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The linking-domain extraction (LDE) decomposition method is a new non-overlapping domain decomposition method for parallel circuit simulation. However, the original LDE method is inefficient in both the computational procedure and storage cost. In this work, a novel hierarchical LDE (H-LDE) method is proposed to further improve the LDE method, which leverages all the hidden features of LDE that are not exploited in the original work to perform a multi-level decomposition of power systems. The LDE-based matrix equation solution computation procedure is first proposed to eliminate the necessity of computing the entire matrix inversion, and then the multi-level computation structure is proposed for fast matrix inversion of the decomposed sub-matrices. The mathematical complexity of the H-LDE method is analyzed, which is used to derive the two principles for decomposing a power system. These principles can be applied on both parallel and sequential compute architecture. The 4-level LDE decomposition is applied on the IEEE 118-bus test power system and implemented in both sequential and parallel, which is used to verify the validity and efficiency of the proposed H-LDE decomposition method. The simulation results of various benchmark test power systems show that the proposed H-LDE method can achieve better performance than the classical LU factorization and sparse KLU method within a certain system scale.

Hierarchical Linking-Domain Extraction Decomposition Method for Fast and Parallel Power System Electromagnetic Transient Simulation