A linear approach to manage input delays while supplying frequency regulation using residential loads

Frequency regulation balances the supply and demand of power within a power network to maintain the network's frequency about its nominal value. Using residential loads to supply frequency regulation while respecting user comfort can require costly communication infrastructure. Developing control algorithms that are resilient to communication network imperfections, e.g., delays, can allow the usage of less costly, lower reliability communication infrastructure. Previous work developed a model predictive control (MPC) approach that enables aggregations of loads to track a desired power signal despite communication delays. This work presents a novel model-reduction method to produce a minimal aggregate load model, and then uses state augmentation to include the effect of input delays. This allows the reformulation of the MPC controller into a linear controller yielding a closed-form control law that reduces online computation. We present simulations that compare the MPC and linear controllers' tracking ability given input delays. The linear controller neglects input constraints explicitly included within the MPC controller, and we characterize the impact of neglecting these constraints through simulations. The linear controller reduces the computation time by a factor of 100, but the RMS tracking error increases 11% in the cases studied.