Spectral and integral methods of determining parameters in selected electric arc models with a forced sinusoid current circuit

The paper discusses problems arising in attempts to accurately represent dynamic processes of an electric arc by means of simple mathematical models. It describes the properties of the universal Pentegov model, employing any shape of static voltagecurrent characteristics of an arc. Next, it presents spectral and integral measuring methods for determining arc parameters in the Mayr, Cassie and Pentegov models of the electric arc with a forced sinusoid current circuit, with the raising static characteristics of hyperbolic-flat and hyperbolic-linear shape. The influence is discussed of the random power supply disturbances on errors of determining the mathematical model parameters. Key words: electric arc, Mayr model, Cassie model, Pentegov model, spectral methods, integral methods 1. Introduction In the process of designing and controlling electrotechnological devices it is often necessary to deploy mathematical models of the electric arc. Such a model should be simple and at the same time it should represent with sufficient accuracy the dynamic voltage-current characteristics of the arc under the conditions of various kinds of disturbances and for a wide range of forcing current amplitude variation. The popular Mayr and Cassie arc models [1, 2] are applicable to limited current ranges, which in turn depend on various external factors of the electric discharge [3, 4]. To overcome the limitations, attempts are being made to create extended mathematical models (e.g. Schwarz-Avdonin, Cassie-Mason, Reider-Urbanek, Kukiekov, Novikov) [5] or to combine simple arc models, for example by joining them in series (the Habedank model [6]) or in parallel (the hybrid model [7]). Extended arc models, however, are not free from drawbacks related to determining a large number of parameters and non-linear static characteristics. In the hybrid model there are problems with determining the optimal forms of the weight function and of the damping factor function. In ad-hoc created...