Complex-Coefficient Complex-Variable Filter for Grid Synchronization Based on Linear Quadratic Regulation

Advanced digital filter is important for grid voltage synchronization, harmonic information extraction, and converter control. The complex variable filter (CVF) such as the reduced order generalized integrator is one of the most prevalent filters. However, it is proven in this paper that the real coefficient CVF achieves performance identical to the real variable filter such as the second-order generalized integrator. It implies that the advantages of CVF are not fully utilized. Therefore, in this paper, the real coefficient is extended to a complex one leading to a complex coefficient CVF (CC-CVF), and the filter performance of CVF for extracting the harmonics is significantly improved. Furthermore, linear quadratic regulation is employed to design the complex coefficients to achieve a better dynamic performance. Finally, the CC-CVF is enhanced with frequency estimation capability. The proposed CC-CVF is verified by extensive simulations and experiments.