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The convergence property of state estimation is a critical issue for its following security assessment functions in energy management system. This paper studies the convergence property of the commonly used weighted least square (WLS) approach for the variations of load levels and system sizes. A new robust bad data processing approach is presented for the purpose of convergence and robustness in this paper. A comparison of robustness between WLS and the proposed approach has been performed. Numerical tests on IEEE 188 bus system and a real system with 5145 bus have been conducted for illustration of the proposed approach.