基于G-范数和sum-范数的三相交流级联系统稳定性判据

G-norm and Sum-norm Based Stability Criterion for Three-phase AC Cascade Systems

在三相交流级联系统中,源模块以及负载模块之间的相互作用将导致整个系统性能下降,甚至有可能导致系统不稳定,尤其是在含有恒功率负载的系统中表现尤为明显。通过分析系统的小信号模型可以看出,模块之间由于相互耦合而产生的稳定性问题和子模块的端口阻抗以及导纳有着直接关系。因此,基于子模块端口阻抗以及导纳的稳定性判据是分析系统级稳定性问题的有效方法。目前,基于子模块阻抗以及导纳的稳定性判据已经广泛应用于直流系统。但是,由于交流系统和直流系统在系统特性上的内在差异,目前广泛应用于直流系统的稳定性判据无法直接使用于交流系统。根据交流系统的系统特性,提出一种基于端口阻抗以及导纳矩阵的G-范数和sum-范数的稳定性判据。且根据矩阵计算的特点,对所提出的稳定性判据做进一步改进,以减少判据的保守性。最终,将所提判据和现有的范数判据进行保守性的比较,可以看出,所提判据的保守性最小,更利于实际应用。

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.