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A method for uncertainty analysis in power system state estimation is proposed. The two-step method uses static weighted least-squares analysis to compute 'point' state estimates. Linear programming is then employed to obtain the upper and lower bounds of the uncertainty interval. It is shown that the method can provide useful additional information for both metered and nonmetered elements of the system. The effects of network parameter errors are also studied. For illustrative purposed, the proposed method is tested using the six-bus and IEEE 30-bus standard systems. Results show that the proposed method is an accurate and reliable tool for estimating the uncertainty bounds in power system state estimation.