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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. [ABSTRACT FROM PUBLISHER]