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Summary form only given. The increased awareness on power quality has resulted in the need to quantify the voltage sag performance of a distribution feeder, similar to what has been done on characterizing the reliability performance of a feeder. Since it is impossible to measure the sag level at every node of a distribution feeder, estimation of sag characteristics at un-metered nodes becomes necessary. This paper proposes the concept of voltage sag state estimation and associated algorithms to achieve this goal. The proposed method has the following characteristics: 1) it makes use of the radial connection characteristic of a distribution feeder, 2) it is based on a limited number of metering points, 3) it employs a least-square method to predict the sag profile along a distribution line. The results of the proposed sag state estimator can be used to calculate the feeder power quality performance indices such as the system average RMS frequency index (SARFIx).