Hydrogen　is　injected　into　the　existing　natural　gas　network　to　form　hydrogen-rich　com-pressed　natural　gas　(HCNG),　effectively　addressing　the　high　cost　of　hydrogen　transmission.　However,　the　traditional　IES　model　cannot　be　used　due　to　the　hydrogen　injection＇s　effect　on　gas　properties　and　the　vague　characteristics　of　the　transport　and　separation　processes.　Therefore,　this　paper　proposes　an　HCNG　penetrated　integrated　energy　system　(HPIES)　optimal　dispatching　method　by　comprehensively　modelling　the　injection,　transmission,　and　separation　processes　of　HCNG.　An　HCNG　mass　flow　rate　model　considering　variable　mixing　ratio　and　unknown　beginning　flow　direction　is　developed　to　describe　the　effect　of　hydrogen　injection.　Furthermore,　the　hydrogen　separation　model　is　established　by　intro-ducing　a　combined　membrane　and　pressure　swing　adsorption　separation　process.　The　tightening　McCormick　algorithm　is　proposed　to　solve　quickly　HPIES　optimal　dispatch　problem　with　an　acceptable　feasibility　check.　Finally,　case　studies　on　the　HPIES　consisting　of　IEEE　39-bus　power　system　and　20-node　natural　gas　system　validate　the　effectiveness　of　the　algorithm　and　model.　The　results　show　that　the　average　error　is　0.031%　for　the　bilinear　term　constraint.(c)　2023　Hydrogen　Energy　Publications　LLC.　Published　by　Elsevier　Ltd.　All　rights　reserved.