We investigate the issue of the convergence error of the consensus based algorithm for the economic dispatch problem (EDP) in the smart grid, where the incremental cost (IC) acts as the consensus variable. The algebraic expression of the convergence error in the context of duration-limited communications is presented. The performance in terms of the convergence error varies with the set of generators selected to be informed the external message associated with the optimal IC. We consider the case of minimizing the convergence error subject to a fixed cardinal number and the case of minimizing the size of the set of generators selected subject to a given bound. By formulating them as corresponding optimization problems, we present algorithm to obtain the optimal set of generators for both cases. The effectiveness of the proposed algorithms is verified by examples.
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