In　recent　years,　the　background　harmonics　in　the　grid　are　increasing　for　the　substantial　increase　of　non-linear　loads.　Background　harmonics　feed　into　the　d-q　coordinate　system　by　reference　frame　transformation,　which　causes　considerable　errors　in　the　d-q　decoupled　control　strategy.　The　traditional　phase-locked　loop　(PLL)　solves　this　problem　by　using　low-pass　filters　(LPFs).　However,　with　the　complication　in　tuning　of　LPF,　the　parameters　in　time　under　the　condition　of　changing　the　operating　mode　is　still　difficult　to　adjust.　To　deal　with　such　issues,　this　paper　proposes　a　novel　technique　to　reduce　the　background　harmonic　in　the　d-q　coordinate　system　by　means　of　reference　frame　transformation.　Named　nested　decoupled　synchronous　reference　frame　(NDSRF)　transformation,　this　technique　decomposes　the　fundamental-frequency　positive-sequence　component　and　harmonic　components　by　multilayer　d-q　synchronous　transformation.　Compared　with　existing　transformation　techniques,　the　proposed　NDSRF　technique　is　able　to　sharply　reduce　the　undesirable　transfer　of　background　harmonic　without　filters.　Furthermore,　the　proposed　NDSRF　is　applicable　to　the　modular　multilevel　converter　(MMC)　controller.　Finally,　the　validity　of　the　NDSRF　technique　and　the　proposed　MMC　controller　are　verified　by　a　three-phase　MMC　based　HVDC　system,　which　is　established　in　PSCAD/EMTDC.　The　simulation　results　show　that　the　proposed　novel　NDSRF　technique　is　superior　over　existing　single　synchronous　reference　frame　(SSRF)　and　decoupled　double　synchronous　reference　frame　(DDSRF)　transformation　techniques,　in　terms　of　less　harmonic　distortion　for　MMC　controller　under　the　background　harmonics　condition.　©　2019　IEEE.