With　the　deregulation　of　electricity　market　and　the　penetration　of　renewable　energy,　microgrid　system　operators　may　encounter　more　difficulties　in　operation　management　when　facing　complex　economic,　technological,　and　political　uncertainties.　In　this　paper,　a　robust　cost-risk　tradeoff　model　is　developed　for　day-ahead　schedule　optimization　in　residential　microgrid　system　under　uncertainties.　This　method　is　an　integration　of　inexact　two-stage　stochastic　programming　and　worst-case　conditional　value-at-risk　theory,　and　could　handle　uncertainties　with　inexact　or　partly　known　probability　distribution　information.　Besides,　by　introducing　the　financial　risk　measurement,　it　could　also　hedge　against　the　worst-case　scenario　caused　by　multiple　independent　uncertainties.　The　proposed　model　was　applied　to　a　hypothetical　residential　microgrid　system　with　combined　heat　and　power　generation　for　obtaining　optimal　day-ahead　schedule　strategies　under　variable　conditions　with　respect　to　renewable　energy　generation,　power　demand,　and　electricity　market　price.　The　obtained　solutions　demonstrate　that　the　proposed　model　could　reflect　better　tradeoff　information　between　economic　operation　and　stable　performance　according　to　different　risk-aversion　attitudes.　In　general,　more　conservative　risk　attitude　would　be　coupled　with　higher　system　cost,　which　implies　higher　system　stability　is　at　the　expense　of　the　economic　costs.　The　developed　robust　cost-risk　tradeoff　method　would　be　expected　to　have　a　potential　for　wide　applications.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.