A Parallel Approach for Solving Network Equations Based on Branch Partition

In the field of Electromagnetic transient (EMT) simulation and transient stability analysis, solving the network equation constitutes a significant portion of the computational workload. Traditional approaches, such as LU decomposition, suffer from inherent sequential nature, making parallelization challenging. On the other hand, matrix multiplication methods, although parallelizable, can be computationally expensive for large-scale systems. This paper introduces an efficient solver that leverages both coarse-grained and fine-grained parallelism to address these challenges. The proposed approach achieves coarse-grained parallelism by partitioning the network into branches connected by cut nodes. Additionally, it employs a parallel forward/backward substitution algorithm based on recursive node reordering to achieve fine-grained parallelism. Experiment on the IEEE 69-bus system shows our approach is 2.7 times faster than sparse LU and 42% faster than parallel BBDF method with LU solver. Moreover, on a synthetic large-scale system, our method is 14 times faster than sparse LU and up to 75% faster than BBDF method with LU solver. These findings highlight the efficiency and scalability of the proposed approach.