The　ongoing　development　of　technology　has　changed　the　nature　of　electric　networks　in　the　field　of　electric　power　generation.　In　the　same　vein,　the　generation　units　and　demands　are　getting　close　by　the　integration　of　distributed　resources　within　the　distribution　system　with　the　aim　of　bringing　more　advantages　to　the　system.　Considering　the　promising　concept　of　hybrid　networks,　which　comprises　different　distributed　resources,　as　a　supportive　element　for　the　power　system,　this　paper　mainly　focuses　on　modeling　a　distributed　hybrid　network,　through　which　both　the　AC　and　DC　loads　can　be　supplied　within　the　hybrid　network.　This　network　is　operated　in　a　distributed　way　where　no　independent　operator　is　assumed　for　the　operation.　The　primal-dual　method　of　multipliers　(PDMM)　as　an　effective　distributed　method　handles　the　operation　of　this　network.　So　far,　this　method　has　only　been　applied　to　the　AC　grid　or　DC　grid　separately,　while　the　presented　method　is　modified　for　the　operation　of　the　hybrid　network.　Convergence　speed　and　preciseness　are　mentioned　as　the　advantages　of　this　method　which　dominates　the　alternating　direction　method　of　multipliers　(ADMM).　In　real　cases,　there　are　some　errors　in　the　output　power　of　the　renewable　resources.　Aiming　to　make　the　presented　PDMM　method　more　applicable,　the　uncertainty　is　also　modelled　using　the　Unscented　Transform　(UT)　approach,　as　a　way　of　uncertainty　modelling　which　has　shown　attractive　features,　especially　the　capability　of　correlation　modelling;　therefore,　it　is　more　preferable　for　uncertainty　modeling　in　many　cases　compared　to　the　other　methods.　The　proposed　work　is　implemented　on　a　smart　island　and　the　authenticity　of　this　work　is　proved　by　comparing　the　performance　of　the　proposed　distributed　approach　with　the　centralized　method.