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State estimation is important for real time power system monitoring and control. State estimation algorithms may suffer divergence under stressed system conditions. Understanding state estimation divergence characteristics is essential for designing more robust state estimation algorithm. This paper investigates impacts of variations of load levels and topology errors on the convergence property of the commonly used weighted least square (WLS) state estimator. The influence of topology errors on the condition number of the gain matrix in the state estimation is also analyzed. The effects of measurement standard deviations are studied. The IEEE 118-bus system is used as the test case and test results are reported.