Grid　synchronization　has　always　been　an　important　challenge　for　grid-connected　converters　under　extremely　distorted　grid　conditions.　Moreover,　how　to　quickly　and　accurately　extract　multiple　required　harmonics　is　also　essential　for　control　systems.　In　this　paper,　two　types　of　generalized　delayed　signal　superposition　(GDSS)　operators　capable　of　extracting　any　arbitrary　harmonic　component　out　of　an　input　signal　are　derived.　In　order　to　show　the　benefits　of　GDSS　operators,　a　new　grid　information　estimation　concept　based　on　multiple　GDSS　operators　(referred　to　as　MGDSS-PLL)　is　proposed　to　track　the　fundamental　and　multiple　targeted　harmonics　under　single-phase　and　three-phase　adverse　grid　conditions.　MGDSS-PLL　can　be　flexibly　tuned　to　extract　any　harmonic　components　according　to　specific　requirements　within　one　fundamental　period,　and　it　also　exhibits　great　robustness　to　grid　disturbances.　Simulations　and　experimental　results　are　presented　for　verifying　the　performance　of　the　MGDSS-PLL.