The Multi-Area Thévenin Equivalent algorithm (MATE) partitions a network into a number of subnetworks connected by links. The solution proceeds in two stages: first the subnetworks are solved independently, with the links open, and then the system formed by the links is solved with the subnetworks represented by their Thévenin equivalents as seen from the link nodes. In this paper, an overview of the MATE technique for solving large power systems on parallel computing architectures will be discussed, along with a performance analysis and applications, including the solution of the WECC system (about 15,000 nodes and 17,000 branches), which was achieved with a 7-time speedup with respect to a sequential sparsity-oriented algorithm. Comparisons with another parallel sparse solver are also presented.
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Tomim et al. (2010) studied this question.