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

We consider demand-side primary frequency control in the power grid provided by smart and flexible loads: loads change consumption to match generation and help the grid while minimizing disutility for consumers incurred by consumption changes. The dual formulation of this problem has been solved previously by Zhao et al. in a decentralized manner for consumer disutilities that are twice continuously differentiable with respect to consumption changes. In this work, we propose a decentralized multi-block alternating-direction-method-of-multipliers (DM-ADMM) algorithm to solve this problem. In contrast to the dual ascent algorithm of Zhao et al., the proposed DM-ADMM algorithm does not require the disutilities to be continuously differentiable; this allows disutility functions that model consumer behavior that may be quite common. In this work, we prove convergence of the DM-ADMM algorithm in the deterministic setting (i.e., when loads may estimate the consumption-generation mismatch from frequency measurements exactly). We test the performance of the DM-ADMM algorithm in simulations, and we compare (when applicable) with the previously proposed solution for the dual formulation. We also present numerical results for a previously proposed ADMM algorithm, whose results were not previously reported.