In　order　to　effectively　analyze　and　manage　the　harmonics,　it　is　particularly　important　to　develop　appropriate　models　to　characterize　harmonic　sources.　The　electric　arc　furnace　is　a　typical　multi-modal　harmonic　source,　and　an　accurate　harmonic　model　is　indispensable　to　assess　the　harmonic　pollution　of　the　electric　arc　furnace.　In　this　paper,　a　harmonic　coupling　model　of　the　arc　furnace　is　proposed　based　on　linear　Cluster-weighted　model　(CWM).　The　proposed　method　divides　the　multi-modal　harmonic　data　into　several　clusters　by　considering　the　linear　coupling　relationship　between　harmonics　at　different　frequencies.　In　addition,　a　family　of　standard　linear　CWM　with　different　kernel　functions　is　defined　and　several　harmonic　source　equivalent　models　are　modeled　in　parallel　based　on　them.　Then,　the　best　model　is　adaptively　selected　by　using　BIC(Bayesian　Information　Criterion)　and　ICL(Completed　Likelihood)　criteria　to　improve　the　generalization　ability　of　the　model　and　its　adaptability　to　different　data　sets.　Finally,　the　experimental　analysis　demonstrates　the　accuracy　and　effectiveness　of　the　proposed　method.　©　2022　IEEE.