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.

中文翻译：

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基于线性二次调节的复系数复变量滤波器用于电网同步

先进的数字滤波器对于电网电压同步，谐波信息提取和转换器控制非常重要。诸如降阶广义积分器之类的复变量滤波器（CVF）是最流行的滤波器之一。但是，本文证明了实系数CVF的性能与二阶广义积分器等实变量滤波器相同。这意味着CVF的优势没有得到充分利用。因此，在本文中，将实系数扩展到一个复系数，从而得到一个复系数CVF（CC-CVF），并且显着提高了CVF提取谐波的滤波器性能。此外，采用线性二次调节来设计复数系数，以实现更好的动态性能。最后，CC-CVF具有频率估计功能。拟议的CC-CVF已通过广泛的仿真和实验验证。