Stability Analysis of Grid-Forming Inverter in DQ Frequency Domain

In near future, power converters will be introduced into transmission grids on a large scale due to increase of renewable energy sources. The control schemes of grid-connected inverters currently assume that there are sufficient synchronous generators (SGs) in the grid for synchronization and integration of electric power. However, when grid-connected inverters significantly outnumber SGs, there is a need for the grid-forming capability to operate the transmission grid autonomously. These inverters should generate AC voltages and are called "grid-forming" inverters. They behave as voltage sources and the cascaded PI controller has been often used. However, it is difficult to tune the control gains because of system couplings and the controller's bandwidths. This paper proposes a new controller based on the linear quadratic regulator (LQR) for voltage regulation and shows comparisons of the performances between them. It is also well known that the instability due to interactions between inverters and a grid is sometimes observed. This paper utilizes the impedance-based method in dq frame to analyze the stability of the grid-forming inverters with both the LQR and the cascaded PI controller. The stability is also investigated using eigenvalue analysis and the results are validated by numerical simulations.