Delay and sampling independence of a consensus algorithm and its application to smart grid privacy

The consensus algorithm can represent many problems in cooperative behavior, and has been widely used in engineering and social sciences. In this work, we prove that the consensus model where the information that each agent receives from its neighbors has time-varying asynchronous delays and sampling, converges to an agreement independent of these communication constraints. This property is useful in the context of “data minimization,” which is one of the principles for privacy. As a practical example, we show how the independence of sampling rate can be used for microgrids with a consensus-based secondary control scheme where participants have incentives to share their states to ensure frequency synchronization, while at the same time minimizing the amount of data shared to preserve their privacy. We then propose two data sharing algorithms: 1) periodic sampling, and 2) discretionary sampling, and study their privacy as well as their performance. We show that even when a discretionary sampling scheme “lies” to their neighbors in order to preserve their privacy, the consensus algorithm performs almost as well as with periodic sampling.