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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 unmetered 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, and 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).