Y-connected　modular　multilevel　converter　(Y-MMC)　is　a　new　topology　of　direct　AC/AC　power　conversion,　with　competitive　application　prospects　in　Fractional　Frequency　Transmission　System　(FFTS).　To　improve　the　uninterrupted　operation　capability　of　Y-MMC,　the　control　strategy　considering　unbalanced　grid　fault　is　proposed　in　this　paper.　This　paper　proposes　the　mathematical　model　of　Y-MMC　under　asymmetric　grid　conditions　according　to　the　symmetrical　component　method　and　superposition　principle　of　linear　systems.　Based　on　the　proposed　mathematical　model,　positive　and　negative　sequence　current　inner　loop　controller,　and　outer　loop　controller　to　suppress　the　negative　sequence　current　are　specially　designed　for　the　stable　operation　of　Y-MMC　under　asymmetric　grid　conditions.　The　effectiveness　of　the　proposed　control　strategy　has　been　verified　by　the　simulation　results　obtained　from　a　10　kV,　10　MW　Y-MMC　system　built　in　MATLAB　/Simulink.　©　2019　IEEE.