Homotopy-Based Re-Initialization for Switched DAEs in Power System Transient Simulation

The simultaneous solution of switched differential-algebraic equations (DAEs) in power system transient simulation may suffer convergence loss following discontinuous events. This difficulty is typically interpreted as a poor post-event initialization problem. This letter presents a geometric framework that explains the underlying convergence mechanism and clarifies why standard convergence-restoration methods may fail at discontinuities. Based on this interpretation, a homotopy-continuation based globalized re-initialization scheme is developed to restore convergence. The proposed method is validated through numerical simulations of representative discontinuities in power system transient simulation. Results show that in the cases where direct post-event solution fails, the proposed scheme can reliably recover convergence.