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Measurement system failures may make it impossible for the power system state estimator to estimate bus voltage angles and magnitudes at all buses in the power system. When confronted with such a measurement deficiency, the state estimator can estimate bus voltages over only a portion of the entire network. This paper presents an algorithm that determines the largest region where bus voltages may be estimated-the maximum observable subnetwork. The theoretical basis of the algorithm is developed, and the underlying concepts are illustrated on an example network.