Power electronic systems are crucial in modern power grids. Accurate offline simulation tools are essential for analyzing such systems. However, the accurate simulation of large-scale power electronic systems is time-consuming especially when stray parameters are considered. This paper proposes a topology-aware iterative method to improve solving efficiency for large-scale power electronic systems with stray parameters. The proposed method includes a topology-aware partitioning strategy and a flexible preconditioning method to efficiently construct preconditioners that can adapt to different topologies and step sizes. With this method, a large-scale solid-state transformer with stray parameters is efficiently simulated. Over 300-fold acceleration is achieved in total compared with commercial software. The method makes it possible to analyze and design large-scale power electronic systems more reliably.