Aiming　at　the　problem　that　existing　affine　power　flow　methods　are　too　conservative　in　complex　systems,　a　high-order　affine　power　flow　algorithm　and　its　recursion　solution　method　are　proposed.　The　proposed　method　defines　an　expanded　affine　form　containing　high-order　partial　deviations　and　applies　it　to　affine　power　flow　modeling.　An　affine　power　flow　model　based　on　recursion　solution　of　high-order　partial　deviation　coefficients　is　proposed　to　address　the　problem　of　excessive　expansion　of　interval　error　resulting　from　the　approximation　of　numerous　nonlinear　partial　deviations.　The　proposed　method　employs　the　recursion　solution　limited　to　second-order　coefficients　of　the　original　partial　deviations,　and　then　transforms　the　calculation　of　higher-order　terms　into　the　determination　and　calculation　of　the　error　partial　deviation　coefficients　of　injected　power,　ensuring　the　completeness　of　the　solution　while　avoiding　redundant　calculations.　Additionally,　a　conversion　method　between　higher-order　affine　and　interval　solution　is　proposed　to　realize　the　affine-interval　conversion　containing　higher-order　partial　deviations　by　utilizing　complex　affine　polygons　to　assist　the　partial　deviation　coefficients　fetching.　Simulation　on　multiple　test　systems　demonstrates　that　the　proposed　method　exhibits　superior　convergence　and　lower　conservatism.　©2025　Chin.Soc.for　Elec.Eng.