Stability and robust performance analysis of grid‐connected inverter with high‐order filter: Resonances beyond the Nyquist frequency

Filters are inevitable for grid‐connected inverters to attenuate the current harmonics caused by the pulse width modulation which is usually used in power conversion systems. High‐order filters have attracted much attention because they attenuate the current harmonics effectively. Nevertheless, the high‐order filters have some resonances which cause instability of the system. In addition, the resonance frequencies shift to high as the inductors and capacitors are smaller. It implies that the resonance frequencies may be beyond the Nyquist frequency in downsizing the filter. This complicates the stability and performance analyses of the system. This paper investigates rigorous input–output stability and analyses a robust performance based on the sampled‐data control theory regardless of whether the resonance frequencies are beyond the Nyquist frequency or not. Our analysis contributes to downsizing the filter synthesis while the stability and the robustness are guaranteed even if the resonance frequencies are beyond the Nyquist frequency. The effectiveness of the proposed method is verified through simulations and experiments.