Periodic solutions of Stiff systems using the Limit Cycle method and an implicit integration technique

This paper presents a powerful tool based on the limit cycle method and an implicit integration technique to compute the periodic steady-state solution of an electric system described by a set of stiff ordinary differential equations. The application of the limit cycle method allows the acceleration of the computation to reach the steady-state by mean of the Poincare map and a Newton method. This time domain approach relies normally on the use of conventional explicit integration techniques to identify a transition matrix, despite the fact that these explicit techniques are extremely inefficient for solving stiff equations. Therefore, the incorporation of an implicit integration approach to the limit cycle method speeds up even more the calculations in the time domain when solving stiff problems. Comparison results for a test case based on the energization of a transformer are reported in terms of convergence to the limit cycle, computational effort and waveforms of the state variables.