期刊名称：International Journal of Soft Computing & Engineering
电子版ISSN：2231-2307
出版年度：2012
卷号：1
期号：6
页码：158-161
出版社：International Journal of Soft Computing & Engineering
摘要：In this work, we propose to apply the conjugate gradient algorithm to the sparse systems; we encounter these in the system admittance matrices, and we will search for a numerical solution to this system using the locally optimal steepest descent method. The system admittance matrices for an IEEE 30-bus or 57-bus system(s) are too large to be handled by direct methods like the Cholesky decomposition method. Hence, we will make use of the flexible preconditioned conjugate-gradient method, which makes use of sophisticated preconditioners, leading to variable preconditioning that change between successive iterations. The Polak–Ribière formula, a highly efficient preconditioner, is applied to the system, to yield drastic improvements in convergence. Our experimental results include a comparison of the Krylov subspace method with traditional methods, assuming the IEEE five-busbar, seven-line reference system as the common basis for all load-flow analysis. The system base quantities are VAbase= 100 MVA and Vbase= 132 kV. The results show an overall better assurance of convergence for all general systems, a lesser dependence on starting voltage profiles assumption and a robustness and efficiency of computation for well-conditioned systems.
