![]() If this frequency is higher than ( f s / 6), the damping method is not needed and the system is stable. The results show that the sampling frequency of 1/6 ( f s / 6) can be used as the critical resonant frequency of the LLCL filter. The stability of LLCL filter considering the effect of time delay was discussed in. But the LLCL filter still has its inherent resonant peak, which causes the instability of the GTI system. In contrast with the LCL filter with the same filtering effect, the inductance value of the LLCL filter is smaller. The resonant frequency is designed at the switching frequency (SF), which can better filter the harmonics at the SF. The series resonant branch of the LLCL filter is composed by connecting a small inductor in series to the filter capacitor branch. In, the LLCL filter topology is proposed to decrease the whole inductance. With the same filtering effect, the LCL filters need smaller volume and lower cost than L filters. Finally, the accuracy of the analysis and the effectiveness of the method is verified by simulations. Furthermore, based on the active damping of the biquad filter, the stability criterion of the control system under a weak power grid is given. Meanwhile, a proportional-integral multiresonant repetitive controller is used to restrain low-frequency current harmonics and improve the steady-state and dynamic performance of the control system. This method makes the system have higher control bandwidth and stronger robustness even in a weak power grid. In this method, the resonance point and the notch point of the biquad filter are placed at the appointed frequency, and the resonant peak is transferred to the stable area by phase transformation, so that the system does not cross −180° at the resonant peak. In this paper, a biquad filter composed of a notch filter and a resonator is introduced to restrain the resonant peak. However, the resonant peak caused by a pair of unstable resonance poles of the LLCL filters is introduced and makes the system become unstable. LLCL filters for grid-tied inverters have been adopted to get better performance for the harmonics near the switching frequency than commonly used LCL filters.
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