The　three-coil　wireless　power　transfer　(WPT)　system　with　relay　coil　can　improve　the　transmission　distance　and　transmission　efficiency　of　the　system.　Based　on　the　coupling　inductance　model,　this　paper　analyzed　and　established　the　mathematical　model　of　the　magnetic　coupling　system　of　three-coil　WPT　with　traditional　series/series/series　(S/S/S)　compensation　structure.　The　mathematical　model　is　not　intuitive　enough,　and　it　is　not　easy　to　analyze　the　determination　methods　of　other　compensation　parameters　of　magnetic　coupling　system　except　self-induced　resonance.　Therefore,　this　paper　proposed　a　new　method　to　model　the　magnetic　coupling　system　of　three-coil　WPT　by　using　transformer　T-network　model.　Compared　with　the　coupling　inductance　model,　a　new　decoupled　circuit　model　was　proposed.　Based　on　the　circuit　model　and　the　equivalent　leakage　inductance　compensation　theory,　the　compensation　structures　of　series/series/series-parallel　(S/S/SP),　parallel/　series/series　(P/S/S)　and　parallel/series/series-parallel　(P/S/SP)　are　determined,　and　the　parameter　determination　methods　of　S/S/S,　S/S/SP,　P/S/S,　P/S/SP　compensation　structures　are　proposed.　In　this　method,　the　variable　gain　and　constant　voltage　output　characteristics　can　be　obtained　by　designing　the　compensation　capacitance　and　equivalent　transformation　ratio　under　the　condition　that　the　magnetic　coupling　system　remains　unchanged.　The　circuit　model　of　this　method　is　simple,　the　design　idea　is　clear　and　flexible　in　parameter　selection,　which　is　helpful　to　broaden　the　range　of　output　voltage　gain.　©　2021　Chin.　Soc.　for　Elec.　Eng.