Modeling and Simulation of Low Voltage Arcs

Modeling and Simulation of Low Voltage Arcs is an attempt to improve the physical understanding, mathematical modeling and numerical simulation of the electric arcs that are found during current interruptions in low voltage circuit breakers. An empirical description is gained by refined electrical measures and fiber optics based imaging. Ways to assess with a graded scale the interruption performance of a circuit breaker are developed. A theoretical review of the arc plasma physics allows to gain an insight in the governing phenomenon, namely the balance between particle energy gain from the electric field and particle energy redistribution through collisions. The elaboration of this idea to a more abstract level of modeling detail allows to develop a new black box model, based on non equilibrium theory and with increased realism, as well as to address the problem with predictive purposes by means of a computational, multi-physics approach.

[1]  Marjan Popov,et al.  Black Box Modeling of Low-Voltage Circuit Breakers , 2010, IEEE Transactions on Power Delivery.

[2]  P. Henrici.  Discrete Variable Methods in Ordinary Differential Equations , 1962 .

[3]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[4]  Enrico Giusti.  Analisi matematica 1 , 1988 .

[5]  John J. Brehm,et al.  Introduction to the Structure of Matter: A Course in Modern Physics , 1988 .

[6]  K. Thompson.  Time-dependent boundary conditions for hyperbolic systems, II , 1990 .

[7]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[8]  Jean-Yves Trépanier,et al.  Modelling and simulation of nozzle ablation in high-voltage circuit-breakers , 2000 .

[9]  O. Mayr.  Beiträge zur Theorie des statischen und des dynamischen Lichtbogens , 1943 .

[10]  Per Christian Hansen,et al.  Solution of Ill-Posed Problems by Means of Truncated SVD , 1988 .

[11]  J.W. McBride,et al.  Electrode processes and arc form in miniature circuit breakers , 1998, Electrical Contacts - 1998. Proceedings of the Forty-Fourth IEEE Holm Conference on Electrical Contacts (Cat. No.98CB36238).

[12]  Douglas M. Bates,et al.  Nonlinear Regression Analysis and Its Applications , 1988 .

[13]  D. Cajal,et al.  Study of re-strike phenomena in a low-voltage breaking device by means of the magnetic camera , 2001 .

[14]  C. W. Gear,et al.  Differential-algebraic equations index transformations , 1988 .

[15]  B. Taylor,et al.  CODATA recommended values of the fundamental physical constants: 2006 | NIST , 2007, 0801.0028.

[16]  A. E. Guile,et al.  The motion of cold-cathode arcs in magnetic fields , 1961 .

[17]  W.R. Rutgers,et al.  A physical arc model for the simulation of current zero behavior of high-voltage circuit breakers , 1991, Proceedings of the 1991 IEEE Power Engineering Society Transmission and Distribution Conference.

[18]  Gene H. Golub,et al.  Matrix computations , 1983 .

[19]  E. Hobson.  The Theory of Spherical and Ellipsoidal Harmonics , 1955 .

[20]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[21]  E. M. Freeman,et al.  A sparse matrix open boundary method for finite element analysis , 1989 .

[22]  C. W. Gear,et al.  Differential-Algebraic Equations , 1984 .

[23]  Andrew Wilkinson.  Compendium of Chemical Terminology , 1997 .

[24]  M. Mercier,et al.  A study of the various phases of the break in a low-voltage circuit breaker thanks to the magnetic camera , 1999 .

[25]  Richard Phillips Feynman,et al.  Mainly Electromagnetism and Matter , 2011 .

[26]  Sven Erik Mattsson,et al.  Index Reduction in Differential-Algebraic Equations Using Dummy Derivatives , 1993, SIAM J. Sci. Comput..

[27]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[28]  M. Landry,et al.  A new concept in post-arc analysis applied to power circuit-breakers , 1988 .

[29]  H. Whitney.  Geometric Integration Theory , 1957 .

[30]  G. Velleaud,et al.  Study of the low-voltage electric breaking arc restrike by means of an inverse method , 1999 .

[31]  W. Egli,et al.  Use of integral arc models in circuit breaker testing and development , 1988 .

[32]  Mario Bertero,et al.  The Stability of Inverse Problems , 1980 .

[33]  Toshiro Matsumura,et al.  Prediction ofCircuit-Breaker Performance Basedona RefinedCybernetic Model , 1986 .

[34]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[35]  Gareth Jones,et al.  Elementary number theory , 2019, The Student Mathematical Library.

[36]  Lawrence F. Shampine,et al.  Solving Index-1 DAEs in MATLAB and Simulink , 1999, SIAM Rev..

[37]  J.J. Shea,et al.  Contact material and arc current effect on post-current zero contact surface temperature , 2006, IEEE Transactions on Components and Packaging Technologies.

[38]  I. Langmuir,et al.  THE REMOVAL OF THORIUM FROM THE SURFACE OF A THORIATED TUNGSTEN FILAMENT BY POSITIVE ION BOMBARDMENT , 1923 .

[39]  David Burton.  Elementary Number Theory , 1976 .

[40]  C. Pantelides.  The consistent intialization of differential-algebraic systems , 1988 .

[41]  A. Quarteroni,et al.  Numerical Approximation of Partial Differential Equations , 2008 .

[42]  Akademii︠a︡ medit︠s︡inskikh nauk Sssr.  Journal of physics , 1939 .

[43]  Wilson A. Sutherland,et al.  Introduction to Metric and Topological Spaces , 1975 .

[44]  R. H. Good,et al.  Thermionic Emission, Field Emission, and the Transition Region , 1956 .

[45]  M. Lindmayer,et al.  Simulation of the gasdynamic and electromagnetic processes in low voltage switching arcs , 1996, Electrical Contacts - 1996. Proceedings of the Forty-Second IEEE Holm Conference on Electrical Contacts. Joint with the 18th International Conference on Electrical Contacts.

[46]  L. Trahms,et al.  An inverse problem of magnetic source localization , 2005, Numerical Algorithms.

[47]  Peeters,et al.  Thermodynamic generalization of the Saha equation for a two-temperature plasma. , 1989, Physical review. A, General physics.

[48]  A. Quarteroni.  Numerical Models for Differential Problems , 2009 .

[49]  J. Rooda,et al.  Index Reduction and Discontinuity Handling Using Substitute Equations , 2001 .

[50]  François Henrotte,et al.  Finite element modelling with transformation techniques , 1999 .

[51]  T. Apostol.  One-variable calculus, with an introduction to linear algebra , 1967 .

[52]  A. Morro,et al.  Thermodynamic derivation of Saha's equation for a multi-temperature plasma , 1988, Journal of Plasma Physics.

[53]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[54]  L. O. Svaasand,et al.  Boundary conditions for the diffusion equation in radiative transfer. , 1994, Journal of the Optical Society of America. A, Optics, image science, and vision.

[55]  R. Ho.  Algebraic Topology , 2022 .

[56]  Richard Phillips Feynman,et al.  Mainly mechanics, radiation, and heat , 1963 .

[57]  Lou van der Sluis,et al.  An Improved Mayr-Type Arc Model Based on Current-Zero Measurements , 2000 .

[58]  B. Dacorogna.  Introduction to the calculus of variations , 2004 .

[59]  D. Povh,et al.  Circuit breaker model for digital simulation based on Mayr's and Cassie's differential arc equations , 1995 .

[60]  X. Brunotte,et al.  An Original Solution for unbounded electromagnetic 2D- and 3D problems throughout the finite element method , 1990, International Conference on Magnetics.

[61]  G. Raithby,et al.  A multigrid method based on the additive correction strategy , 1986 .

[62]  M. Lindmayer,et al.  The process of arc splitting between metal plates in low voltage arc chutes , 2006, IEEE Transactions on Components and Packaging Technologies.

[63]  J. Toumazet,et al.  Optical and magnetic diagnostics of the electric arc dynamics in a low voltage circuit breaker , 2002 .

[64]  Mofreh R. Zaghloul.  On the vaporization of Teflon and heated compound-materials in ablation-controlled arcs , 2004 .

[65]  K. Han,et al.  Study of the preparation and properties of UV‐blocking fabrics of a PET/TiO2 nanocomposite prepared by in situ polycondensation , 2006 .

[66]  C. Paul.  Introduction to electromagnetic compatibility , 2005 .

[67]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[68]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[69]  Hermann A. Haus,et al.  Electromagnetic fields, energy, and waves , 1972 .

[70]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[71]  I. Madsen,et al.  From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes , 1997 .

[72]  A. W. Trivelpiece,et al.  Introduction to Plasma Physics , 1976 .

[73]  L. van der Sluis,et al.  Current Interruption in Low-Voltage Circuit Breakers , 2010, IEEE Transactions on Power Delivery.

[74]  T. Sakuta,et al.  Measurement of arc properties and spectrum intensity in AC arcs surrounded by plastics , 2002 .

[75]  A. Savitzky,et al.  Smoothing and Differentiation of Data by Simplified Least Squares Procedures. , 1964 .

[76]  Xingwen Li,et al.  Study of the Effect of Gassing Material on Arc Behavior in Low Voltage Circuit Breaker , 2007, IEICE Trans. Electron..

[77]  C. W. Gear,et al.  ODE METHODS FOR THE SOLUTION OF DIFFERENTIAL/ALGEBRAIC SYSTEMS , 1984 .

[78]  L. M. M.-T..  Spherical Harmonics: an Elementary Treatise on Harmonic Functions, with Applications , 1928, Nature.

[79]  P. Hettwer.  Arc-Interruption and Gas-Evolution Characteristics of Common Polymeric Materials , 1982, IEEE Transactions on Power Apparatus and Systems.

[80]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[81]  Heating of refractory cathodes by high-pressure arc plasmas: II , 2002 .

[82]  A. Tikhonov.  On the stability of inverse problems , 1943 .

[83]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[84]  S. Markutsyaa,et al.  Intensive electric arc interaction with polymer surfaces : reorganization of surface morphology and microstructure , 2005 .

[86]  P. Chevrier,et al.  Arc - wall interaction modelling in a low-voltage circuit breaker , 1997 .

[87]  L. Niemeyer,et al.  Ablation Controlled Arcs , 1986, IEEE Transactions on Plasma Science.

[88]  B. Cordani.  The Kepler problem : group theoretical aspects, regularization and quantization, with application to the study of perturbations , 2003 .

[89]  Barry Smith,et al.  Domain Decomposition Methods for Partial Differential Equations , 1997 .

[90]  A. Gleizes,et al.  Net emission coefficient of air thermal plasmas , 2002 .

[91]  E. V. Bonin,et al.  Quenching Processes of Axially Inhomogeneous Arcs in SF6 Circuit Breakers , 1980, IEEE Transactions on Plasma Science.

[92]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[93]  Fei Yang,et al.  Three-Dimensional Numerical Analysis with P-1 Radiation Model in Low Voltage Switching Arc , 2007, IEICE Trans. Electron..

[94]  D. Givoli.  Non-reflecting boundary conditions , 1991 .

[95]  Hans Sagan,et al.  Introduction to the Calculus of Variations. , 1969 .

[96]  J. McBride,et al.  Magnetic and gas dynamic effects on arc motion in miniature circuit breakers , 1993 .

[97]  P. H. Schavemaker,et al.  Digital testing of high-voltage circuit breakers , 2000 .

[98]  Anil Date,et al.  Introduction to Computational Fluid Dynamics , 2023, essentials.

[99]  Raffaele Albanese,et al.  Magnetostatic field computations in terms of two‐component vector potentials , 1990 .

[100]  W.,et al.  Time Dependent Boundary Conditions for Hyperbolic Systems , 2003 .

[101]  V. V. Nossov,et al.  Simulation of the thermal radiation effect of an arc on polymer walls in low-voltage circuit breakers , 2007 .

[102]  R. Penrose.  On best approximate solutions of linear matrix equations , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[103]  M. Modest.  Radiative heat transfer , 1993 .

[104]  M. Benilov.  Understanding and modelling plasma–electrode interaction in high-pressure arc discharges: a review , 2008 .

[105]  J. Didier,et al.  Arc-contact-insulating wall interactions in low voltage circuit-breakers , 1998 .

[106]  Fei Yang,et al.  Numerical analysis of arc plasma behaviour during contact opening process in low-voltage switching device , 2007 .

[107]  M. N. Özişik.  Radiative Transfer And Interactions With Conduction And Convection , 1985 .

[108]  P. H. Schavemaker,et al.  Quantification of the interrupting performance of high-voltage circuit breakers , 2002 .

[109]  E. Heine.  Die Elemente der Functionenlehre. , .

[110]  J. Navarro-Pedreño.  Numerical Methods for Least Squares Problems , 1996 .

[111]  Andrew S. Glassner,et al.  An introduction to ray tracing , 1989 .

[112]  H. Maecker,et al.  Elektrische Bögen und thermisches Plasma , 1956 .

[113]  A Tikhonov,et al.  Solution of Incorrectly Formulated Problems and the Regularization Method , 1963 .

[114]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[115]  R. Penrose.  A Generalized inverse for matrices , 1955 .

[116]  J. McBride,et al.  Anode and cathode arc root movement during contact opening at high current , 1999 .

[117]  John Henry Poynting,et al.  On the transfer of energy in the electromagnetic field , 1883, Proceedings of the Royal Society of London.

[118]  Yasunori Tanaka,et al.  Numerical and experimental investigations on thermal interaction between thermal plasma and solid polymer powders using induction thermal plasma technique , 2008 .

[119]  J. Nédélec.  A new family of mixed finite elements in ℝ3 , 1986 .

[120]  Yi Wu,et al.  Simulation Study of the Influence of Wall Ablation on Arc Behavior in a Low-Voltage Circuit Breaker , 2009, IEEE Transactions on Plasma Science.

[121]  M. Dresser.  The Saha‐Langmuir Equation and its Application , 1968 .

[122]  Y. Wong,et al.  Differentiable Manifolds , 2009 .

[123]  Y. Nakamichi,et al.  Analysis of Electric Arcs in AC Circuits , 1983, IEEE Transactions on Power Apparatus and Systems.

[124]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[125]  E van Bonin,et al.  Advanced Methods of Circuit-breaker Engineering , 1979 .

[126]  Wp Legros,et al.  Circuit Breaker Stochastic Behaviour Simulation , 1979 .

[127]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[128]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[129]  J.W. McBride,et al.  Arc root mobility during contact opening at high current , 1996, Electrical Contacts - 1996. Proceedings of the Forty-Second IEEE Holm Conference on Electrical Contacts. Joint with the 18th International Conference on Electrical Contacts.

[130]  R. Bachmann,et al.  ON METHODS FOR REDUCING THE INDEX OF DIFFERENTIAL ALGEBRAIC EQUATIONS , 1990 .

[131]  Loring W. Tu,et al.  Differential forms in algebraic topology , 1982, Graduate texts in mathematics.

[132]  M Claessens,et al.  A computational fluid dynamics simulation of high- and low-current arcs in self-blast circuit breakers , 1997 .

[133]  Cecie Starr,et al.  Biology: Concepts and Applications , 2005 .