Interval　power　flow　(IPF)　analysis　is　a　promising　approach　to　handling　the　uncertainty　of　renewable　energy　sources　and　loads　in　power　systems.　However,　most　existing　studies　are　based　on　standard　interval　arithmetic　or　affine　arithmetic.　Little　work　can　be　found　that　employs　traditional　optimization　methods　to　obtain　the　interval　results,　especially　based　on　convexified　power　flow　formulation.　Therefore,　this　paper　proposes　an　IPF　method　based　on　a　hybrid　second-order　cone　and　linear　programming　for　radial　distribution　systems.　First,　the　optimization　process　of　IPF　based　on　the　standard　power　flow　model　is　introduced.　Given　the　non-convexity　of　the　standard　power　flow　model,　an　IPF　framework　based　on　second-order　cone　programming　(SOCP)　for　radial　distribution　systems　is　proposed.　Moreover,　considering　that　the　SOCP　formulation　can　only　achieve　half　of　the　whole　IPF　process,　a　revised　linear　DistFlow　formulation　is　adopted,　and　the　IPF　method　based　on　a　hybrid　second-order　cone　and　linear　programming　is　devised.　Finally,　the　proposed　IPF　method　is　compared　with　the　standard　power　flow　equation-based　IPF　method　and　the　Monte　Carlo　method.　The　simulation　results　on　modified　IEEE　33-node　and　69-node　distribution　systems　demonstrate　the　effectiveness　and　prospects　of　the　proposed　IPF　method.　©　2023　Elsevier　Ltd