold at a smaller current value. Based on the least squares solution of the Mayr model, the time of decay of arc energy is prolonged when interruption fails, which is disadvantageous to the breaking process. On the other hand, the eddy effect is enhanced by higher frequency, which increases the residual magnetic induction intensity and the hysteresis phase of AMF after CZ. As a result, the diffusion of plasma is blocked. In the experiments, we find that the position of arc reignition always appears at the margin of contacts. It is shown by calculation that the electric field at the marginal area is twice as strong as that inside the contact. The current density is high, where the electric field is strong, leading to the higher probability of field emission. Arc images are analyzed by frame differential method. The sputtering velocity of macroscopic particles is estimated to be 10-20 m/s. The dissipation time of the macroscopic particles is longer than the arc time of IF vacuum arc, and the presence of macroscopic particles leads to the arc reignition. The findings of this paper would be beneficial to the parameter design of IF vacuum circuit breakers, such as the magnetic flux density of AMF, the chamfering of contact margin, and contact materials.

Dynamical Models of Electric Arcs and Memristors: The Common Properties

We discuss the memristive properties (or fingerprints) of the hybrid Cassie–Mayr model of electric arcs. In particular, we prove that: 1) the voltage–current characteristic of the model has the pinched hysteresis nature; 2) the voltage and current zero crossings occur at the same instants; and 3) when the frequency $f$ of the power supply increases, the voltage–current pinched hysteresis characteristic tends closer to a single-valued one, meaning that the voltage–current graph becomes that of a resistor (with an increased linearity for $f\rightarrow \infty $ ). The conductance $g$ of the Cassie–Mayr model decreases when the frequency increases. The hybrid Cassie–Mayr model describes, therefore, an interesting case of a memristive phenomenon.

Generalised Cassie–Mayr electric arc furnace models

Electric arc furnace (EAF) is one of the largest loads in the power systems. Unfortunately, it is highly non-linear and time varying which causes power quality problems such as harmonics and flicker. Therefore, having an accurate EAF model is necessary. Cassie model is one of the most utilised EAF models in the related fields. However, actual data from electrical system of Mobarakeh Steel Company in Isfahan/Iran show that this model is unable to take into account some important quantities such as the active power and harmonics. Hence, as the first step in this study, different Cassie–Mayr model variants (include the Cassie model) are investigated and the best variant is attained. A novel procedure using large number of recorded actual data is utilised for the models assessment. In the second step, two generalised types of the original Cassie–Mayr model are proposed. Both the generalised types are more accurate than the best-selected Cassie–Mayr variant. All the proposed models have time-varying parameters. Their time-varying nature is studied and by analysing the time series, the proper auto regressive moving average models are attained for every parameter.

Memristive behaviour of high‐impedance faults

In this reported work, the analogy between parallel electrical arcs and memristors is extended to high-impedance faults such as carbonised paths and circuit openings. First, it is demonstrated that the conductance from the high-impedance Mayr model behaves like a particular memductance sensitive to the integral of the squared current. Then, the current–voltage plot confirms the memristive behaviour of high-impedance faults, both by simulation and with experimental results.

Model for Variable-Length Electrical Arc Plasmas Under AC Conditions

This paper proposes a mathematical model for electrical discharge plasmas between moving electrodes under ac condition, which happens in ac switching apparatuses. The modeling work is started by converting the problem to a conventional RL network that treats the arcing phenomenon as a black box and proposing a transient differential equation to represent the breaking arc process. A resistance–time relation model developed from the classic Mayr model is then proposed. A conceptual unit-arc approach is used to deal with the issue of variable arc length as the contacts move. Experimental data from ac contactor tests are used to approximate the resistance–time function by a nonlinear curve fitting. The model is solved computationally and compared with the experimental data. It is that the model adequately describes the breaking arc phenomenon.

Arcing Model of a Disconnector and its Effect on VFTO

In the computational process of very fast transient over-voltage (VFTO), it is essential to find an accurate model for a gas insulated substation. The arcing model of the disconnector is particularly important. The general arcing model is not able to give a good description of the arc development process. In this paper, based on the physical process of arcing and existing arc models (the exponential time-varying resistance model and the segmental arcing models), a dynamic arcing model is proposed, which is divided into two stages before and after the zero crossing. The dynamic arcing model combines hyperbola time-varying resistance and the Mayr model to describe the dynamic process of arcing. The present paper creates an arc model blockset upon the Matlab/Simulink software platform. Moreover for a specific 1100 kV station, VFTO is simulated in detail based on different arcing models. It is demonstrated that the dynamic arcing model can describe the physical arc process precisely and is useful for improving the accuracy of VFTO simulations.

Hybrid model of electric arcs in high voltage circuit breakers

In this work, a 0D hybrid model for arc quenching in a high voltage (HV) SF6 circuit breaker is developed. It integrates the thermal radiation of the plasma and enables to simulate the arc voltage and the conductance evolution through varying current ranges. We also show that the overvoltage peaks due to the transition between the developed model and Mayr model decrease when gases of weak ionization constant are used. The numerical solving of the model equations is based on the direct programming of Runge–Kutta method for default currents of about 90% of the breaking capacity in an SF6 circuit breaker (245kV/50kA/50Hz).

Improved Mayr Model of Electrical Arc Furnace to Analyse Harmonic

Voltage flicker and harmonics are power quality problems which are imposed on power system by electrical arc furnace. To study furnaces and find a solution to remove the negative effects of them, it is needed to have an appropriate electrical arc furnace model. Several methods in time and frequency domain have been presented. One of the time domain methods is Mayr model which has two problems. Firstly, it shows the harmonic components more than the real values. Secondly, it does not involve voltage flicker phenomenon. In this article with the comparison of harmonic components of Mayr model and measured values of arc furnace, an improved Mayr model is introduced. In the presented model, the problems of Mayr model are removed and it shows the real behavior of arc furnace

Mayr's Equation-Based Model for Pantograph Arc of High-Speed Railway Traction System

This letter presents an extended Mayr's equation-based model for the pantograph detachment arc of the high-speed railway traction system. The proposed model is composed of Mayr's model for arc behavior control and time-controlled switches for starting pantograph detachment and reattachment events, which are developed by MODELS language and TACS in Electromagnetic Transients Program/Alternate Transients Program. With the combination of a traction motor drive circuit, an effective simulation is performed to observe the harmonic spectrum of pantograph current that is caused by pantograph detachment arcs. By comparing this with the actual measurements for validation, it shows that the proposed arc model is useful for estimating the harmonic frequency range of the pantograph arc current and for power-quality studies.

Simulation of SLF Interrupting Performance for SF6 Gas Circuit Breaker based on Serially Connected 3 Arc Models

This paper shows the simulation of SLF interrupting performances for SF6 gas circuit breakers. From the measurements using 300kV-SF6 gas model circuit breakers, it was shown that the extinction peak voltages were varying with arcing times. But, the current values at the extinction peak were the same.To simulate the SLF interrupting performances for the circuit breakers, serially connected 3 arc models were used. Cassie arc model and two Mayr arc models were serially connected. In this arc model, the Cassie model simulates the high current arc. One of the Mayr arc model (Mayr model 1) simulates the arc around the voltage extinction peak. And the other Mayr arc model simulates the arc around current zero. In this model, arc voltage of the Cassie model and arc power loss of the Mayr model 1 are only estimated from the experiments. It was good agreement with the measurements and simulations.

The simulation of circuit breaker switching using a composite Cassie-modified Mayr model

In substation electromagnetic compatibility studies or insulation coordination studies it is desirable to obtain as accurate a representation as possible of the transients generated by faults and switching events. A method of simulating the voltage and current transients generated by gas blast circuit breaker operation using a composite Cassie-modified Mayr model of the circuit breaker arc is described. It is demonstrated that this gives good agreement with published laboratory measurements of the circuit breaker voltage and current. The transmission line modelling method is used in the construction of the simulation algorithm of the circuit breaker circuit. A method, based on describing the circuit breaker using a transmission-line model is used to decouple the nonlinear characteristics from the rest of the network.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>