Undervoltage load shedding serves to maintain voltage stability when a majority of loads are fast acting. An undervoltage load shedding scheme should address two tasks: The detection of voltage instability following a large disturbance and the determination of the amount of load to be shed. Additionally, in case of short-term voltage instability, the scheme should be fast. This paper proposes a method to predict voltage instability arising due to a large disturbance. The amount of load to be shed to maintain voltage stability is then determined from the Thevenin equivalent of the network as seen from the local bus. The proposed method uses local measurements of bus voltage and power, and does not require knowledge of the network. The method is validated by simulation of three test systems subjected to a large disturbance. The proposed scheme is fairly accurate in estimating the minimum amount of load to be shed to maintain stability. The method is also successful in maintaining stability in cases where voltage collapse is detected at multiple buses. © 2016 by De Gruyter.