Current　research　on　microgrid　(MG)　energy　management　based　on　federated　deep　reinforcement　learning　has　not　considered　the　problem　of　multiple　types　of　energy　conversion　and　power　trading　among　MGs,　while　frequent　interaction　of　model　parameters　leads　to　large　communication　latency.　Based　on　this,　an　MC　including　multiple　types　of　energies　such　as　wind,　solar,　electricity,　and　gas　is　studied.　An　energy　management　model　that　allows　for　inter-MG　electricity　trading　and　intra-MG　energy　conversion　is　constructed.　A　federated　dueling　deep　Q-network　(Dueling　DQN)　learning　algorithm　based　on　the　sine　cosine　algorithm　(SCA)　is　proposed,　and　a　multi-microgrid　energy　management　and　optimization　strategy　considering　energy　conversion　and　trading　is　designed　based　on　the　proposed　algorithm.　The　simulation　results　show　that　the　proposed　energy　management　strategy　can　achieve　higher　rewards　to　maximize　microgrid　economic　benefits　while　protecting　data　privacy　and　reducing　communication　latency.　©　2024　Automation　of　Electric　Power　Systems　Press.　All　rights　reserved.