The　uncertain　operating　state　of　integrated　energy　systems　(IESs)　increases　significantly　with　the　ever-increasing　renewable　energy　penetration.　In　order　to　evaluate　the　operation　state　of　IES　more　reasonably,　this　paper　proposes　an　interval　energy　flow　(IEF)　method　and　applies　it　to　an　IES　that　utilizes　hydrogen　as　an　energy　conversion　carrier.　Firstly,　a　steady-state　energy　flow　model　for　an　electricity-heat-hydrogen　system　is　presented.　Then,　the　parallelogram　model　is　employed　to　describe　the　correlation　between　interval　variables　to　acquire　more　accurate　results.　Furtherly,　combined　with　the　above　two　models,　the　IEF　is　transformed　into　minimum　and　maximum　optimization　models.　Due　to　the　complexity　of　nonlinear　optimization　calculation,　the　interval　solution　is　procured　by　the　alternating　iterative　method　based　on　linear　optimization　and　deterministic　energy　flow　for　the　sake　of　accuracy　and　simplicity.　Finally,　a　case　study　demonstrates　the　effectiveness　of　the　proposed　method,　and　a　detailed　discussion　about　the　impact　of　correlation　on　interval　solutions　is　given.　The　calculation　speed　of　the　proposed　method　is　6.5　times　faster　than　Monte　Carlo　simulation.　The　interval　ranges　of　state　variables　are　narrowed　significantly　after　considering　correlation,　with　a　maximum　narrowing　range　of　up　to　63.08%.　©　2022　Elsevier　Ltd