G-norm and sum-norm based stability criterion for three-phase AC cascade systems

In an AC cascade system, the interaction between converters and the non-ideal source may cause instability issues, especially when the converters operate as a constant power load. From the view of the small signal model, the stability issues can be assessed according to the relationship between the terminal impedance and the admittance of sub-modules. Therefore, the stability criterion based on the terminal impedance and admittance is an effective way to estimate the stability of the total cascade system. The impedance/admittance-based stability criteria have been widely accepted in the DC cascade system. However, the stability criterion for the DC cascade system cannot be applied to the AC cascade system directly due to the difference in complexity of system behaviors. In this paper, a norm type stability criterion was proposed to analyze the stability issues in the AC cascade system. G-norm and sum-norm were employed and a modified method was also proposed to reduce the conservatism. Finally, the conservatism of different norm type criteria were evaluated and compared. The results show that the proposed criterion is better than other criteria in practical applications.