Study on chaotic dynamic arc behavior in SF6 circuit breaker

Based on the arc mathematical model for the SF₆ circuit breaker (CB), the equations describing the arc chaotic behavior were deduced by considering the velocity and temperature effect in the model as the chaotic characteristics and expending in 2D form using the convergence of Fourier series. The time series, and Lyapunov exponents diagram reflecting the chaotic behavior of arc were obtained based on the numerical analyses, which proved that the arc behavior exist chaos during the arc quenching. In order to reflect the interactions of the coupling of the electric field, magnetic field and gas flow field and confirm the factors affecting the arc chaotic behavior, third-order nonlinear differential equations with constant coefficient for arc in SF₆ CB has been obtained by introducing Maxwell and current density equations in the arc mathematical model and linearizing a set of nonlinear differential equation for the arc model according to the stability theory. The results show that the shock wave is one of the origin of the arc instability. By adjusting the parameters for SF₆ CB closely related to the temperature, the system has significant chaotic behavior, which indicates that the system stability can be effectively controlled according to the temperature.