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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.

Domain decomposition of the network conductance matrix is one of the efficient approaches to solve large-scale networks in parallel, wherein the most commonly-used non-iterative method is the Schur complement (SC) method. However, the SC method could not obtain the network conductance matrix inversion directly, and the computational cost will increase fast when the overlapping domain expands. In this work, a novel Linking-Domain Extraction (LDE) based decomposition method is proposed, in which the network matrix is expressed as the sum of a linking-domain matrix (LDM) and a diagonal block matrix (DBM) composed of multiple block matrices in diagonal. Through mathematical analysis over LDM, one lemma about the nature of LDM and its proof are proposed. Based on this lemma, the general formulation of the inverse matrix of the sum of LDM and DBM can be found using the Woodbury matrix identity, and based on the formulation the network matrix inversion can be directly computed in parallel to significantly accelerate the matrix inversion process. Test systems were implemented on both the FPGA and GPU parallel architectures, and the simulation results and speed-ups over the SC method and Gauss-Jordan elimination demonstrate the validity and efficiency of the proposed LDE method. [ABSTRACT FROM AUTHOR]