基于预处理BICGSTAB法的电力系统潮流并行计算方法

为实现大规模电力系统潮流的准确、快速求解，以非精确牛顿法为基础，提出一种基于CPU-GPU异构平台的电力系统潮流并行计算方法。修正方程组的求解是牛拉法潮流计算中最为耗时的部分，提升修正方程组的求解效率可有效提升潮流计算效率。为此，根据雅可比矩阵的不对称不定性，采用稳定双正交共轭梯度(bi-conjugate gradient stabilized, BICGSTAB)法进行修正方程组的求解。进一步，为改善BICGSTAB法的收敛性，根据雅可比矩阵的稀疏性和类对角占优性，提出一种改进PPAT(Preconditioner with sparsity Pattern of AT, PPAT)预处理器和改进Jacobi预处理器相结合的两阶段预处理方法，并对雅可比矩阵进行预处理，提升BICGSTAB法的收敛性能。然后，将上述潮流算法移植到CPU-GPU异构平台，实现电力系统潮流的并行求解。最后，通过不同测试系统算例对所提方法进行验证、分析。结果表明，所提潮流并行计算方法可实现电力系统潮流的准确、快速求解。

Parallel power flow computing in power grids based on a preconditioned BICGSTAB method

In order to solve the large-scale power flow problem accurately and quickly, a parallel algorithm for power flow calculation based on the inexact Newton and CPU-GPU heterogeneous platform is proposed. The efficiency of power flow computing can be effectively enhanced by improving the solving efficiency of the correction equations which are the most time-consuming part of the Newton-Raphson method. For this reason, the Bi-Conjugate Gradient Stabilized (BICGSTAB) method is adopted to solve the correction equations according to the asymmetric and indefinite characteristics of a Jacobian matrix. Then, in order to improve the convergence performance of the BICGSTAB method, a two-step preconditioner for the Jacobian matrix is proposed given the characteristic that the Jacobian matrix is analogous to a sparse diagonally dominant matrix. The convergence performance of the BICGSTAB method can be improved with the two-step preconditioner that consists of the improved Preconditioner with sparsity Pattern of AT (PPAT) preconditioner and the improved Jacobi preconditioner. Next, the above power flow algorithm is transplanted to a CPU-GPU heterogeneous platform to achieve power flow parallel computing. Finally, different test systems are further used to verify and analyze the performance of the proposed method. The results validate that the proposed power flow algorithm can solve the power flow calculation problem accurately and quickly.This work is supported by National Natural Science Foundation of China (No. 51607033 and No. 51677023).