This paper proposes a new structure for grid synchronization based on generalized integrators (GI) that lead to fast detection of positive and negative components of the grid voltage. The GI are used as a band pass filter (GI-BPF) mainly to provide in-phase and quadrature components of grid voltage. The proposed structure consists in the cascaded connection of multiple GI-BPF to achieve a faster time response than a single GI-BPF but with the same bandwidth characteristics. This structure is used with a frequency locked loop and a positive sequence detector to operate under unbalanced voltage sags. Simulations and experimental results of a photovoltaic power system injecting power to the grid in the stationary reference frame are shown to validate this proposal. Comparisons between this proposal and one that uses a single GI-BPF in the sequence detector are provided. The results show that the proposed cascaded GI-BPF achieves a considerably time response reduction in the sequence grid detection under a fault with the same quality-filter characteristics.