Discrete Multiple Second-Order Generalized Integrator with Low-Pass Filters and Frequency-Locked Loop for DC Rejection

The multiple second-order generalized integrator (MSOGI), which is composed of parallel second-order generalized integrators (SOGI), is widely used in grid synchronization and signal extraction, and it usually suffers from dc offset issue. In continuous domain, low-pass filter (LPF) can be added to SOGI to eliminate the dc offset in its quadrature channel. However, in digital implementation, directly discretized LPF-based methods may not be able to eliminate dc offset and ac discretization error simultaneously, where the steady-state error will also be introduced by the conventional frequency-locked loop (FLL). In this article, a modified impulse invariant method is adopted to discretize SOGIs, which presents zero ac errors and good dynamics, but shows dc offset in both output channels. Then, an LPF is introduced to eliminate the dc offset of the discrete SOGI, forming a discrete SOGI-LPF. And, a discrete MSOGI-LPF (DMSOGI-LPF) is formed by paralleling multiple DSOGI-LPFs, which can extract different frequency components. Furthermore, a discrete FLL is proposed to estimate the frequency of the input signal, which suppresses the influence of the dc offset and achieves good dynamics. Finally, the stability analysis of the proposed method based on discrete linear-time periodic (LTP) model is provided. The effectiveness of the proposed method and its discrete LTP model are validated through experimental results.