基于预条件处理GMRES的不精确牛顿法潮流计算

结合大规模电力系统修正方程组高维超稀疏性以及短向量的特点,提出以Krylov子空间方法研究电力系统方程计算问题.针对牛顿法潮流计算,采用预条件处理的GMRES方法求解高维稀疏的修正方程组,提出一种完整的基于预条件处理GMRES的不精确牛顿潮流算法,设计实现不同的预条件子,并以此为基础详细比较各类预条件子的预处理效果.通过对IEEE30、IEEE118和多个合成的大规模电力系统进行潮流计算,结果表明ILU预条件子比其他预条件子需要更少的迭代次数和浮点运算次数,当系统规模达到3000节点左右时,基于ILU预条件子的不精确牛顿法与传统的LU直接分解法相比,浮点运算次数减少了50%,内存使用量减少了将近10%,并且随着系统规模的增大,浮点运算次数基本上保持在LU直接法的50%左右,对大规模电力系统的潮流计算极为有利.

Inexact Newton Flow Computation Based on Preconditioned GMRES Method

This paper utilizes two characteristics of the large scale power system: the correction equation is large sparse and the vector is short, and studies the power system computation based on Krylov subspace method. For Newton flow computation, the paper uses preconditioned generalized minimal residual method(GMRES)to solve large sparse sets of correction equation. An inexact Newton method with a preconditioned GMRES linear solver is presented. Studies comparing the performance of kinds of preconditioners have been performed. Tests have been done with networks of IEEE test systems and synthesized bulk systems, and shown the better effectiveness in computation for the ILU preconditioner than other preconditioners. When the system scale reaches nearly 3000 buses, comparing with traditional LU direct method, floating point operations persecond (FLOPS)and reguired memory capacity of inexact Newton method with ILU preconditioner can be reduce more than 50% and nearly 10% respectively, and as the increase of the system scale, the percentage of FLOPS keeps nearly 50%, which is especially efficacious for large scale power system computation.