In　order　to　maximize　the　return　on　equity　(ROE)　of　wind-hydrogen　system　investors,　take　full　advantage　of　the　wind　power　as　well　as　smooth　the　wind　power　output　of　a　wind　farm,　an　optimal　sizing　model　of　a　coupled　wind-hydrogen　system　(CWHS)　is　established　considering　the　requirements　of　wind　power　grid-connection　technology.　The　fluctuating　cost　of　wind　power　is　calculated　by　an　“equal-kWh　following　load”　method　and　the　chance-constrained　programming　is　introduced　to　deal　with　the　uncertainty　generated　by　the　wind　power.　The　optimal　capacity　of　each　unit　for　a　CWHS,　including　the　wind　power　transmission　project,　electrolyser,　compressor　and　so　on,　is　acquired　and　the　economic　analysis　is　evaluated　under　comprehensive　aspects,　e.g.　wind　curtailment　decisions,　hydrogen　prices,　the　correlations　between　wind　power　output　and　system　load,　and　the　fluctuation　degrees　of　wind　power　generation.　The　simulation　is　established　by　the　realistic　historical　data　from　a　wind　farm　in　Fujian,　China.　When　the　confidence　level　is　92%,　the　capacity　of　electrolysers　increases　with　the　increase　of　the　hydrogen　price　when　it　is　larger　than　the　equivalent　value　4.34　€/kg.　In　addition,　the　smaller　the　correlation　between　wind　power　output　and　load　and　the　bigger　the　volatility　index　of　wind　power　output,　the　less　the　smoothing　benefit　of　the　CWHS,　where　the　smaller　capacity　of　the　transmission　project　and　bigger　capacities　of　electrolysers　and　compressors　are　required.　©　2019　Hydrogen　Energy　Publications　LLC