Analysis of Bifurcation Phenomenon in a Grid-Connected Electric Arc Furnace

This paper aims to study the stability and dynamic behavior of a grid-connected electric arc furnace system, using bifurcation theory. This theory introduces a systematic method for stability analysis of dynamic systems, under changes in the system parameters. In fact, a parameter is constantly changed in each step, using MATLAB and/or AUTO software, and system eigenvalues are monitored simultaneously. Considering how the eigenvalues approach the system’s imaginary axis on S plain in accordance with the changes in the targeted parameter, the occurred saddle-node and/or Hopf bifurcation of the system is extracted. In this paper, at first, electric arc furnace is modeled by the differential-algebraic equations and then based on the projection method, two-dimensional center manifold at the Hopf bifurcation happens in the electric arc furnace system is achieved analytically. Projection method is discussed in the bifurcation theory and is presented totally in this paper. Finally, the results are compared by the computer simulations.