Microgrids　(MGs)　have　attracted　growing　attention　due　to　self-sufficiency　and　self-healing　properties.　Nonetheless,　the　intermittent　nature　and　uncertainty　of　distributed　energy　resources　and　load　demands　remain　challenging　issues　in　balancing　demands　and　managing　energy　resources　in　MGs.　Existing　research　efforts　mainly　focus　on　developing　techniques　to　enable　interactions　between　local　MGs　and　the　utility　grid,　which　leads　to　high　line　power　losses　and　operation　costs.　In　this　paper,　we　present　the　Sto2Auc　framework　to　address　the　issue　of　stochastic　optimal　bidding　problem　for　a　system　with　MGs.　First,　the　optimal　bidding　problem　is　formulated　as　a　two-stage　stochastic　programming　process,　which　aims　to　minimize　the　system　operation　cost　and　obtain　optimal　energy　capacity　of　MGs　by　the　MG　center　controller　(MGCC).　Uncertainties　arise　from　both　energy　supply　and　demand,　which　are　considered　in　the　stochastic　model,　and　random　parameters　representing　those　uncertainties　are　captured　by　using　the　Monte　Carlo　method.　Second,　to　enable　optimal　electricity　trading　between　the　insufficient　and　surplus　MGs,　we　propose　a　distributed　double　auction　(DDA)-based　scheme,　which　is　proven　to　converge　to　the　optimal　social　welfare　of　the　system　with　MGs,　and　achieves　the　economical　properties　of　being　strategy-proof,　individually　rational,　and　(weak)　budget　balanced.　Extensive　experiments　on　an　MG　system　composed　of　IEEE-33　buses　demonstrate　the　effectiveness　of　proposed　scheme.　The　experimental　results　show　that　Sto2Auc　framework　is　capable　of　reducing　the　operational　cost　of　MG　systems,　while　the　implemented　DDA　scheme　achieves　good　performance　with　respect　to　social　welfare,　demand　insufficiency,　and　MGCC　profit.