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The problem of estimating the state variables from measurements in an electric-power system is considered. The conventional linearised least-squares solution is shown to be ineffective in the presence of gross measurement errors. Reformulating the problem as a linear program leads to a state estimator that combines the advantages of noise filtering and bad-data elimination, and may be implemented straightforwardly by application of the simplex method. The solution of various examples based on three test networks confirms the advantages of the method especially where the data are corrupted by a number of gross errors. Depending on the degree of redundancy in the measurement set, the computational requirements of the method are comparable with conventional least-squares solution. For real-time power-system monitoring and control where process variables have unknown statistics, the linear-programming method is believed to be more efficient than conventional algorithms.