Nonlinear oscillations due to nonlinear Arc characteristics

Abstract

The negative U-I-characteristic of a high-pressure arc causes unstable current oscillations in selected LC-networks. In the present paper three different types of oscillations are analyzed. The relevant nonlinear differential equations are solved by numerical and analytical methods as well as by graphical integration procedures. Two types of stable oscillations occur. They can be represented either by stable sinusoidal or almost triangular waveforms or by a Van der Pol oscillation. The third kind of oscillation is unstable and grows exponentially only for small amplitudes whilst it increases considerably faster for larger amplitudes. Our results agree with the experimentally observed features of arcs in electrical power networks.