This　paper　proposes　a　novel　branch　voltage-balancing　control　strategy　for　a　hexagonal　converter　(Hexverter).　First,　the　state-space　model　based　on　the　double-dq　transformation　is　analyzed　in-depth　along　with　the　necessary　basic　mathematical　derivation,　and　the　active/reactive　power　control　model　in　the　dq　reference　frame　for　the　Hexverter　is　proposed.　Second,　a　zero-sequence　double-loop　network　consisting　of　a　Y-loop　and　a　Hex-loop　circulating　current　was　established.　This　study　proposes　a　method　to　suppress　the　Y-loop　circulating　current　by　connecting　a　capacitor　at　the　neutral　point.　We　then　establish　a　novel　branch　voltage-balancing　control　strategy　based　on　the　transfer　power　model.　The　essence　of　the　proposed　control　strategy　is　to　control　the　charging　and　discharging　states　of　each　submodule　via　the　zero-sequence　voltages　and　the　Hex-loop　circulating　current　to　regulate　the　power　transfer　between　adjacent　submodules　and　branches,　thereby　effectively　ensuring　the　dynamic　balance　of　the　DC　voltages　of　the　submodules.　The　branch　voltage-balancing　control　model　and　power　control　model　proposed　in　this　paper　are　based　on　zero-sequence　and　positive-sequence　networks,　respectively.　The　relative　independence　of　the　positive-　and　zero-sequence　networks　leads　to　decoupling　of　the　branch　voltage-balancing　control　model　and　the　power　control　model;　thus,　the　respective　control　objectives　can　be　achieved　by　adjusting　the　respective　control　variables　independently.　It　has　a　stronger　adaptability　to　diverse　power　grid　operating　parameters.　Finally,　the　validity　and　correctness　of　the　mathematical　model　and　control　strategy　proposed　in　this　study　are　verified　using　MATLAB/Simulink.