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We present a systematic method to design ubiquitous continuous fast-acting distributed load control for primary frequency regulation in power networks, by formulating an optimal load control (OLC) problem where the objective is to minimize the aggregate cost of tracking an operating point subject to power balance over the network. We prove that the swing dynamics and the branch power flows, coupled with frequency-based load control, serve as a distributed primal-dual algorithm to solve OLC. Wedoi:10.1109/tac.2014.2298140 fatcat:caywa4x44rhu5ksjb5nw5buwle