Nieliniowe modele matematyczne łuku elektrycznego

Mathematical Differential and Integral Models in the Macromodelling of Electric Arc Using Voltage and Current Controlled Sources Part 2. Selected Mathematical Arc Macromodels with Explicitly Defined Current and Voltage Characteristics

“…If the static current-voltage characteristic U(I) is used, the power of arc dissipation is described by the following dependence (3), where G(I) -static characteristic of column conductance. By substituting formulas (2) and (3) to (1) it is possible to obtain the Mayr modified equations in the conductance form (4),…”

“…The application of static characteristics for the development of dynamic models of electric arc facilitates the following: 1. identification of certain parameters of dynamic models in the differential and integral form [2]; 2. taking into consideration disturbances in the form of interference and control effects in mathematical models; 3. control of changes in characteristic parameters of electric arc (e.g. ignition voltage, residual conductance) [2][3][4]; 4. in certain cases, interpretation of physical processes in circuits with electric arc. Engineering practice uses several wellknown mathematical differential models of electric arc including current-voltage characteristics.…”

Classical and Modified Mathematical Models of Electric Arc

“…The extent, to which such assumptions can be fulfilled depends on excitation (range of current amplitude and frequency) and other arc burning physical conditions (e.g. temperature, pressure, the chemical composition of gas) [9][10]. The objective of the implementation of modifications in classical models or combining them to form hybrid models [11] is the extension of their application ranges when simulating electromagnetic processes in technological devices.…”

“…In certain cases related to the analysis of circuits operating within a wide range of current amplitude changes, other modifications are assumed, e.g. by applying a non-linear damping functions depending on column current q(i) or conductance q(g) [9][10][11][12]. Because of the adopted initial assumptions and accuracy of approximation, the Mayr model and its modifications are used to represent processes in circuits with low-current arc, whereas the Cassie model and its modifications are used to represent processes in circuits with high-current arc.…”

Mathematical models of the electric arc of variable geometrical parameters based on static voltage-current characteristics

“…In some devices however, the changes in the working conditions occur very fast, which may lead to deteriorating the discharge stability and to undesirable changes in technological effects. This indicates the conditions with rapid changes have to be taken into account in simulation tests [1,17].…”