With the remarkable growth of renewables, distributed power generation systems (DPGSs) are starting to take over the dominant role of synchronous machines. As an essential interface between renewables and power grids, the grid-connected inverter plays an important role in the safe and stable operation of DPGSs. Among two types of grid-connected inverters, i.e., grid-following (GFL) and grid-forming (GFM) ones, attention has gradually turned to the GFM inverter in recent decades, owing to its synchronous-machine-like characteristics and capability of operating in weak grid or even forming a stand-alone grid. However, similar to the GFL inverter, the GFM inverter may exhibit non-passive characteristics in the mid/high-frequency bands, leading to mid/high-frequency resonance risk.

The existing research mainly focuses on sub-synchronous oscillation, but the mid/high-frequency resonance issue still needs to be explored. In order to mitigate the mid/high-frequency resonance and harvest the desired performance, this paper provides the optimal design procedure for controller parameters from the perspective of internal stability and the impedance reshaping method via the grid current feedforward from the perspective of external stability.

Firstly, a mathematical model of the voltage-current double-loop controlled GFM inverter is established. The control block diagram of the inverter’s control system is depicted, and its equivalent transformation is performed. Accordingly, the impedance model of the GFM inverter is obtained as a controlled source in series with the output impedance.

After that, the stability of the GFM inverter is divided into internal stability and external stability, which characterize the stability of the equivalent voltage source and the interaction stability between the equivalent impedance and the grid, respectively. From these two stability dimensions, the stability mechanism and resonance risk of the GFM inverter are analyzed based on the Nyquist stability criterion and the passivity theory, and the main factors affecting the system stability are revealed.

According to the internal stability constraints, stability margin requirements, and steady-state error, an optimal design procedure for the control parameters is provided, which avoids repeated trials and ensures internal stability and low steady-state error. Additionally, based on the external stability constraints, the impedance shaping scheme with the grid current feedforward is proposed, and the corresponding feedforward function is derived. The proposed scheme is simple to implement and can effectively enhance the inverter's robustness against grid impedance variations.

Finally, experiments are carried out on a 10 kW GFM inverter prototype. The results confirm that under different grid conditions, the inverter can with the designed parameters and the proposed scheme continuously operate stably, and the power quality is high, which verifies the theoretical analyses and the proposed scheme.