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This paper presents an efficient method for power system static state estimation along with a statistical technique of bad data detection and identification. In the estimation process, the exponential function is utilized to modify the variances of measurements in anticipation of maintaining the estimation performance under the bad data scenario. Besides, with the aid of the proposed gap statistic method, those bad data can be effectively detected and identified from the set of raw measurements. To validate the effectiveness of the proposed approach, this method has been tested under different simulated scenarios. Test results help confirm the feasibility of the method for the applications considered.