In electromagnetic transient (EMT) simulation, 80-97% of the computational time is devoted to solving the network equations. A key observation is that the sub-matrix representing the interaction between two far-away groups of buses is usually sparse and can be approximated by a low-rank matrix. Based on this observation, we propose a novel low-rank approximation method which permits ${O(N \log N)}$ -time matrix-vector multiplication for each network solution time step. Comprehensive numerical studies are conducted on a 39-bus system and a 179- bus system from the literature, and large cases created from the two systems. The results demonstrate that the proposed approach is up to 2:8× faster than the state-of-the-art sparse LU factorization based network solution, without compromising simulation accuracy. Since our low-rank approximation is highly parallelizable, further speedup may be possible.

中文翻译：

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用于 EMT 仿真的基于分层低秩近似的网络求解器

在电磁瞬态 (EMT) 仿真中，80-97% 的计算时间用于求解网络方程。一个关键的观察结果是，代表两个相距较远的公共汽车组之间相互作用的子矩阵通常是稀疏的，可以用低秩矩阵来近似。基于这一观察，我们提出了一种新的低秩近似方法，该方法允许每个网络解决方案时间步的 ${O(N \log N)}$ -time 矩阵向量乘法。对文献中的 39 总线系统和 179 总线系统以及从这两个系统创建的大型案例进行了全面的数值研究。结果表明，在不影响仿真精度的情况下，所提出的方法比最先进的基于稀疏 LU 分解的网络解决方案快 2:8 倍。