Due　to　the　prevalence　of　communication　link　delay　in　communication　networks,　the　study　of　communication　delays　in　smart　grids　and　their　impact　on　economic　dispatch　is　of　great　practical　value.　In　this　paper,　a　Gossip-based　economic　dispatch　protocol　perfected　under　constant　time　delay　is　considered,　and　it　is　proved　by　augmented　matrix　theory　and　matrix　perturbation　theory　that　a　sufficiently　small　control　gain　parameter　always　exists　to　guarantee　the　convergence　over　a　constant　delay　in　the　communication　network.　Iterative　update　rules　are　given　when　the　neighboring　generation　units　do　not　receive　the　initial　state　due　to　the　time　delay　to　ensure　the　optimal　solution　can　be　obtained.　Finally,　simulation　cases　are　provided　to　verify　the　effectiveness　and　plug-and-play　capability　of　the　algorithm,　as　well　as　its　feasibility　for　large-scale　systems.　©　2024　IEEE.