The　economic　dispatch　problem　(EDP)　in　smart　grid　mainly　is　investigated　in　this　paper.　The　transmission　losses　of　power　produced　by　generator　will　be　taken　into　account,　which　introduces　nonlinear　constraints　in　the　EDP.　By　viewing　the　losses　as　a　quadratic　function,　a　broadcast　gossip　economic　dispatch　algorithm　is　proposed　to　work　out　the　EDP.　This　distributed　algorithm　makes　all　neighbors　of　the　node　update　the　information　of　each　iteration　through　broadcast.　The　convergence　of　the　algorithm　will　be　certified　by　the　approximation　as　well　as　matrix　perturbation　theory.　Three　simulation　experiments　show　the　distributed　algorithm’s　availability　as　well　as　plug-and-play　capability,　and　a　comparison　with　the　algorithm　in　which　the　transmission　loss　is　not　considered　is　further　given.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.