Affine　power　flow　algorithm　is　critical　for　addressing　the　uncertainty　of　power　flow.　However,　for　existing　affine　power　flow　algorithms　which　are　based　on　rectangular　affine　arithmetic,　it　is　difficult　to　analyze　the　interactions　between　the　magnitude　and　angle　of　voltage　and　the　injected　power.　This　paper　proposes　an　affine　coordinate　conversion　(ACC)　method　that　allows　an　affine　variable　to　be　transformed　between　different　coordinate　systems.　Based　on　the　ACC　method,　the　hybrid　coordinates　affine　arithmetic　(HCAA)　is　proposed,　which　uses　rectangular　affine　arithmetic　in　addition　operation　and　uses　polar　affine　arithmetic　in　multiplication　and　division　operation.　Finally,　an　affine　power　flow　algorithm　based　on　HCAA　is　proposed,　which　is　computed　by　Ybus-Gauss　iteration　algorithm.　In　numerical　experiments,　the　Monte　Carlo　method　are　used　as　benchmarks　for　evaluating　the　completeness　of　the　exact　solution,　and　the　results　demonstrated　the　method　proposed　in　this　paper　presents　a　more　compact　solution　region　than　existing　affine　power　flow　algorithms.　Meanwhile,　the　simulation　results　on　IEEE33-bus　distribution　network　with　injected　power　fluctuation　shows　the　accuracy　of　the　proposed　method　in　solving　the　uncertain　power　flow.　©　2022　IEEE.