Stability analysis of grid-connected inverters with LCL-filter based on harmonic balance and Floquet theory

The inherent resonance of the grid-connected inverter with LCL-filter can lead to an instability of such a system. Normally, a damping resistor in series with the capacitor in the LCL-filter will be used to suppress the resonance, and the damping resistance is designed roughly based on the Routh-Hurwitz stability criterion. But, in practice, the resistance should be bigger than the designed value to make the inverter stable and reliable, which results in the arbitrariness of the parameter selection. In this paper, a novel method is provided based on the harmonic balance and Floquet theory to analyze the stability of the inverter. In detail, the approximate analytical periodic expressions of the inverter are obtained by using the harmonic balance method; following, the stability of the inverter versus damping resistance is analyzed according to Floquet theory. By comparing with the damping resistance got by Routh-Hurwitz stability criterion, the resistance obtained by the provided stability analysis is more practical, therefore, the provided method can be used to optimize the damping resistance.