Convergence analysis of ADMM-based power system mode estimation under asynchronous wide-area communication delays

In our recent paper [1], we proposed a distributed PMU-PDC architecture for estimating power system oscillation modes by integrating a Prony-based algorithm with Alternating Direction Method of Multipliers (ADMM). A critical assumption behind the proposed method was that the communication between local PDCs and the central averager is completely synchronized. In realistic wide-area networks, however, such synchronous communication may not always be possible. In this paper we address this issue of asynchronous communication, and its impact on the convergence of the distributed estimation. We first impose a probability model for the communication delays between the central PDC and the local PDCs, and then implement two strategies of averaging at the central PDC based on a chosen delay threshold. We carry out simulations to show possible instabilities and sensitivities of the ADMM convergence on delay distribution parameters under these two averaging strategies. Our results exhibit a broad view of how the convergence of distributed estimation algorithms in physical processes depends strongly on the uncertainties in the underlying communications in a generic cyber-physical system.