Abstract
In this paper, we focus on the convergence of autonomous demand side management (A-DSM) algorithms which are widely discussed in the literature of smart grid. We prove that the Nash equilibrium of these algorithms is not unique, however, the Nash equilibria form a convex set, and each consumer's payoff is the same over this set. Moreover, it is proved that the A-DSM program is convergent to the equilibria set if the consumers take turns in the algorithm. When a large number of consumers participate in the A-DSM program, it takes a long time to converge. Therefore, we modify the A-DSM algorithm such that the consumers can make decision in parallel. The proposed algorithm increases the convergence rate by several folds while the scheduled load profile and the system cost remain very close to those of the original A-DSM algorithm.