Classical and Modified Mathematical Models of Electric Arc

Abstract

The article presents classical mathematical models of electric arc characterised by undetermined or unreduced ignition voltage. The aforementioned models include the well-known Mayr and Cassie models and their well-known Schwartz extensions with the power functions of the Mayr and Cassie voltage as well as the increased dissipation of energy within the high-current range. The modified models contain residual conductance, enabling the determination of arc ignition voltage. A similar approach was applied to modify the approximating functions of voltage and current characteristics used in the Pentegov model. Computer simulations were used to examine the influence of the parameters of the mathematical models on the shapes of static and dynamic characteristics of arc located in a circuit with sinusoidal current excitation.

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

“…Afterwards, constant parameter Q p and the remaining parameters connected with the dynamics of processes in arc (e.g. residual conductance) are identified [10].…”

“…The derivative of the aforesaid conductance is the following Discussed below are cases of the approximation of static current-voltage characteristics including the determinacy of ignition voltage [10]. Based on the modification of approximating function (10) it is possible to obtain the following formula where, approximately, the value of current I M -corresponds to the abscissa of the extreme point on the static characteristic.…”

“…Based on the modification of approximating function (10) it is possible to obtain the following formula where, approximately, the value of current I M -corresponds to the abscissa of the extreme point on the static characteristic. The aforesaid current is related to the value of residual conductance [10]. The static conductance of the column can be calculated using the following formula:…”

General earth fault protection for MV networks using wavelet decomposition and Bayesian criterion

“…The maximum permissible content of 3rd harmonic equal to 5% [10] has been assumed. The non-linear earth-fault resistance R F was modeled as a series circuit consisting of the arc resistance R arc [11][12][13][14] and the transition resistance R T . The arc model has been used with parameters [11,12]: ignition voltage U ig = 10 kV, voltage in the arc column in a conducting state U k = 1000 V, resistance in a conducting state R 1 = 0.1 , time constant  = 0.1 ms.…”

The influence of the network asymmetry on the settings and sensitivity of an earth fault protection using higher harmonics

“…suited. The asymmetry reactive power for third harmonics is the smallest, and, as shown in [4][5][6], the non-linear resistance of the earth fault, especially an arc resistance [13][14][15][16], generates mainly the third harmonics of the zero sequence current and voltage. The protection using criterion Q 031 will have the lowest setting and the highest sensitivity.…”