This paper describes a generalized integral solution method to solve the power system state estimation problems for well-conditioned and ill-conditioned power systems. By simple graph analysis, the condition number, which is derived from the simple graph analysis, can be used for justification and determination of various power system operating situations. The modified fast decoupled state estimation method for well-conditioned power systems and the Crout decomposition method for ill-conditioned power systems are formulated and discussed in this paper. Simulations and results are discussed to support the feasibility and effectiveness of the proposed methods for well- and ill-conditioned power system state estimation.
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