A Coding based Approach to Load Flow Analysis using Krylov Subspace Methods for well conditioned systems
Dibyendu Chowdhury1, Souvik Singha2 

1Dibyendu Chowdhury, Department of Electronics & Communication Engineering, Haldia Institute of technology, Haldia, India.
2Souvik Singha, Department of Computer Science & Informatics, Bengal Institute of Technology & Management, Santiniketan, India.
Manuscript received on December 02, 2011. | Revised Manuscript received on December 14, 2011. | Manuscript published on January 05, 2012. | PP: 158-161 | Volume-1 Issue-6, January 2012. | Retrieval Number: F0289111611/2012©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: 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.
Keywords: Krylov subspace methods, conjugate gradient algorithm, preconditioners, Polak–Ribière formula, assured convergence.