大规模电力系统快速潮流计算方法研究

摘要

Direct and iterative methods are two common solution methods for linear equations. Three methods for power flow calculation in large-scale power systems are compared, namely multifrontal algorithm (MA), GMRES method and FGMRES method. Numerical simulation tests on seven systems including IEEE 118, 300 buses and five Poland test systems indicate that the FGMRES method obviously has fewer inner iterative numbers than the GMRES method with ILU preconditioner,but it takes more computing time on the whole. Overall, MA is the fastest. Based on PQ preconditioning, this paper presents a combined GMRES-MA method. MA is used to solve the assisted preconditioning equations, after the Krylov subspace is generated by the GMRES method for each step in the outer-iterations. The results show that, with the scale expanding, this new method has fewer inner iterative numbers than the GMRES method. Furthermore, compared with both MA and GMRES method, the computing time of the new method is decreased. Therefore, this new method is applicable to the fast power flow calculation in large-scale power systems.%直接法和迭代法是求解线性方程组的两类常见方法,比较了多波前算法(MA)、GMRES算法、FGMRES算法在大规模电力系统潮流计算中的求解效率.经IEEE 118节点、300节点和Poland共7个算例仿真测试表明,基于ILU分解法预条件子的FGMRES算法的内迭代次数较GMRES算法明显减少,但整体求解时间较GMRES算法长；多波前算法的求解速度较二者快.基于PQ分解法预条件子,提出一种GMRES-MA混合算法,在GMRES算法每步迭代过程生成Krylov子空间后,利用多波前算法(MA)直接求解辅助预处理方程组.算例测试结果表明,随着系统规模的增长,该方法的内迭代次数较GMRES算法有所减少,并且计算时间较GMRES算法和多波前算法(MA)均有所降低,适合于大规模电力系统潮流计算的快速求解.