A Frequency-Fixed Dual Third-Order Generalized Integrator PLL with Complex Rotation Compensation for Three-Phase Grid Synchronization

Frequency deviations and DC offsets challenge the synchronization of grid-connected converters in power systems with high renewable energy penetration. Frequency-adaptive filter-based phase-locked loops (PLLs) introduce coupling between resonator tuning and frequency estimation, whereas frequency-fixed filters exhibit amplitude and phase errors when the grid frequency departs from its nominal value. This paper proposes a frequency-fixed dual third-order generalized integrator PLL with complex rotation compensation (FFDTOGI-CRC-PLL). Both channels of the dual third-order generalized integrator have a zero at the origin, so the input dc offset is rejected with zero steady-state error; second-order generalized integrator and all-pass prefilters, by contrast, have a non-zero gain at zero frequency and require an additional filter to remove the dc offset. A complex coefficient, obtained from the prefilter transfer function evaluated at the estimated frequency, corrects the amplitude and phase errors through a single complex multiplication. The coefficient is updated without retuning the resonators, removing the resonant-parameter feedback path. A small-signal model is established to analyze the PLL dynamics and guide parameter tuning. Experimental comparisons under frequency deviations and DC offsets demonstrate effective DC rejection, reduced amplitude and phase errors, and fast, accurate phase and frequency tracking.