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We consider demand-side primary frequency control in the power grid providedby smart and flexible loads: loads change consumption to match generation andhelp the grid while minimizing disutility for consumers incurred by consumptionchanges. The dual formulation of this problem has been solved previously byZhao et al. in a decentralized manner for consumer disutilities that are twicecontinuously differentiable with respect to consumption changes. In this work,we propose a decentralized multi-blockalternating-direction-method-of-multipliers (DM-ADMM) algorithm to solve thisproblem. In contrast to the dual ascent algorithm of Zhao et al., the proposedDM-ADMM algorithm does not require the disutilities to be continuouslydifferentiable; this allows disutility functions that model consumer behaviorthat may be quite common. In this work, we prove convergence of the DM-ADMMalgorithm in the deterministic setting (i.e., when loads may estimate theconsumption-generation mismatch from frequency measurements exactly). We testthe performance of the DM-ADMM algorithm in simulations, and we compare (whenapplicable) with the previously proposed solution for the dual formulation. Wealso present numerical results for a previously proposed ADMM algorithm, whoseresults were not previously reported.

A Decentralized Multi-block ADMM for Demand-side Primary Frequency Control using Local Frequency Measurements