Dynamic Power Allocation for Smart Grids via ADMM

Electric power distribution systems will encounter fluctuations in supply due to the introduction of renewable sources with high variability in generation capacity. It is therefore necessary to provide algorithms that are capable of dynamically finding approximate solutions. We propose two semi-distributed algorithms based on ADMM and discuss their advantages and disadvantages. One of the algorithms computes a feasible approximate of the optimal power allocation at each instance. We require coordination between the nodes to guarantee feasibility of each of the iterates. We bound the distance from the approximate solutions to the optimal solution as a function of the variation in optimal power allocation. Finally, we verify our results via experiments.